From 51a7e53f65e93cbdb46f5ff885ff1a68cc738fbc Mon Sep 17 00:00:00 2001
From: Christophe Geuzaine <cgeuzaine@ulg.ac.be>
Date: Wed, 3 Apr 2013 05:35:30 +0000
Subject: [PATCH]
---
Common/OS.cpp | 1 -
contrib/Tetgen1.5/predicates.cxx | 742 +-
contrib/Tetgen1.5/tetgen.cxx | 15011 +++++++++++++----------------
contrib/Tetgen1.5/tetgen.h | 1962 ++--
4 files changed, 8019 insertions(+), 9697 deletions(-)
diff --git a/Common/OS.cpp b/Common/OS.cpp
index 961da73fcc..a6f3f59a71 100644
--- a/Common/OS.cpp
+++ b/Common/OS.cpp
@@ -27,7 +27,6 @@
#include <io.h>
#include <direct.h>
#include <fcntl.h>
-#include <io.h>
#include <iostream>
#include <fstream>
#endif
diff --git a/contrib/Tetgen1.5/predicates.cxx b/contrib/Tetgen1.5/predicates.cxx
index 4120704c35..5fe852e211 100644
--- a/contrib/Tetgen1.5/predicates.cxx
+++ b/contrib/Tetgen1.5/predicates.cxx
@@ -125,6 +125,13 @@
#include "tetgen.h" // Defines the symbol REAL (float or double).
+#ifdef USE_CGAL_PREDICATES
+ #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+ typedef CGAL::Exact_predicates_inexact_constructions_kernel cgalEpick;
+ typedef cgalEpick::Point_3 Point;
+ cgalEpick cgal_pred_obj;
+#endif // #ifdef USE_CGAL_PREDICATES
+
/* On some machines, the exact arithmetic routines might be defeated by the */
/* use of internal extended precision floating-point registers. Sometimes */
/* this problem can be fixed by defining certain values to be volatile, */
@@ -149,8 +156,8 @@
/* which is disastrously slow. A faster way on IEEE machines might be to */
/* mask the appropriate bit, but that's difficult to do in C. */
-#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
-/* #define Absolute(a) fabs(a) */
+//#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
+#define Absolute(a) fabs(a)
/* Many of the operations are broken up into two pieces, a main part that */
/* performs an approximate operation, and a "tail" that computes the */
@@ -375,271 +382,144 @@ static REAL o3derrboundA, o3derrboundB, o3derrboundC;
static REAL iccerrboundA, iccerrboundB, iccerrboundC;
static REAL isperrboundA, isperrboundB, isperrboundC;
-/*****************************************************************************/
-/* */
-/* doubleprint() Print the bit representation of a double. */
-/* */
-/* Useful for debugging exact arithmetic routines. */
-/* */
-/*****************************************************************************/
+// Options to choose types of geometric computtaions.
+// Added by H. Si, 2012-08-23.
+static int _use_inexact_arith; // -X option.
+static int _use_static_filter; // Default option, disable it by -X1
+
+// Static filters for orient3d() and insphere().
+// They are pre-calcualted and set in exactinit().
+// Added by H. Si, 2012-08-23.
+static REAL o3dstaticfilter;
+static REAL ispstaticfilter;
+
+
+
+// The following codes were part of "IEEE 754 floating-point test software"
+// http://www.math.utah.edu/~beebe/software/ieee/
+// The original program was "fpinfo2.c".
-/*
-void doubleprint(number)
-double number;
+double fppow2(int n)
{
- unsigned long long no;
- unsigned long long sign, expo;
- int exponent;
- int i, bottomi;
-
- no = *(unsigned long long *) &number;
- sign = no & 0x8000000000000000ll;
- expo = (no >> 52) & 0x7ffll;
- exponent = (int) expo;
- exponent = exponent - 1023;
- if (sign) {
- printf("-");
- } else {
- printf(" ");
- }
- if (exponent == -1023) {
- printf(
- "0.0000000000000000000000000000000000000000000000000000_ ( )");
- } else {
- printf("1.");
- bottomi = -1;
- for (i = 0; i < 52; i++) {
- if (no & 0x0008000000000000ll) {
- printf("1");
- bottomi = i;
- } else {
- printf("0");
- }
- no <<= 1;
- }
- printf("_%d (%d)", exponent, exponent - 1 - bottomi);
- }
+ double x, power;
+ x = (n < 0) ? ((double)1.0/(double)2.0) : (double)2.0;
+ n = (n < 0) ? -n : n;
+ power = (double)1.0;
+ while (n-- > 0)
+ power *= x;
+ return (power);
}
-*/
-/*****************************************************************************/
-/* */
-/* floatprint() Print the bit representation of a float. */
-/* */
-/* Useful for debugging exact arithmetic routines. */
-/* */
-/*****************************************************************************/
+#ifdef SINGLE
-/*
-void floatprint(number)
-float number;
+float fstore(float x)
{
- unsigned no;
- unsigned sign, expo;
- int exponent;
- int i, bottomi;
-
- no = *(unsigned *) &number;
- sign = no & 0x80000000;
- expo = (no >> 23) & 0xff;
- exponent = (int) expo;
- exponent = exponent - 127;
- if (sign) {
- printf("-");
- } else {
- printf(" ");
- }
- if (exponent == -127) {
- printf("0.00000000000000000000000_ ( )");
- } else {
- printf("1.");
- bottomi = -1;
- for (i = 0; i < 23; i++) {
- if (no & 0x00400000) {
- printf("1");
- bottomi = i;
- } else {
- printf("0");
- }
- no <<= 1;
- }
- printf("_%3d (%3d)", exponent, exponent - 1 - bottomi);
- }
+ return (x);
}
-*/
-/*****************************************************************************/
-/* */
-/* expansion_print() Print the bit representation of an expansion. */
-/* */
-/* Useful for debugging exact arithmetic routines. */
-/* */
-/*****************************************************************************/
-
-/*
-void expansion_print(elen, e)
-int elen;
-REAL *e;
+int test_float(int verbose)
{
- int i;
+ float x;
+ int pass = 1;
- for (i = elen - 1; i >= 0; i--) {
- REALPRINT(e[i]);
- if (i > 0) {
- printf(" +\n");
- } else {
- printf("\n");
- }
+ //(void)printf("float:\n");
+
+ if (verbose) {
+ (void)printf(" sizeof(float) = %2u\n", (unsigned int)sizeof(float));
+#ifdef CPU86 // <float.h>
+ (void)printf(" FLT_MANT_DIG = %2d\n", FLT_MANT_DIG);
+#endif
}
-}
-*/
-/*****************************************************************************/
-/* */
-/* doublerand() Generate a double with random 53-bit significand and a */
-/* random exponent in [0, 511]. */
-/* */
-/*****************************************************************************/
+ x = (float)1.0;
+ while (fstore((float)1.0 + x/(float)2.0) != (float)1.0)
+ x /= (float)2.0;
+ if (verbose)
+ (void)printf(" machine epsilon = %13.5e ", x);
-/*
-double doublerand()
-{
- double result;
- double expo;
- long a, b, c;
- long i;
-
- a = random();
- b = random();
- c = random();
- result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
- for (i = 512, expo = 2; i <= 131072; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
+ if (x == (float)fppow2(-23)) {
+ if (verbose)
+ (void)printf("[IEEE 754 32-bit macheps]\n");
+ } else {
+ (void)printf("[not IEEE 754 conformant] !!\n");
+ pass = 0;
}
- return result;
-}
-*/
-/*****************************************************************************/
-/* */
-/* narrowdoublerand() Generate a double with random 53-bit significand */
-/* and a random exponent in [0, 7]. */
-/* */
-/*****************************************************************************/
-
-/*
-double narrowdoublerand()
-{
- double result;
- double expo;
- long a, b, c;
- long i;
-
- a = random();
- b = random();
- c = random();
- result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
- for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
+ x = (float)1.0;
+ while (fstore(x / (float)2.0) != (float)0.0)
+ x /= (float)2.0;
+ if (verbose)
+ (void)printf(" smallest positive number = %13.5e ", x);
+
+ if (x == (float)fppow2(-149)) {
+ if (verbose)
+ (void)printf("[smallest 32-bit subnormal]\n");
+ } else if (x == (float)fppow2(-126)) {
+ if (verbose)
+ (void)printf("[smallest 32-bit normal]\n");
+ } else {
+ (void)printf("[not IEEE 754 conformant] !!\n");
+ pass = 0;
}
- return result;
+
+ return pass;
}
-*/
-/*****************************************************************************/
-/* */
-/* uniformdoublerand() Generate a double with random 53-bit significand. */
-/* */
-/*****************************************************************************/
+# else
-/*
-double uniformdoublerand()
+double dstore(double x)
{
- double result;
- long a, b;
-
- a = random();
- b = random();
- result = (double) (a - 1073741824) * 8388608.0 + (double) (b >> 8);
- return result;
+ return (x);
}
-*/
-
-/*****************************************************************************/
-/* */
-/* floatrand() Generate a float with random 24-bit significand and a */
-/* random exponent in [0, 63]. */
-/* */
-/*****************************************************************************/
-/*
-float floatrand()
+int test_double(int verbose)
{
- float result;
- float expo;
- long a, c;
- long i;
-
- a = random();
- c = random();
- result = (float) ((a - 1073741824) >> 6);
- for (i = 512, expo = 2; i <= 16384; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
+ double x;
+ int pass = 1;
+
+ // (void)printf("double:\n");
+ if (verbose) {
+ (void)printf(" sizeof(double) = %2u\n", (unsigned int)sizeof(double));
+#ifdef CPU86 // <float.h>
+ (void)printf(" DBL_MANT_DIG = %2d\n", DBL_MANT_DIG);
+#endif
}
- return result;
-}
-*/
-/*****************************************************************************/
-/* */
-/* narrowfloatrand() Generate a float with random 24-bit significand and */
-/* a random exponent in [0, 7]. */
-/* */
-/*****************************************************************************/
+ x = 1.0;
+ while (dstore(1.0 + x/2.0) != 1.0)
+ x /= 2.0;
+ if (verbose)
+ (void)printf(" machine epsilon = %13.5le ", x);
-/*
-float narrowfloatrand()
-{
- float result;
- float expo;
- long a, c;
- long i;
-
- a = random();
- c = random();
- result = (float) ((a - 1073741824) >> 6);
- for (i = 512, expo = 2; i <= 2048; i *= 2, expo = expo * expo) {
- if (c & i) {
- result *= expo;
- }
+ if (x == (double)fppow2(-52)) {
+ if (verbose)
+ (void)printf("[IEEE 754 64-bit macheps]\n");
+ } else {
+ (void)printf("[not IEEE 754 conformant] !!\n");
+ pass = 0;
}
- return result;
-}
-*/
-
-/*****************************************************************************/
-/* */
-/* uniformfloatrand() Generate a float with random 24-bit significand. */
-/* */
-/*****************************************************************************/
-/*
-float uniformfloatrand()
-{
- float result;
- long a;
+ x = 1.0;
+ while (dstore(x / 2.0) != 0.0)
+ x /= 2.0;
+ if (verbose)
+ (void)printf(" smallest positive number = %13.5le ", x);
+
+ if (x == (double)fppow2(-1074)) {
+ if (verbose)
+ (void)printf("[smallest 64-bit subnormal]\n");
+ } else if (x == (double)fppow2(-1022)) {
+ if (verbose)
+ (void)printf("[smallest 64-bit normal]\n");
+ } else {
+ (void)printf("[not IEEE 754 conformant] !!\n");
+ pass = 0;
+ }
- a = random();
- result = (float) ((a - 1073741824) >> 6);
- return result;
+ return pass;
}
-*/
+
+#endif
/*****************************************************************************/
/* */
@@ -660,7 +540,8 @@ float uniformfloatrand()
/* */
/*****************************************************************************/
-REAL exactinit()
+void exactinit(int verbose, int noexact, int nofilter, REAL maxx, REAL maxy,
+ REAL maxz)
{
REAL half;
REAL check, lastcheck;
@@ -687,6 +568,24 @@ REAL exactinit()
_FPU_SETCW(cword);
#endif /* LINUX */
+ if (verbose) {
+ printf(" Initializing robust predicates.\n");
+ }
+
+#ifdef USE_CGAL_PREDICATES
+ if (cgal_pred_obj.Has_static_filters) {
+ printf(" Use static filter.\n");
+ } else {
+ printf(" No static filter.\n");
+ }
+#endif // USE_CGAL_PREDICATES
+
+#ifdef SINGLE
+ test_float(verbose);
+#else
+ test_double(verbose);
+#endif
+
every_other = 1;
half = 0.5;
epsilon = 1.0;
@@ -722,7 +621,31 @@ REAL exactinit()
isperrboundB = (5.0 + 72.0 * epsilon) * epsilon;
isperrboundC = (71.0 + 1408.0 * epsilon) * epsilon * epsilon;
- return epsilon; /* Added by H. Si 30 Juli, 2004. */
+ // Set TetGen options. Added by H. Si, 2012-08-23.
+ _use_inexact_arith = noexact;
+ _use_static_filter = !nofilter;
+
+ // Calculate the two static filters for orient3d() and insphere() tests.
+ // Added by H. Si, 2012-08-23.
+
+ // Sort maxx < maxy < maxz. Re-use 'half' for swapping.
+ assert(maxx > 0);
+ assert(maxy > 0);
+ assert(maxz > 0);
+
+ if (maxx > maxz) {
+ half = maxx; maxx = maxz; maxz = half;
+ }
+ if (maxy > maxz) {
+ half = maxy; maxy = maxz; maxz = half;
+ }
+ else if (maxy < maxx) {
+ half = maxy; maxy = maxx; maxx = half;
+ }
+
+ o3dstaticfilter = 5.1107127829973299e-15 * maxx * maxy * maxz;
+ ispstaticfilter = 1.2466136531027298e-13 * maxx * maxy * maxz * (maxz * maxz);
+
}
/*****************************************************************************/
@@ -1869,16 +1792,6 @@ REAL orient3dadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
REAL fin1[192], fin2[192];
int finlength;
- ////////////////////////////////////////////////////////
- // To avoid uninitialized warnings reported by valgrind.
- int i;
- for (i = 0; i < 8; i++) {
- adet[i] = bdet[i] = cdet[i] = 0.0;
- }
- for (i = 0; i < 16; i++) {
- abdet[i] = 0.0;
- }
- ////////////////////////////////////////////////////////
REAL adxtail, bdxtail, cdxtail;
REAL adytail, bdytail, cdytail;
@@ -1916,6 +1829,7 @@ REAL orient3dadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
INEXACT REAL _i, _j, _k;
REAL _0;
+
adx = (REAL) (pa[0] - pd[0]);
bdx = (REAL) (pb[0] - pd[0]);
cdx = (REAL) (pc[0] - pd[0]);
@@ -2263,27 +2177,16 @@ REAL orient3dadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL permanent)
return finnow[finlength - 1];
}
-#ifdef INEXACT_GEOM_PRED
+#ifdef USE_CGAL_PREDICATES
REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
- REAL adx, bdx, cdx;
- REAL ady, bdy, cdy;
- REAL adz, bdz, cdz;
-
- adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
- ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
- adz = pa[2] - pd[2];
- bdz = pb[2] - pd[2];
- cdz = pc[2] - pd[2];
-
- return adx * (bdy * cdz - bdz * cdy)
- + bdx * (cdy * adz - cdz * ady)
- + cdx * (ady * bdz - adz * bdy);
+ return (REAL)
+ - cgal_pred_obj.orientation_3_object()
+ (Point(pa[0], pa[1], pa[2]),
+ Point(pb[0], pb[1], pb[2]),
+ Point(pc[0], pc[1], pc[2]),
+ Point(pd[0], pd[1], pd[2]));
}
#else
@@ -2293,16 +2196,16 @@ REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
REAL adx, bdx, cdx, ady, bdy, cdy, adz, bdz, cdz;
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
REAL det;
- REAL permanent, errbound;
+
adx = pa[0] - pd[0];
- bdx = pb[0] - pd[0];
- cdx = pc[0] - pd[0];
ady = pa[1] - pd[1];
- bdy = pb[1] - pd[1];
- cdy = pc[1] - pd[1];
adz = pa[2] - pd[2];
+ bdx = pb[0] - pd[0];
+ bdy = pb[1] - pd[1];
bdz = pb[2] - pd[2];
+ cdx = pc[0] - pd[0];
+ cdy = pc[1] - pd[1];
cdz = pc[2] - pd[2];
bdxcdy = bdx * cdy;
@@ -2318,6 +2221,19 @@ REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
+ bdz * (cdxady - adxcdy)
+ cdz * (adxbdy - bdxady);
+ if (_use_inexact_arith) {
+ return det;
+ }
+
+ if (_use_static_filter) {
+ //if (fabs(det) > o3dstaticfilter) return det;
+ if (det > o3dstaticfilter) return det;
+ if (det < -o3dstaticfilter) return det;
+ }
+
+
+ REAL permanent, errbound;
+
permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adz)
+ (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdz)
+ (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdz);
@@ -2329,7 +2245,7 @@ REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
return orient3dadapt(pa, pb, pc, pd, permanent);
}
-#endif // ifdef INEXACT_GEOM_PRED
+#endif // #ifdef USE_CGAL_PREDICATES
/*****************************************************************************/
/* */
@@ -3362,6 +3278,7 @@ REAL insphereexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
INEXACT REAL _i, _j;
REAL _0;
+
Two_Product(pa[0], pb[1], axby1, axby0);
Two_Product(pb[0], pa[1], bxay1, bxay0);
Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);
@@ -3938,6 +3855,7 @@ REAL insphereadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe,
INEXACT REAL _i, _j;
REAL _0;
+
aex = (REAL) (pa[0] - pe[0]);
bex = (REAL) (pb[0] - pe[0]);
cex = (REAL) (pc[0] - pe[0]);
@@ -4114,50 +4032,19 @@ REAL insphereadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe,
return insphereexact(pa, pb, pc, pd, pe);
}
-#ifdef INEXACT_GEOM_PRED
+#ifdef USE_CGAL_PREDICATES
REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
{
- REAL aex, bex, cex, dex;
- REAL aey, bey, cey, dey;
- REAL aez, bez, cez, dez;
- REAL alift, blift, clift, dlift;
- REAL ab, bc, cd, da, ac, bd;
- REAL abc, bcd, cda, dab;
-
- aex = pa[0] - pe[0];
- bex = pb[0] - pe[0];
- cex = pc[0] - pe[0];
- dex = pd[0] - pe[0];
- aey = pa[1] - pe[1];
- bey = pb[1] - pe[1];
- cey = pc[1] - pe[1];
- dey = pd[1] - pe[1];
- aez = pa[2] - pe[2];
- bez = pb[2] - pe[2];
- cez = pc[2] - pe[2];
- dez = pd[2] - pe[2];
-
- ab = aex * bey - bex * aey;
- bc = bex * cey - cex * bey;
- cd = cex * dey - dex * cey;
- da = dex * aey - aex * dey;
-
- ac = aex * cey - cex * aey;
- bd = bex * dey - dex * bey;
-
- abc = aez * bc - bez * ac + cez * ab;
- bcd = bez * cd - cez * bd + dez * bc;
- cda = cez * da + dez * ac + aez * cd;
- dab = dez * ab + aez * bd + bez * da;
-
- alift = aex * aex + aey * aey + aez * aez;
- blift = bex * bex + bey * bey + bez * bez;
- clift = cex * cex + cey * cey + cez * cez;
- dlift = dex * dex + dey * dey + dez * dez;
-
- return (dlift * abc - clift * dab) + (blift * cda - alift * bcd);
+ return (REAL)
+ - cgal_pred_obj.side_of_oriented_sphere_3_object()
+ (Point(pa[0], pa[1], pa[2]),
+ Point(pb[0], pb[1], pb[2]),
+ Point(pc[0], pc[1], pc[2]),
+ Point(pd[0], pd[1], pd[2]),
+ Point(pe[0], pe[1], pe[2]));
}
+
#else
REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
@@ -4170,12 +4057,8 @@ REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
REAL alift, blift, clift, dlift;
REAL ab, bc, cd, da, ac, bd;
REAL abc, bcd, cda, dab;
- REAL aezplus, bezplus, cezplus, dezplus;
- REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
- REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
- REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
REAL det;
- REAL permanent, errbound;
+
aex = pa[0] - pe[0];
bex = pb[0] - pe[0];
@@ -4222,6 +4105,23 @@ REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
det = (dlift * abc - clift * dab) + (blift * cda - alift * bcd);
+ if (_use_inexact_arith) {
+ return det;
+ }
+
+ if (_use_static_filter) {
+ if (fabs(det) > ispstaticfilter) return det;
+ //if (det > ispstaticfilter) return det;
+ //if (det < minus_ispstaticfilter) return det;
+
+ }
+
+ REAL aezplus, bezplus, cezplus, dezplus;
+ REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
+ REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
+ REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
+ REAL permanent, errbound;
+
aezplus = Absolute(aez);
bezplus = Absolute(bez);
cezplus = Absolute(cez);
@@ -4262,7 +4162,7 @@ REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe)
return insphereadapt(pa, pb, pc, pd, pe, permanent);
}
-#endif // #ifdef INEXACT_GEOM_PRED
+#endif // #ifdef USE_CGAL_PREDICATES
/*****************************************************************************/
/* */
@@ -4327,6 +4227,7 @@ REAL orient4dexact(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
INEXACT REAL _i, _j;
REAL _0;
+
Two_Product(pa[0], pb[1], axby1, axby0);
Two_Product(pb[0], pa[1], bxay1, bxay0);
Two_Two_Diff(axby1, axby0, bxay1, bxay0, ab[3], ab[2], ab[1], ab[0]);
@@ -4540,6 +4441,7 @@ REAL orient4dadapt(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
INEXACT REAL _i, _j;
REAL _0;
+
aex = (REAL) (pa[0] - pe[0]);
bex = (REAL) (pb[0] - pe[0]);
cex = (REAL) (pc[0] - pe[0]);
@@ -4699,108 +4601,106 @@ REAL orient4d(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
REAL aheight, REAL bheight, REAL cheight, REAL dheight,
REAL eheight)
{
- REAL aex, bex, cex, dex;
- REAL aey, bey, cey, dey;
- REAL aez, bez, cez, dez;
- REAL aexbey, bexaey, bexcey, cexbey, cexdey, dexcey, dexaey, aexdey;
- REAL aexcey, cexaey, bexdey, dexbey;
- REAL aeheight, beheight, ceheight, deheight;
- REAL ab, bc, cd, da, ac, bd;
- REAL abc, bcd, cda, dab;
- REAL aezplus, bezplus, cezplus, dezplus;
- REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
- REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
- REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
- REAL det;
- REAL permanent, errbound;
-
- //orient4dcount++;
-
- aex = pa[0] - pe[0];
- bex = pb[0] - pe[0];
- cex = pc[0] - pe[0];
- dex = pd[0] - pe[0];
- aey = pa[1] - pe[1];
- bey = pb[1] - pe[1];
- cey = pc[1] - pe[1];
- dey = pd[1] - pe[1];
- aez = pa[2] - pe[2];
- bez = pb[2] - pe[2];
- cez = pc[2] - pe[2];
- dez = pd[2] - pe[2];
- aeheight = aheight - eheight;
- beheight = bheight - eheight;
- ceheight = cheight - eheight;
- deheight = dheight - eheight;
-
- aexbey = aex * bey;
- bexaey = bex * aey;
- ab = aexbey - bexaey;
- bexcey = bex * cey;
- cexbey = cex * bey;
- bc = bexcey - cexbey;
- cexdey = cex * dey;
- dexcey = dex * cey;
- cd = cexdey - dexcey;
- dexaey = dex * aey;
- aexdey = aex * dey;
- da = dexaey - aexdey;
-
- aexcey = aex * cey;
- cexaey = cex * aey;
- ac = aexcey - cexaey;
- bexdey = bex * dey;
- dexbey = dex * bey;
- bd = bexdey - dexbey;
-
- abc = aez * bc - bez * ac + cez * ab;
- bcd = bez * cd - cez * bd + dez * bc;
- cda = cez * da + dez * ac + aez * cd;
- dab = dez * ab + aez * bd + bez * da;
-
- det = (deheight * abc - ceheight * dab) + (beheight * cda - aeheight * bcd);
+ REAL aex, bex, cex, dex;
+ REAL aey, bey, cey, dey;
+ REAL aez, bez, cez, dez;
+ REAL aexbey, bexaey, bexcey, cexbey, cexdey, dexcey, dexaey, aexdey;
+ REAL aexcey, cexaey, bexdey, dexbey;
+ REAL aeheight, beheight, ceheight, deheight;
+ REAL ab, bc, cd, da, ac, bd;
+ REAL abc, bcd, cda, dab;
+ REAL aezplus, bezplus, cezplus, dezplus;
+ REAL aexbeyplus, bexaeyplus, bexceyplus, cexbeyplus;
+ REAL cexdeyplus, dexceyplus, dexaeyplus, aexdeyplus;
+ REAL aexceyplus, cexaeyplus, bexdeyplus, dexbeyplus;
+ REAL det;
+ REAL permanent, errbound;
+
+
+ aex = pa[0] - pe[0];
+ bex = pb[0] - pe[0];
+ cex = pc[0] - pe[0];
+ dex = pd[0] - pe[0];
+ aey = pa[1] - pe[1];
+ bey = pb[1] - pe[1];
+ cey = pc[1] - pe[1];
+ dey = pd[1] - pe[1];
+ aez = pa[2] - pe[2];
+ bez = pb[2] - pe[2];
+ cez = pc[2] - pe[2];
+ dez = pd[2] - pe[2];
+ aeheight = aheight - eheight;
+ beheight = bheight - eheight;
+ ceheight = cheight - eheight;
+ deheight = dheight - eheight;
+
+ aexbey = aex * bey;
+ bexaey = bex * aey;
+ ab = aexbey - bexaey;
+ bexcey = bex * cey;
+ cexbey = cex * bey;
+ bc = bexcey - cexbey;
+ cexdey = cex * dey;
+ dexcey = dex * cey;
+ cd = cexdey - dexcey;
+ dexaey = dex * aey;
+ aexdey = aex * dey;
+ da = dexaey - aexdey;
+
+ aexcey = aex * cey;
+ cexaey = cex * aey;
+ ac = aexcey - cexaey;
+ bexdey = bex * dey;
+ dexbey = dex * bey;
+ bd = bexdey - dexbey;
+
+ abc = aez * bc - bez * ac + cez * ab;
+ bcd = bez * cd - cez * bd + dez * bc;
+ cda = cez * da + dez * ac + aez * cd;
+ dab = dez * ab + aez * bd + bez * da;
+
+ det = (deheight * abc - ceheight * dab) + (beheight * cda - aeheight * bcd);
+
+ aezplus = Absolute(aez);
+ bezplus = Absolute(bez);
+ cezplus = Absolute(cez);
+ dezplus = Absolute(dez);
+ aexbeyplus = Absolute(aexbey);
+ bexaeyplus = Absolute(bexaey);
+ bexceyplus = Absolute(bexcey);
+ cexbeyplus = Absolute(cexbey);
+ cexdeyplus = Absolute(cexdey);
+ dexceyplus = Absolute(dexcey);
+ dexaeyplus = Absolute(dexaey);
+ aexdeyplus = Absolute(aexdey);
+ aexceyplus = Absolute(aexcey);
+ cexaeyplus = Absolute(cexaey);
+ bexdeyplus = Absolute(bexdey);
+ dexbeyplus = Absolute(dexbey);
+ permanent = ((cexdeyplus + dexceyplus) * bezplus
+ + (dexbeyplus + bexdeyplus) * cezplus
+ + (bexceyplus + cexbeyplus) * dezplus)
+ * Absolute(aeheight)
+ + ((dexaeyplus + aexdeyplus) * cezplus
+ + (aexceyplus + cexaeyplus) * dezplus
+ + (cexdeyplus + dexceyplus) * aezplus)
+ * Absolute(beheight)
+ + ((aexbeyplus + bexaeyplus) * dezplus
+ + (bexdeyplus + dexbeyplus) * aezplus
+ + (dexaeyplus + aexdeyplus) * bezplus)
+ * Absolute(ceheight)
+ + ((bexceyplus + cexbeyplus) * aezplus
+ + (cexaeyplus + aexceyplus) * bezplus
+ + (aexbeyplus + bexaeyplus) * cezplus)
+ * Absolute(deheight);
+ errbound = isperrboundA * permanent;
+ if ((det > errbound) || (-det > errbound)) {
+ return det;
+ }
+
+ return orient4dadapt(pa, pb, pc, pd, pe,
+ aheight, bheight, cheight, dheight, eheight, permanent);
+}
- if (0) { //if (noexact) {
- return det;
- }
- aezplus = Absolute(aez);
- bezplus = Absolute(bez);
- cezplus = Absolute(cez);
- dezplus = Absolute(dez);
- aexbeyplus = Absolute(aexbey);
- bexaeyplus = Absolute(bexaey);
- bexceyplus = Absolute(bexcey);
- cexbeyplus = Absolute(cexbey);
- cexdeyplus = Absolute(cexdey);
- dexceyplus = Absolute(dexcey);
- dexaeyplus = Absolute(dexaey);
- aexdeyplus = Absolute(aexdey);
- aexceyplus = Absolute(aexcey);
- cexaeyplus = Absolute(cexaey);
- bexdeyplus = Absolute(bexdey);
- dexbeyplus = Absolute(dexbey);
- permanent = ((cexdeyplus + dexceyplus) * bezplus
- + (dexbeyplus + bexdeyplus) * cezplus
- + (bexceyplus + cexbeyplus) * dezplus)
- * aeheight
- + ((dexaeyplus + aexdeyplus) * cezplus
- + (aexceyplus + cexaeyplus) * dezplus
- + (cexdeyplus + dexceyplus) * aezplus)
- * beheight
- + ((aexbeyplus + bexaeyplus) * dezplus
- + (bexdeyplus + dexbeyplus) * aezplus
- + (dexaeyplus + aexdeyplus) * bezplus)
- * ceheight
- + ((bexceyplus + cexbeyplus) * aezplus
- + (cexaeyplus + aexceyplus) * bezplus
- + (aexbeyplus + bexaeyplus) * cezplus)
- * deheight;
- errbound = isperrboundA * permanent;
- if ((det > errbound) || (-det > errbound)) {
- return det;
- }
- return orient4dadapt(pa, pb, pc, pd, pe,
- aheight, bheight, cheight, dheight, eheight, permanent);
-}
diff --git a/contrib/Tetgen1.5/tetgen.cxx b/contrib/Tetgen1.5/tetgen.cxx
index 0a66de153c..df7fb43790 100644
--- a/contrib/Tetgen1.5/tetgen.cxx
+++ b/contrib/Tetgen1.5/tetgen.cxx
@@ -2,21 +2,17 @@
// //
// TetGen //
// //
-// A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator //
+// A Quality Tetrahedral Mesh Generator and A 3D Delaunay Triangulator //
// //
// Version 1.5 //
-// February 21, 2012 //
+// (March 27, 2013) //
// //
-// PRE-RELEASE TEST CODE. //
-// PLEASE DO NOT DISTRIBUTE !! //
-// PLEASE HELP ME TO IMPROVE IT !! //
-// //
-// Copyright (C) 2002--2012 //
+// Copyright (C) 2002--2013 //
// Hang Si //
// Research Group: Numerical Mathematics and Scientific Computing //
// Weierstrass Institute for Applied Analysis and Stochastics (WIAS) //
// Mohrenstr. 39, 10117 Berlin, Germany //
-// Hang.Si@wias-berlin.de //
+// si@wias-berlin.de //
// //
// TetGen is freely available through the website: http://www.tetgen.org. //
// It may be copied, modified, and redistributed for non-commercial use. //
@@ -335,6 +331,10 @@ bool tetgenio::load_edge(char* filebasename)
}
edgelist[index++] = corner;
}
+ if (numberofcorners == 10) {
+ // Skip an extra vertex (generated by a previous -o2 option).
+ stringptr = findnextnumber(stringptr);
+ }
// Read the edge marker if it has.
if (markers) {
stringptr = findnextnumber(stringptr);
@@ -419,6 +419,12 @@ bool tetgenio::load_face(char* filebasename)
}
trifacelist[index++] = corner;
}
+ if (numberofcorners == 10) {
+ // Skip 3 extra vertices (generated by a previous -o2 option).
+ for (j = 0; j < 3; j++) {
+ stringptr = findnextnumber(stringptr);
+ }
+ }
// Read the boundary marker if it exists.
if (markers) {
stringptr = findnextnumber(stringptr);
@@ -627,7 +633,6 @@ bool tetgenio::load_var(char* filebasename)
if (infile != (FILE *) NULL) {
printf("Opening %s.\n", varfilename);
} else {
- // No such file. Ignore it without a message.
return false;
}
@@ -740,7 +745,6 @@ bool tetgenio::load_mtr(char* filebasename)
if (infile != (FILE *) NULL) {
printf("Opening %s.\n", mtrfilename);
} else {
- // No such file. Return.
return false;
}
@@ -1381,14 +1385,11 @@ bool tetgenio::load_off(char* filebasename)
return false;
}
- // Check whether read all points
if (iverts != nverts) {
printf("Expected %d vertices, but read only %d vertices in file %s\n",
nverts, iverts, infilename);
return false;
}
-
- // Check whether read all faces
if (ifaces != nfaces) {
printf("Expected %d faces, but read only %d faces in file %s\n",
nfaces, ifaces, infilename);
@@ -1603,14 +1604,11 @@ bool tetgenio::load_ply(char* filebasename)
return false;
}
- // Check whether read all points
if (iverts != nverts) {
printf("Expected %d vertices, but read only %d vertices in file %s\n",
nverts, iverts, infilename);
return false;
}
-
- // Check whether read all faces
if (ifaces != nfaces) {
printf("Expected %d faces, but read only %d faces in file %s\n",
nfaces, ifaces, infilename);
@@ -2389,6 +2387,7 @@ bool tetgenio::load_plc(char* filebasename, int object)
}
if (success) {
+ // Try to load the following files (.edge, .var, .mtr).
load_edge(filebasename);
load_var(filebasename);
load_mtr(filebasename);
@@ -2415,6 +2414,7 @@ bool tetgenio::load_tetmesh(char* filebasename, int object)
success = load_tet(filebasename);
}
if (success) {
+ // Try to load the following files (.face, .edge, .vol).
load_face(filebasename);
load_edge(filebasename);
load_vol(filebasename);
@@ -2422,6 +2422,7 @@ bool tetgenio::load_tetmesh(char* filebasename, int object)
}
if (success) {
+ // Try to load the following files (.var, .mtr).
load_var(filebasename);
load_mtr(filebasename);
}
@@ -2902,16 +2903,22 @@ char* tetgenio::findnextnumber(char *string)
void tetgenbehavior::syntax()
{
- printf(" tetgen [-pYrq_a_AiS_T_dzfenvgKJBNEFICQVh] input_file\n");
+ printf(" tetgen [-pYq_Aa_mriO_S_T_XMwcdzfenvgkJBNEFICQVh] input_file\n");
printf(" -p Tetrahedralizes a piecewise linear complex (PLC).\n");
- printf(" -Y No splitting of input boundaries (facets and segments).\n");
- printf(" -r Reconstructs a previously generated mesh.\n");
+ printf(" -Y Preserves the input surface mesh (does not modify it).\n");
printf(" -q Refines mesh (to improve mesh quality).\n");
- printf(" -a Applies a maximum tetrahedron volume constraint.\n");
printf(" -A Assigns attributes to tetrahedra in different regions.\n");
- printf(" -i Inserts a list of additional points into mesh.\n");
+ printf(" -a Applies a maximum tetrahedron volume constraint.\n");
+ printf(" -m Applies a mesh sizing function.\n");
+ printf(" -r Reconstructs a previously generated mesh.\n");
+ printf(" -i Inserts a list of additional points.\n");
+ printf(" -O Specifies the level of mesh optimization.\n");
printf(" -S Specifies maximum number of added points.\n");
printf(" -T Sets a tolerance for coplanar test (default 1e-8).\n");
+ printf(" -X Suppresses use of exact arithmetic.\n");
+ printf(" -M No merge of coplanar facets or very close vertices.\n");
+ printf(" -w Generates weighted Delaunay (regular) triangulation.\n");
+ printf(" -c Retains the convex hull of the PLC.\n");
printf(" -d Detects self-intersections of facets of the PLC.\n");
printf(" -z Numbers all output items starting from zero.\n");
printf(" -f Outputs all faces to .face file.\n");
@@ -2919,12 +2926,12 @@ void tetgenbehavior::syntax()
printf(" -n Outputs tetrahedra neighbors to .neigh file.\n");
printf(" -v Outputs Voronoi diagram to files.\n");
printf(" -g Outputs mesh to .mesh file for viewing by Medit.\n");
- printf(" -K Outputs mesh to .vtk file for viewing by Paraview.\n");
+ printf(" -k Outputs mesh to .vtk file for viewing by Paraview.\n");
printf(" -J No jettison of unused vertices from output .node file.\n");
printf(" -B Suppresses output of boundary information.\n");
printf(" -N Suppresses output of .node file.\n");
printf(" -E Suppresses output of .ele file.\n");
- printf(" -F Suppresses output of .face file.\n");
+ printf(" -F Suppresses output of .face and .edge file.\n");
printf(" -I Suppresses mesh iteration numbers.\n");
printf(" -C Checks the consistency of the final mesh.\n");
printf(" -Q Quiet: No terminal output except errors.\n");
@@ -2943,20 +2950,18 @@ void tetgenbehavior::usage()
printf("TetGen\n");
printf("A Quality Tetrahedral Mesh Generator and 3D Delaunay ");
printf("Triangulator\n");
- printf("Version 1.5 (February 21, 2012).\n");
+ printf("Version 1.5\n");
+ printf("(March 27, 2013)\n");
printf("\n");
- printf("Copyright (C) 2002 - 2012\n");
+ printf("Copyright (C) 2002 - 2013\n");
printf("Hang Si\n");
printf("Mohrenstr. 39, 10117 Berlin, Germany\n");
- printf("Hang.Si@wias-berlin.de\n");
+ printf("si@wias-berlin.de\n");
printf("\n");
printf("What Can TetGen Do?\n");
printf("\n");
- printf(" TetGen generates exact Delaunay tetrahedralizations, exact\n");
- printf(" constrained Delaunay tetrahedralizations, and quality ");
- printf("tetrahedral\n meshes. The latter are nicely graded and whose ");
- printf("tetrahedra have\n radius-edge ratio bounded, thus are suitable ");
- printf("for finite element and\n finite volume analysis.\n");
+ printf(" TetGen generates Delaunay tetrahedralizations, constrained\n");
+ printf(" Delaunay tetrahedralizations, and quality tetrahedral meshes.\n");
printf("\n");
printf("Command Line Syntax:\n");
printf("\n");
@@ -2977,19 +2982,21 @@ void tetgenbehavior::usage()
printf("Examples of How to Use TetGen:\n");
printf("\n");
printf(" \'tetgen object\' reads vertices from object.node, and writes ");
- printf("their\n Delaunay tetrahedralization to object.1.node and ");
- printf("object.1.ele.\n");
+ printf("their\n Delaunay tetrahedralization to object.1.node, ");
+ printf("object.1.ele\n (tetrahedra), and object.1.face");
+ printf(" (convex hull faces).\n");
printf("\n");
printf(" \'tetgen -p object\' reads a PLC from object.poly or object.");
printf("smesh (and\n possibly object.node) and writes its constrained ");
- printf("Delaunay\n tetrahedralization to object.1.node, object.1.ele and ");
- printf("object.1.face.\n");
+ printf("Delaunay\n tetrahedralization to object.1.node, object.1.ele, ");
+ printf("object.1.face,\n");
+ printf(" (boundary faces) and object.1.edge (boundary edges).\n");
printf("\n");
printf(" \'tetgen -pq1.414a.1 object\' reads a PLC from object.poly or\n");
printf(" object.smesh (and possibly object.node), generates a mesh ");
printf("whose\n tetrahedra have radius-edge ratio smaller than 1.414 and ");
printf("have volume\n of 0.1 or less, and writes the mesh to ");
- printf("object.1.node, object.1.ele\n and object.1.face.\n");
+ printf("object.1.node, object.1.ele,\n object.1.face, and object.1.edge\n");
printf("\n");
printf("Please send bugs/comments to Hang Si <si@wias-berlin.de>\n");
terminatetetgen(0);
@@ -3004,19 +3011,6 @@ void tetgenbehavior::usage()
// of a C/C++ program. They together represent the command line user invoked //
// from an environment in which TetGen is running. //
// //
-// When TetGen is invoked from an environment. 'argc' is nonzero, switches //
-// and input filename should be supplied as zero-terminated strings in //
-// argv[0] through argv[argc - 1] and argv[0] shall be the name used to //
-// invoke TetGen, i.e. "tetgen". Switches are previously started with a //
-// dash '-' to identify them from the input filename. //
-// //
-// When TetGen is called from within another program. 'argc' is set to zero. //
-// switches are given in one zero-terminated string (no previous dash is //
-// required.), and 'argv' is a pointer points to this string. No input //
-// filename is required (usually the input data has been directly created by //
-// user in the 'tetgenio' structure). A default filename 'tetgen-tmpfile' //
-// will be created for debugging output purpose. //
-// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenbehavior::parse_commandline(int argc, char **argv)
@@ -3024,7 +3018,6 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
int startindex;
int increment;
int meshnumber;
- int scount, ocount;
int i, j, k;
char workstring[1024];
@@ -3038,12 +3031,9 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
strcpy(commandline, argv[0]);
strcat(commandline, " ");
}
-
- // Count the number of '-O' and '-o' be used.
- scount = ocount = 0;
for (i = startindex; i < argc; i++) {
- // Remember the command line switches.
+ // Remember the command line for output.
strcat(commandline, argv[i]);
strcat(commandline, " ");
if (startindex == 1) {
@@ -3051,7 +3041,6 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
if (argv[i][0] != '-') {
strncpy(infilename, argv[i], 1024 - 1);
infilename[1024 - 1] = '\0';
- // Go to the next string directly.
continue;
}
}
@@ -3072,11 +3061,17 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
facet_ang_tol = (REAL) strtod(workstring, (char **) NULL);
}
} else if (argv[i][j] == 's') {
- psc = 1;
+ psc = 1;
+ } else if (argv[i][j] == 'Y') {
+ nobisect = 1;
+ if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
+ nobisect_param = (argv[i][j + 1] - '0');
+ j++;
+ }
} else if (argv[i][j] == 'r') {
- refine++;
+ refine = 1;
} else if (argv[i][j] == 'q') {
- quality++;
+ quality = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3087,30 +3082,47 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- if (quality == 1) { // -q#
- minratio = (REAL) strtod(workstring, (char **) NULL);
- } else if (quality == 2) { // -qq#
+ minratio = (REAL) strtod(workstring, (char **) NULL);
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
mindihedral = (REAL) strtod(workstring, (char **) NULL);
}
}
- } else if (argv[i][j] == 'm') {
- metric++;
- } else if (argv[i][j] == 'Y') {
- nobisect = 1;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
+ optmaxdihedral = (REAL) strtod(workstring, (char **) NULL);
}
- workstring[k] = '\0';
- nobisect_param = (int) strtol(workstring, (char **) NULL, 0);
}
} else if (argv[i][j] == 'w') {
weighted = 1;
+ if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
+ weighted_param = (argv[i][j + 1] - '0');
+ j++;
+ }
+ } else if (argv[i][j] == 'b') {
+ // -b(brio_threshold/brio_ratio/hilbert_limit/hilbert_order)
+ brio_hilbert = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3121,8 +3133,66 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- weighted_param = (int) strtol(workstring, (char **) NULL, 0);
+ brio_threshold = (int) strtol(workstring, (char **) &workstring, 0);
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
+ brio_ratio = (REAL) strtod(workstring, (char **) NULL);
+ }
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
+ hilbert_limit = (int) strtol(workstring, (char **) &workstring, 0);
+ }
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
+ hilbert_order = (REAL) strtod(workstring, (char **) NULL);
+ }
+ }
+ if (brio_threshold == 0) { // -b0
+ brio_hilbert = 0; // Turn off BRIO-Hilbert sorting.
}
+ if (brio_ratio >= 1.0) { // -b/1
+ no_sort = 1;
+ brio_hilbert = 0; // Turn off BRIO-Hilbert sorting.
+ }
+ } else if (argv[i][j] == 'l') {
+ incrflip = 1;
+ } else if (argv[i][j] == 'L') {
+ flipinsert = 1;
+ } else if (argv[i][j] == 'm') {
+ metric = 1;
} else if (argv[i][j] == 'a') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
@@ -3141,71 +3211,44 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
varvolume = 1;
}
} else if (argv[i][j] == 'A') {
- regionattrib++;
- } else if (argv[i][j] == 'l') {
- incrflip = 1;
- // Check if a smallest edge length is given.
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- minedgelength = (REAL) strtod(workstring, (char **) NULL);
- }
- } else if (argv[i][j] == 'L') {
- flipinsert++;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- if (flipinsert == 1) { // -L
- fliplinklevel = (int) strtol(workstring, (char **) NULL, 0);
- } else if (flipinsert == 2) { // -LL
- flipstarsize = (int) strtol(workstring, (char **) NULL, 0);
- }
- }
- } else if (argv[i][j] == 'u') {
- // Set the maximum btree node size, -u0 means do not use btree.
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- max_btreenode_size = (int) strtol(workstring, (char **) NULL, 0);
- }
- if (max_btreenode_size == 0) {
- btree = 0;
+ regionattrib = 1;
+ } else if (argv[i][j] == 'D') {
+ conforming = 1;
+ if ((argv[i][j + 1] >= '1') && (argv[i][j + 1] <= '3')) {
+ reflevel = (argv[i][j + 1] - '1') + 1;
+ j++;
}
- } else if (argv[i][j] == 'U') {
- hilbertcurve = 1;
- btree = 0;
} else if (argv[i][j] == 'i') {
insertaddpoints = 1;
} else if (argv[i][j] == 'd') {
diagnose = 1;
} else if (argv[i][j] == 'c') {
convex = 1;
+ } else if (argv[i][j] == 'M') {
+ nomergefacet = 1;
+ nomergevertex = 1;
+ if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '1')) {
+ nomergefacet = (argv[i][j + 1] - '0');
+ j++;
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '1')) {
+ nomergevertex = (argv[i][j + 1] - '0');
+ j++;
+ }
+ }
+ } else if (argv[i][j] == 'X') {
+ if (argv[i][j + 1] == '1') {
+ nostaticfilter = 1;
+ j++;
+ } else {
+ noexact = 1;
+ }
} else if (argv[i][j] == 'z') {
zeroindex = 1;
} else if (argv[i][j] == 'f') {
- facesout = 1;
+ facesout++;
} else if (argv[i][j] == 'e') {
edgesout++;
} else if (argv[i][j] == 'n') {
@@ -3214,10 +3257,8 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
voroout = 1;
} else if (argv[i][j] == 'g') {
meditview = 1;
- } else if (argv[i][j] == 'K') {
+ } else if (argv[i][j] == 'k') {
vtkview = 1;
- } else if (argv[i][j] == 'M') {
- nomerge = 1;
} else if (argv[i][j] == 'J') {
nojettison = 1;
} else if (argv[i][j] == 'B') {
@@ -3226,10 +3267,6 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
nonodewritten = 1;
} else if (argv[i][j] == 'E') {
noelewritten = 1;
- if (argv[i][j + 1] == '2') {
- j++;
- noelewritten = 2;
- }
} else if (argv[i][j] == 'F') {
nofacewritten = 1;
} else if (argv[i][j] == 'I') {
@@ -3249,53 +3286,38 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
steinerleft = (int) strtol(workstring, (char **) NULL, 0);
}
} else if (argv[i][j] == 'o') {
- ocount++;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
- j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- if (ocount == 1) { // -o#
+ if (argv[i][j + 1] == '2') {
+ order = 2;
+ j++;
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ k = 0;
+ while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
+ (argv[i][j + 1] == '.')) {
+ j++;
+ workstring[k] = argv[i][j];
+ k++;
+ }
+ workstring[k] = '\0';
optmaxdihedral = (REAL) strtod(workstring, (char **) NULL);
- } else if (ocount == 2) { // -oo#
- optminsmtdihed = (REAL) strtod(workstring, (char **) NULL);
- } else if (ocount == 3) { // -ooo#
- optminslidihed = (REAL) strtod(workstring, (char **) NULL);
- }
+ }
}
} else if (argv[i][j] == 'O') {
- scount++;
- if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.')) {
- k = 0;
- while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
- (argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
- (argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
+ if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
+ optlevel = (argv[i][j + 1] - '0');
+ j++;
+ }
+ if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
+ j++;
+ if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '7')) {
+ optscheme = (argv[i][j + 1] - '0');
j++;
- workstring[k] = argv[i][j];
- k++;
- }
- workstring[k] = '\0';
- if (scount == 1) { // -O
- optlevel = (int) strtol(workstring, (char **) NULL, 0);
- } else if (scount == 2) { // -OO
- optpasses = (int) strtol(workstring, (char **) NULL, 0);
- } else if (scount == 3) { // -OOO
- optmaxfliplevel = (int) strtol(workstring, (char **) NULL, 0);
- } else if (scount == 4) { // -OOOO
- delmaxfliplevel = (int) strtol(workstring, (char **) NULL, 0);
- } else if (scount == 5) { // -OOOOO (5 Os)
- optmaxflipstarsize = (int) strtol(workstring, (char **) NULL, 0);
}
}
- } else if (argv[i][j] == 'D') {
- conforming = 1;
+ } else if (argv[i][j] == 'T') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3307,9 +3329,17 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- reflevel = (int) strtol(workstring, (char **) NULL, 0);
+ epsilon = (REAL) strtod(workstring, (char **) NULL);
}
- } else if (argv[i][j] == 'T') {
+ } else if (argv[i][j] == 'R') {
+ reversetetori = 1;
+ } else if (argv[i][j] == 'C') {
+ docheck++;
+ } else if (argv[i][j] == 'Q') {
+ quiet = 1;
+ } else if (argv[i][j] == 'V') {
+ verbose++;
+ } else if (argv[i][j] == 'x') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3321,14 +3351,14 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- epsilon = (REAL) strtod(workstring, (char **) NULL);
+ tetrahedraperblock = (int) strtol(workstring, (char **) NULL, 0);
+ if (tetrahedraperblock > 8188) {
+ vertexperblock = tetrahedraperblock / 2;
+ shellfaceperblock = vertexperblock / 2;
+ } else {
+ tetrahedraperblock = 8188;
+ }
}
- } else if (argv[i][j] == 'C') {
- docheck++;
- } else if (argv[i][j] == 'Q') {
- quiet = 1;
- } else if (argv[i][j] == 'V') {
- verbose++;
} else if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
(argv[i][j] == '?')) {
usage();
@@ -3395,6 +3425,10 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
if (diagnose && !plc) { // -d
plc = 1;
}
+ if (plc && !quality && !nobisect) { // -p only
+ // Create a CDT, do not do mesh optimization.
+ optlevel = 0;
+ }
// Detect improper combinations of switches.
if (plc && refine) {
@@ -3430,18 +3464,16 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
}
}
}
- if (ocount == 0) {
- // No user-specified dihedral angle bound. Use default ones.
- if (!quality) {
- if (optmaxdihedral < 179.0) {
- optmaxdihedral = 179.0;
- }
- if (optminsmtdihed < 179.999) {
- optminsmtdihed = 179.999;
- }
- if (optminslidihed < 179.999) {
- optminslidihed = 179.99;
- }
+ // No user-specified dihedral angle bound. Use default ones.
+ if (!quality) {
+ if (optmaxdihedral < 179.0) {
+ optmaxdihedral = 179.0;
+ }
+ if (optminsmtdihed < 179.999) {
+ optminsmtdihed = 179.999;
+ }
+ if (optminslidihed < 179.999) {
+ optminslidihed = 179.999;
}
}
@@ -3497,18 +3529,25 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
// Initialize fast lookup tables for mesh maniplulation primitives.
-int tetgenmesh::mod12[36] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
-
-int tetgenmesh::mod6[18] = {0, 1, 2, 3, 4, 5,
- 0, 1, 2, 3, 4, 5,
- 0, 1, 2, 3, 4, 5};
-
-// Table 'edgepivot' takes an directed edge (version) as input, returns the
+int tetgenmesh::bondtbl[12][12] = {{0,},};
+int tetgenmesh::enexttbl[12] = {0,};
+int tetgenmesh::eprevtbl[12] = {0,};
+int tetgenmesh::enextesymtbl[12] = {0,};
+int tetgenmesh::eprevesymtbl[12] = {0,};
+int tetgenmesh::eorgoppotbl[12] = {0,};
+int tetgenmesh::edestoppotbl[12] = {0,};
+int tetgenmesh::fsymtbl[12][12] = {{0,},};
+int tetgenmesh::facepivot1[12] = {0,};
+int tetgenmesh::facepivot2[12][12] = {{0,},};
+int tetgenmesh::tsbondtbl[12][6] = {{0,},};
+int tetgenmesh::stbondtbl[12][6] = {{0,},};
+int tetgenmesh::tspivottbl[12][6] = {{0,},};
+int tetgenmesh::stpivottbl[12][6] = {{0,},};
+
+// Table 'esymtbl' takes an directed edge (version) as input, returns the
// inversed edge (version) of it.
-int tetgenmesh::edgepivot[12] = {9, 6, 11, 4, 3, 7, 1, 5, 10, 0, 8, 2};
+int tetgenmesh::esymtbl[12] = {9, 6, 11, 4, 3, 7, 1, 5, 10, 0, 8, 2};
// The following four tables give the 12 permutations of the set {0,1,2,3}.
// An offset 4 is added to each element for a direct access of the points
@@ -3525,6 +3564,11 @@ int tetgenmesh::oppopivot[12] = {4, 5, 6, 7, 4, 5, 6, 7, 4, 5, 6, 7};
int tetgenmesh::ver2edge[12] = {0, 1, 2, 3, 3, 5, 1, 5, 4, 0, 4, 2};
int tetgenmesh::edge2ver[ 6] = {0, 1, 2, 3, 8, 5};
+// Edge versions whose apex or opposite may be dummypoint.
+
+int tetgenmesh::epivot[12] = {4, 5, 2, 11, 4, 5, 2, 11, 4, 5, 2, 11};
+
+
// Table 'snextpivot' takes an edge version as input, returns the next edge
// version in the same edge ring.
@@ -3538,11 +3582,91 @@ int tetgenmesh::sorgpivot [6] = {3, 4, 4, 5, 5, 3};
int tetgenmesh::sdestpivot[6] = {4, 3, 5, 4, 3, 5};
int tetgenmesh::sapexpivot[6] = {5, 5, 3, 3, 4, 4};
-// Edge versions whose apex or opposite may be dummypoint.
+///////////////////////////////////////////////////////////////////////////////
+// //
+// inittable() Initialize the look-up tables. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::inittables()
+{
+ int i, j;
+
+
+ // i = t1.ver; j = t2.ver;
+ for (i = 0; i < 12; i++) {
+ for (j = 0; j < 12; j++) {
+ bondtbl[i][j] = (j & 3) + (((i & 12) + (j & 12)) % 12);
+ }
+ }
+
+
+ // i = t1.ver; j = t2.ver
+ for (i = 0; i < 12; i++) {
+ for (j = 0; j < 12; j++) {
+ fsymtbl[i][j] = (j + 12 - (i & 12)) % 12;
+ }
+ }
-int tetgenmesh::epivot[4] = {4, 5, 2, 11};
+
+ for (i = 0; i < 12; i++) {
+ facepivot1[i] = (esymtbl[i] & 3);
+ }
+
+ for (i = 0; i < 12; i++) {
+ for (j = 0; j < 12; j++) {
+ facepivot2[i][j] = fsymtbl[esymtbl[i]][j];
+ }
+ }
+
+ for (i = 0; i < 12; i++) {
+ enexttbl[i] = (i + 4) % 12;
+ eprevtbl[i] = (i + 8) % 12;
+ }
+
+ for (i = 0; i < 12; i++) {
+ enextesymtbl[i] = esymtbl[enexttbl[i]];
+ eprevesymtbl[i] = esymtbl[eprevtbl[i]];
+ }
+
+ for (i = 0; i < 12; i++) {
+ eorgoppotbl [i] = eprevtbl[esymtbl[enexttbl[i]]];
+ edestoppotbl[i] = enexttbl[esymtbl[eprevtbl[i]]];
+ }
+
+ int soffset, toffset;
+
+ // i = t.ver, j = s.shver
+ for (i = 0; i < 12; i++) {
+ for (j = 0; j < 6; j++) {
+ if ((j & 1) == 0) {
+ soffset = (6 - ((i & 12) >> 1)) % 6;
+ toffset = (12 - ((j & 6) << 1)) % 12;
+ } else {
+ soffset = (i & 12) >> 1;
+ toffset = (j & 6) << 1;
+ }
+ tsbondtbl[i][j] = (j & 1) + (((j & 6) + soffset) % 6);
+ stbondtbl[i][j] = (i & 3) + (((i & 12) + toffset) % 12);
+ }
+ }
+ // i = t.ver, j = s.shver
+ for (i = 0; i < 12; i++) {
+ for (j = 0; j < 6; j++) {
+ if ((j & 1) == 0) {
+ soffset = (i & 12) >> 1;
+ toffset = (j & 6) << 1;
+ } else {
+ soffset = (6 - ((i & 12) >> 1)) % 6;
+ toffset = (12 - ((j & 6) << 1)) % 12;
+ }
+ tspivottbl[i][j] = (j & 1) + (((j & 6) + soffset) % 6);
+ stpivottbl[i][j] = (i & 3) + (((i & 12) + toffset) % 12);
+ }
+ }
+}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -3576,6 +3700,7 @@ void tetgenmesh::arraypool::poolinit(int sizeofobject, int log2objperblk)
log2objectsperblock = log2objperblk;
// Compute the number of objects in each block.
objectsperblock = ((int) 1) << log2objectsperblock;
+ objectsperblockmark = objectsperblock - 1;
// No memory has been allocated.
totalmemory = 0l;
@@ -3753,6 +3878,7 @@ int tetgenmesh::arraypool::newindex(void **newptr)
return newindex;
}
+
///////////////////////////////////////////////////////////////////////////////
// //
// memorypool() The constructors of memorypool. //
@@ -3766,7 +3892,6 @@ tetgenmesh::memorypool::memorypool()
deaditemstack = (void *) NULL;
pathblock = (void **) NULL;
pathitem = (void *) NULL;
- itemwordtype = POINTER;
alignbytes = 0;
itembytes = itemwords = 0;
itemsperblock = 0;
@@ -3775,10 +3900,10 @@ tetgenmesh::memorypool::memorypool()
pathitemsleft = 0;
}
-tetgenmesh::memorypool::
-memorypool(int bytecount, int itemcount, enum wordtype wtype, int alignment)
+tetgenmesh::memorypool::memorypool(int bytecount, int itemcount, int wsize,
+ int alignment)
{
- poolinit(bytecount, itemcount, wtype, alignment);
+ poolinit(bytecount, itemcount, wsize, alignment);
}
///////////////////////////////////////////////////////////////////////////////
@@ -3812,14 +3937,9 @@ tetgenmesh::memorypool::~memorypool()
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::memorypool::
-poolinit(int bytecount, int itemcount, enum wordtype wtype, int alignment)
+void tetgenmesh::memorypool::poolinit(int bytecount,int itemcount,int wordsize,
+ int alignment)
{
- int wordsize;
-
- // Initialize values in the pool.
- itemwordtype = wtype;
- wordsize = (itemwordtype == POINTER) ? sizeof(void *) : sizeof(REAL);
// Find the proper alignment, which must be at least as large as:
// - The parameter `alignment'.
// - The primary word type, to avoid unaligned accesses.
@@ -3929,11 +4049,7 @@ void* tetgenmesh::memorypool::alloc()
// Allocate a new item.
newitem = nextitem;
// Advance `nextitem' pointer to next free item in block.
- if (itemwordtype == POINTER) {
- nextitem = (void *) ((void **) nextitem + itemwords);
- } else {
- nextitem = (void *) ((REAL *) nextitem + itemwords);
- }
+ nextitem = (void *) ((uintptr_t) nextitem + itembytes);
unallocateditems--;
maxitems++;
}
@@ -4017,25 +4133,18 @@ void* tetgenmesh::memorypool::traverse()
}
newitem = pathitem;
// Find the next item in the block.
- if (itemwordtype == POINTER) {
- pathitem = (void *) ((void **) pathitem + itemwords);
- } else {
- pathitem = (void *) ((REAL *) pathitem + itemwords);
- }
+ pathitem = (void *) ((uintptr_t) pathitem + itembytes);
pathitemsleft--;
return newitem;
}
-
-
///////////////////////////////////////////////////////////////////////////////
// //
// makeindex2pointmap() Create a map from index to vertices. //
// //
// 'idx2verlist' returns the created map. Traverse all vertices, a pointer //
// to each vertex is set into the array. The pointer to the first vertex is //
-// saved in 'idx2verlist[0]'. Don't forget to minus 'in->firstnumber' when //
-// to get the vertex form its index. //
+// saved in 'idx2verlist[in->firstnumber]'. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -4052,14 +4161,13 @@ void tetgenmesh::makeindex2pointmap(point*& idx2verlist)
points->traversalinit();
pointloop = pointtraverse();
- idx = in->firstnumber;;
+ idx = in->firstnumber;
while (pointloop != (point) NULL) {
idx2verlist[idx++] = pointloop;
pointloop = pointtraverse();
}
}
-
///////////////////////////////////////////////////////////////////////////////
// //
// makesubfacemap() Create a map from vertex to subfaces incident at it. //
@@ -4163,15 +4271,13 @@ void tetgenmesh::tetrahedrondealloc(tetrahedron *dyingtetrahedron)
// dead tetrahedra when traversing the list of all tetrahedra.
dyingtetrahedron[4] = (tetrahedron) NULL;
- //if (b->plc || b->refine) { //if (b->useshelles) {
- // Dealloc the space to subfaces/subsegments.
- if (dyingtetrahedron[8] != NULL) {
- tet2segpool->dealloc((shellface *) dyingtetrahedron[8]);
- }
- if (dyingtetrahedron[9] != NULL) {
- tet2subpool->dealloc((shellface *) dyingtetrahedron[9]);
- }
- //}
+ // Dealloc the space to subfaces/subsegments.
+ if (dyingtetrahedron[8] != NULL) {
+ tet2segpool->dealloc((shellface *) dyingtetrahedron[8]);
+ }
+ if (dyingtetrahedron[9] != NULL) {
+ tet2subpool->dealloc((shellface *) dyingtetrahedron[9]);
+ }
tetrahedrons->dealloc((void *) dyingtetrahedron);
}
@@ -4244,38 +4350,6 @@ tetgenmesh::shellface* tetgenmesh::shellfacetraverse(memorypool *pool)
return newshellface;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// badfacedealloc() Deallocate space for a badface, marking it dead. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::badfacedealloc(memorypool *pool, badface *dying)
-{
- // Set badface's forg to NULL. This makes it possible to detect dead
- // ones when traversing the list of all items.
- dying->forg = (point) NULL;
- pool->dealloc((void *) dying);
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// badfacetraverse() Traverse the pools, skipping dead ones. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-tetgenmesh::badface* tetgenmesh::badfacetraverse(memorypool *pool)
-{
- badface *newsh;
-
- do {
- newsh = (badface *) pool->traverse();
- if (newsh == (badface *) NULL) {
- return (badface *) NULL;
- }
- } while (newsh->forg == (point) NULL); // Skip dead ones.
- return newsh;
-}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -4319,6 +4393,7 @@ tetgenmesh::point tetgenmesh::pointtraverse()
void tetgenmesh::maketetrahedron(triface *newtet)
{
newtet->tet = (tetrahedron *) tetrahedrons->alloc();
+
// Initialize the four adjoining tetrahedra to be "outer space".
newtet->tet[0] = NULL;
newtet->tet[1] = NULL;
@@ -4332,9 +4407,9 @@ void tetgenmesh::maketetrahedron(triface *newtet)
// No attached segments and sbfaces yet.
newtet->tet[8] = NULL;
newtet->tet[9] = NULL;
- // Initialize the marker (for flags).
+ // Initialize the marker (clear all flags).
setelemmarker(newtet->tet, 0);
- for (int i = 0; i < in->numberoftetrahedronattributes; i++) {
+ for (int i = 0; i < numelemattrib; i++) {
setelemattribute(newtet->tet, i, 0.0);
}
if (b->varvolume) {
@@ -4355,6 +4430,7 @@ void tetgenmesh::maketetrahedron(triface *newtet)
void tetgenmesh::makeshellface(memorypool *pool, face *newface)
{
newface->sh = (shellface *) pool->alloc();
+
// No adjointing subfaces.
newface->sh[0] = NULL;
newface->sh[1] = NULL;
@@ -4382,7 +4458,7 @@ void tetgenmesh::makeshellface(memorypool *pool, face *newface)
setshellmark(*newface, 0);
// Set the default face type.
setshelltype(*newface, NSHARP);
- // Initialize the version to be Zero.
+
newface->shver = 0;
}
@@ -4394,9 +4470,14 @@ void tetgenmesh::makeshellface(memorypool *pool, face *newface)
void tetgenmesh::makepoint(point* pnewpoint, enum verttype vtype)
{
- int ptmark, i;
+ int i;
*pnewpoint = (point) points->alloc();
+
+ // Initialize the point attributes.
+ for (i = 0; i < numpointattrib; i++) {
+ (*pnewpoint)[3 + i] = 0.0;
+ }
// Initialize the metric tensor.
for (i = 0; i < sizeoftensor; i++) {
(*pnewpoint)[pointmtrindex + i] = 0.0;
@@ -4411,20 +4492,11 @@ void tetgenmesh::makepoint(point* pnewpoint, enum verttype vtype)
}
}
// Initialize the point marker (starting from in->firstnumber).
- ptmark = (int) points->items - (in->firstnumber == 1 ? 0 : 1);
- setpointmark(*pnewpoint, ptmark);
- // Initialize the point type.
+ setpointmark(*pnewpoint, (int) (points->items) - (!in->firstnumber));
+ // Clear all flags.
+ ((int *) (*pnewpoint))[pointmarkindex + 1] = 0;
+ // Initialize (set) the point type.
setpointtype(*pnewpoint, vtype);
- // Clear the point flags.
- puninfect(*pnewpoint);
- punmarktest(*pnewpoint);
- if (b->psc) {
- // Initialize the u,v coordinates.
- setpointgeomuv(*pnewpoint, 0, 0);
- setpointgeomuv(*pnewpoint, 1, 0);
- // Initialize the geometry tag.
- setpointgeomtag(*pnewpoint, 0);
- }
}
///////////////////////////////////////////////////////////////////////////////
@@ -4440,11 +4512,36 @@ void tetgenmesh::makepoint(point* pnewpoint, enum verttype vtype)
void tetgenmesh::initializepools()
{
- enum memorypool::wordtype wtype;
- int pointsize, elesize, shsize;
+ int pointsize = 0, elesize = 0, shsize = 0;
+ int i;
if (b->verbose) {
printf(" Initializing memorypools.\n");
+ printf(" tetrahedron per block: %d.\n", b->tetrahedraperblock);
+ }
+
+ inittables();
+
+ // There are three input point lists available, which are in, addin,
+ // and bgm->in. These point lists may have different number of
+ // attributes. Decide the maximum number.
+ numpointattrib = in->numberofpointattributes;
+ if (bgm != NULL) {
+ if (bgm->in->numberofpointattributes > numpointattrib) {
+ numpointattrib = bgm->in->numberofpointattributes;
+ }
+ }
+ if (addin != NULL) {
+ if (addin->numberofpointattributes > numpointattrib) {
+ numpointattrib = addin->numberofpointattributes;
+ }
+ }
+ if (b->weighted || b->flipinsert) { // -w or -L.
+ // The internal number of point attribute needs to be at least 1
+ // (for storing point weights).
+ if (numpointattrib == 0) {
+ numpointattrib = 1;
+ }
}
// Default varconstraint = 0;
@@ -4452,17 +4549,16 @@ void tetgenmesh::initializepools()
checkconstraints = 1;
}
- // Each vertex has three coordinates plus a weight, hence 4 REALs.
// The index within each point at which its metric tensor is found.
+ // Each vertex has three coordinates.
if (b->psc) {
- // For '-s' option (PSC), the u,v coordinates are provided. It is
- // saved directly after the list of point attributes.
- pointmtrindex = 6 + in->numberofpointattributes;
+ // '-s' option (PSC), the u,v coordinates are provided.
+ pointmtrindex = 5 + numpointattrib;
} else {
- pointmtrindex = 4 + in->numberofpointattributes;
+ pointmtrindex = 3 + numpointattrib;
}
// The index within each point at which its u, v coordinates are found.
- pointparamindex = pointmtrindex - 2;
+ pointparamindex = 3 + (numpointattrib > 0);
// For '-m' option. A tensor field is provided (*.mtr or *.b.mtr file).
if (b->metric) {
// Decide the size (1, 3, or 6) of the metric tensor.
@@ -4491,19 +4587,11 @@ void tetgenmesh::initializepools()
// - a pointer to a parent point, read by point2ppt()).
// - a pointer to a subface or segment, read by point2sh();
if (b->metric && (bgm != (tetgenmesh *) NULL)) {
- // Increase one pointer to into the background mesh, point2bgmtet().
+ // Increase one pointer into the background mesh, point2bgmtet().
pointsize = (point2simindex + 4) * sizeof(tetrahedron);
} else {
pointsize = (point2simindex + 3) * sizeof(tetrahedron);
}
- // The index within each point at which a pbc point is found.
- point2pbcptindex = (pointsize + sizeof(tetrahedron) - 1)
- / sizeof(tetrahedron);
- if (checkpbcs) {
- // Increase the size by one pointer to a corresponding pbc point,
- // read by point2pbcpt().
- pointsize = (point2pbcptindex + 1) * sizeof(tetrahedron);
- }
} else {
// Increase the point size by two pointer, which are:
// - a pointer to a tet, read by point2tet();
@@ -4517,14 +4605,10 @@ void tetgenmesh::initializepools()
// - an integer for boundary marker;
// - an integer for vertex type;
// - an integer for geometry tag (optional, -s option).
- //pointsize = (pointmarkindex + 2)*sizeof(int); // Wrong for 64 bit system.
pointsize = (pointmarkindex + 2 + (b->psc ? 1 : 0)) * sizeof(tetrahedron);
- // Decide the wordtype used in vertex pool.
- wtype = (sizeof(REAL) >= sizeof(tetrahedron)) ?
- memorypool::FLOATINGPOINT : memorypool::POINTER;
// Initialize the pool of vertices.
- points = new memorypool(pointsize, b->vertexperblock, wtype, 0);
+ points = new memorypool(pointsize, b->vertexperblock, sizeof(REAL), 0);
if (b->verbose) {
printf(" Size of a point: %d bytes.\n", points->itembytes);
@@ -4532,7 +4616,32 @@ void tetgenmesh::initializepools()
// Initialize the infinite vertex.
dummypoint = (point) new char[pointsize];
- setpointmark(dummypoint, -1);
+ // Initialize all fields of this point.
+ dummypoint[0] = 0.0;
+ dummypoint[1] = 0.0;
+ dummypoint[2] = 0.0;
+ for (i = 0; i < numpointattrib; i++) {
+ dummypoint[3 + i] = 0.0;
+ }
+ // Initialize the metric tensor.
+ for (i = 0; i < sizeoftensor; i++) {
+ dummypoint[pointmtrindex + i] = 0.0;
+ }
+ setpoint2tet(dummypoint, NULL);
+ setpoint2ppt(dummypoint, NULL);
+ if (b->plc || b->psc || b->refine) {
+ // Initialize the point-to-simplex field.
+ setpoint2sh(dummypoint, NULL);
+ if (b->metric && (bgm != NULL)) {
+ setpoint2bgmtet(dummypoint, NULL);
+ }
+ }
+ // Initialize the point marker (starting from in->firstnumber).
+ setpointmark(dummypoint, -1); // The unique marker for dummypoint.
+ // Clear all flags.
+ ((int *) (dummypoint))[pointmarkindex + 1] = 0;
+ // Initialize (set) the point type.
+ setpointtype(dummypoint, UNUSEDVERTEX); // Does not matter.
// The number of bytes occupied by a tetrahedron is varying by the user-
// specified options. The contents of the first 12 pointers are listed
@@ -4558,26 +4667,28 @@ void tetgenmesh::initializepools()
assert((sizeof(tetrahedron) % sizeof(int)) == 0);
elemmarkerindex = (elesize - sizeof(tetrahedron)) / sizeof(int);
+ // The actual number of element attributes. Note that if the
+ // `b->regionattrib' flag is set, an additional attribute will be added.
+ numelemattrib = in->numberoftetrahedronattributes + (b->regionattrib > 0);
+
// The index within each element at which its attributes are found, where
// the index is measured in REALs.
elemattribindex = (elesize + sizeof(REAL) - 1) / sizeof(REAL);
// The index within each element at which the maximum voulme bound is
- // found, where the index is measured in REALs. Note that if the
- // `b->regionattrib' flag is set, an additional attribute will be added.
- volumeboundindex = elemattribindex + in->numberoftetrahedronattributes
- + (b->regionattrib > 0);
+ // found, where the index is measured in REALs.
+ volumeboundindex = elemattribindex + numelemattrib;
// If element attributes or an constraint are needed, increase the number
// of bytes occupied by an element.
if (b->varvolume) {
elesize = (volumeboundindex + 1) * sizeof(REAL);
- } else if (in->numberoftetrahedronattributes + b->regionattrib > 0) {
+ } else if (numelemattrib > 0) {
elesize = volumeboundindex * sizeof(REAL);
}
// Having determined the memory size of an element, initialize the pool.
- tetrahedrons = new memorypool(elesize, b->tetrahedraperblock,
- memorypool::POINTER, 16);
+ tetrahedrons = new memorypool(elesize, b->tetrahedraperblock, sizeof(void *),
+ 16);
if (b->verbose) {
printf(" Size of a tetrahedron: %d (%d) bytes.\n", elesize,
@@ -4604,13 +4715,12 @@ void tetgenmesh::initializepools()
shmarkindex = (shsize + sizeof(int) - 1) / sizeof(int);
// Increase the number of bytes by two or three integers, one for facet
// marker, one for shellface type, and optionally one for pbc group.
- shsize = (shmarkindex + 2 + checkpbcs) * sizeof(shellface);
+ shsize = (shmarkindex + 2) * sizeof(shellface);
// Initialize the pool of subfaces. Each subface record is eight-byte
// aligned so it has room to store an edge version (from 0 to 5) in
// the least three bits.
- subfaces = new memorypool(shsize, b->shellfaceperblock,
- memorypool::POINTER, 8);
+ subfaces = new memorypool(shsize, b->shellfaceperblock, sizeof(void *), 8);
if (b->verbose) {
printf(" Size of a shellface: %d (%d) bytes.\n", shsize,
@@ -4619,40 +4729,37 @@ void tetgenmesh::initializepools()
// Initialize the pool of subsegments. The subsegment's record is same
// with subface.
- subsegs = new memorypool(shsize, b->shellfaceperblock,
- memorypool::POINTER, 8);
+ subsegs = new memorypool(shsize, b->shellfaceperblock, sizeof(void *), 8);
// Initialize the pool for tet-subseg connections.
tet2segpool = new memorypool(6 * sizeof(shellface), b->shellfaceperblock,
- memorypool::POINTER, 0);
+ sizeof(void *), 0);
// Initialize the pool for tet-subface connections.
tet2subpool = new memorypool(4 * sizeof(shellface), b->shellfaceperblock,
- memorypool::POINTER, 0);
+ sizeof(void *), 0);
// Initialize arraypools for segment & facet recovery.
subsegstack = new arraypool(sizeof(face), 10);
subfacstack = new arraypool(sizeof(face), 10);
subvertstack = new arraypool(sizeof(point), 8);
-
suppsteinerptlist = new arraypool(sizeof(point), 8);
- // Initialize arraypools for surface Bowyer-Watson algorithm.
+ // Initialize arraypools for surface point insertion/deletion.
caveshlist = new arraypool(sizeof(face), 8);
caveshbdlist = new arraypool(sizeof(face), 8);
cavesegshlist = new arraypool(sizeof(face), 4);
cavetetshlist = new arraypool(sizeof(face), 8);
cavetetseglist = new arraypool(sizeof(face), 8);
-
caveencshlist = new arraypool(sizeof(face), 8);
caveencseglist = new arraypool(sizeof(face), 8);
}
- // Initialize the pool for flips.
- flippool = new memorypool(sizeof(badface), 1024, memorypool::POINTER, 0);
+ // Initialize the pools for flips.
+ flippool = new memorypool(sizeof(badface), 1024, sizeof(void *), 0);
unflipqueue = new arraypool(sizeof(badface), 10);
- // Initialize the arraypools for Bowyer-Watson algorithm.
+ // Initialize the arraypools for point insertion.
cavetetlist = new arraypool(sizeof(triface), 10);
cavebdrylist = new arraypool(sizeof(triface), 10);
caveoldtetlist = new arraypool(sizeof(triface), 10);
@@ -4668,9 +4775,148 @@ void tetgenmesh::initializepools()
//// ////
// PI is the ratio of a circle's circumference to its diameter.
-
REAL tetgenmesh::PI = 3.14159265358979323846264338327950288419716939937510582;
+///////////////////////////////////////////////////////////////////////////////
+// //
+// insphere_s() Insphere test with symbolic perturbation. //
+// //
+// Given four points pa, pb, pc, and pd, test if the point pe lies inside or //
+// outside the circumscirbed sphere of the four points. //
+// //
+// Here we assume that the 3d orientation of the point sequence {pa, pb, pc, //
+// pd} is positive (NOT zero), i.e., pd lies above the plane passing through //
+// points pa, pb, and pc. Otherwise, the returned sign is flipped. //
+// //
+// Return a positive value (> 0) if pe lies inside, a negative value (< 0) //
+// if pe lies outside the sphere, the returned value will not be zero. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+REAL tetgenmesh::insphere_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe)
+{
+ REAL sign;
+
+ sign = insphere(pa, pb, pc, pd, pe);
+ if (sign != 0.0) {
+ return sign;
+ }
+
+ // Symbolic perturbation.
+ point pt[5], swappt;
+ REAL oriA, oriB;
+ int swaps, count;
+ int n, i;
+
+ pt[0] = pa;
+ pt[1] = pb;
+ pt[2] = pc;
+ pt[3] = pd;
+ pt[4] = pe;
+
+ // Sort the five points such that their indices are in the increasing
+ // order. An optimized bubble sort algorithm is used, i.e., it has
+ // the worst case O(n^2) runtime, but it is usually much faster.
+ swaps = 0; // Record the total number of swaps.
+ n = 5;
+ do {
+ count = 0;
+ n = n - 1;
+ for (i = 0; i < n; i++) {
+ if (pointmark(pt[i]) > pointmark(pt[i+1])) {
+ swappt = pt[i]; pt[i] = pt[i+1]; pt[i+1] = swappt;
+ count++;
+ }
+ }
+ swaps += count;
+ } while (count > 0); // Continue if some points are swapped.
+
+ oriA = orient3d(pt[1], pt[2], pt[3], pt[4]);
+ if (oriA != 0.0) {
+ // Flip the sign if there are odd number of swaps.
+ if ((swaps % 2) != 0) oriA = -oriA;
+ return oriA;
+ }
+
+ oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]);
+ assert(oriB != 0.0); // SELF_CHECK
+ // Flip the sign if there are odd number of swaps.
+ if ((swaps % 2) != 0) oriB = -oriB;
+ return oriB;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// orient4d_s() 4d orientation test with symbolic perturbation. //
+// //
+// Given four lifted points pa', pb', pc', and pd' in R^4,test if the lifted //
+// point pe' in R^4 lies below or above the hyperplance passing through the //
+// four points pa', pb', pc', and pd'. //
+// //
+// Here we assume that the 3d orientation of the point sequence {pa, pb, pc, //
+// pd} is positive (NOT zero), i.e., pd lies above the plane passing through //
+// the points pa, pb, and pc. Otherwise, the returned sign is flipped. //
+// //
+// Return a positive value (> 0) if pe' lies below, a negative value (< 0) //
+// if pe' lies above the hyperplane, the returned value should not be zero. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+REAL tetgenmesh::orient4d_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
+ REAL aheight, REAL bheight, REAL cheight,
+ REAL dheight, REAL eheight)
+{
+ REAL sign;
+
+ sign = orient4d(pa, pb, pc, pd, pe,
+ aheight, bheight, cheight, dheight, eheight);
+ if (sign != 0.0) {
+ return sign;
+ }
+
+ // Symbolic perturbation.
+ point pt[5], swappt;
+ REAL oriA, oriB;
+ int swaps, count;
+ int n, i;
+
+ pt[0] = pa;
+ pt[1] = pb;
+ pt[2] = pc;
+ pt[3] = pd;
+ pt[4] = pe;
+
+ // Sort the five points such that their indices are in the increasing
+ // order. An optimized bubble sort algorithm is used, i.e., it has
+ // the worst case O(n^2) runtime, but it is usually much faster.
+ swaps = 0; // Record the total number of swaps.
+ n = 5;
+ do {
+ count = 0;
+ n = n - 1;
+ for (i = 0; i < n; i++) {
+ if (pointmark(pt[i]) > pointmark(pt[i+1])) {
+ swappt = pt[i]; pt[i] = pt[i+1]; pt[i+1] = swappt;
+ count++;
+ }
+ }
+ swaps += count;
+ } while (count > 0); // Continue if some points are swapped.
+
+ oriA = orient3d(pt[1], pt[2], pt[3], pt[4]);
+ if (oriA != 0.0) {
+ // Flip the sign if there are odd number of swaps.
+ if ((swaps % 2) != 0) oriA = -oriA;
+ return oriA;
+ }
+
+ oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]);
+ assert(oriB != 0.0); // SELF_CHECK
+ // Flip the sign if there are odd number of swaps.
+ if ((swaps % 2) != 0) oriB = -oriB;
+ return oriB;
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// tri_edge_test() Triangle-edge intersection test. //
@@ -4693,6 +4939,10 @@ REAL tetgenmesh::PI = 3.14159265358979323846264338327950288419716939937510582;
// //
///////////////////////////////////////////////////////////////////////////////
+#define SETVECTOR3(V, a0, a1, a2) (V)[0] = (a0); (V)[1] = (a1); (V)[2] = (a2)
+
+#define SWAP2(a0, a1, tmp) (tmp) = (a0); (a0) = (a1); (a1) = (tmp)
+
int tetgenmesh::tri_edge_2d(point A, point B, point C, point P, point Q,
point R, int level, int *types, int *pos)
{
@@ -4709,14 +4959,14 @@ int tetgenmesh::tri_edge_2d(point A, point B, point C, point P, point Q,
REAL n[3], len;
// Calculate a lift point, saved in dummypoint.
facenormal(A, B, C, n, 1, NULL);
- len = sqrt(DOT(n, n));
+ len = sqrt(dot(n, n));
if (len != 0) {
n[0] /= len;
n[1] /= len;
n[2] /= len;
- len = DIST(A, B);
- len += DIST(B, C);
- len += DIST(C, A);
+ len = distance(A, B);
+ len += distance(B, C);
+ len += distance(C, A);
len /= 3.0;
R = abovept; //dummypoint;
R[0] = A[0] + len * n[0];
@@ -4737,7 +4987,6 @@ int tetgenmesh::tri_edge_2d(point A, point B, point C, point P, point Q,
sB = orient3d(P, Q, R, B);
sC = orient3d(P, Q, R, C);
- triedgcopcount++;
if (sA < 0) {
if (sB < 0) {
@@ -5321,7 +5570,6 @@ int tetgenmesh::tri_edge_tail(point A,point B,point C,point P,point Q,point R,
REAL s1, s2, s3;
int z1;
- triedgcount++;
if (sP < 0) {
if (sQ < 0) { // (--) disjoint
@@ -5816,6 +6064,9 @@ void tetgenmesh::lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N)
// Return a negative value if pd is inside the circumcircle of the triangle //
// pa, pb, and pc. //
// //
+// IMPORTANT: It assumes that [a,b] is the common edge, i.e., the two input //
+// triangles are [a,b,c] and [b,a,d]. //
+// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::incircle3d(point pa, point pb, point pc, point pd)
@@ -5825,19 +6076,19 @@ REAL tetgenmesh::incircle3d(point pa, point pb, point pc, point pd)
// Calculate the areas of the two triangles [a, b, c] and [b, a, d].
facenormal(pa, pb, pc, n1, 1, NULL);
- area2[0] = DOT(n1, n1);
+ area2[0] = dot(n1, n1);
facenormal(pb, pa, pd, n2, 1, NULL);
- area2[1] = DOT(n2, n2);
+ area2[1] = dot(n2, n2);
if (area2[0] > area2[1]) {
// Choose [a, b, c] as the base triangle.
circumsphere(pa, pb, pc, NULL, c, &r);
- d = DIST(c, pd);
+ d = distance(c, pd);
} else {
// Choose [b, a, d] as the base triangle.
if (area2[1] > 0) {
circumsphere(pb, pa, pd, NULL, c, &r);
- d = DIST(c, pc);
+ d = distance(c, pc);
} else {
// The four points are collinear. This case only happens on the boundary.
return 0; // Return "not inside".
@@ -5854,235 +6105,86 @@ REAL tetgenmesh::incircle3d(point pa, point pb, point pc, point pd)
///////////////////////////////////////////////////////////////////////////////
// //
-// insphere_s() Insphere test with symbolic perturbation. //
-// //
-// Given four points pa, pb, pc, and pd, test if the point pe lies inside or //
-// outside the circumscirbed sphere of the four points. //
+// facenormal() Calculate the normal of the face. //
// //
-// Here we assume that the 3d orientation of the point sequence {pa, pb, pc, //
-// pd} is positive (NOT zero), i.e., pd lies above the plane passing through //
-// points pa, pb, and pc. Otherwise, the returned sign is flipped. //
+// The normal of the face abc can be calculated by the cross product of 2 of //
+// its 3 edge vectors. A better choice of two edge vectors will reduce the //
+// numerical error during the calculation. Burdakov proved that the optimal //
+// basis problem is equivalent to the minimum spanning tree problem with the //
+// edge length be the functional, see Burdakov, "A greedy algorithm for the //
+// optimal basis problem", BIT 37:3 (1997), 591-599. If 'pivot' > 0, the two //
+// short edges in abc are chosen for the calculation. //
// //
-// Return a positive value (> 0) if pe lies inside, a negative value (< 0) //
-// if pe lies outside the sphere, the returned value will not be zero. //
+// If 'lav' is not NULL and if 'pivot' is set, the average edge length of //
+// the edges of the face [a,b,c] is returned. //
// //
///////////////////////////////////////////////////////////////////////////////
-REAL tetgenmesh::insphere_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe)
+void tetgenmesh::facenormal(point pa, point pb, point pc, REAL *n, int pivot,
+ REAL* lav)
{
- REAL sign;
+ REAL v1[3], v2[3], v3[3], *pv1, *pv2;
+ REAL L1, L2, L3;
- inspherecount++;
+ v1[0] = pb[0] - pa[0]; // edge vector v1: a->b
+ v1[1] = pb[1] - pa[1];
+ v1[2] = pb[2] - pa[2];
+ v2[0] = pa[0] - pc[0]; // edge vector v2: c->a
+ v2[1] = pa[1] - pc[1];
+ v2[2] = pa[2] - pc[2];
- sign = insphere(pa, pb, pc, pd, pe);
- if (sign != 0.0) {
- return sign;
+ // Default, normal is calculated by: v1 x (-v2) (see Fig. fnormal).
+ if (pivot > 0) {
+ // Choose edge vectors by Burdakov's algorithm.
+ v3[0] = pc[0] - pb[0]; // edge vector v3: b->c
+ v3[1] = pc[1] - pb[1];
+ v3[2] = pc[2] - pb[2];
+ L1 = dot(v1, v1);
+ L2 = dot(v2, v2);
+ L3 = dot(v3, v3);
+ // Sort the three edge lengths.
+ if (L1 < L2) {
+ if (L2 < L3) {
+ pv1 = v1; pv2 = v2; // n = v1 x (-v2).
+ } else {
+ pv1 = v3; pv2 = v1; // n = v3 x (-v1).
+ }
+ } else {
+ if (L1 < L3) {
+ pv1 = v1; pv2 = v2; // n = v1 x (-v2).
+ } else {
+ pv1 = v2; pv2 = v3; // n = v2 x (-v3).
+ }
+ }
+ if (lav) {
+ // return the average edge length.
+ *lav = (sqrt(L1) + sqrt(L2) + sqrt(L3)) / 3.0;
+ }
+ } else {
+ pv1 = v1; pv2 = v2; // n = v1 x (-v2).
}
- insphere_sos_count++;
+ // Calculate the face normal.
+ cross(pv1, pv2, n);
+ // Inverse the direction;
+ n[0] = -n[0];
+ n[1] = -n[1];
+ n[2] = -n[2];
+}
- // Symbolic perturbation.
- point pt[5], swappt;
- REAL oriA, oriB;
- int swaps, count;
- int n, i;
-
- pt[0] = pa;
- pt[1] = pb;
- pt[2] = pc;
- pt[3] = pd;
- pt[4] = pe;
-
- // Sort the five points such that their indices are in the increasing
- // order. An optimized bubble sort algorithm is used, i.e., it has
- // the worst case O(n^2) runtime, but it is usually much faster.
- swaps = 0; // Record the total number of swaps.
- n = 5;
- do {
- count = 0;
- n = n - 1;
- for (i = 0; i < n; i++) {
- if (pointmark(pt[i]) > pointmark(pt[i+1])) {
- swappt = pt[i]; pt[i] = pt[i+1]; pt[i+1] = swappt;
- count++;
- }
- }
- swaps += count;
- } while (count > 0); // Continue if some points are swapped.
-
- oriA = orient3d(pt[1], pt[2], pt[3], pt[4]);
- if (oriA != 0.0) {
- // Flip the sign if there are odd number of swaps.
- if ((swaps % 2) != 0) oriA = -oriA;
- return oriA;
- }
-
- oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]);
- assert(oriB != 0.0); // SELF_CHECK
- // Flip the sign if there are odd number of swaps.
- if ((swaps % 2) != 0) oriB = -oriB;
- return oriB;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// orient4d_s() 4d orientation test with symbolic perturbation. //
-// //
-// Given four lifted points pa', pb', pc', and pd' in R^4,test if the lifted //
-// point pe' in R^4 lies below or above the hyperplance passing through the //
-// four points pa', pb', pc', and pd'. //
-// //
-// Here we assume that the 3d orientation of the point sequence {pa, pb, pc, //
-// pd} is positive (NOT zero), i.e., pd lies above the plane passing through //
-// the points pa, pb, and pc. Otherwise, the returned sign is flipped. //
-// //
-// Return a positive value (> 0) if pe' lies below, a negative value (< 0) //
-// if pe' lies above the hyperplane, the returned value should not be zero. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-REAL tetgenmesh::orient4d_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
- REAL aheight, REAL bheight, REAL cheight,
- REAL dheight, REAL eheight)
-{
- REAL sign;
-
- inspherecount++;
-
- sign = orient4d(pa, pb, pc, pd, pe,
- aheight, bheight, cheight, dheight, eheight);
- if (sign != 0.0) {
- return sign;
- }
-
- insphere_sos_count++;
-
- // Symbolic perturbation.
- point pt[5], swappt;
- REAL oriA, oriB;
- int swaps, count;
- int n, i;
-
- pt[0] = pa;
- pt[1] = pb;
- pt[2] = pc;
- pt[3] = pd;
- pt[4] = pe;
-
- // Sort the five points such that their indices are in the increasing
- // order. An optimized bubble sort algorithm is used, i.e., it has
- // the worst case O(n^2) runtime, but it is usually much faster.
- swaps = 0; // Record the total number of swaps.
- n = 5;
- do {
- count = 0;
- n = n - 1;
- for (i = 0; i < n; i++) {
- if (pointmark(pt[i]) > pointmark(pt[i+1])) {
- swappt = pt[i]; pt[i] = pt[i+1]; pt[i+1] = swappt;
- count++;
- }
- }
- swaps += count;
- } while (count > 0); // Continue if some points are swapped.
-
- oriA = orient3d(pt[1], pt[2], pt[3], pt[4]);
- if (oriA != 0.0) {
- // Flip the sign if there are odd number of swaps.
- if ((swaps % 2) != 0) oriA = -oriA;
- return oriA;
- }
-
- oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]);
- assert(oriB != 0.0); // SELF_CHECK
- // Flip the sign if there are odd number of swaps.
- if ((swaps % 2) != 0) oriB = -oriB;
- return oriB;
-}
-
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// facenormal() Calculate the normal of the face. //
-// //
-// The normal of the face abc can be calculated by the cross product of 2 of //
-// its 3 edge vectors. A better choice of two edge vectors will reduce the //
-// numerical error during the calculation. Burdakov proved that the optimal //
-// basis problem is equivalent to the minimum spanning tree problem with the //
-// edge length be the functional, see Burdakov, "A greedy algorithm for the //
-// optimal basis problem", BIT 37:3 (1997), 591-599. If 'pivot' > 0, the two //
-// short edges in abc are chosen for the calculation. //
-// //
-// If 'lav' is not NULL and if 'pivot' is set, the average edge length of //
-// the edges of the face [a,b,c] is returned. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::facenormal(point pa, point pb, point pc, REAL *n, int pivot,
- REAL* lav)
-{
- REAL v1[3], v2[3], v3[3], *pv1, *pv2;
- REAL L1, L2, L3;
-
- v1[0] = pb[0] - pa[0]; // edge vector v1: a->b
- v1[1] = pb[1] - pa[1];
- v1[2] = pb[2] - pa[2];
- v2[0] = pa[0] - pc[0]; // edge vector v2: c->a
- v2[1] = pa[1] - pc[1];
- v2[2] = pa[2] - pc[2];
-
- // Default, normal is calculated by: v1 x (-v2) (see Fig. fnormal).
- if (pivot > 0) {
- // Choose edge vectors by Burdakov's algorithm.
- v3[0] = pc[0] - pb[0]; // edge vector v3: b->c
- v3[1] = pc[1] - pb[1];
- v3[2] = pc[2] - pb[2];
- L1 = DOT(v1, v1);
- L2 = DOT(v2, v2);
- L3 = DOT(v3, v3);
- // Sort the three edge lengths.
- if (L1 < L2) {
- if (L2 < L3) {
- pv1 = v1; pv2 = v2; // n = v1 x (-v2).
- } else {
- pv1 = v3; pv2 = v1; // n = v3 x (-v1).
- }
- } else {
- if (L1 < L3) {
- pv1 = v1; pv2 = v2; // n = v1 x (-v2).
- } else {
- pv1 = v2; pv2 = v3; // n = v2 x (-v3).
- }
- }
- if (lav) {
- // return the average edge length.
- *lav = (sqrt(L1) + sqrt(L2) + sqrt(L3)) / 3.0;
- }
- } else {
- pv1 = v1; pv2 = v2; // n = v1 x (-v2).
- }
-
- // Calculate the face normal.
- CROSS(pv1, pv2, n);
- // Inverse the direction;
- n[0] = -n[0];
- n[1] = -n[1];
- n[2] = -n[2];
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// shortdistance() Returns the shortest distance from point p to a line //
-// defined by two points e1 and e2. //
-// //
-// First compute the projection length l_p of the vector v1 = p - e1 along //
-// the vector v2 = e2 - e1. Then Pythagoras' Theorem is used to compute the //
-// shortest distance. //
-// //
-// This routine allows that p is collinear with the line. In this case, the //
-// return value is zero. The two points e1 and e2 should not be identical. //
-// //
-///////////////////////////////////////////////////////////////////////////////
+///////////////////////////////////////////////////////////////////////////////
+// //
+// shortdistance() Returns the shortest distance from point p to a line //
+// defined by two points e1 and e2. //
+// //
+// First compute the projection length l_p of the vector v1 = p - e1 along //
+// the vector v2 = e2 - e1. Then Pythagoras' Theorem is used to compute the //
+// shortest distance. //
+// //
+// This routine allows that p is collinear with the line. In this case, the //
+// return value is zero. The two points e1 and e2 should not be identical. //
+// //
+///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2)
{
@@ -6097,9 +6199,8 @@ REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2)
v2[2] = p[2] - e1[2];
len = sqrt(dot(v1, v1));
-#ifdef SELF_CHECK
assert(len != 0.0);
-#endif
+
v1[0] /= len;
v1[1] /= len;
v1[2] /= len;
@@ -6108,7 +6209,6 @@ REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2)
return sqrt(dot(v2, v2) - l_p * l_p);
}
-
///////////////////////////////////////////////////////////////////////////////
// //
// triarea() Return the area of a triangle. //
@@ -6132,6 +6232,27 @@ REAL tetgenmesh::triarea(REAL* pa, REAL* pb, REAL* pc)
return 0.5 * sqrt(dot(A[2], A[2])); // The area of [a,b,c].
}
+REAL tetgenmesh::orient3dfast(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
+{
+ REAL adx, bdx, cdx;
+ REAL ady, bdy, cdy;
+ REAL adz, bdz, cdz;
+
+ adx = pa[0] - pd[0];
+ bdx = pb[0] - pd[0];
+ cdx = pc[0] - pd[0];
+ ady = pa[1] - pd[1];
+ bdy = pb[1] - pd[1];
+ cdy = pc[1] - pd[1];
+ adz = pa[2] - pd[2];
+ bdz = pb[2] - pd[2];
+ cdz = pc[2] - pd[2];
+
+ return adx * (bdy * cdz - bdz * cdy)
+ + bdx * (cdy * adz - cdz * ady)
+ + cdx * (ady * bdz - adz * bdy);
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// interiorangle() Return the interior angle (0 - 2 * PI) between vectors //
@@ -6161,9 +6282,8 @@ REAL tetgenmesh::interiorangle(REAL* o, REAL* p1, REAL* p2, REAL* n)
len1 = sqrt(dot(v1, v1));
len2 = sqrt(dot(v2, v2));
lenlen = len1 * len2;
-#ifdef SELF_CHECK
assert(lenlen != 0.0);
-#endif
+
costheta = dot(v1, v2) / lenlen;
if (costheta > 1.0) {
costheta = 1.0; // Roundoff.
@@ -6205,9 +6325,7 @@ void tetgenmesh::projpt2edge(REAL* p, REAL* e1, REAL* e2, REAL* prj)
v2[2] = p[2] - e1[2];
len = sqrt(dot(v1, v1));
-#ifdef SELF_CHECK
assert(len != 0.0);
-#endif
v1[0] /= len;
v1[1] /= len;
v1[2] /= len;
@@ -6249,7 +6367,6 @@ void tetgenmesh::projpt2face(REAL* p, REAL* f1, REAL* f2, REAL* f3, REAL* prj)
prj[2] = p[2] - dist * fnormal[2];
}
-
///////////////////////////////////////////////////////////////////////////////
// //
// facedihedral() Return the dihedral angle (in radian) between two //
@@ -6371,6 +6488,7 @@ bool tetgenmesh::tetalldihedral(point pa, point pb, point pc, point pd,
}
cosd = -dot(N[f1], N[f2]);
if (cosd < -1.0) cosd = -1.0; // Rounding.
+ if (cosd > 1.0) cosd = 1.0; // Rounding.
if (cosdd) cosdd[i] = cosd;
if (cosmaxd || cosmind) {
if (i == 0) {
@@ -6559,7 +6677,59 @@ bool tetgenmesh::circumsphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd,
return true;
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// orthosphere() Calulcate the orthosphere of four weighted points. //
+// //
+// A weighted point (p, P^2) can be interpreted as a sphere centered at the //
+// point 'p' with a radius 'P'. The 'height' of 'p' is pheight = p[0]^2 + //
+// p[1]^2 + p[2]^2 - P^2. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::orthosphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd,
+ REAL aheight, REAL bheight, REAL cheight,
+ REAL dheight, REAL* orthocent, REAL* radius)
+{
+ REAL A[4][4], rhs[4], D;
+ int indx[4];
+
+ // Set the coefficient matrix A (4 x 4).
+ A[0][0] = 1.0; A[0][1] = pa[0]; A[0][2] = pa[1]; A[0][3] = pa[2];
+ A[1][0] = 1.0; A[1][1] = pb[0]; A[1][2] = pb[1]; A[1][3] = pb[2];
+ A[2][0] = 1.0; A[2][1] = pc[0]; A[2][2] = pc[1]; A[2][3] = pc[2];
+ A[3][0] = 1.0; A[3][1] = pd[0]; A[3][2] = pd[1]; A[3][3] = pd[2];
+
+ // Set the right hand side vector (4 x 1).
+ rhs[0] = 0.5 * aheight;
+ rhs[1] = 0.5 * bheight;
+ rhs[2] = 0.5 * cheight;
+ rhs[3] = 0.5 * dheight;
+
+ // Solve the 4 by 4 equations use LU decomposition with partial pivoting
+ // and backward and forward substitute..
+ if (!lu_decmp(A, 4, indx, &D, 0)) {
+ if (radius != (REAL *) NULL) *radius = 0.0;
+ return false;
+ }
+ lu_solve(A, 4, indx, rhs, 0);
+ if (orthocent != (REAL *) NULL) {
+ orthocent[0] = rhs[1];
+ orthocent[1] = rhs[2];
+ orthocent[2] = rhs[3];
+ }
+ if (radius != (REAL *) NULL) {
+ // rhs[0] = - rheight / 2;
+ // rheight = - 2 * rhs[0];
+ // = r[0]^2 + r[1]^2 + r[2]^2 - radius^2
+ // radius^2 = r[0]^2 + r[1]^2 + r[2]^2 -rheight
+ // = r[0]^2 + r[1]^2 + r[2]^2 + 2 * rhs[0]
+ *radius = sqrt(rhs[1] * rhs[1] + rhs[2] * rhs[2] + rhs[3] * rhs[3]
+ + 2.0 * rhs[0]);
+ }
+ return true;
+}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -6607,8 +6777,6 @@ void tetgenmesh::planelineint(REAL* pa, REAL* pb, REAL* pc, REAL* e1, REAL* e2,
}
}
-
-
///////////////////////////////////////////////////////////////////////////////
// //
// tetprismvol() Calculate the volume of a tetrahedral prism in 4D. //
@@ -6656,44 +6824,145 @@ REAL tetgenmesh::tetprismvol(REAL* p0, REAL* p1, REAL* p2, REAL* p3)
return fabs(vol[0]) + fabs(vol[1]) + fabs(vol[2]) + fabs(vol[3]);
}
-//// ////
-//// ////
-//// geom_cxx /////////////////////////////////////////////////////////////////
-
-//// flip_cxx /////////////////////////////////////////////////////////////////
-//// ////
-//// ////
-
///////////////////////////////////////////////////////////////////////////////
// //
-// flippush() Push a face (possibly will be flipped) into flipstack. //
-// //
-// The face is marked. The flag is used to check the validity of the face on //
-// its popup. Some other flips may change it already. //
+// calculateabovepoint() Calculate a point above a facet in 'dummypoint'. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::flippush(badface*& fstack, triface* flipface)
+bool tetgenmesh::calculateabovepoint(arraypool *facpoints, point *ppa,
+ point *ppb, point *ppc)
{
- badface *newflipface;
+ point *ppt, pa, pb, pc;
+ REAL v1[3], v2[3], n[3];
+ REAL lab, len, A, area;
+ REAL x, y, z;
+ int i;
- if (!facemarked(*flipface)) {
- newflipface = (badface *) flippool->alloc();
- newflipface->tt = *flipface;
- markface(newflipface->tt);
- // Push this face into stack.
- newflipface->nextitem = fstack;
- fstack = newflipface;
- }
-}
+ ppt = (point *) fastlookup(facpoints, 0);
+ pa = *ppt; // a is the first point.
+ pb = pc = NULL; // Avoid compiler warnings.
-///////////////////////////////////////////////////////////////////////////////
-// //
-// flip23() Perform a 2-to-3 flip (face-to-edge flip). //
-// //
-// 'fliptets' is an array of tetrahedra. On input it contains two tets //
-// [a,b,c,d] and [b,a,c,e]. It returns three new tets: [e,d,a,b], [e,d,b,c], //
-// [e,d,c,a]. The face [a,b,c] is removed, and the edge [d,e] is created. //
+ // Get a point b s.t. the length of [a, b] is maximal.
+ lab = 0;
+ for (i = 1; i < facpoints->objects; i++) {
+ ppt = (point *) fastlookup(facpoints, i);
+ x = (*ppt)[0] - pa[0];
+ y = (*ppt)[1] - pa[1];
+ z = (*ppt)[2] - pa[2];
+ len = x * x + y * y + z * z;
+ if (len > lab) {
+ lab = len;
+ pb = *ppt;
+ }
+ }
+ lab = sqrt(lab);
+ if (lab == 0) {
+ if (!b->quiet) {
+ printf("Warning: All points of a facet are coincident with %d.\n",
+ pointmark(pa));
+ }
+ return false;
+ }
+
+ // Get a point c s.t. the area of [a, b, c] is maximal.
+ v1[0] = pb[0] - pa[0];
+ v1[1] = pb[1] - pa[1];
+ v1[2] = pb[2] - pa[2];
+ A = 0;
+ for (i = 1; i < facpoints->objects; i++) {
+ ppt = (point *) fastlookup(facpoints, i);
+ v2[0] = (*ppt)[0] - pa[0];
+ v2[1] = (*ppt)[1] - pa[1];
+ v2[2] = (*ppt)[2] - pa[2];
+ cross(v1, v2, n);
+ area = dot(n, n);
+ if (area > A) {
+ A = area;
+ pc = *ppt;
+ }
+ }
+ if (A == 0) {
+ // All points are collinear. No above point.
+ if (!b->quiet) {
+ printf("Warning: All points of a facet are collinaer with [%d, %d].\n",
+ pointmark(pa), pointmark(pb));
+ }
+ return false;
+ }
+
+ // Calculate an above point of this facet.
+ facenormal(pa, pb, pc, n, 1, NULL);
+ len = sqrt(dot(n, n));
+ n[0] /= len;
+ n[1] /= len;
+ n[2] /= len;
+ lab /= 2.0; // Half the maximal length.
+ dummypoint[0] = pa[0] + lab * n[0];
+ dummypoint[1] = pa[1] + lab * n[1];
+ dummypoint[2] = pa[2] + lab * n[2];
+
+ if (ppa != NULL) {
+ // Return the three points.
+ *ppa = pa;
+ *ppb = pb;
+ *ppc = pc;
+ }
+
+ return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Calculate an above point. It lies above the plane containing the subface //
+// [a,b,c], and save it in dummypoint. Moreover, the vector pa->dummypoint //
+// is the normal of the plane. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::calculateabovepoint4(point pa, point pb, point pc, point pd)
+{
+ REAL n1[3], n2[3], *norm;
+ REAL len, len1, len2;
+
+ // Select a base.
+ facenormal(pa, pb, pc, n1, 1, NULL);
+ len1 = sqrt(dot(n1, n1));
+ facenormal(pa, pb, pd, n2, 1, NULL);
+ len2 = sqrt(dot(n2, n2));
+ if (len1 > len2) {
+ norm = n1;
+ len = len1;
+ } else {
+ norm = n2;
+ len = len2;
+ }
+ assert(len > 0);
+ norm[0] /= len;
+ norm[1] /= len;
+ norm[2] /= len;
+ len = distance(pa, pb);
+ dummypoint[0] = pa[0] + len * norm[0];
+ dummypoint[1] = pa[1] + len * norm[1];
+ dummypoint[2] = pa[2] + len * norm[2];
+}
+
+//// ////
+//// ////
+//// geom_cxx /////////////////////////////////////////////////////////////////
+
+//// flip_cxx /////////////////////////////////////////////////////////////////
+//// ////
+//// ////
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// flip23() Perform a 2-to-3 flip (face-to-edge flip). //
+// //
+// 'fliptets' is an array of three tets (handles), where the [0] and [1] are //
+// [a,b,c,d] and [b,a,c,e]. The three new tets: [e,d,a,b], [e,d,b,c], and //
+// [e,d,c,a] are returned in [0], [1], and [2] of 'fliptets'. As a result, //
+// The face [a,b,c] is removed, and the edge [d,e] is created. //
// //
// If 'hullflag' > 0, hull tets may be involved in this flip, i.e., one of //
// the five vertices may be 'dummypoint'. There are two canonical cases: //
@@ -6704,27 +6973,19 @@ void tetgenmesh::flippush(badface*& fstack, triface* flipface)
// rotate the three input tets counterclockwisely (right-hand rule) //
// until a or b is in c's position. //
// //
-// If 'flipflag > 0', faces on the convex hull of the five vertices might //
-// need to be flipped, e.g., for incremental DT construction or mesh quality //
-// improvement. They will be queued in 'flipstack'. //
-// //
-// If 'flipflag = 1', it is in the process of incrmental flip DT algorithm, //
-// and we assume that 'd' must be the newly inserted vertex. In such case, //
-// only the link faces at 'd', i.e., three faces [a,b,e], [b,c,e], and [c,a, //
-// e] needs to be queued, see [Edelsbrunner & Shah'1996] and [M\"ucke'1998]. //
+// If 'fc->enqflag' is set, convex hull faces will be queued for flipping. //
+// In particular, if 'fc->enqflag' is 1, it is called by incrementalflip() //
+// after the insertion of a new point. It is assumed that 'd' is the new //
+// point. IN this case, only link faces of 'd' are queued. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
- int chkencflag)
+void tetgenmesh::flip23(triface* fliptets, int hullflag, flipconstraints *fc)
{
triface topcastets[3], botcastets[3];
triface newface, casface;
- face checksh;
- face checkseg;
- badface *bface; // used by chkencflag
point pa, pb, pc, pd, pe;
- REAL volneg[2], volpos[3], vol_diff; // volumes of involved tet-prisms.
+ REAL attrib, volume;
int dummyflag = 0; // range = {-1, 0, 1, 2}.
int i;
@@ -6752,16 +7013,12 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
}
}
- pa = org(fliptets[0]);
+ pa = org(fliptets[0]);
pb = dest(fliptets[0]);
pc = apex(fliptets[0]);
pd = oppo(fliptets[0]);
pe = oppo(fliptets[1]);
- if (b->verbose > 3) {
- printf(" flip 2-to-3: (%d, %d, %d, %d, %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pe));
- }
flip23count++;
// Get the outer boundary faces.
@@ -6779,6 +7036,7 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
fliptets[1].ver = 11;
setelemmarker(fliptets[0].tet, 0); // Clear all flags.
setelemmarker(fliptets[1].tet, 0);
+ // NOTE: the element attributes and volume constraint remain unchanged.
if (checksubsegflag) {
// Dealloc the space to subsegments.
if (fliptets[0].tet[8] != NULL) {
@@ -6803,6 +7061,15 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
}
// Create a new tet.
maketetrahedron(&(fliptets[2]));
+ // The new tet have the same attributes from the old tet.
+ for (i = 0; i < numelemattrib; i++) {
+ attrib = elemattribute(fliptets[0].tet, i);
+ setelemattribute(fliptets[2].tet, i, attrib);
+ }
+ if (b->varvolume) {
+ volume = volumebound(fliptets[0].tet);
+ setvolumebound(fliptets[2].tet, volume);
+ }
if (hullflag > 0) {
// Check if d is dummytet.
@@ -6836,7 +7103,8 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
setvertices(fliptets[2], pe, pd, pc, pa); // [e,d,c,a] *
}
- if (calc_tetprism_vol) {
+ if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol
+ REAL volneg[2], volpos[3], vol_diff;
if (pd != dummypoint) {
if (pc != dummypoint) {
volpos[0] = tetprismvol(pe, pd, pa, pb);
@@ -6859,8 +7127,8 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
volneg[1] = tetprismvol(pb, pa, pc, pe);
}
vol_diff = volpos[0] + volpos[1] + volpos[2] - volneg[0] - volneg[1];
- tetprism_vol_sum += vol_diff; // Update the total sum.
- } // if (check_tetprism_vol_diff)
+ fc->tetprism_vol_sum += vol_diff; // Update the total sum.
+ }
// Bond three new tets together.
for (i = 0; i < 3; i++) {
@@ -6869,43 +7137,36 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
}
// Bond to top outer boundary faces (at [a,b,c,d]).
for (i = 0; i < 3; i++) {
- enextesym(fliptets[i], newface);
- eprevself(newface); // At edges [b,a], [c,b], [a,c].
+ eorgoppo(fliptets[i], newface); // At edges [b,a], [c,b], [a,c].
bond(newface, topcastets[i]);
}
// Bond bottom outer boundary faces (at [b,a,c,e]).
for (i = 0; i < 3; i++) {
- eprevesym(fliptets[i], newface);
- enextself(newface); // At edges [a,b], [b,c], [c,a].
+ edestoppo(fliptets[i], newface); // At edges [a,b], [b,c], [c,a].
bond(newface, botcastets[i]);
}
- // Bond 15 subsegments if there are.
if (checksubsegflag) {
+ // Bond subsegments if there are.
+ // Each new tet has 5 edges to be checked (except the edge [e,d]).
+ face checkseg;
// The middle three: [a,b], [b,c], [c,a].
- for (i = 0; i < 3; i++) {
- tsspivot1(topcastets[i], checkseg);
- if (checkseg.sh != NULL) {
- enextesym(fliptets[i], newface);
- eprevself(newface); // At edges [b,a], [c,b], [a,c].
+ for (i = 0; i < 3; i++) {
+ if (issubseg(topcastets[i])) {
+ tsspivot1(topcastets[i], checkseg);
+ eorgoppo(fliptets[i], newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
}
// The top three: [d,a], [d,b], [d,c]. Two tets per edge.
for (i = 0; i < 3; i++) {
- eprev(topcastets[i], casface);
- tsspivot1(casface, checkseg);
- if (checkseg.sh != NULL) {
+ eprev(topcastets[i], casface);
+ if (issubseg(casface)) {
+ tsspivot1(casface, checkseg);
enext(fliptets[i], newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
@@ -6913,22 +7174,16 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
eprevself(newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
}
// The bot three: [a,e], [b,e], [c,e]. Two tets per edge.
for (i = 0; i < 3; i++) {
enext(botcastets[i], casface);
- tsspivot1(casface, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(casface)) {
+ tsspivot1(casface, checkseg);
eprev(fliptets[i], newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
@@ -6936,75 +7191,53 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
enextself(newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
}
- }
+ } // if (checksubsegflag)
- // Bond 6 subfaces if there are.
if (checksubfaceflag) {
- for (i = 0; i < 3; i++) {
- tspivot(topcastets[i], checksh);
- if (checksh.sh != NULL) {
- enextesym(fliptets[i], newface);
- eprevself(newface); // At edge [b,a], [c,b], [a,c].
+ // Bond 6 subfaces if there are.
+ face checksh;
+ for (i = 0; i < 3; i++) {
+ if (issubface(topcastets[i])) {
+ tspivot(topcastets[i], checksh);
+ eorgoppo(fliptets[i], newface);
sesymself(checksh);
tsbond(newface, checksh);
- if (chkencflag & 2) {
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface
- }
+ if (fc->chkencflag & 2) {
+ enqueuesubface(badsubfacs, &checksh);
}
}
}
for (i = 0; i < 3; i++) {
- tspivot(botcastets[i], checksh);
- if (checksh.sh != NULL) {
- eprevesym(fliptets[i], newface);
- enextself(newface); // At edge [a,b], [b,c], [c,a]
+ if (issubface(botcastets[i])) {
+ tspivot(botcastets[i], checksh);
+ edestoppo(fliptets[i], newface);
sesymself(checksh);
tsbond(newface, checksh);
- if (chkencflag & 2) {
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface
- }
+ if (fc->chkencflag & 2) {
+ enqueuesubface(badsubfacs, &checksh);
}
}
}
- }
+ } // if (checksubfaceflag)
- if (chkencflag & 4) {
+ if (fc->chkencflag & 4) {
// Put three new tets into check list.
for (i = 0; i < 3; i++) {
- if (!marktest2ed(fliptets[i])) {
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = fliptets[i];
- marktest2(bface->tt);
- bface->forg = org(fliptets[i]);
- }
+ enqueuetetrahedron(&(fliptets[i]));
}
}
// Update the point-to-tet map.
- setpoint2tet(pa, encode(fliptets[0]));
- setpoint2tet(pb, encode(fliptets[0]));
- setpoint2tet(pc, encode(fliptets[1]));
- setpoint2tet(pd, encode(fliptets[0]));
- setpoint2tet(pe, encode(fliptets[0]));
+ setpoint2tet(pa, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pb, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pc, (tetrahedron) fliptets[1].tet);
+ setpoint2tet(pd, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pe, (tetrahedron) fliptets[0].tet);
if (hullflag > 0) {
if (dummyflag != 0) {
@@ -7037,19 +7270,15 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
}
}
- if (flipflag > 0) {
+ if (fc->enqflag > 0) {
// Queue faces which may be locally non-Delaunay.
- //pd = dest(fliptets[0]); // 'd' may be a new vertex.
for (i = 0; i < 3; i++) {
eprevesym(fliptets[i], newface);
- //flippush(flipstack, &newface, pd);
flippush(flipstack, &newface);
}
- if (flipflag > 1) {
- //pe = org(fliptets[0]);
+ if (fc->enqflag > 1) {
for (i = 0; i < 3; i++) {
enextesym(fliptets[i], newface);
- //flippush(flipstack, &newface, pe);
flippush(flipstack, &newface);
}
}
@@ -7062,9 +7291,10 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
// //
// flip32() Perform a 3-to-2 flip (edge-to-face flip). //
// //
-// 'fliptets' is an array of three tetrahedra. On input, it contains three //
-// tets: [e,d,a,b], [e,d,b,c], and [e,d,c,a]. It returns tw tets: [a,b,c,d], //
-// and [b,a,c,e]. The edge [e,d] is replaced by the face [a,b,c]. //
+// 'fliptets' is an array of three tets (handles), which are [e,d,a,b], //
+// [e,d,b,c], and [e,d,c,a]. The two new tets: [a,b,c,d] and [b,a,c,e] are //
+// returned in [0] and [1] of 'fliptets'. As a result, the edge [e,d] is //
+// replaced by the face [a,b,c]. //
// //
// If 'hullflag' > 0, hull tets may be involved in this flip, i.e., one of //
// the five vertices may be 'dummypoint'. There are two canonical cases: //
@@ -7075,35 +7305,36 @@ void tetgenmesh::flip23(triface* fliptets, int hullflag, int flipflag,
// three old tets counterclockwisely (right-hand rule) until a or b //
// is in c's position. //
// //
-// If 'flipflag > 0', faces on the convex hull of the five vertices might //
-// need to be flipped, e.g., for incremental DT construction or mesh quality //
-// improvement. They will be queued in 'flipstack'. //
-// //
-// If 'flipflag = 1', it is in the process of incrmental flip DT algorithm, //
-// and we assume that 'a' must be the newly inserted vertex. In such case, //
-// only the link faces at 'a', i.e., two faces [c,b,d] and [b,c,e] needs to //
-// be queued, refer to [Edelsbrunner & Shah'1996] and [M\"ucke'1998]. //
+// If 'fc->enqflag' is set, convex hull faces will be queued for flipping. //
+// In particular, if 'fc->enqflag' is 1, it is called by incrementalflip() //
+// after the insertion of a new point. It is assumed that 'a' is the new //
+// point. In this case, only link faces of 'a' are queued. //
// //
+// If 'checksubfaceflag' is on (global variable), and assume [e,d] is not a //
+// segment. There may be two (interior) subfaces sharing at [e,d], which are //
+// [e,d,p] and [e,d,q], where the pair (p,q) may be either (a,b), or (b,c), //
+// or (c,a) In such case, a 2-to-2 flip is performed on these two subfaces //
+// and two new subfaces [p,q,e] and [p,q,d] are created. They are inserted //
+// back into the tetrahedralization. However, it is possible that the new //
+// subface ([p,q,e] or [p,q,d] already exists. In such case, we just delete //
+// the conflict subface. As a result, either 'd' or 'e' is removed from the //
+// surface mesh. An alternative solution would be to detect this case in //
+// advance and perform a 3-to-1 flip to remove 'd' or 'e' (see 2011-11-15). //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
- int chkencflag)
+void tetgenmesh::flip32(triface* fliptets, int hullflag, flipconstraints *fc)
{
triface topcastets[3], botcastets[3];
triface newface, casface;
- face checksh;
+ face flipshs[3];
face checkseg;
- badface *bface; // used by chkencflag
point pa, pb, pc, pd, pe;
- REAL volneg[3], volpos[2], vol_diff; // volumes of involved tet-prisms.
+ REAL attrib, volume;
int dummyflag = 0; // Rangle = {-1, 0, 1, 2}
- int i;
-
- // For 2-to-2 flip (subfaces).
- face flipshs[3], flipfaces[2];
- point rempt;
- int spivot = -1, scount = 0;
+ int spivot = -1, scount = 0; // for flip22()
+ int t1ver;
+ int i, j;
if (hullflag > 0) {
// Check if e is 'dummypoint'.
@@ -7143,36 +7374,24 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
pd = dest(fliptets[0]);
pe = org(fliptets[0]);
- if (b->verbose > 3) {
- printf(" flip 3-to-2: (%d, %d, %d, %d, %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pe));
- }
flip32count++;
// Get the outer boundary faces.
for (i = 0; i < 3; i++) {
- enextesym(fliptets[i], casface);
- eprevself(casface);
+ eorgoppo(fliptets[i], casface);
fsym(casface, topcastets[i]);
}
for (i = 0; i < 3; i++) {
- eprevesym(fliptets[i], casface);
- enextself(casface);
+ edestoppo(fliptets[i], casface);
fsym(casface, botcastets[i]);
}
if (checksubfaceflag) {
// Check if there are interior subfaces at the edge [e,d].
- spivot = -1;
- scount = 0;
for (i = 0; i < 3; i++) {
tspivot(fliptets[i], flipshs[i]);
if (flipshs[i].sh != NULL) {
- if (b->verbose > 3) {
- printf(" Found an interior subface (%d, %d, %d).\n",
- pointmark(sorg(flipshs[i])), pointmark(sdest(flipshs[i])),
- pointmark(sapex(flipshs[i])));
- }
+ // Found an interior subface.
stdissolve(flipshs[i]); // Disconnect the sub-tet bond.
scount++;
} else {
@@ -7208,7 +7427,28 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
fliptets[1].tet[9] = NULL;
}
}
-
+ if (checksubfaceflag) {
+ if (scount > 0) {
+ // The element attributes and volume constraint must be set correctly.
+ // There are two subfaces involved in this flip. The three tets are
+ // separated into two different regions, one may be exterior. The
+ // first region has two tets, and the second region has only one.
+ // The two created tets must be in the same region as the first region.
+ // The element attributes and volume constraint must be set correctly.
+ //assert(spivot != -1);
+ // The tet fliptets[spivot] is in the first region.
+ for (j = 0; j < 2; j++) {
+ for (i = 0; i < numelemattrib; i++) {
+ attrib = elemattribute(fliptets[spivot].tet, i);
+ setelemattribute(fliptets[j].tet, i, attrib);
+ }
+ if (b->varvolume) {
+ volume = volumebound(fliptets[spivot].tet);
+ setvolumebound(fliptets[j].tet, volume);
+ }
+ }
+ }
+ }
// Delete an old tet.
tetrahedrondealloc(fliptets[2].tet);
@@ -7232,14 +7472,15 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
esymself(fliptets[0]);
// Adjust abec -> bace.
esymself(fliptets[1]);
- // The hullsize does not changle.
+ // The hullsize does not change.
}
} else {
setvertices(fliptets[0], pa, pb, pc, pd);
setvertices(fliptets[1], pb, pa, pc, pe);
}
- if (calc_tetprism_vol) {
+ if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol
+ REAL volneg[3], volpos[2], vol_diff;
if (pc != dummypoint) {
if (pd != dummypoint) {
volneg[0] = tetprismvol(pe, pd, pa, pb);
@@ -7262,7 +7503,7 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
volpos[1] = 0.;
}
vol_diff = volpos[0] + volpos[1] - volneg[0] - volneg[1] - volneg[2];
- tetprism_vol_sum += vol_diff; // Update the total sum.
+ fc->tetprism_vol_sum += vol_diff; // Update the total sum.
}
// Bond abcd <==> bace.
@@ -7281,133 +7522,91 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
}
if (checksubsegflag) {
- // Bond segments to new (flipped) tets.
- for (i = 0; i < 3; i++) {
- tsspivot1(topcastets[i], checkseg);
- if (checkseg.sh != NULL) {
+ // Bond 9 segments to new (flipped) tets.
+ for (i = 0; i < 3; i++) { // edges a->b, b->c, c->a.
+ if (issubseg(topcastets[i])) {
+ tsspivot1(topcastets[i], checkseg);
tssbond1(fliptets[0], checkseg);
sstbond1(checkseg, fliptets[0]);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ tssbond1(fliptets[1], checkseg);
+ sstbond1(checkseg, fliptets[1]);
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
+ eprevself(fliptets[1]);
}
// The three top edges.
- for (i = 0; i < 3; i++) {
+ for (i = 0; i < 3; i++) { // edges b->d, c->d, a->d.
esym(fliptets[0], newface);
- eprevself(newface); // edge b->d, c->d, a->d.
- enext(topcastets[i], casface);
- tsspivot1(casface, checkseg);
- if (checkseg.sh != NULL) {
+ eprevself(newface);
+ enext(topcastets[i], casface);
+ if (issubseg(casface)) {
+ tsspivot1(casface, checkseg);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
}
- // Process the bottom tet bace.
- for (i = 0; i < 3; i++) {
- tsspivot1(botcastets[i], checkseg);
- if (checkseg.sh != NULL) {
- tssbond1(fliptets[1], checkseg);
- sstbond1(checkseg, fliptets[1]);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
- }
- }
- eprevself(fliptets[1]);
- }
// The three bot edges.
- for (i = 0; i < 3; i++) {
+ for (i = 0; i < 3; i++) { // edges b<-e, c<-e, a<-e.
esym(fliptets[1], newface);
- enextself(newface); // edge b<-e, c<-e, a<-e.
+ enextself(newface);
eprev(botcastets[i], casface);
- tsspivot1(casface, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(casface)) {
+ tsspivot1(casface, checkseg);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
eprevself(fliptets[1]);
}
- }
+ } // if (checksubsegflag)
if (checksubfaceflag) {
+ face checksh;
// Bond the top three casing subfaces.
- for (i = 0; i < 3; i++) {
- tspivot(topcastets[i], checksh);
- if (checksh.sh != NULL) {
- esym(fliptets[0], newface); // At edge [b,a], [c,b], [a,c]
+ for (i = 0; i < 3; i++) { // At edges [b,a], [c,b], [a,c]
+ if (issubface(topcastets[i])) {
+ tspivot(topcastets[i], checksh);
+ esym(fliptets[0], newface);
sesymself(checksh);
tsbond(newface, checksh);
- if (chkencflag & 2) {
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface
- }
+ if (fc->chkencflag & 2) {
+ enqueuesubface(badsubfacs, &checksh);
}
}
enextself(fliptets[0]);
}
// Bond the bottom three casing subfaces.
- for (i = 0; i < 3; i++) {
- tspivot(botcastets[i], checksh);
- if (checksh.sh != NULL) {
- esym(fliptets[1], newface); // // At edge [a,b], [b,c], [c,a]
+ for (i = 0; i < 3; i++) { // At edges [a,b], [b,c], [c,a]
+ if (issubface(botcastets[i])) {
+ tspivot(botcastets[i], checksh);
+ esym(fliptets[1], newface);
sesymself(checksh);
tsbond(newface, checksh);
- if (chkencflag & 2) {
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface
- }
+ if (fc->chkencflag & 2) {
+ enqueuesubface(badsubfacs, &checksh);
}
}
eprevself(fliptets[1]);
}
- }
- if (checksubfaceflag) {
if (scount > 0) {
assert(spivot != -1); // spivot = i, in {0,1,2}
+ face flipfaces[2];
+ point rempt;
// Perform a 2-to-2 flip in subfaces.
flipfaces[0] = flipshs[(spivot + 1) % 3];
flipfaces[1] = flipshs[(spivot + 2) % 3];
sesymself(flipfaces[1]);
- flip22(flipfaces, 0, chkencflag);
+ flip22(flipfaces, 0, fc->chkencflag);
// Connect the flipped subfaces to flipped tets.
// First go to the corresponding flipping edge.
// Re-use top- and botcastets[0].
@@ -7435,9 +7634,6 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
assert(checkseg.sh == NULL);
// Delete the two duplicated subfaces.
rempt = sapex(checksh);
- if (b->verbose > 2) {
- printf(" Remove vertex %d from surface.\n", pointmark(rempt));
- }
// Make sure we do not delete a Steiner points in segment.
assert(pointtype(rempt) == FREEFACETVERTEX);
setpointtype(rempt, FREEVOLVERTEX);
@@ -7494,9 +7690,6 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
// the surface triangulation.
// Delete the two duplicated subfaces.
rempt = sapex(checksh);
- if (b->verbose > 2) {
- printf(" Remove vertex %d from surface.\n", pointmark(rempt));
- }
// Make sure we do not delete a Steiner points in segment.
assert(pointtype(rempt) == FREEFACETVERTEX);
setpointtype(rempt, FREEVOLVERTEX);
@@ -7530,26 +7723,21 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
// // Push botcastets[0] into queue for checking new sliver.
// assert(oppo(botcastets[0]) != dummypoint);
// flippush(&(botcastets[0]), oppo(botcastets[0]));
- }
- }
+ } // if (scount > 0)
+ } // if (checksubfaceflag)
- if (chkencflag & 4) {
+ if (fc->chkencflag & 4) {
// Put two new tets into check list.
for (i = 0; i < 2; i++) {
- if (!marktest2ed(fliptets[i])) {
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = fliptets[i];
- marktest2(bface->tt);
- bface->forg = org(fliptets[i]);
- }
+ enqueuetetrahedron(&(fliptets[i]));
}
}
- setpoint2tet(pa, encode(fliptets[0]));
- setpoint2tet(pb, encode(fliptets[0]));
- setpoint2tet(pc, encode(fliptets[0]));
- setpoint2tet(pd, encode(fliptets[0]));
- setpoint2tet(pe, encode(fliptets[1]));
+ setpoint2tet(pa, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pb, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pc, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pd, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pe, (tetrahedron) fliptets[1].tet);
if (hullflag > 0) {
if (dummyflag != 0) {
@@ -7572,14 +7760,14 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
}
}
- if (flipflag > 0) {
+ if (fc->enqflag > 0) {
// Queue faces which may be locally non-Delaunay.
// pa = org(fliptets[0]); // 'a' may be a new vertex.
enextesym(fliptets[0], newface);
flippush(flipstack, &newface);
eprevesym(fliptets[1], newface);
flippush(flipstack, &newface);
- if (flipflag > 1) {
+ if (fc->enqflag > 1) {
//pb = dest(fliptets[0]);
eprevesym(fliptets[0], newface);
flippush(flipstack, &newface);
@@ -7605,28 +7793,28 @@ void tetgenmesh::flip32(triface* fliptets, int hullflag, int flipflag,
// four tets in 'fliptets' are: [p,d,a,b], [p,d,b,c], [p,d,c,a], and [a,b,c, //
// p]. On return, 'fliptets[0]' is the new tet [a,b,c,d]. //
// //
-// If 'hullflag' is set (> 0), one of the four vertices may be 'duumypoint'. //
-// The 'hullsize' may be changed. //
+// If 'hullflag' is set (> 0), one of the five vertices may be 'dummypoint'. //
+// The 'hullsize' may be changed. Note that p may be dummypoint. In this //
+// case, four hull tets are replaced by one real tet. //
// //
// If 'checksubface' flag is set (>0), it is possible that there are three //
// interior subfaces connecting at p. If so, a 3-to-1 flip is performed to //
// to remove p from the surface triangulation. //
// //
+// If it is called by the routine incrementalflip(), we assume that d is the //
+// newly inserted vertex. //
+// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
- int chkencflag)
+void tetgenmesh::flip41(triface* fliptets, int hullflag, flipconstraints *fc)
{
triface topcastets[3], botcastet;
triface newface, neightet;
face flipshs[4];
- face checksh;
- face checkseg;
point pa, pb, pc, pd, pp;
- badface *bface; // used by chkencflag
- REAL volneg[4], volpos[1], vol_diff; // volumes of involved tet-prisms.
int dummyflag = 0; // in {0, 1, 2, 3, 4}
int spivot = -1, scount = 0;
+ int t1ver;
int i;
pa = org(fliptets[3]);
@@ -7635,11 +7823,7 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
pd = dest(fliptets[0]);
pp = org(fliptets[0]); // The removing vertex.
- if (b->verbose > 3) {
- printf(" flip 4-to-1: (%d, %d, %d, %d, %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pp));
- }
- // flip41count++;
+ flip41count++;
// Get the outer boundary faces.
for (i = 0; i < 3; i++) {
@@ -7652,8 +7836,6 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
if (checksubfaceflag) {
// Check if there are three subfaces at 'p'.
// Re-use 'newface'.
- spivot = -1;
- scount = 0;
for (i = 0; i < 3; i++) {
fnext(fliptets[3], newface); // [a,b,p,d],[b,c,p,d],[c,a,p,d].
tspivot(newface, flipshs[i]);
@@ -7683,9 +7865,11 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
}
} // if (checksubfaceflag)
+
// Re-use fliptets[0] for [a,b,c,d].
fliptets[0].ver = 11;
setelemmarker(fliptets[0].tet, 0); // Clean all flags.
+ // NOTE: the element attributes and volume constraint remain unchanged.
if (checksubsegflag) {
// Dealloc the space to subsegments.
if (fliptets[0].tet[8] != NULL) {
@@ -7700,19 +7884,20 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
fliptets[0].tet[9] = NULL;
}
}
-
// Delete the other three tets.
for (i = 1; i < 4; i++) {
tetrahedrondealloc(fliptets[i].tet);
}
- // Mark the point pp as unused.
- setpointtype(pp, UNUSEDVERTEX);
- unuverts++;
+ if (pp != dummypoint) {
+ // Mark the point pp as unused.
+ setpointtype(pp, UNUSEDVERTEX);
+ unuverts++;
+ }
// Create the new tet [a,b,c,d].
if (hullflag > 0) {
- // One of the four vertices may be 'dummypoint'.
+ // One of the five vertices may be 'dummypoint'.
if (pa == dummypoint) {
// pa is dummypoint.
setvertices(fliptets[0], pc, pb, pd, pa);
@@ -7733,17 +7918,26 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
dummyflag = 4;
} else {
setvertices(fliptets[0], pa, pb, pc, pd);
- dummyflag = 0;
+ if (pp == dummypoint) {
+ dummyflag = -1;
+ } else {
+ dummyflag = 0;
+ }
}
if (dummyflag > 0) {
- // We delete 3 hull tets, and create 1 hull tet.
+ // We deleted 3 hull tets, and create 1 hull tet.
hullsize -= 2;
+ } else if (dummyflag < 0) {
+ // We deleted 4 hull tets.
+ hullsize -= 4;
+ // meshedges does not change.
}
} else {
setvertices(fliptets[0], pa, pb, pc, pd);
}
- if (calc_tetprism_vol) {
+ if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol
+ REAL volneg[4], volpos[1], vol_diff;
if (dummyflag > 0) {
if (pa == dummypoint) {
volneg[0] = 0.;
@@ -7767,6 +7961,12 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
volneg[3] = tetprismvol(pa, pb, pc, pp);
}
volpos[0] = 0.;
+ } else if (dummyflag < 0) {
+ volneg[0] = 0.;
+ volneg[1] = 0.;
+ volneg[2] = 0.;
+ volneg[3] = 0.;
+ volpos[0] = tetprismvol(pa, pb, pc, pd);
} else {
volneg[0] = tetprismvol(pp, pd, pa, pb);
volneg[1] = tetprismvol(pp, pd, pb, pc);
@@ -7775,7 +7975,7 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
volpos[0] = tetprismvol(pa, pb, pc, pd);
}
vol_diff = volpos[0] - volneg[0] - volneg[1] - volneg[2] - volneg[3];
- tetprism_vol_sum += vol_diff; // Update the total sum.
+ fc->tetprism_vol_sum += vol_diff; // Update the total sum.
}
// Bond the new tet to adjacent tets.
@@ -7787,40 +7987,29 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
bond(fliptets[0], botcastet);
if (checksubsegflag) {
+ face checkseg;
// Bond 6 segments (at edges of [a,b,c,d]) if there there are.
for (i = 0; i < 3; i++) {
eprev(topcastets[i], newface); // At edges [d,a],[d,b],[d,c].
- tsspivot1(newface, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(newface)) {
+ tsspivot1(newface, checkseg);
esym(fliptets[0], newface);
enextself(newface); // At edges [a,d], [b,d], [c,d].
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
}
for (i = 0; i < 3; i++) {
- tsspivot1(topcastets[i], checkseg); // At edges [a,b],[b,c],[c,a].
- if (checkseg.sh != NULL) {
+ if (issubseg(topcastets[i])) {
+ tsspivot1(topcastets[i], checkseg); // At edges [a,b],[b,c],[c,a].
tssbond1(fliptets[0], checkseg);
sstbond1(checkseg, fliptets[0]);
- if (chkencflag & 1) {
- // Skip it if it has already queued.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
+ if (fc->chkencflag & 1) {
+ enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
@@ -7828,40 +8017,29 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
}
if (checksubfaceflag) {
+ face checksh;
// Bond 4 subfaces (at faces of [a,b,c,d]) if there are.
for (i = 0; i < 3; i++) {
- tspivot(topcastets[i], checksh); // At faces [a,b,d],[b,c,d],[c,a,d]
- if (checksh.sh != NULL) {
+ if (issubface(topcastets[i])) {
+ tspivot(topcastets[i], checksh); // At faces [a,b,d],[b,c,d],[c,a,d]
esym(fliptets[0], newface); // At faces [b,a,d],[c,b,d],[a,c,d]
sesymself(checksh);
tsbond(newface, checksh);
- if (chkencflag & 2) {
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface
- }
+ if (fc->chkencflag & 2) {
+ enqueuesubface(badsubfacs, &checksh);
}
}
enextself(fliptets[0]);
}
- tspivot(botcastet, checksh); // At face [b,a,c]
- if (checksh.sh != NULL) {
+ if (issubface(botcastet)) {
+ tspivot(botcastet, checksh); // At face [b,a,c]
sesymself(checksh);
tsbond(fliptets[0], checksh);
- if (chkencflag & 2) {
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface
- }
+ if (fc->chkencflag & 2) {
+ enqueuesubface(badsubfacs, &checksh);
}
}
- }
- if (checksubfaceflag) {
if (spivot >= 0) {
// Perform a 3-to-1 flip in surface triangulation.
// Depending on the value of 'spivot', the three subfaces are:
@@ -7895,30 +8073,26 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
} // if (spivot > 0)
} // if (checksubfaceflag)
- if (chkencflag & 4) {
- // Put the new tet into check list.
- if (!marktest2ed(fliptets[0])) {
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = fliptets[0];
- marktest2(bface->tt);
- bface->forg = org(fliptets[0]);
- }
+ if (fc->chkencflag & 4) {
+ enqueuetetrahedron(&(fliptets[0]));
}
// Update the point-to-tet map.
- setpoint2tet(pa, encode(fliptets[0]));
- setpoint2tet(pb, encode(fliptets[0]));
- setpoint2tet(pc, encode(fliptets[0]));
- setpoint2tet(pd, encode(fliptets[0]));
+ setpoint2tet(pa, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pb, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pc, (tetrahedron) fliptets[0].tet);
+ setpoint2tet(pd, (tetrahedron) fliptets[0].tet);
- if (flipflag > 0) {
+ if (fc->enqflag > 0) {
// Queue faces which may be locally non-Delaunay.
- for (i = 0; i < 3; i++) {
- esym(fliptets[0], newface);
- flippush(flipstack, &newface);
- enextself(fliptets[0]);
+ flippush(flipstack, &(fliptets[0])); // [a,b,c] (opposite to new point).
+ if (fc->enqflag > 1) {
+ for (i = 0; i < 3; i++) {
+ esym(fliptets[0], newface);
+ flippush(flipstack, &newface);
+ enextself(fliptets[0]);
+ }
}
- flippush(flipstack, &(fliptets[0]));
}
recenttet = fliptets[0];
@@ -7926,7 +8100,7 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
///////////////////////////////////////////////////////////////////////////////
// //
-// flipnm() Try to flip an edge through a sequence of elementary flips. //
+// flipnm() Flip an edge through a sequence of elementary flips. //
// //
// 'abtets' is an array of 'n' tets in the star of edge [a,b].These tets are //
// ordered in a counterclockwise cycle with respect to the vector a->b, i.e.,//
@@ -7951,7 +8125,6 @@ void tetgenmesh::flip41(triface* fliptets, int hullflag, int flipflag,
// - Neither a nor b is 'dummypoint'. //
// - [a,b] must not be a segment. //
// //
-// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
@@ -7959,27 +8132,19 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
{
triface fliptets[3], spintet, flipedge;
triface *tmpabtets, *parytet;
- face checksh;
- face checkseg, *paryseg;
point pa, pb, pc, pd, pe, pf;
- point tmppts[3];
- REAL abovept[3];
- REAL ori, ori1, ori2;
- int reducflag, rejflag;
+ REAL ori;
int hullflag;
+ int reducflag, rejflag;
int reflexlinkedgecount;
int edgepivot;
int n1, nn;
+ int t1ver;
int i, j;
pa = org(abtets[0]);
pb = dest(abtets[0]);
- if (b->verbose > 2) {
- printf(" flipnm(%d): (%d, %d) - n(%d), e(%d).\n", level, pointmark(pa),
- pointmark(pb), n, abedgepivot);
- }
-
if (n > 3) {
// Try to reduce the size of the Star(ab) by flipping a face in it.
reflexlinkedgecount = 0;
@@ -7987,9 +8152,7 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
for (i = 0; i < n; i++) {
// Let the face of 'abtets[i]' be [a,b,c].
if (checksubfaceflag) {
- // Do not flip this face if it is a constraining face.
- tspivot(abtets[i], checksh);
- if (checksh.sh != NULL) {
+ if (issubface(abtets[i])) {
continue; // Skip a subface.
}
}
@@ -7998,30 +8161,28 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
(elemcounter(abtets[(i - 1 + n) % n]) > 1)) {
continue;
}
+
pc = apex(abtets[i]);
pd = apex(abtets[(i + 1) % n]);
pe = apex(abtets[(i - 1 + n) % n]);
if ((pd == dummypoint) || (pe == dummypoint)) {
- // [a,b,c] is a hull face, it is not flipable.
- continue;
+ continue; // [a,b,c] is a hull face.
}
+
if (checkinverttetflag) {
// The mesh contains inverted (or degenerated) elements.
// Only do check if both elements are valid.
- if (pc != dummypoint) {
- ori = orient3d(pa, pb, pc, pd);
- if (ori < 0) {
- ori = orient3d(pb, pa, pc, pe);
- }
- if (ori >= 0) {
- continue; // An invalid tet.
- }
- } else {
- continue;
+ ori = orient3d(pa, pb, pc, pd);
+ if (ori < 0) {
+ ori = orient3d(pb, pa, pc, pe);
+ }
+ if (ori >= 0) {
+ continue; // An invalid tet.
}
} // if (checkinverttetflag)
- reducflag = 0; // Not reducible.
+ // Decide whether [a,b,c] is flippable or not.
+ reducflag = 0;
hullflag = (pc == dummypoint); // pc may be dummypoint.
if (hullflag == 0) {
@@ -8072,7 +8233,7 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
if (reducflag) {
// [a,b,c] could be removed by a 2-to-3 flip.
rejflag = 0;
- if (fc != NULL) {
+ if (fc->checkflipeligibility) {
// Check if the flip can be performed.
rejflag = checkflipeligibility(1, pa, pb, pc, pd, pe, level,
abedgepivot, fc);
@@ -8081,7 +8242,7 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// Do flip: [a,b,c] => [e,d].
fliptets[0] = abtets[i];
fsym(fliptets[0], fliptets[1]); // abtets[i-1].
- flip23(fliptets, hullflag, 0, 0);
+ flip23(fliptets, hullflag, fc);
// Shrink the array 'abtets', maintain the original order.
// Two tets 'abtets[i-1] ([a,b,e,c])' and 'abtets[i] ([a,b,c,d])'
@@ -8099,11 +8260,9 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// [n-2] |___________| [n-2] |___________|
// [n-1] |___________| [n-1] |_[i]_2-t-3_|
//
- eprevself(fliptets[0]);
- esymself(fliptets[0]);
- enextself(fliptets[0]); // [a,b,e,d]
+ edestoppoself(fliptets[0]); // [a,b,e,d]
// Increase the counter of this new tet (it is in Star(ab)).
- increaseelemcounter(fliptets[0]); //marktest(fliptets[0]);
+ increaseelemcounter(fliptets[0]);
abtets[(i - 1 + n) % n] = fliptets[0];
for (j = i; j < n - 1; j++) {
abtets[j] = abtets[j + 1]; // Upshift
@@ -8134,7 +8293,10 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// Star(ab) is reduced. Try to flip the edge [a,b].
nn = flipnm(abtets, n - 1, level, abedgepivot, fc);
- if (nn > 2) {
+ if (nn == 2) {
+ // The edge has been flipped.
+ return nn;
+ } else { // if (nn > 2)
// The edge is not flipped.
if (fc->unflip || (ori == 0)) {
// Undo the previous 2-to-3 flip, i.e., do a 3-to-2 flip to
@@ -8144,17 +8306,15 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// Remeber that 'abtets[i-1]' is [a,b,e,d]. We can use it to
// find another two tets [e,d,b,c] and [e,d,c,a].
fliptets[0] = abtets[(i-1 + (n-1)) % (n-1)]; // [a,b,e,d]
- eprevself(fliptets[0]);
- esymself(fliptets[0]);
- enextself(fliptets[0]); // [e,d,a,b]
+ edestoppoself(fliptets[0]); // [e,d,a,b]
fnext(fliptets[0], fliptets[1]); // [1] is [e,d,b,c]
fnext(fliptets[1], fliptets[2]); // [2] is [e,d,c,a]
assert(apex(fliptets[0]) == oppo(fliptets[2])); // SELF_CHECK
// Restore the two original tets in Star(ab).
- flip32(fliptets, hullflag, 0, 0);
+ flip32(fliptets, hullflag, fc);
// Marktest the two restored tets in Star(ab).
for (j = 0; j < 2; j++) {
- increaseelemcounter(fliptets[j]); //marktest(fliptets[j]);
+ increaseelemcounter(fliptets[j]);
}
// Expand the array 'abtets', maintain the original order.
for (j = n - 2; j>= i; j--) {
@@ -8173,27 +8333,14 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
} // if (upflip || (ori == 0))
} // if (nn > 2)
- if (nn == 2) { //if ((nn == 2) || !fullsearch) {
- // The edge has been flipped.
- return nn;
- }
if (!fc->unflip) {
// The flips are not reversed. The current Star(ab) can not be
- // further reduced. Return its size (# of tets).
+ // further reduced. Return its current size (# of tets).
return nn;
}
// unflip is set.
// Continue the search for flips.
- } else {
- if (b->verbose > 2) {
- printf(" -- Reject a 2-to-3 flip at star face (%d, %d, %d)",
- pointmark(pa), pointmark(pb), pointmark(pc));
- printf(", link (%d)\n", level);
- }
- if (fc != NULL) {
- fc->rejf23count++;
- }
- } // if (rejflag)
+ }
} // if (reducflag)
} // i
@@ -8202,16 +8349,6 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// There are reflex edges in the Link(ab).
if (((b->fliplinklevel < 0) && (level < autofliplinklevel)) ||
((b->fliplinklevel >= 0) && (level < b->fliplinklevel))) {
- // Record the largest level.
- if ((level + 1) > maxfliplinklevel) {
- maxfliplinklevel = level + 1;
- }
- if (fc != NULL) {
- // Increase the link level counter.
- if ((level + 1) > fc->maxflippedlinklevelcount) {
- fc->maxflippedlinklevelcount = level + 1;
- }
- }
// Try to reduce the Star(ab) by flipping a reflex edge in Link(ab).
for (i = 0; i < n; i++) {
// Do not flip this face [a,b,c] if there are two Stars involved.
@@ -8221,13 +8358,14 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
}
pc = apex(abtets[i]);
if (pc == dummypoint) {
- continue; // [a,b,dummypoint] is a hull edge.
+ continue; // [a,b] is a hull edge.
}
pd = apex(abtets[(i + 1) % n]);
pe = apex(abtets[(i - 1 + n) % n]);
if ((pd == dummypoint) || (pe == dummypoint)) {
continue; // [a,b,c] is a hull face.
}
+
if (checkinverttetflag) {
// The mesh contains inverted (or degenerated) elements.
// Only do check if both elements are valid.
@@ -8265,21 +8403,15 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// An edge is selected.
if (checksubsegflag) {
// Do not flip it if it is a segment.
- tsspivot1(flipedge, checkseg);
- if (checkseg.sh != NULL) {
- if (b->verbose > 2) {
- printf(" -- Can't flip a link(%d) segment (%d, %d).\n",
- level, pointmark(org(flipedge)), pointmark(dest(flipedge)));
- }
- if (fc != NULL) {
- fc->encsegcount++;
- if (fc->collectencsegflag) {
- if (!sinfected(checkseg)) {
- // Queue this segment in list.
- sinfect(checkseg);
- caveencseglist->newindex((void **) &paryseg);
- *paryseg = checkseg;
- }
+ if (issubseg(flipedge)) {
+ if (fc->collectencsegflag) {
+ face checkseg, *paryseg;
+ tsspivot1(flipedge, checkseg);
+ if (!sinfected(checkseg)) {
+ // Queue this segment in list.
+ sinfect(checkseg);
+ caveencseglist->newindex((void **) &paryseg);
+ *paryseg = checkseg;
}
}
continue;
@@ -8294,7 +8426,7 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
spintet = flipedge;
while (1) {
n1++;
- j += (elemcounter(spintet)); //if (marktested(spintet)) j++;
+ j += (elemcounter(spintet));
fnextself(spintet);
if (spintet.tet == flipedge.tet) break;
}
@@ -8306,14 +8438,8 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// Only two tets can be marktested.
assert(j == 2);
- flipstarcount++;
- // Record the maximum star size.
- if (n1 > maxflipstarsize) {
- maxflipstarsize = n1;
- }
if ((b->flipstarsize > 0) && (n1 > b->flipstarsize)) {
- // The star size exceeds the given limit (-LL__).
- skpflipstarcount++;
+ // The star size exceeds the given limit.
continue; // Do not flip it.
}
@@ -8330,15 +8456,6 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
fnextself(spintet);
if (spintet.tet == flipedge.tet) break;
}
- // SELF_CHECK BEGIN
- // These two tets are inside both of the Stars.
- assert(elemcounter(tmpabtets[0]) == 2);
- assert(elemcounter(tmpabtets[1]) == 2);
- // Marktest the tets in Star(flipedge) but not in Star(ab).
- for (j = 2; j < n1; j++) {
- assert(elemcounter(tmpabtets[j]) == 1);
- //marktest(tmpabtets[j]);
- }
// Try to flip the selected edge away.
nn = flipnm(tmpabtets, n1, level + 1, edgepivot, fc);
@@ -8359,10 +8476,8 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
esymself(spintet);
eprevself(spintet); // [a,b,e,d]
} // edgepivot == 2
- //assert(!marktested(spintet)); // It's a new tet.
- assert(elemcounter(spintet) == 0);
- //marktest(spintet); // It is in Star(ab).
- increaseelemcounter(spintet);
+ assert(elemcounter(spintet) == 0); // It's a new tet.
+ increaseelemcounter(spintet); // It is in Star(ab).
// Put the new tet at [i-1]-th entry.
abtets[(i - 1 + n) % n] = spintet;
for (j = i; j < n - 1; j++) {
@@ -8389,7 +8504,10 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// Continue to flip the edge [a,b].
nn = flipnm(abtets, n - 1, level, abedgepivot, fc);
- if (nn > 2) {
+ if (nn == 2) {
+ // The edge has been flipped.
+ return nn;
+ } else { // if (nn > 2) {
// The edge is not flipped.
if (fc->unflip) {
// Recover the flipped edge ([c,b] or [a,c]).
@@ -8455,10 +8573,6 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
} // if (unflip)
} // if (nn > 2)
- if (nn == 2) { //if ((nn == 2) || !fullsearch) {
- // The edge has been flipped.
- return nn;
- }
if (!fc->unflip) {
// The flips are not reversed. The current Star(ab) can not be
// further reduced. Return its size (# of tets).
@@ -8484,70 +8598,56 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
delete [] tmpabtets;
}
} // i
- } else {
- if (b->verbose > 2) {
- printf(" -- Maximal link level (%d) reached at edge (%d, %d).\n",
- level, pointmark(org(abtets[0])), pointmark(dest(abtets[0])));
- }
- if (fc != NULL) {
- fc->misfliplinklevelcount++;
- }
} // if (level...)
} // if (reflexlinkedgecount > 0)
} else {
// Check if a 3-to-2 flip is possible.
- pc = apex(abtets[0]);
- pd = apex(abtets[1]);
- pe = apex(abtets[2]);
-
- // Check if one of them is dummypoint. If so, we rearrange the vertices
- // c, d, and e into p0, p1, and p2, such that p2 is the dummypoint.
+ // Let the three apexes be c, d,and e. Hull tets may be involved. If so,
+ // we rearrange them such that the vertex e is dummypoint.
hullflag = 0;
- if (pc == dummypoint) {
- hullflag = 1;
- tmppts[0] = pd;
- tmppts[1] = pe;
- tmppts[2] = pc;
- } else if (pd == dummypoint) {
+
+ if (apex(abtets[0]) == dummypoint) {
+ pc = apex(abtets[1]);
+ pd = apex(abtets[2]);
+ pe = apex(abtets[0]);
hullflag = 1;
- tmppts[0] = pe;
- tmppts[1] = pc;
- tmppts[2] = pd;
- } else if (pe == dummypoint) {
+ } else if (apex(abtets[1]) == dummypoint) {
+ pc = apex(abtets[2]);
+ pd = apex(abtets[0]);
+ pe = apex(abtets[1]);
hullflag = 1;
- tmppts[0] = pc;
- tmppts[1] = pd;
- tmppts[2] = pe;
} else {
- tmppts[0] = pc;
- tmppts[1] = pd;
- tmppts[2] = pe;
- }
+ pc = apex(abtets[0]);
+ pd = apex(abtets[1]);
+ pe = apex(abtets[2]);
+ hullflag = (pe == dummypoint);
+ }
reducflag = 0;
rejflag = 0;
if (checkinverttetflag) {
- // Only do flip if no tet is inverted (or degenerated).
+ // Only do flip if no tet is inverted.
+ // NOTE: [a,b,c,d] may be degenerated (ori == 0). For instance,
+ // it is in the middle of a 4-to-4 flip.
if (hullflag == 0) {
- ori = orient3d(pa, pb, pc, pd);
- if (ori < 0) {
+ ori = orient3d(pa, pb, pc, pd);
+ if (ori <= 0) {
ori = orient3d(pa, pb, pd, pe);
if (ori < 0) {
ori = orient3d(pa, pb, pe, pc);
}
+ if (ori >= 0) {
+ return 3; // Either [a,b,d,e] or [a,b,e,c] is inverted.
+ }
+ } else {
+ return 3; // [a,b,c,d] is inverted.
}
} else {
- ori = orient3d(pa, pb, tmppts[0], tmppts[1]);
- }
- if (ori >= 0) {
- if (b->verbose > 2) {
- printf(" -- Hit a non-valid tet (%d, %d) - (%d, %d, %d)",
- pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd),
- pointmark(pe));
- printf(" at link(%d)\n", level);
+ ori = orient3d(pa, pb, pc, pd);
+ if (ori > 0) {
+ return 3; // [a,b,c,d] is inverted.
}
- return 3;
}
} // if (checkinverttetflag)
@@ -8560,97 +8660,29 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
if (ori < 0) {
reducflag = 1;
}
- } else {
- if (b->verbose > 2) {
- printf(" -- Hit a chrismastree (%d, %d) - (%d, %d, %d)",
- pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd),
- pointmark(pe));
- printf(" at link(%d)\n", level);
- }
- if (fc != NULL) {
- fc->chrismastreecount++;
- }
}
} else {
- // [a,b] is a hull edge. Moreover, the tet [a,b,p0,p1] is a hull tet
- // ([a,b,p0] and [a,b,p1] are two hull faces).
+ // [a,b] is a hull edge.
// This can happen when it is in the middle of a 4-to-4 flip.
// Note that [a,b] may even be a non-convex hull edge.
if (!nonconvex) {
- // [a,b], [a,b,p0] and [a,b,p1] are on the convex hull.
- ori = orient3d(pa, pb, tmppts[0], tmppts[1]);
- if (ori == 0) {
- // They four vertices are coplanar. A 2-to-2 flip is possible if
- // [a,b] and [p0,p1] are intersecting each other.
- // NOTE: The following test is not robust, should be replaced in
- // the future. 2011-12-01.
- calculateabovepoint4(pa, pb, tmppts[0], tmppts[1]);
- for (j = 0; j < 3; j++) {
- abovept[j] = dummypoint[j];
- }
- // Make sure that no inverted face will be created, i.e., [p1,p0,
- // abvpt,pa] and [p0,p1,abvpt,pb] must be valid tets.
- ori1 = orient3d(tmppts[0], tmppts[1], abovept, pa);
- ori2 = orient3d(tmppts[0], tmppts[1], abovept, pb);
- if (ori1 * ori2 < 0) {
- reducflag = 1; // Flipable.
- }
- if (!reducflag) {
- if (b->verbose > 2) {
- printf(" -- Hit a degenerate chrismastree (%d, %d)",
- pointmark(pa), pointmark(pb));
- printf(" - (%d, %d, -1) at link(%d)\n",
- pointmark(tmppts[0]), pointmark(tmppts[1]), level);
- }
- if (fc != NULL) {
- fc->chrismastreecount++;
- }
- }
- } else {
- if (b->verbose > 2) {
- printf(" -- Hit a convex hull edge (%d, %d) at link(%d).\n",
- pointmark(pa), pointmark(pb), level);
- }
- if (fc != NULL) {
- fc->convexhulledgecount++;
- }
- }
- } else { // if (nonconvex)
- // [a,b,p0] and [a,b,p1] must be two subfaces.
- // Since [a,b] is not a segment. A 3-to-2 flip (including a 2-to-2
- // flip) is possible.
- // Here we only do flip if there are exactly three tets containing
- // the edge [p0,p1]. In this case, the other two tets at [p0,p1]
- // (not [a,b,p0,p1]) must be valid. Since they already exist.
- for (j = 0; j < 3; j++) {
- if (apex(abtets[j]) == dummypoint) {
- flipedge = abtets[(j + 1) % 3]; // [a,b,p0,p1].
- break;
- }
- }
- // assert(j < 3);
- eprevself(flipedge);
- esymself(flipedge);
- enextself(flipedge); // [p0,p1,a,b].
- assert(apex(flipedge) == pa);
- spintet = flipedge;
- j = 0;
- while (1) {
- j++;
- fnextself(spintet);
- if (spintet.tet == flipedge.tet) break;
- }
- if (j == 3) {
- reducflag = 1;
- } else {
- if (b->verbose > 2) {
- printf(" -- Hit a hull edge (%d, %d) at link(%d).\n",
- pointmark(pa), pointmark(pb), level);
- }
- //if (fc != NULL) {
- // fc->convexhulledgecount++;
- //}
- }
+ // [a,b], [a,b,c] and [a,b,d] are on the convex hull.
+ // They four vertices are coplanar. A 2-to-2 flip is possible if
+ // [a,b] and [c,d] are intersecting each other.
+ // NOTE: The following test is not robust, should be replaced in
+ // the future. 2011-12-01.
+ REAL abovept[3], ori1, ori2;
+ calculateabovepoint4(pa, pb, pc, pd);
+ for (j = 0; j < 3; j++) abovept[j] = dummypoint[j];
+ ori1 = orient3d(pc, pd, abovept, pa);
+ ori2 = orient3d(pc, pd, abovept, pb);
+ if (ori1 * ori2 < 0) {
+ reducflag = 1; // Flipable.
+ }
+ }
+ else { // if (nonconvex)
+ // A hull edge. The case is not fully handled. We do not flip it.
+ reducflag = 0;
}
} // if (hullflag == 1)
@@ -8663,8 +8695,7 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// 3-to-2 flip.
nn = 0;
for (j = 0; j < 3; j++) {
- tspivot(abtets[j], checksh);
- if (checksh.sh != NULL) {
+ if (issubface(abtets[j])) {
nn++; // Found a subface.
}
}
@@ -8674,34 +8705,38 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
// the boundary recovery phase. The neighbor subface is not yet
// recovered. This edge should not be flipped at this moment.
rejflag = 1;
+ } else if (nn == 2) {
+ // Found two subfaces. A 2-to-2 flip is possible.
+ if (nonconvex) {
+ // However, do not flip if one of the endpoints of this edge is a
+ // Steiner point on segment. This case may cause the vertex to be
+ // removed. It is not handled yet.
+ if ((pointtype(pa) == FREESEGVERTEX) ||
+ (pointtype(pb) == FREESEGVERTEX)) {
+ rejflag = 1;
+ }
+ }
}
}
- if (!rejflag && (fc != NULL)) {
- //rejflag = checkflipeligibility(2, tmppts[0], tmppts[1], tmppts[2],
- // pa, pb, level, abedgepivot, fc);
- // Here we must permute 'a' and 'b'. Since in the check... function,
+ if (!rejflag && fc->checkflipeligibility) {
+ // Here we must exchange 'a' and 'b'. Since in the check... function,
// we assume the following point sequence, 'a,b,c,d,e', where
// the face [a,b,c] will be flipped and the edge [e,d] will be
// created. The two new tets are [a,b,c,d] and [b,a,c,e].
- rejflag = checkflipeligibility(2, tmppts[0], tmppts[1], tmppts[2],
- pb, pa, level, abedgepivot, fc);
+ rejflag = checkflipeligibility(2, pc, pd, pe, pb, pa, level,
+ abedgepivot, fc);
}
if (!rejflag) {
// Do flip: [a,b] => [c,d,e]
- flip32(abtets, hullflag, 0, 0);
- sucflipstarcount++;
+ flip32(abtets, hullflag, fc);
if (fc->remove_ndelaunay_edge) {
if (level == 0) {
- // It is the desired removing edge.
- if (tetprism_vol_sum >= fc->bak_tetprism_vol) {
- if (b->verbose > 2) {
- printf(" -- Reject to flip (%d, %d) at link(%d)\n",
- pointmark(pa), pointmark(pb), level);
- printf(" due to an increased volume (%.17g).\n",
- tetprism_vol_sum - fc->bak_tetprism_vol);
- }
- // flip back: [c,d,e] => [a,b].
- flip23(abtets, hullflag, 0, 0);
+ // It is the desired removing edge. Check if we have improved
+ // the objective function.
+ if ((fc->tetprism_vol_sum >= 0.0) ||
+ (fabs(fc->tetprism_vol_sum) < fc->bak_tetprism_vol)) {
+ // No improvement! flip back: [c,d,e] => [a,b].
+ flip23(abtets, hullflag, fc);
// Increase the element counter -- They are in cavity.
for (j = 0; j < 3; j++) {
increaseelemcounter(abtets[j]);
@@ -8731,15 +8766,7 @@ int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
}
} // if (fc->collectnewtets)
return 2;
- } else {
- if (b->verbose > 2) {
- printf(" -- Reject a 3-to-2 flip (%d, %d) at link(%d).\n",
- pointmark(pa), pointmark(pb), level);
- }
- if (fc != NULL) {
- fc->rejf32count++;
- }
- } // if (rejflag)
+ }
} // if (reducflag)
} // if (n == 3)
@@ -8794,7 +8821,7 @@ int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot,
// 'abtets[1]' is [d,c,e,a] or [#,#,#,a].
if (fc->unflip) {
// Do a 2-to-3 flip to recover the edge [a,b]. There may be hull tets.
- flip23(abtets, 1, 0, 0);
+ flip23(abtets, 1, fc);
if (fc->collectnewtets) {
// Pop up new (flipped) tets from the stack.
if (abedgepivot == 0) {
@@ -8808,9 +8835,7 @@ int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot,
}
// The initial size of Star(ab) is 3.
nn++;
- } else { // nn > 2.
- // The edge [a,b] exists.
- }
+ }
// Walk through the performed flips.
for (i = nn; i < n; i++) {
@@ -8836,7 +8861,7 @@ int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot,
fnext(fliptets[1], fliptets[2]); // [e,d,c,a]
// Do a 3-to-2 flip: [e,d] => [a,b,c].
// NOTE: hull tets may be invloved.
- flip32(fliptets, 1, 0, 0);
+ flip32(fliptets, 1, fc);
// Expand the array 'abtets', maintain the original order.
// The new array length is (i+1).
for (j = i - 1; j >= t; j--) {
@@ -8923,9 +8948,6 @@ int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot,
printf(" Release %d spaces at f[%d].\n", n1, i);
}
delete [] tmpabtets;
- } else {
- assert(fliptype == 0); // Not a saved flip.
- assert(0); // Should be not possible.
}
} // i
@@ -8934,916 +8956,178 @@ int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot,
///////////////////////////////////////////////////////////////////////////////
// //
-// lawsonflip3d() A three-dimensional Lawson's flip algorithm. //
-// //
-// The basic idea of Lawson's algorithm is to flip every face of the triang- //
-// ulation which is not locally Delaunay until no such face exists, then the //
-// triangulation is a DT. However, in 3D, it is common that a face which is //
-// not locally Delaunay and is not flippable. Hence, Laowson's algorithm may //
-// get stuck. It is still an open problem, whether there exists a flip algo- //
-// rithm which has a guarantee to create a DT in 3D. //
-// //
-// If only one vertex is added into a DT, then Lawson's flip algorithm is //
-// guaranteed to transform it into a new DT [Joe'91]. Moreover, an arbitrary //
-// order of flips is sufficient [Edelsbrunner & Shah'96]. //
-// //
-// In practice, it is desired to remove not locally Delaunay faces by flips //
-// as many as possible. For this purpose, a second queue is used to store //
-// the not locally Delaunay faces which are not flippable, and try them at a //
-// later time. //
-// //
-// If 'newpt' (p) is not NULL, it is a new vertex just inserted into the //
-// tetrahedralization T. //
-// //
-// 'flipflag' indicates the property of the tetrahedralization 'T' which //
-// does not include 'p' yet. //
+// insertpoint() Insert a point into current tetrahedralization. //
// //
-// If 'peelsliverflag' is set, the purpose of calling Lawson's flip is to //
-// remove "hull slivers". This flag only works with a non-convex mesh, i.e., //
-// the mesh must contains boundaries (segments and subfaces). //
-// //
-// 'chkencflag' indicates whether segments, subfaces, and tets should be //
-// checked (for encroaching and quality) after flips. //
+// The Bowyer-Watson (B-W) algorithm is used to add a new point p into the //
+// tetrahedralization T. It first finds a "cavity", denoted as C, in T, C //
+// consists of tetrahedra in T that "conflict" with p. If T is a Delaunay //
+// tetrahedralization, then all boundary faces (triangles) of C are visible //
+// by p, i.e.,C is star-shaped. We can insert p into T by first deleting all //
+// tetrahedra in C, then creating new tetrahedra formed by boundary faces of //
+// C and p. If T is not a DT, then C may be not star-shaped. It must be //
+// modified so that it becomes star-shaped. //
// //
///////////////////////////////////////////////////////////////////////////////
-long tetgenmesh::lawsonflip3d(point newpt, int flipflag, int peelsliverflag,
- int chkencflag, int flipedgeflag)
+int tetgenmesh::insertpoint(point insertpt, triface *searchtet, face *splitsh,
+ face *splitseg, insertvertexflags *ivf)
{
- badface *popface, *bface;
- triface fliptets[5], baktets[2];
- triface fliptet, neightet, *parytet;
- face checksh, *parysh;
+ arraypool *swaplist;
+ triface *cavetet, spintet, neightet, neineitet, *parytet;
+ triface oldtet, newtet, newneitet;
+ face checksh, neighsh, *parysh;
face checkseg, *paryseg;
- point *ppt, pd, pe, pf;
- long flipcount;
+ point *pts, pa, pb, pc, *parypt;
+ enum locateresult loc = OUTSIDE;
REAL sign, ori;
- int convflag;
- int n, i;
-
- // For removing hull slivers.
- face neighsh;
- point p1, p2;
- point pa, pb, pc, rempt;
- REAL ang;
- long tetpeelcount;
- int remflag;
-
- flipconstraints fc;
+ REAL attrib, volume;
+ bool enqflag;
+ int t1ver;
+ int i, j, k, s;
if (b->verbose > 2) {
- printf(" Lawson flip %ld faces.\n", flippool->items);
+ printf(" Insert point %d\n", pointmark(insertpt));
}
- flipcount = flip23count + flip32count + flip44count;
- tetpeelcount = opt_sliver_peels;
-
- if (flipedgeflag) {
- fc.remove_ndelaunay_edge = 1;
- fc.unflip = 1; // Unflip if the edge is not flipped.
- fc.collectnewtets = 1;
- assert(cavetetlist->objects == 0l);
- assert(calc_tetprism_vol == 1); // Swith on.
- } else {
- assert(unflipqueue->objects == 0); // The second queue must be empty.
+ // Locate the point.
+ if (searchtet->tet != NULL) {
+ loc = (enum locateresult) ivf->iloc;
}
- while (1) {
-
- while (flipstack != (badface *) NULL) {
-
- // Pop a face from the stack.
- popface = flipstack;
- flipstack = flipstack->nextitem; // The next top item in stack.
- fliptet = popface->tt;
- flippool->dealloc((void *) popface);
-
- // Skip it if it is a dead tet (destroyed by previous flips).
- if (isdeadtet(fliptet)) continue;
- // Skip it if it is not the same tet as we saved.
- if (!facemarked(fliptet)) continue;
+ if (loc == OUTSIDE) {
+ if (searchtet->tet == NULL) {
+ if (!b->weighted) {
+ randomsample(insertpt, searchtet);
+ } else {
+ // Weighted DT. There may exist dangling vertex.
+ *searchtet = recenttet;
+ }
+ }
+ // Locate the point.
+ loc = locate(insertpt, searchtet, ivf->chkencflag);
+ }
- unmarkface(fliptet);
+ ivf->iloc = (int) loc; // The return value.
- // FOR DEBUG
- if (flipflag == 1) {
- assert(oppo(fliptet) == newpt);
+ if (b->weighted) {
+ if (loc != OUTSIDE) {
+ // Check if this vertex is regular.
+ pts = (point *) searchtet->tet;
+ assert(pts[7] != dummypoint);
+ sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt,
+ pts[4][3], pts[5][3], pts[6][3], pts[7][3],
+ insertpt[3]);
+ if (sign > 0) {
+ // This new vertex does not lie below the lower hull. Skip it.
+ setpointtype(insertpt, NREGULARVERTEX);
+ nonregularcount++;
+ ivf->iloc = (int) NONREGULAR;
+ return 0;
}
+ }
+ }
- if (ishulltet(fliptet)) {
- // It is a hull tet.
- if (((flipflag == 4) || peelsliverflag) && !b->convex) {
- fliptet.ver = epivot[fliptet.ver & 3];
- if (oppo(fliptet) == dummypoint) {
- // It's a hull face (oppo(fliptet) == dummypoint).
- // Check if there exists a "hull sliver".
- fsymself(fliptet);
- tspivot(fliptet, checksh);
- assert(checksh.sh != NULL);
- for (i = 0; i < 3; i++) {
- sspivot(checksh, checkseg);
- if (checkseg.sh == NULL) {
- spivot(checksh, neighsh);
- assert(neighsh.sh != NULL);
- if (sorg(checksh) != sdest(neighsh)) {
- sesymself(neighsh);
- }
- stpivot(neighsh, neightet);
- if (neightet.tet == fliptet.tet) {
- // Found a hull sliver 'neightet' [d,e,a,b], where [d,e,a]
- // and [e,d,b] are two hull faces. Normally, a 3-to-2 flip
- // (including a 2-to-2 flip on hull subfaces) can remove
- // this hull sliver.
- // A special case is the existence of a hull tet [b,a,d,-1]
- // or [a,b,e,-1]. It was creared by a previous hull tet
- // removal. Moreover, 'd' or 'e' might be Steiner points
- // on segments [a,b]. In this case, eithe [a,d],[b,d] or
- // [a,e],[b,e] are subsegments. If so, a 4-to-1 flip
- // (including a 3-to-1, and maybe a 2-to-1 flip) should be
- // applied to remove an exterior vertex.
- // See figures (2011-11-13 and 15) for illustraions.
-
- // First check if the face [b,a,d] is a hull face.
- eprev(neightet, fliptets[0]);
- esymself(fliptets[0]); // [d,a,b,e]
- enextself(fliptets[0]); // [a,b,d,e]
- fsymself(fliptets[0]); // [b,a,d,#]
- if (oppo(fliptets[0]) != dummypoint) {
- // Second check if the face [a,b,e] is a hull face.
- enext(neightet, fliptets[0]);
- esymself(fliptets[0]); // [a,e,b,d]
- eprevself(fliptets[0]); // [b,a,e,d]
- fsymself(fliptets[0]); // [b,a,e,#]
- }
-
- if (oppo(fliptets[0]) != dummypoint) {
- // Make sure we do not create an "inverted triangle" in the
- // boundary, i.e., in exactly planar case, d and e must
- // lie in the different sides of the edge [a,b].
- // If the dihedral angle formed by [a,b,e] and [a,b,d] is
- // larger than 90 degree, we can remove [a,b,e,d].
- fliptets[0] = neightet; // [e,d,a,b]
- eprevself(fliptets[0]);
- esymself(fliptets[0]);
- enextself(fliptets[0]); // [a,b,e,d].
- pa = org(fliptets[0]);
- pb = dest(fliptets[0]);
- p1 = apex(fliptets[0]); // pe
- p2 = oppo(fliptets[0]); // pd
- ang = facedihedral(pa, pb, p1, p2);
- ang *= 2.0;
- if (ang > PI) {
- if (b->verbose > 2) {
- printf(" Remove a hull sliver (%d, %d, %d, %d).\n",
- pointmark(org(fliptet)), pointmark(dest(fliptet)),
- pointmark(apex(fliptet)), pointmark(oppo(fliptet)));
- }
- // Remove the ill tet from bounday.
- fliptets[0] = neightet; // [e,d,a,b]
- fnext(fliptets[0], fliptets[1]); // [e,d,b,c]
- fnext(fliptets[1], fliptets[2]); // [e,d,c,a]
- // FOR DEBUG
- fnext(fliptets[2], fliptets[3]);
- assert(fliptets[3].tet == neightet.tet);
- assert(oppo(fliptets[1]) == dummypoint);
- // Do a 3-to-2 flip to remove the ill tet. Two hull tets
- // are removed toether. Two hull subfaces are flipped.
- flip32(fliptets, 1, flipflag, 0);
- // Update counters.
- flip32count--;
- flip22count--;
- opt_sliver_peels++;
- }
- } else {
- // There exists a thrid hull tet at vertex.
- rempt = apex(fliptets[0]);
- if (pointmark(rempt) >
- (in->numberofpoints - (in->firstnumber ? 0 : 1))) {
- if (pointtype(rempt) == FREESEGVERTEX) {
- st_segref_count--;
- } else if (pointtype(rempt) == FREEFACETVERTEX) {
- st_facref_count--;
- } else {
- assert(0); // Impossible.
- }
- if (b->verbose > 2) {
- printf(" Remove an exterior Steiner vertex %d.\n",
- pointmark(rempt));
- }
- if (removevertexbyflips(rempt)) {
- // exsteinercount++;
- } else {
- assert(0); // Not possible.
- }
- } else {
- //if (b->verbose > 2) {
- // printf(" Remove an exterior input vertex %d.\n",
- // pointmark(rempt));
- //}
- // Comment: We do not remove an input point.
- }
- }
- break;
- }
- } // if (checkseg.sh == NULL)
- senextself(checksh);
- } // i
- } else {
- // It's a hull edge.
- assert(apex(fliptet) == dummypoint);
- if (!peelsliverflag) {
- // The hull edge may be not locally Delaunay. Put interior
- // faces at this edge into 'flipstack' for flipping.
- neightet = fliptet; // [a,b,c,d] ('c' is dummypoint).
- fnextself(neightet); // [a,b,d,#1] ([a,b,d] is a hull face).
- while (1) {
- fnextself(neightet); // [a,b,#1,#2]
- if (oppo(neightet) != dummypoint) {
- // It is an interior face.
- flippush(flipstack, &neightet);
- } else {
- // We assume the interior of the domain is connected.
- // Hence we can hit hull faces only twice.
- break;
- }
- } // while (1)
- } // if (!peelsliverflag)
- }
- } // if ((flipflag == 4) || peelsliverflag)
+ // Create the initial cavity C(p) which contains all tetrahedra that
+ // intersect p. It may include 1, 2, or n tetrahedra.
+ // If p lies on a segment or subface, also create the initial sub-cavity
+ // sC(p) which contains all subfaces (and segment) which intersect p.
- // Do not flip a hull face/edge UNLESS it is in the process of
- // incrementally creating a DT in which the convex hull may be
- // enlarged by the flips (when p lies outside of it).
- if (flipflag != 1) {
- continue;
- }
- } // if (ishulltet(fliptet))
+ if (loc == OUTSIDE) {
+ flip14count++;
+ // The current hull will be enlarged.
+ // Add four adjacent boundary tets into list.
+ for (i = 0; i < 4; i++) {
+ decode(searchtet->tet[i], neightet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = neightet;
+ }
+ infect(*searchtet);
+ caveoldtetlist->newindex((void **) &parytet);
+ *parytet = *searchtet;
+ } else if (loc == INTETRAHEDRON) {
+ flip14count++;
+ // Add four adjacent boundary tets into list.
+ for (i = 0; i < 4; i++) {
+ decode(searchtet->tet[i], neightet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = neightet;
+ }
+ infect(*searchtet);
+ caveoldtetlist->newindex((void **) &parytet);
+ *parytet = *searchtet;
+ } else if (loc == ONFACE) {
+ flip26count++;
+ // Add six adjacent boundary tets into list.
+ j = (searchtet->ver & 3); // The current face number.
+ for (i = 1; i < 4; i++) {
+ decode(searchtet->tet[(j + i) % 4], neightet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = neightet;
+ }
+ decode(searchtet->tet[j], spintet);
+ j = (spintet.ver & 3); // The current face number.
+ for (i = 1; i < 4; i++) {
+ decode(spintet.tet[(j + i) % 4], neightet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = neightet;
+ }
+ infect(spintet);
+ caveoldtetlist->newindex((void **) &parytet);
+ *parytet = spintet;
+ infect(*searchtet);
+ caveoldtetlist->newindex((void **) &parytet);
+ *parytet = *searchtet;
- if (peelsliverflag) {
- continue; // Only check hull tets.
+ if (ivf->splitbdflag) {
+ if (splitsh != NULL) {
+ // Create the initial sub-cavity sC(p).
+ smarktest(*splitsh);
+ caveshlist->newindex((void **) &parysh);
+ *parysh = *splitsh;
}
+ } // if (splitbdflag)
+ } else if (loc == ONEDGE) {
+ flipn2ncount++;
+ // Add all adjacent boundary tets into list.
+ spintet = *searchtet;
+ while (1) {
+ eorgoppo(spintet, neightet);
+ decode(neightet.tet[neightet.ver & 3], neightet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = neightet;
+ edestoppo(spintet, neightet);
+ decode(neightet.tet[neightet.ver & 3], neightet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = neightet;
+ infect(spintet);
+ caveoldtetlist->newindex((void **) &parytet);
+ *parytet = spintet;
+ fnextself(spintet);
+ if (spintet.tet == searchtet->tet) break;
+ } // while (1)
- // Let 'fliptet' be [a,b,c,d], the face [a,b,c] is the flip face.
- // Get its opposite tet [b,a,c,e].
- fsym(fliptet, neightet);
-
- if (ishulltet(neightet)) {
- // It is a hull tet.
- if (flipflag == 1) {
- // Check if the new point is visible by the hull face.
- ppt = (point *) neightet.tet;
- ori = orient3d(ppt[4], ppt[5], ppt[6], newpt); orient3dcount++;
- if (ori < 0) {
- // Visible. Perform a 2-to-3 flip on the flip face.
- fliptets[0] = fliptet; // [a,b,c,d], d = newpt.
- fliptets[1] = neightet; // [b,a,c,e], c = dummypoint.
- flip23(fliptets, 1, flipflag, chkencflag); // flip a hull tet.
- //recenttet = fliptets[0];
- } else if (ori == 0) {
- // Handle degenerate case ori == 0.
- if (oppo(neightet) == newpt) {
- // Two hull tets have the same base face.
- if (b->verbose > 2) {
- printf(" Close an open face (%d, %d, %d)\n",
- pointmark(org(fliptet)), pointmark(dest(fliptet)),
- pointmark(apex(fliptet)));
- }
- // The following code connect adjacent tets at corresponding
- // sides of the two hull tets. It is hard to understand.
- // See an example in 2011-11-11.
- // First infect the two hull tets (they will be deleted).
- infect(fliptet);
- infect(neightet);
- // Connect the actual adjacent tets.
- for (i = 0; i < 3; i++) {
- fnext(fliptet, fliptets[0]);
- fnext(neightet, fliptets[1]);
- if (!infected(fliptets[0])) {
- assert(!infected(fliptets[1]));
- bond(fliptets[0], fliptets[1]);
- // Update the point-to-tet map.
- pa = org(fliptet);
- pb = dest(fliptet);
- setpoint2tet(pa, encode(fliptets[0]));
- setpoint2tet(pb, encode(fliptets[0]));
- // Remeber a recent tet for point location.
- recenttet = fliptets[0];
- // apex(fliptets[0]) is the new point. The opposite face may
- // be not locally Delaunay. Put it in flip stack.
- assert(apex(fliptets[0]) == newpt); // SELF_CHECK
- esymself(fliptets[0]);
- flippush(flipstack, &(fliptets[0]));
- assert(apex(fliptets[1]) == newpt); // SELF_CHECK
- esymself(fliptets[1]);
- flippush(flipstack, &(fliptets[1]));
- }
- enextself(fliptet);
- eprevself(neightet);
- }
- // Delete the two tets.
- tetrahedrondealloc(fliptet.tet);
- tetrahedrondealloc(neightet.tet);
- // Update the hull size.
- hullsize -= 2;
- }
- }
- } // if (flipflag == 1)
-
- continue; // Do not flip a hull face.
- } // if (ishulltet(neightet))
-
- if (ishulltet(fliptet)) {
- continue; // Do not flip a hull tet.
+ if (ivf->splitbdflag) {
+ // Create the initial sub-cavity sC(p).
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
+ smarktest(*splitseg);
+ splitseg->shver = 0;
+ spivot(*splitseg, *splitsh);
}
-
- if ((flipflag == 3) || (flipflag == 4)) {
- if (checksubfaceflag) {
- // Do not flip a subface.
- tspivot(fliptet, checksh);
- if (checksh.sh != NULL) {
- if (chkencflag & 2) {
- // Mesh refinement.
- // Put this subface into list.
- if (!smarktest2ed(checksh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(checksh); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface.
- }
- }
- continue;
- }
- }
- } // if ((flipflag == 3) || (flipflag == 4))
-
- ppt = (point *) fliptet.tet;
- pe = oppo(neightet);
-
- sign = insphere_s(ppt[4], ppt[5], ppt[6], ppt[7], pe);
-
- if (sign < 0) {
- if (b->verbose > 3) {
- printf(" A non-Delaunay face (%d, %d, %d) - %d, %d\n",
- pointmark(org(fliptet)), pointmark(dest(fliptet)),
- pointmark(apex(fliptet)), pointmark(oppo(fliptet)),
- pointmark(pe));
- }
-
- // Try to flip this face.
- pd = oppo(fliptet);
- // Check the convexity of its three edges.
- convflag = 1;
- for (i = 0; i < 3; i++) {
- p1 = org(fliptet);
- p2 = dest(fliptet);
- ori = orient3d(p1, p2, pd, pe); orient3dcount++;
- if (ori < 0) {
- // A locally non-convex edge.
- convflag = -1;
- break;
- } else if (ori == 0) {
- // A locally flat edge.
- convflag = 0;
- break;
- }
- enextself(fliptet);
- }
-
- if (convflag > 0) {
- // A 2-to-3 flip is found.
- fliptets[0] = fliptet; // abcd, d may be the new vertex.
- fliptets[1] = neightet; // bace.
- if ((flipflag == 1) || (flipflag == 2)) { // CDT boundary recovery.
- if (checksubfaceflag) {
- // Check if a subface will be flipped.
- tspivot(fliptets[0], checksh);
- if (checksh.sh != NULL) {
- assert(flipflag < 3); // 1 or 2.
- // It is updateing a conforming DT or a CDT.
- if (b->verbose > 3) {
- printf(" Queue a flipped subface (%d, %d, %d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- for (i = 0; i < 2; i++) {
- tsdissolve(fliptets[i]); // Disconnect the tet->sub bond.
- }
- stdissolve(checksh); // Disconnect the sub->tet bond.
- // Add the missing subface into list.
- subfacstack->newindex((void **) &parysh);
- *parysh = checksh;
- } // if (checksh.sh != NULL)
- }
- } // if ((flipflag == 1) || (flipflag == 2))
- flip23(fliptets, 0, flipflag, chkencflag);
- //recenttet = fliptets[0]; // for point location.
- } else {
- // The edge ('fliptet') is non-convex or flat.
- if ((flipflag == 3) || (flipflag == 4)) {
- // Do not flip a subsegment.
- tsspivot1(fliptet, checkseg);
- if (checkseg.sh != NULL) {
- if (b->verbose > 3) {
- printf(" Found a non-Delaunay segment (%d, %d).\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
- // Comment: this should be only possible when a new Steiner
- // point is inserted on a segment nearby.
- if (chkencflag & 1) {
- // Put this segment into list.
- if (!smarktest2ed(checkseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(checkseg); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
- }
- }
- continue;
- }
- }
-
- // A 3-to-2 or 4-to-4 may be possible.
- esym(fliptet, fliptets[0]); // [b,a,d,c]
- // assert(apex(fliptets[0]) == pd);
- n = 0;
- do {
- fnext(fliptets[n], fliptets[n + 1]);
- n++;
- } while ((fliptets[n].tet != fliptet.tet) && (n < 5));
-
- if (n == 3) {
- // Found a 3-to-2 flip.
- if ((flipflag == 1) || (flipflag == 2)) { // CDT boundary recovery.
- if (checksubsegflag) {
- // Check if the flip edge is subsegment.
- tsspivot1(fliptets[0], checkseg);
- if (checkseg.sh != NULL) {
- if (!sinfected(checkseg)) {
- // This subsegment will be flipped. Queue it.
- if (b->verbose > 3) {
- printf(" Queue a flipped segment (%d, %d).\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
- sinfect(checkseg); // Only save it once.
- subsegstack->newindex((void **) &paryseg);
- *paryseg = checkseg;
- }
- // Clean tet-to-seg pointers.
- for (i = 0; i < 3; i++) {
- tssdissolve1(fliptets[i]);
- }
- // Clean the seg-to-tet pointer.
- sstdissolve1(checkseg);
- }
- }
- if (checksubfaceflag) {
- // Check if there are subfaces to be flipped.
- for (i = 0; i < 3; i++) {
- tspivot(fliptets[i], checksh);
- if (checksh.sh != NULL) {//if (flipshs[i].sh != NULL) {
- if (b->verbose > 2) {
- printf(" Queue a flipped subface (%d, %d, %d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- tsdissolve(fliptets[i]); // Disconnect the tet->sub bond.
- stdissolve(checksh); // Disconnect the sub->tet bond.
- // Add the missing subface into list.
- subfacstack->newindex((void **) &parysh);
- *parysh = checksh;
- }
- }
- }
- } // if ((flipflag == 1) || (flipflag == 2))
-
- // Now flip the edge.
- flip32(fliptets, 0, flipflag, chkencflag);
- //recenttet = fliptets[0]; // for point location.
- } else {
- // There are more than 3 tets shared at this edge.
- if ((n == 4) && (convflag < 0)) {
- // Check if a 4-to-4 flip is possible.
- pf = apex(fliptets[3]);
- if (pf == dummypoint) {
- // It is a non-convex hull edge shared by four tets (two hull
- // tets and two interior tets).
- // Let the two interior tets be [a,b,c,d] and [b,a,c,e] where
- // [a,b] be the hull edge, [a,b,c] be the interior face.
- // [a,b,d] and [a,b,e] are two hull faces.
- // A 4-to-4 flip is possible if the two new tets [e,d,b,c]
- // and [e,d,c,a] are valid tets.
- // Current status:
- // 'fliptets[0]' is [a,b,e,c]
- // 'fliptets[1]' is [a,b,c,d]
- // 'fliptets[2]' is [a,b,d,f] (hull tet)
- // 'fliptets[3]' is [a,b,f,e] (hull tet)
- pa = org(fliptets[1]);
- pb = dest(fliptets[1]);
- pc = apex(fliptets[1]);
- p1 = oppo(fliptets[1]); // pd
- p2 = apex(fliptets[0]); // pe
- ori = orient3d(p2, p1, pb, pc);
- if (ori < 0) {
- ori = orient3d(p2, p1, pc, pa);
- if (ori < 0) {
- convflag = -2; // A 4-to-4 flip is possible.
- }
- }
- }
- } // if ((n == 4) && (convflag < 0))
- if ((n == 4) && ((convflag == 0) || (convflag == -2))) {
- // Found a 4-to-4 flip.
- if (b->verbose > 3) {
- printf(" A 4-to-4 flip (%d, %d) - (%d, %d).\n",
- pointmark(org(fliptet)), pointmark(dest(fliptet)),
- pointmark(pd), pointmark(pe));
- }
- if ((flipflag == 1) || (flipflag == 2)) { // CDT boundary recovery
- if (checksubsegflag) {
- // Check if the flip edge is subsegment.
- tsspivot1(fliptets[0], checkseg);
- if (checkseg.sh != NULL) {
- if (!sinfected(checkseg)) {
- // This subsegment will be flipped. Queue it.
- if (b->verbose > 3) {
- printf(" Queue a flipped segment (%d, %d).\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
- sinfect(checkseg); // Only save it once.
- subsegstack->newindex((void **) &paryseg);
- *paryseg = checkseg;
- }
- // Clean the tet-to-seg pointers.
- for (i = 0; i < 4; i++) {
- tssdissolve1(fliptets[i]);
- }
- // Clean the seg-to-tet pointer.
- sstdissolve1(checkseg);
- }
- }
- if (checksubfaceflag) {
- // Check if there are subfaces to be flipped.
- for (i = 0; i < 4; i++) {
- tspivot(fliptets[i], checksh);
- if (checksh.sh != NULL) {
- if (b->verbose > 3) {
- printf(" Queue a flipped subface (%d,%d,%d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- tsdissolve(fliptets[i]); // Disconnect the tet->sub bond.
- stdissolve(checksh); // Disconnect the sub->tet bond.
- // Add the missing subface into list.
- subfacstack->newindex((void **) &parysh);
- *parysh = checksh;
- }
- }
- }
- } // if ((flipflag == 1) || (flipflag == 2))
-
- // First do a 2-to-3 flip.
- // Comment: This flip temporarily creates either a degenerated
- // tet (convflag == 0) or an inverted tet (convflag < 0).
- // It is removed by the followed 3-to-2 flip.
- fliptets[0] = fliptet; // tet abcd, d is the new vertex.
- baktets[0] = fliptets[2];
- baktets[1] = fliptets[3];
- // The flip may involve hull tets.
- flip23(fliptets, 1, flipflag, chkencflag);
- // Then do a 3-to-2 flip.
- enextesymself(fliptets[0]); // fliptets[0] is edab.
- eprevself(fliptets[0]); // tet badc, d is the new vertex.
- fliptets[1] = baktets[0];
- fliptets[2] = baktets[1];
- flip32(fliptets, 1, flipflag, chkencflag);
- flip23count--;
- flip32count--;
- flip44count++;
- //recenttet = fliptets[0]; // for point location.
- } else {
- // This edge is shared by more than 4 tets.
- if (b->verbose > 2) {
- printf(" An unflippable non-Delaunay edge (%d,%d).\n",
- pointmark(org(fliptet)), pointmark(dest(fliptet)));
- }
- remflag = 0;
- if (flipedgeflag == 2) {
- // Try to flip this edge by my edge flip algorithm.
- // Remember the the objective value (volume of all tetprisms).
- fc.bak_tetprism_vol = tetprism_vol_sum;
- if (removeedgebyflips(&fliptet, &fc) == 2) {
- if (b->verbose > 2) {
- printf(" Decreased quantity: %.17g.\n",
- fc.bak_tetprism_vol - tetprism_vol_sum);
- }
- // Queue new faces in flipstack.
- for (i = 0; i < cavetetlist->objects; i++) {
- parytet = (triface *) fastlookup(cavetetlist, i);
- if (!isdeadtet(*parytet)) { // Skip a dead tet.
- for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) {
- // Avoid queue a face twice.
- fsym(*parytet, neightet);
- if (!facemarked(neightet)) {
- //flippush(flipstack, parytet);
- bface = (badface *) flippool->alloc();
- bface->tt = *parytet;
- markface(bface->tt);
- bface->forg = org(bface->tt); // An alive badface.
- bface->fdest = dest(bface->tt);
- bface->fapex = apex(bface->tt);
- // bface->foppo = oppo(bface->tt);
- // Push this face into stack.
- bface->nextitem = flipstack;
- flipstack = bface;
- }
- } // parytet->ver
- }
- } // i
- cavetetlist->restart();
- remflag = 1;
- }
- }
- if (!remflag) {
- // Found an unflippable non-Delaunay edge.
- if (flipedgeflag > 0) { // if (flipflag > 1) {
- // Save this face (of the edge) in a second queue.
- unflipqueue->newindex((void **) &bface);
- bface->tt = fliptet;
- bface->forg = org(fliptet);
- bface->fdest = dest(fliptet);
- bface->fapex = apex(fliptet); // FOR DEBUG.
- }
- }
- }
- } // if (n > 3)
- } // if (convflag <= 0)
- } // if (sign < 0)
-
- } // while (flipstack != NULL)
-
-
- break;
-
- } // while (1)
-
-
- if (b->verbose > 2) {
- printf(" Total %ld flips", flip23count + flip32count + flip44count
- - flipcount);
- if ((flipflag == 4) || peelsliverflag) {
- printf(", %ld sliver peels", opt_sliver_peels - tetpeelcount);
- }
- printf("\n");
- }
-
-
- return flip23count + flip32count + flip44count - flipcount;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertvertex() Insert a point into current tetrahedralization. //
-// //
-// This routine implements the famous Bowyer-Watson (B-W) algorithm to add a //
-// new point p into current tetrahedralization, denoted as T. The baisc idea //
-// of B-W algorithm is: first finds a "cavity", denoted as C inside T, where //
-// C is a simplicial polyhedron formed by a union of tetrahedra in T. If all //
-// boundary faces (triangles) of C are visible by p, i.e., C is star-shaped, //
-// then T can be re-tetrahedralized by first deleting all old tetrahedra in //
-// C, then replacing new tetrahedra formed by boundary faces of C and p. The //
-// result is that p becomesis a vertex of T. //
-// //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
- face *splitseg, insertvertexflags *ivf)
-{
- arraypool *swaplist; // for updating cavity.
- triface *cavetet, spintet, neightet, neineitet, *parytet;
- triface oldtet, newtet, newneitet;
- face checksh, *parysh, neighsh, spinsh;
- face checkseg, *paryseg;
- point *pts, pa, pb, pc, *parypt;
- badface *bface;
- enum locateresult loc;
- REAL sign, ori;
- REAL rd, cent[3];
- REAL attrib, volume;
- long cutcount, cutshcount, tetcount = 0;
- long bakhullsize;
- bool enqflag;
- int i, j, k, s;
-
- int rejptflag, encptflag; // for protecting balls.
- int bgmloc;
-
-#ifdef WITH_RUNTIME_COUNTERS
- clock_t tstart, tend;
-#endif
-
- if (b->verbose > 2) {
- printf(" Insert point %d\n", pointmark(insertpt));
- }
-
-
- // Locate the point.
- loc = OUTSIDE; // Set a default value.
-
- if (searchtet->tet != NULL) {
- loc = (enum locateresult) ivf->iloc;
- }
-
- if (loc == OUTSIDE) {
-#ifdef WITH_RUNTIME_COUNTERS
- tstart = clock();
-#endif
- tetcount = ptloc_count; // Count the number of walked tets.
- if (searchtet->tet == NULL) {
- if (!b->weighted) {
- if (b->btree) {
- btree_search(insertpt, searchtet);
- } else if (b->hilbertcurve) { // -U
- *searchtet = recenttet;
- } else { // -u0
- randomsample(insertpt, searchtet);
- }
- } else {
- // There may exist dangling vertex.
- *searchtet = recenttet;
- }
- }
- // Locate the point. Use 'randflag' if the mesh is non-convex.
- loc = locate(insertpt, searchtet, ivf->chkencflag, checksubfaceflag);
- if (b->verbose > 3) {
- printf(" Walk distance (# tets): %ld\n", ptloc_count-tetcount);
- }
- if (ptloc_max_count < (ptloc_count - tetcount)) {
- ptloc_max_count = (ptloc_count - tetcount);
- }
-#ifdef WITH_RUNTIME_COUNTERS
- tend = clock();
- t_ptloc += (tend - tstart);
-#endif
- }
-
- if (b->verbose > 3) {
- printf(" Located tet (%d, %d, %d, %d).\n",
- pointmark(org(*searchtet)), pointmark(dest(*searchtet)),
- pointmark(apex(*searchtet)), pointmark(oppo(*searchtet)));
- }
-
-#ifdef WITH_RUNTIME_COUNTERS
- tstart = clock();
-#endif
-
- if (b->weighted) {
- if (loc != OUTSIDE) {
- // Check if this vertex is regular.
- pts = (point *) searchtet->tet;
- assert(pts[7] != dummypoint);
- sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt,
- pts[4][3], pts[5][3], pts[6][3], pts[7][3],
- insertpt[3]);
- if (sign > 0) {
- // This new vertex does not lie below the lower hull. Skip it.
- if (b->verbose > 2) {
- printf(" The point is above the lower hull, skipped.\n");
- }
- return OUTSIDE;
- }
- }
- }
-
- // Create the initial cavity C(p) which contains all tetrahedra directly
- // intersect with p.
- // If 'bowywat > 2' and p lies on a segment or subface, also create the
- // initial sub-cavity sC(p) which contains all subfaces (and segment)
- // which directly intersect with p.
- // If 'bowywat > 2', the initial C(p) is validated, i.e., all boundary
- // faces of C(p) should be visible by p.
-
- // Remember the current hullsize. It is used to restore the hullsize
- // if the new point is rejected for insertion.
- bakhullsize = hullsize;
-
- if (loc == OUTSIDE) {
- if (b->verbose > 3) {
- printf(" Outside hull.\n");
- }
- // The current hull will be enlarged.
- // Add four adjacent boundary tets into list.
- for (i = 0; i < 4; i++) {
- decode(searchtet->tet[i], neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- }
- if ((point) searchtet->tet[7] == dummypoint) hullsize--;
- // tetrahedrondealloc(searchtet->tet);
- infect(*searchtet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = *searchtet;
- flip14count++;
- } else if (loc == INTETRAHEDRON) {
- if (b->verbose > 3) {
- printf(" Inside tet.\n");
- }
- // Add four adjacent boundary tets into list.
- for (i = 0; i < 4; i++) {
- decode(searchtet->tet[i], neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- }
- // tetrahedrondealloc(searchtet->tet);
- infect(*searchtet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = *searchtet;
- flip14count++;
- } else if (loc == ONFACE) {
- if (b->verbose > 3) {
- printf(" On face.\n");
- }
- // Add six adjacent boundary tets into list.
- j = (searchtet->ver & 3); // The current face number.
- for (i = 1; i < 4; i++) {
- decode(searchtet->tet[(j + i) % 4], neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- }
- decode(searchtet->tet[j], spintet);
- j = (spintet.ver & 3); // The current face number.
- for (i = 1; i < 4; i++) {
- decode(spintet.tet[(j + i) % 4], neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- }
- if ((point) spintet.tet[7] == dummypoint) hullsize--;
- if ((point) searchtet->tet[7] == dummypoint) hullsize--;
- // tetrahedrondealloc(spintet.tet);
- infect(spintet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = spintet;
- // tetrahedrondealloc(searchtet->tet);
- infect(*searchtet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = *searchtet;
- flip26count++;
-
- if (ivf->splitbdflag) { //if (bowywat > 2) {
- if (splitsh != NULL) {
- // Create the initial sub-cavity sC(p).
- smarktest(*splitsh);
- caveshlist->newindex((void **) &parysh);
- *parysh = *splitsh;
- }
- } // if (splitbdflag)
- } else if (loc == ONEDGE) {
- if (b->verbose > 3) {
- printf(" On edge.\n");
- }
- // Add all adjacent boundary tets into list.
- spintet = *searchtet;
- while (1) {
- enextesym(spintet, neightet);
- fsymself(neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- eprevesym(spintet, neightet);
- fsymself(neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- if ((point) spintet.tet[7] == dummypoint) hullsize--;
- // tetrahedrondealloc(spintet.tet);
- infect(spintet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = spintet;
- fnextself(spintet);
- if (spintet.tet == searchtet->tet) break;
- } // while (1)
- flipn2ncount++;
-
- if (ivf->splitbdflag) { //if (bowywat > 2) {
- // Create the initial sub-cavity sC(p).
- if (splitseg != NULL) {
- smarktest(*splitseg);
- splitseg->shver = 0;
- spivot(*splitseg, *splitsh);
- }
- if (splitsh != NULL) {
- if (splitsh->sh != NULL) {
- // Collect all subfaces share at this edge.
- pa = sorg(*splitsh);
- neighsh = *splitsh;
- while (1) {
- // Adjust the origin of its edge to be 'pa'.
- if (sorg(neighsh) != pa) {
- sesymself(neighsh);
+ if (splitsh != NULL) {
+ if (splitsh->sh != NULL) {
+ // Collect all subfaces share at this edge.
+ pa = sorg(*splitsh);
+ neighsh = *splitsh;
+ while (1) {
+ // Adjust the origin of its edge to be 'pa'.
+ if (sorg(neighsh) != pa) {
+ sesymself(neighsh);
}
// Add this face into list (in B-W cavity).
smarktest(neighsh);
@@ -9862,9 +9146,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
} // if (splitbdflag)
} else if (loc == INSTAR) {
- if (b->verbose > 3) {
- printf(" Inside star.\n");
- }
// We assume that all tets in the star are given in 'caveoldtetlist',
// and they are all infected.
assert(caveoldtetlist->objects > 0);
@@ -9876,140 +9157,53 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
decode(cavetet->tet[j], neightet);
if (!infected(neightet)) {
// It's a boundary face.
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
+ neightet.ver = epivot[neightet.ver];
+ cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
}
}
}
} else if (loc == ONVERTEX) {
- pa = org(*searchtet);
- if (b->verbose > 3) {
- printf(" On vertex %d.\n", pointmark(pa));
- }
- if (insertpt != pa) {
- // Remember it is a duplicated point.
- setpointtype(insertpt, DUPLICATEDVERTEX);
- // Set a pointer to the point it duplicates.
- setpoint2ppt(insertpt, pa);
- }
// The point already exist. Do nothing and return.
- return (int) loc;
+ return 0;
} else if (loc == ENCSUBFACE) {
- if (b->verbose > 3) {
- printf(" Encroached.\n");
- }
- // The vertex lies outside of the region boundary.
- // Treated it as outside
- loc = OUTSIDE;
- return (int) loc;
- } else {
- assert(0); // Unknown type.
+ // Treat it as outside.
+ ivf->iloc = (int) OUTSIDE;
+ return 0;
}
if (ivf->assignmeshsize) {
// Assign mesh size for the new point.
- if (bgm != NULL) {
- // Interpolate the mesh size from the background mesh.
- pa = org(*searchtet);
- bgm->decode(point2bgmtet(pa), neightet); // neightet is in 'bgm'!
- bgmloc = bgm->scoutpoint(insertpt, &neightet, 0); // randflag = 0
- if (bgmloc != (int) OUTSIDE) {
- insertpt[pointmtrindex] = // posflag = 1
- bgm->getpointmeshsize(insertpt, &neightet, bgmloc, 1);
- setpoint2bgmtet(insertpt, bgm->encode(neightet));
- }
- } else {
- insertpt[pointmtrindex] = // posflag = 1
- getpointmeshsize(insertpt, searchtet, (int) loc, 1);
- }
- } // if (assignmeshsize)
-
- if (ivf->validflag) { //if (bowywat > 2) {
- // Validate the initial C(p). Enlarge it at a face which is not visible
- // by p. This removes (interior) slivers. Re-use 'cavebdrylist'.
- tetcount = 0l;
-
- for (i = 0; i < cavetetlist->objects; i++) {
- cavetet = (triface *) fastlookup(cavetetlist, i);
- // Other expansions may make this face inside C(p).
- if (!infected(*cavetet)) {
- pc = apex(*cavetet);
- // Do valid if it is a face (not a hull edge).
- if (pc != dummypoint) {
- pa = org(*cavetet);
- pb = dest(*cavetet);
- ori = orient3d(pa, pb, pc, insertpt);
- if (ori <= 0) {
- // An invalid face. Enlarge the cavity.
- //if (oppo(*cavetet) != dummypoint) {
- if (b->verbose > 3) {
- printf(" Enlarge cavity at (%d, %d, %d)\n",
- pointmark(pa), pointmark(pb), pointmark(pc));
- }
- // Add the other three faces into list.
- j = (cavetet->ver & 3); // The current face number.
- for (k = 1; k < 4; k++) {
- decode(cavetet->tet[(j + k) % 4], neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- }
- if ((point) cavetet->tet[7] == dummypoint) hullsize--;
- infect(*cavetet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = *cavetet;
- tetcount++;
- //} else {
- // printf("Error in insertvertex %d: ", pointmark(insertpt));
- // printf("Invalid initial cavity at face %d.\n", i + 1);
- // assert(0);
- //}
- } else {
- // A valid face.
- cavebdrylist->newindex((void **) &parytet);
- *parytet = *cavetet;
- }
- } else {
- // A hull edge is valid.
- cavebdrylist->newindex((void **) &parytet);
- *parytet = *cavetet;
- }
- } // if (!infected(*cavetet))
- } // i
-
- if (tetcount > 0l) {
- // The cavity has been enlarged. Update it.
- cavetetlist->restart();
- for (i = 0; i < cavebdrylist->objects; i++) {
- cavetet = (triface *) fastlookup(cavebdrylist, i);
- if (!infected(*cavetet)) {
- cavetetlist->newindex((void **) &parytet);
- *parytet = *cavetet;
- }
- } // i
- } // if (tetcount)
-
- cavebdrylist->restart();
- tetcount = 0l;
- } // if (bowywat > 2)
-
- // Update the cavity C(p) using the Bowyer-Watson approach (bowywat > 0).
+ if (bgm != NULL) {
+ // Interpolate the mesh size from the background mesh.
+ bgm->decode(point2bgmtet(org(*searchtet)), neightet);
+ int bgmloc = (int) bgm->scoutpoint(insertpt, &neightet, 0);
+ if (bgmloc != (int) OUTSIDE) {
+ insertpt[pointmtrindex] =
+ bgm->getpointmeshsize(insertpt, &neightet, bgmloc);
+ setpoint2bgmtet(insertpt, bgm->encode(neightet));
+ }
+ } else {
+ insertpt[pointmtrindex] = getpointmeshsize(insertpt,searchtet,(int)loc);
+ }
+ } // if (assignmeshsize)
- for (i = 0; i < cavetetlist->objects; i++) {
- // 'cavetet' is an adjacent tet at outside of the cavity.
- cavetet = (triface *) fastlookup(cavetetlist, i);
- // The tet may be tested and included in the (enlarged) cavity.
- if (!infected(*cavetet)) {
- // Check for two possible cases for this tet:
- // (1) It is a cavity tet, or
- // (2) it is a cavity boundary face.
- // In case (1), this tet is grabbed in the cavity and three adjacent
- // tets on other faces of this tet are added into 'cavetetlist'.
- enqflag = false;
- if (!marktested(*cavetet)) {
- if (ivf->bowywat) {
+ if (ivf->bowywat) {
+ // Update the cavity C(p) using the Bowyer-Watson algorithm.
+ swaplist = cavetetlist;
+ cavetetlist = cavebdrylist;
+ cavebdrylist = swaplist;
+ for (i = 0; i < cavetetlist->objects; i++) {
+ // 'cavetet' is an adjacent tet at outside of the cavity.
+ cavetet = (triface *) fastlookup(cavetetlist, i);
+ // The tet may be tested and included in the (enlarged) cavity.
+ if (!infected(*cavetet)) {
+ // Check for two possible cases for this tet:
+ // (1) It is a cavity tet, or
+ // (2) it is a cavity boundary face.
+ enqflag = false;
+ if (!marktested(*cavetet)) {
// Do Delaunay (in-sphere) test.
pts = (point *) cavetet->tet;
if (pts[7] != dummypoint) {
@@ -10026,20 +9220,17 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
if (!nonconvex) {
// Test if this hull face is visible by the new point.
ori = orient3d(pts[4], pts[5], pts[6], insertpt);
- orient3dcount++;
if (ori < 0) {
// A visible hull face.
//if (!nonconvex) {
// Include it in the cavity. The convex hull will be enlarged.
enqflag = true; // (ori < 0.0);
- //}
+ //}
} else if (ori == 0.0) {
// A coplanar hull face. We need to test if this hull face is
// Delaunay or not. We test if the adjacent tet (not faked)
// of this hull face is Delaunay or not.
- neightet = *cavetet;
- neightet.ver = 3; // The face opposite to dummypoint.
- fsym(neightet, neineitet);
+ decode(cavetet->tet[3], neineitet);
if (!infected(neineitet)) {
if (!marktested(neineitet)) {
// Do Delaunay test on this tet.
@@ -10053,12 +9244,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
sign = insphere_s(pts[4],pts[5],pts[6],pts[7], insertpt);
}
enqflag = (sign < 0.0);
- } else {
- // The adjacent tet has been tested (marktested), and it
- // is Delaunay (not get infected). Hence the the hull
- // face is Delaunay as well.
- // enqflag = false;
- }
+ }
} else {
// The adjacent tet is non-Delaunay. The hull face is non-
// Delaunay as well. Include it in the cavity.
@@ -10067,15 +9253,11 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
} // if (ori == 0.0)
} else {
// A hull face (must be a subface).
- assert(checksubfaceflag);
- assert(ivf->validflag);
// We FIRST include it in the initial cavity if the adjacent tet
// (not faked) of this hull face is not Delaunay wrt p.
// Whether it belongs to the final cavity will be determined
// during the validation process. 'validflag'.
- neightet = *cavetet;
- neightet.ver = 3; // The face opposite to dummypoint.
- fsym(neightet, neineitet);
+ decode(cavetet->tet[3], neineitet);
if (!infected(neineitet)) {
if (!marktested(neineitet)) {
// Do Delaunay test on this tet.
@@ -10089,12 +9271,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
sign = insphere_s(pts[4],pts[5],pts[6],pts[7], insertpt);
}
enqflag = (sign < 0.0);
- } else {
- // The adjacent tet has been tested (marktested), and it
- // is Delaunay (not get infected). Hence the the hull
- // face is Delaunay as well.
- // enqflag = false;
- } // if (marktested(neineitet))
+ }
} else {
// The adjacent tet is non-Delaunay. The hull face is non-
// Delaunay as well. Include it in the cavity.
@@ -10102,200 +9279,124 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
} // if (infected(neineitet))
} // if (nonconvex)
} // if (pts[7] != dummypoint)
- } // if (bowywat)
- marktest(*cavetet); // Only test it once.
- } // if (!marktested(*cavetet))
-
- if (enqflag) {
- // Found a tet in the cavity. Put other three faces in check list.
- k = (cavetet->ver & 3); // The current face number
- for (j = 1; j < 4; j++) {
- decode(cavetet->tet[(j + k) % 4], neightet);
- neightet.ver = epivot[neightet.ver & 3];
- cavetetlist->newindex((void **) &parytet);
- *parytet = neightet;
- }
- if ((point) cavetet->tet[7] == dummypoint) hullsize--;
- // tetrahedrondealloc(cavetet->tet);
- infect(*cavetet);
- caveoldtetlist->newindex((void **) &parytet);
- *parytet = *cavetet;
- } else {
- // Found a boundary face of the cavity. It may be a face of a hull
- // tet which contains 'dummypoint'. Choose the edge in the face
- // such that its endpoints are not 'dummypoint', while its apex
- // may be 'dummypoint'.
- //j = (cavetet->ver & 3); // j is the face number.
- //cavetet->ver = epivot[j]; // [4,5,2,11]
- cavebdrylist->newindex((void **) &parytet);
- *parytet = *cavetet;
- }
- } // if (!infected(*cavetet))
- } // i
+ marktest(*cavetet); // Only test it once.
+ } // if (!marktested(*cavetet))
- if (b->verbose > 3) {
- printf(" Initial cavity size: %ld tets, %ld faces.\n",
- caveoldtetlist->objects, cavebdrylist->objects);
- }
+ if (enqflag) {
+ // Found a tet in the cavity. Put other three faces in check list.
+ k = (cavetet->ver & 3); // The current face number
+ for (j = 1; j < 4; j++) {
+ decode(cavetet->tet[(j + k) % 4], neightet);
+ cavetetlist->newindex((void **) &parytet);
+ *parytet = neightet;
+ }
+ infect(*cavetet);
+ caveoldtetlist->newindex((void **) &parytet);
+ *parytet = *cavetet;
+ } else {
+ // Found a boundary face of the cavity.
+ cavetet->ver = epivot[cavetet->ver];
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = *cavetet;
+ }
+ } // if (!infected(*cavetet))
+ } // i
+ cavetetlist->restart(); // Clear the working list.
+ } // if (ivf->bowywat)
if (checksubsegflag) {
// Collect all segments of C(p).
+ shellface *ssptr;
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
- for (j = 0; j < 6; j++) {
- cavetet->ver = edge2ver[j];
- tsspivot1(*cavetet, checkseg);
- if (checkseg.sh != NULL) {
- if (!sinfected(checkseg)) {
- sinfect(checkseg);
- cavetetseglist->newindex((void **) &paryseg);
- *paryseg = checkseg;
+ if ((ssptr = (shellface*) cavetet->tet[8]) != NULL) {
+ for (j = 0; j < 6; j++) {
+ if (ssptr[j]) {
+ sdecode(ssptr[j], checkseg);
+ if (!sinfected(checkseg)) {
+ sinfect(checkseg);
+ cavetetseglist->newindex((void **) &paryseg);
+ *paryseg = checkseg;
+ }
}
- }
+ } // j
}
- }
+ } // i
// Uninfect collected segments.
for (i = 0; i < cavetetseglist->objects; i++) {
- checkseg = * (face *) fastlookup(cavetetseglist, i);
- suninfect(checkseg);
+ paryseg = (face *) fastlookup(cavetetseglist, i);
+ suninfect(*paryseg);
+ }
+
+ if (ivf->rejflag & 1) {
+ // Reject this point if it encroaches upon any segment.
+ face *paryseg1;
+ for (i = 0; i < cavetetseglist->objects; i++) {
+ paryseg1 = (face *) fastlookup(cavetetseglist, i);
+ if (checkseg4encroach((point) paryseg1->sh[3], (point) paryseg1->sh[4],
+ insertpt)) {
+ encseglist->newindex((void **) &paryseg);
+ *paryseg = *paryseg1;
+ }
+ } // i
+ if (encseglist->objects > 0) {
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) ENCSEGMENT;
+ return 0;
+ }
}
} // if (checksubsegflag)
if (checksubfaceflag) {
// Collect all subfaces of C(p).
+ shellface *sptr;
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
- oldtet = *cavetet;
- for (oldtet.ver = 0; oldtet.ver < 4; oldtet.ver++) {
- tspivot(oldtet, checksh);
- if (checksh.sh != NULL) {
- if (!sinfected(checksh)) {
- sinfect(checksh);
- cavetetshlist->newindex((void **) &parysh);
- *parysh = checksh;
+ if ((sptr = (shellface*) cavetet->tet[9]) != NULL) {
+ for (j = 0; j < 4; j++) {
+ if (sptr[j]) {
+ sdecode(sptr[j], checksh);
+ if (!sinfected(checksh)) {
+ sinfect(checksh);
+ cavetetshlist->newindex((void **) &parysh);
+ *parysh = checksh;
+ }
}
- }
+ } // j
}
- }
+ } // i
// Uninfect collected subfaces.
for (i = 0; i < cavetetshlist->objects; i++) {
- checksh = * (face *) fastlookup(cavetetshlist, i);
- suninfect(checksh);
- }
- } // if (checksubfaceflag)
-
- if (ivf->rejflag & 1) {
- // Reject insertion of this point if it encroaches upon any segment.
- for (i = 0; i < cavetetseglist->objects; i++) {
- checkseg = * (face *) fastlookup(cavetetseglist, i);
- pa = sorg(checkseg);
- pb = sdest(checkseg);
- if (checkseg4encroach(pa, pb, insertpt)) {
- if (b->verbose > 3) {
- printf(" Found an encroached seg (%d, %d).\n",
- pointmark(pa), pointmark(pb));
- }
- encseglist->newindex((void **) &paryseg);
- *paryseg = checkseg;
- }
- } // i
- if (encseglist->objects > 0) {
- if (b->verbose > 3) {
- printf(" Found %ld encroached segments. Reject it.\n",
- encseglist->objects);
- }
- for (i = 0; i < caveoldtetlist->objects; i++) {
- cavetet = (triface *) fastlookup(caveoldtetlist, i);
- uninfect(*cavetet);
- unmarktest(*cavetet);
- }
- for (i = 0; i < cavebdrylist->objects; i++) {
- cavetet = (triface *) fastlookup(cavebdrylist, i);
- unmarktest(*cavetet); // Unmark it.
- }
- // Clear working lists.
- cavetetlist->restart();
- cavebdrylist->restart();
- caveoldtetlist->restart();
- cavetetseglist->restart();
- cavetetshlist->restart();
- if (ivf->splitbdflag) { //if (bowywat > 2) {
- if (splitseg != NULL) {
- sunmarktest(*splitseg);
- }
- for (i = 0; i < caveshlist->objects; i++) {
- parysh = (face *) fastlookup(caveshlist, i);
- assert(smarktested(*parysh));
- sunmarktest(*parysh);
- }
- caveshlist->restart();
- cavesegshlist->restart();
- }
- // Restore the hullsize.
- hullsize = bakhullsize;
- return (int) ENCSEGMENT;
+ parysh = (face *) fastlookup(cavetetshlist, i);
+ suninfect(*parysh);
}
- } // if (reject & 1)
- if (ivf->rejflag & 2) {
- // Reject insertion of this point if it encroaches upon any subface.
- for (i = 0; i < cavetetshlist->objects; i++) {
- checksh = * (face *) fastlookup(cavetetshlist, i);
- pa = sorg(checksh);
- pb = sdest(checksh);
- pc = sapex(checksh);
- if (checkfac4encroach(pa, pb, pc, insertpt, cent, &rd)) {
- if (b->verbose > 3) {
- printf(" Found an encroached subface (%d, %d, %d).\n",
- pointmark(pa), pointmark(pb), pointmark(pc));
+ if (ivf->rejflag & 2) {
+ REAL rd, cent[3];
+ badface *bface;
+ // Reject this point if it encroaches upon any subface.
+ for (i = 0; i < cavetetshlist->objects; i++) {
+ parysh = (face *) fastlookup(cavetetshlist, i);
+ if (checkfac4encroach((point) parysh->sh[3], (point) parysh->sh[4],
+ (point) parysh->sh[5], insertpt, cent, &rd)) {
+ encshlist->newindex((void **) &bface);
+ bface->ss = *parysh;
+ bface->forg = (point) parysh->sh[3]; // Not a dad one.
+ for (j = 0; j < 3; j++) bface->cent[j] = cent[j];
+ bface->key = rd;
}
- encshlist->newindex((void **) &bface);
- bface->ss = checksh;
- bface->forg = pa; // Not a dad one.
- for (j = 0; j < 3; j++) bface->cent[j] = cent[j];
- bface->key = rd;
- }
- } // i
- if (encshlist->objects > 0) {
- if (b->verbose > 3) {
- printf(" Found %ld encroached subfaces. Reject it.\n",
- caveencshlist->objects);
- }
- for (i = 0; i < caveoldtetlist->objects; i++) {
- cavetet = (triface *) fastlookup(caveoldtetlist, i);
- uninfect(*cavetet);
- unmarktest(*cavetet);
- }
- for (i = 0; i < cavebdrylist->objects; i++) {
- cavetet = (triface *) fastlookup(cavebdrylist, i);
- unmarktest(*cavetet); // Unmark it.
}
- cavetetlist->restart();
- cavebdrylist->restart();
- caveoldtetlist->restart();
- cavetetseglist->restart();
- cavetetshlist->restart();
- if (ivf->splitbdflag) { //if (bowywat > 2) {
- if (splitseg != NULL) {
- sunmarktest(*splitseg);
- }
- for (i = 0; i < caveshlist->objects; i++) {
- parysh = (face *) fastlookup(caveshlist, i);
- assert(smarktested(*parysh));
- sunmarktest(*parysh);
- }
- caveshlist->restart();
- cavesegshlist->restart();
+ if (encshlist->objects > 0) {
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) ENCSUBFACE;
+ return 0;
}
- // Restore the hullsize.
- hullsize = bakhullsize;
- return (int) ENCSUBFACE;
}
- } // if (reject & 2)
+ } // if (checksubfaceflag)
- if (ivf->splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
- // Update the sC(p).
+ if (ivf->splitbdflag) {
+ // The new point locates in surface mesh. Update the sC(p).
// We have already 'smarktested' the subfaces which directly intersect
// with p in 'caveshlist'. From them, we 'smarktest' their neighboring
// subfaces which are included in C(p). Do not across a segment.
@@ -10304,16 +9405,15 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
assert(smarktested(*parysh));
checksh = *parysh;
for (j = 0; j < 3; j++) {
- sspivot(checksh, checkseg);
- if (checkseg.sh == NULL) {
+ if (!isshsubseg(checksh)) {
spivot(checksh, neighsh);
assert(neighsh.sh != NULL);
if (!smarktested(neighsh)) {
- // Add this subface if it is inside C(p).
stpivot(neighsh, neightet);
if (infected(neightet)) {
fsymself(neightet);
if (infected(neightet)) {
+ // This subface is inside C(p).
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
*parysh = neighsh;
@@ -10324,48 +9424,34 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
senextself(checksh);
} // j
} // i
- if (b->verbose > 3) {
- printf(" Initial subcavity size: %ld subfacess.\n",
- caveshlist->objects);
- }
- }
-
- cutcount = 0l;
+ } // if (ivf->splitbdflag)
- if (ivf->validflag) {
- //if (bowywat > 1) { // if (bowywat == 2 || bowywat == 3) {
- // T is a CT. Validation is needed (fig/dump-cavity-case8).
- cavetetlist->restart(); // Re-use it.
+ if (ivf->validflag) {
+ // Validate C(p) and update it if it is not star-shaped.
+ int cutcount = 0;
- //if (splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
if (ivf->respectbdflag) {
// The initial cavity may include subfaces which are not on the facets
- // being splitting. Find them and make them as boundary of C(p).
- // Comment: We have already 'smarktested' the subfaces in sC(p).
- // It is needed by 'splitbdflag'.
+ // being splitting. Find them and make them as boundary of C(p).
+ // Comment: We have already 'smarktested' the subfaces in sC(p). They
+ // are completely inside C(p).
for (i = 0; i < cavetetshlist->objects; i++) {
parysh = (face *) fastlookup(cavetetshlist, i);
stpivot(*parysh, neightet);
if (infected(neightet)) {
fsymself(neightet);
if (infected(neightet)) {
+ // Found a subface inside C(p).
if (!smarktested(*parysh)) {
- if (b->verbose > 3) {
- printf(" Found a subface (%d, %d, %d) inside cavity.\n",
- pointmark(sorg(*parysh)), pointmark(sdest(*parysh)),
- pointmark(sapex(*parysh)));
- }
// It is possible that this face is a boundary subface.
// Check if it is a hull face.
- assert(apex(neightet) != dummypoint);
+ //assert(apex(neightet) != dummypoint);
if (oppo(neightet) != dummypoint) {
fsymself(neightet);
}
if (oppo(neightet) != dummypoint) {
- pa = org(neightet);
- pb = dest(neightet);
- pc = apex(neightet);
- ori = orient3d(pa, pb, pc, insertpt);
+ ori = orient3d(org(neightet), dest(neightet), apex(neightet),
+ insertpt);
if (ori < 0) {
// A visible face, get its neighbor face.
fsymself(neightet);
@@ -10377,27 +9463,20 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
// Cut this tet if it is either invisible by or coplanar with p.
if (ori >= 0) {
- if (b->verbose > 3) {
- printf(" Cut tet (%d, %d, %d, %d)\n",
- pointmark(org(neightet)), pointmark(dest(neightet)),
- pointmark(apex(neightet)), pointmark(oppo(neightet)));
- }
uninfect(neightet);
unmarktest(neightet);
cutcount++;
- neightet.ver = epivot[neightet.ver & 3];
+ neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
// Add three new faces to find new boundaries.
for (j = 0; j < 3; j++) {
esym(neightet, neineitet);
- neineitet.ver = epivot[neineitet.ver & 3];
+ neineitet.ver = epivot[neineitet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neineitet;
enextself(neightet);
}
- // Update hullsize.
- if (oppo(neightet) == dummypoint) hullsize++;
} // if (ori >= 0)
}
}
@@ -10419,10 +9498,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
if (spintet.tet == neightet.tet) break;
}
if (infected(spintet)) {
- if (b->verbose > 3) {
- printf(" Found an interior segment (%d, %d).\n",
- pointmark(sorg(*paryseg)), pointmark(sdest(*paryseg)));
- }
// Find an adjacent tet at this segment such that both faces
// at this segment are not visible by p.
pa = org(neightet);
@@ -10447,7 +9522,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
}
}
- } else {
}
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
@@ -10465,42 +9539,34 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
uninfect(neightet);
unmarktest(neightet);
cutcount++;
- neightet.ver = epivot[neightet.ver & 3];
+ neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
// Add three new faces to find new boundaries.
for (j = 0; j < 3; j++) {
esym(neightet, neineitet);
- neineitet.ver = epivot[neineitet.ver & 3];
+ neineitet.ver = epivot[neineitet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neineitet;
enextself(neightet);
}
- // Update hullsize.
- //if (oppo(neightet) == dummypoint) hullsize++;
- if ((point) (neightet.tet[7]) == dummypoint) hullsize++;
}
}
} // i
- } // if (bowywat > 2)
+ } // if (ivf->respectbdflag)
// Update the cavity by removing invisible faces until it is star-shaped.
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
- // 'cavetet' is an exterior tet adjacent to the cavity.
- assert(cavetet->ver == epivot[cavetet->ver & 3]); // SELF_CHECK
- // It must be not inside the cavity (since we only cut tets).
- assert(!infected(*cavetet));
+ // 'cavetet' is an exterior tet adjacent to the cavity.
// Check if its neighbor is inside C(p).
fsym(*cavetet, neightet);
if (infected(neightet)) {
if (apex(*cavetet) != dummypoint) {
// It is a cavity boundary face. Check its visibility.
if (oppo(neightet) != dummypoint) {
- pa = org(*cavetet);
- pb = dest(*cavetet);
- pc = apex(*cavetet);
- ori = orient3d(pa, pb, pc, insertpt); orient3dcount++;
+ ori = orient3d(org(*cavetet), dest(*cavetet), apex(*cavetet),
+ insertpt);
enqflag = (ori > 0);
// Comment: if ori == 0 (coplanar case), we also cut the tet.
} else {
@@ -10517,24 +9583,17 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
cavetetlist->newindex((void **) &parytet);
*parytet = *cavetet;
} else {
- if (b->verbose > 3) {
- printf(" Cut tet (%d, %d, %d, %d)\n",
- pointmark(org(neightet)), pointmark(dest(neightet)),
- pointmark(apex(neightet)), pointmark(oppo(neightet)));
- }
uninfect(neightet);
unmarktest(neightet);
cutcount++;
// Add three new faces to find new boundaries.
for (j = 0; j < 3; j++) {
esym(neightet, neineitet);
- neineitet.ver = epivot[neineitet.ver & 3];
+ neineitet.ver = epivot[neineitet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neineitet;
enextself(neightet);
}
- // Update the hullsize.
- if (oppo(neightet) == dummypoint) hullsize++;
// 'cavetet' is not on the cavity boundary anymore.
unmarktest(*cavetet);
}
@@ -10546,14 +9605,11 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
if (cutcount > 0) {
// The cavity has been updated.
-
// Update the cavity boundary faces.
cavebdrylist->restart();
for (i = 0; i < cavetetlist->objects; i++) {
cavetet = (triface *) fastlookup(cavetetlist, i);
// 'cavetet' was an exterior tet adjacent to the cavity.
- assert(cavetet->ver == epivot[cavetet->ver & 3]); // SELF_CHECK
- assert(!infected(*cavetet));
fsym(*cavetet, neightet);
if (infected(neightet)) {
// It is a cavity boundary face.
@@ -10581,12 +9637,13 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// The cavity should contain at least one tet.
if (caveoldtetlist->objects == 0l) {
- printf("Invalid cavity of Steiner point %d.\n", pointmark(insertpt));
- assert(0);
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) BADELEMENT;
+ return 0;
}
- if (ivf->splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
- cutshcount = 0;
+ if (ivf->splitbdflag) {
+ int cutshcount = 0;
// Update the sub-cavity sC(p).
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
@@ -10600,11 +9657,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
}
if (!enqflag) {
- if (b->verbose > 3) {
- printf(" Cut subface (%d, %d, %d).\n",
- pointmark(sorg(*parysh)), pointmark(sdest(*parysh)),
- pointmark(sapex(*parysh)));
- }
sunmarktest(*parysh);
// Use the last entry of this array to fill this entry.
j = caveshlist->objects - 1;
@@ -10652,127 +9704,140 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
if (i > 0) {
// The updated sC(p) is invalid. Do not insert this vertex.
- if (b->verbose > 3) {
- printf(" Found %d invalid items. Reject it.\n", i);
- }
- for (i = 0; i < caveoldtetlist->objects; i++) {
- cavetet = (triface *) fastlookup(caveoldtetlist, i);
- uninfect(*cavetet);
- unmarktest(*cavetet);
- }
- for (i = 0; i < cavebdrylist->objects; i++) {
- cavetet = (triface *) fastlookup(cavebdrylist, i);
- unmarktest(*cavetet); // Unmark it.
- }
- cavetetlist->restart();
- cavebdrylist->restart();
- caveoldtetlist->restart();
- cavetetseglist->restart();
- cavetetshlist->restart();
- if (ivf->splitbdflag) { //if (bowywat > 2) {
- if (splitseg != NULL) {
- sunmarktest(*splitseg);
- }
- for (i = 0; i < caveshlist->objects; i++) {
- parysh = (face *) fastlookup(caveshlist, i);
- assert(smarktested(*parysh));
- sunmarktest(*parysh);
- }
- caveshlist->restart();
- cavesegshlist->restart();
- }
- // Restore the hullsize.
- hullsize = bakhullsize;
- return (int) BADELEMENT;
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) BADELEMENT;
+ return 0;
}
} // if (cutshcount > 0)
- } // if (bowywat > 2)
-
+ } // if (ivf->splitbdflag)
} // if (cutcount > 0)
- } // if (validflag) // if (bowywat > 1)
-
- if (b->verbose > 3) {
- printf(" Final cavity: %ld tets, %ld faces.",
- caveoldtetlist->objects, cavebdrylist->objects);
- if (cutcount > 0l) {
- printf(" Updated %ld times.", cutcount);
- }
- printf("\n");
- }
-
+ } // if (ivf->validflag)
if (ivf->refineflag) {
// The new point is inserted by Delaunay refinement, i.e., it is the
// circumcenter of a tetrahedron, or a subface, or a segment.
// Do not insert this point if the tetrahedron, or subface, or segment
// is not inside the final cavity.
- rejptflag = 0;
- if (ivf->refineflag == 1) {
- // The new point is the circumcenter of a tetrahedron.
- assert(!isdeadtet(ivf->refinetet));
- if (!infected(ivf->refinetet)) {
- rejrefinetetcount++;
- rejptflag = 1;
- }
- } else if (ivf->refineflag == 2) {
- // The new point is the circumcenter of a subface.
- assert(ivf->refinesh.sh != NULL);
- if (!smarktested(ivf->refinesh)) {
- rejrefineshcount++;
- rejptflag = 1;
- }
- }
- if (rejptflag) {
- if (b->verbose > 2) {
- printf(" Point %d does not refine its element. Rejected.\n",
- pointmark(insertpt));
+ if (((ivf->refineflag == 1) && !infected(ivf->refinetet)) ||
+ ((ivf->refineflag == 2) && !smarktested(ivf->refinesh))) {
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) BADELEMENT;
+ return 0;
+ }
+ } // if (ivf->refineflag)
+
+ if (b->plc && (loc != INSTAR)) {
+ // Reject the new point if it lies too close to an existing point (b->plc),
+ // or it lies inside a protecting ball of near vertex (ivf->rejflag & 4).
+ // Collect the list of vertices of the initial cavity.
+ if (loc == OUTSIDE) {
+ pts = (point *) &(searchtet->tet[4]);
+ for (i = 0; i < 3; i++) {
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = pts[i];
}
- // Restore the original status.
- for (i = 0; i < caveoldtetlist->objects; i++) {
- cavetet = (triface *) fastlookup(caveoldtetlist, i);
- uninfect(*cavetet);
- unmarktest(*cavetet);
+ } else if (loc == INTETRAHEDRON) {
+ pts = (point *) &(searchtet->tet[4]);
+ for (i = 0; i < 4; i++) {
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = pts[i];
+ }
+ } else if (loc == ONFACE) {
+ pts = (point *) &(searchtet->tet[4]);
+ for (i = 0; i < 3; i++) {
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = pts[i];
}
- for (i = 0; i < cavebdrylist->objects; i++) {
- cavetet = (triface *) fastlookup(cavebdrylist, i);
- unmarktest(*cavetet); // Unmark it.
+ if (pts[3] != dummypoint) {
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = pts[3];
}
- // Clear working lists.
- cavetetlist->restart();
- cavebdrylist->restart();
- caveoldtetlist->restart();
- cavetetshlist->restart();
- cavetetseglist->restart();
- cavetetvertlist->restart();
- if (ivf->splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
- if (splitseg != NULL) {
- sunmarktest(*splitseg);
- }
- for (i = 0; i < caveshlist->objects; i++) {
- parysh = (face *) fastlookup(caveshlist, i);
- assert(smarktested(*parysh));
- sunmarktest(*parysh);
+ fsym(*searchtet, spintet);
+ if (oppo(spintet) != dummypoint) {
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = oppo(spintet);
+ }
+ } else if (loc == ONEDGE) {
+ spintet = *searchtet;
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = org(spintet);
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = dest(spintet);
+ while (1) {
+ if (apex(spintet) != dummypoint) {
+ cavetetvertlist->newindex((void **) &parypt);
+ *parypt = apex(spintet);
}
- caveshlist->restart();
- cavesegshlist->restart();
+ fnextself(spintet);
+ if (spintet.tet == searchtet->tet) break;
}
+ }
- // Restore the hullsize.
- hullsize = bakhullsize;
- loc = BADELEMENT;
- return (int) loc;
- } // if (rejptflag)
- } // if (ivf->refineflag)
+ int rejptflag = (ivf->rejflag & 4);
+ REAL rd;
+ pts = NULL;
+
+ for (i = 0; i < cavetetvertlist->objects; i++) {
+ parypt = (point *) fastlookup(cavetetvertlist, i);
+ rd = distance(*parypt, insertpt);
+ // Is the point very close to an existing point?
+ if (rd < b->minedgelength) {
+ pts = parypt;
+ loc = NEARVERTEX;
+ break;
+ }
+ if (rejptflag) {
+ // Is the point encroaches upon an existing point?
+ if (rd < (*parypt)[pointmtrindex]) {
+ pts = parypt;
+ loc = ENCVERTEX;
+ break;
+ }
+ }
+ }
+ cavetetvertlist->restart(); // Clear the work list.
- rejptflag = (ivf->rejflag & 4);
- encptflag = 0;
+ if (pts != NULL) {
+ // The point is either too close to an existing vertex (NEARVERTEX)
+ // or encroaches upon (isndie the protecting ball) of that vertex.
+ if (loc == NEARVERTEX) {
+ if (b->nomergevertex) { // -M0/1 option.
+ // In this case, we still insert this vertex. Although it is very
+ // close to an existing vertex. Give a warning, anyway.
+ if (!b->quiet) {
+ printf("Warning: Two points, %d and %d, are very close.\n",
+ pointmark(insertpt), pointmark(*pts));
+ printf(" Creating a very short edge (len = %g) (< %g).\n",
+ rd, b->minedgelength);
+ printf(" You may try a smaller tolerance (-T) (current is %g)\n",
+ b->epsilon);
+ printf(" to avoid this warning.\n");
+ }
+ } else {
+ insertpt[3] = rd; // Only for reporting.
+ setpoint2ppt(insertpt, *pts);
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) loc;
+ return 0;
+ }
+ } else { // loc == ENCVERTEX
+ // The point lies inside the protection ball.
+ setpoint2ppt(insertpt, *pts);
+ insertpoint_abort(splitseg, ivf);
+ ivf->iloc = (int) loc;
+ return 0;
+ }
+ }
+ } // if (b->plc && (loc != INSTAR))
- if (b->weighted || b->plc || rejptflag) {
+ if (b->weighted || ivf->cdtflag
+ ) {
+ // There may be other vertices inside C(p). We need to find them.
// Collect all vertices of C(p).
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
- assert(infected(*cavetet));
+ //assert(infected(*cavetet));
pts = (point *) &(cavetet->tet[4]);
for (j = 0; j < 4; j++) {
if (pts[j] != dummypoint) {
@@ -10784,118 +9849,33 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
} // j
} // i
- if (b->verbose > 3) {
- printf(" %ld cavity vertices.\n", cavetetvertlist->objects);
- }
// Uninfect all collected (cavity) vertices.
for (i = 0; i < cavetetvertlist->objects; i++) {
parypt = (point *) fastlookup(cavetetvertlist, i);
puninfect(*parypt);
}
- if (b->plc || rejptflag) {
- // Check if p is too close to an existing vertex.
- pts = NULL;
- for (i = 0; i < cavetetvertlist->objects; i++) {
- parypt = (point *) fastlookup(cavetetvertlist, i);
- rd = distance(*parypt, insertpt);
- // Is the point very close to an existing point?
- if (rd < b->minedgelength) {
- pts = parypt;
- break;
- }
- if (rejptflag) {
- // Is the point encroaches upon an existing point?
- if (rd < (*parypt)[pointmtrindex]) {
- // The point lies inside the protection ball.
- if (b->verbose > 2) {
- printf(" Point %d lies in protball of %d. Rejected.\n",
- pointmark(insertpt), pointmark(*parypt));
- }
- pts = parypt;
- encptflag = 1;
- break;
- }
- }
- } // i
- if (pts != NULL) {
- // p is too close to *pts.
- if (ivf->iloc != (int) INSTAR) {
- if (pointmark(insertpt) <= in->numberofpoints) {
- // It's an input point.
- if (!b->quiet) {
- printf("Warning: Point %d is replaced by point %d.\n",
- pointmark(insertpt), pointmark(*pts));
- }
- // Count the number of duplicated points.
- dupverts++;
- } else { // It's a Steiner point.
- if (b->verbose) {
- if (!rejptflag) {
- printf("Warning: Reject a Steiner point %d (close to %d).\n",
- pointmark(insertpt), pointmark(*pts));
- }
- }
- }
- // Remember it is a duplicated point.
- setpointtype(insertpt, DUPLICATEDVERTEX);
- // Set a pointer to the point it duplicates.
- setpoint2ppt(insertpt, *pts);
-
- // Restore the original status.
- for (i = 0; i < caveoldtetlist->objects; i++) {
- cavetet = (triface *) fastlookup(caveoldtetlist, i);
- uninfect(*cavetet);
- unmarktest(*cavetet);
- }
- for (i = 0; i < cavebdrylist->objects; i++) {
- cavetet = (triface *) fastlookup(cavebdrylist, i);
- unmarktest(*cavetet); // Unmark it.
- }
- // Clear working lists.
- cavetetlist->restart();
- cavebdrylist->restart();
- caveoldtetlist->restart();
- cavetetshlist->restart();
- cavetetseglist->restart();
- cavetetvertlist->restart();
- if (ivf->splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
- if (splitseg != NULL) {
- sunmarktest(*splitseg);
- }
- for (i = 0; i < caveshlist->objects; i++) {
- parysh = (face *) fastlookup(caveshlist, i);
- assert(smarktested(*parysh));
- sunmarktest(*parysh);
- }
- caveshlist->restart();
- cavesegshlist->restart();
- }
+ }
- // Restore the hullsize.
- hullsize = bakhullsize;
- if (!encptflag) {
- loc = NEARVERTEX;
- } else {
- loc = ENCVERTEX;
- }
- return (int) loc;
- } else { // (iloc == (int) INSTAR)
- // The cavity is guaranteed to be valid by the caller of this
- // function. We still insert this vertex.
- if (b->verbose) {
- printf("Warning: The Steiner point %d is very close to %d.\n",
- pointmark(insertpt), pointmark(*pts));
- }
- }
- } // if (pts != NULL)
- }
- }
- // The new point will be inserted.
- totaldeadtets += caveoldtetlist->objects;
- totalbowatcavsize += cavebdrylist->objects;
- if (maxbowatcavsize < cavebdrylist->objects) {
- maxbowatcavsize = cavebdrylist->objects;
+ if (ivf->cdtflag) {
+ // Unmark tets.
+ for (i = 0; i < caveoldtetlist->objects; i++) {
+ cavetet = (triface *) fastlookup(caveoldtetlist, i);
+ unmarktest(*cavetet);
+ }
+ for (i = 0; i < cavebdrylist->objects; i++) {
+ cavetet = (triface *) fastlookup(cavebdrylist, i);
+ unmarktest(*cavetet);
+ }
+ // Clean up arrays which are not needed.
+ cavetetlist->restart();
+ if (checksubsegflag) {
+ cavetetseglist->restart();
+ }
+ if (checksubfaceflag) {
+ cavetetshlist->restart();
+ }
+ return 1;
}
// Before re-mesh C(p). Process the segments and subfaces which are on the
@@ -10917,7 +9897,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
while (1) {
j++;
if (!infected(spintet)) {
- neineitet = spintet; // An outer tet. Remember it.
+ neineitet = spintet; // An outer tet. Remember it.
} else {
k++; // An in tet.
}
@@ -10938,12 +9918,8 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
sstbond1(*paryseg, neineitet);
} else { // k == j
// The segment is inside C(p).
- if (!ivf->splitbdflag) {//if (bowywat < 3) { // if (bowywat == 2) {
+ if (!ivf->splitbdflag) {
checkseg = *paryseg;
- if (b->verbose > 3) {
- printf(" Queueing a missing seg (%d, %d)\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
sinfect(checkseg); // Flag it as an interior segment.
caveencseglist->newindex((void **) &paryseg);
*paryseg = checkseg;
@@ -10958,10 +9934,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
sinfect(*paryseg);
}
} // i
- if (b->verbose > 3) {
- printf(" %ld (%ld) cavity (interior) segments.\n",
- cavetetseglist->objects, caveencseglist->objects);
- }
} // if (checksubsegflag)
if (checksubfaceflag) {
@@ -10991,13 +9963,8 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// This side is the outer boundary of C(p).
*parysh = checksh;
} else { // k == 2
- if (!ivf->splitbdflag) { //if (bowywat < 3) { // if (bowywat == 2) {
+ if (!ivf->splitbdflag) {
checksh = *parysh;
- if (b->verbose > 3) {
- printf(" Queueing a missing subface (%d, %d, %d)\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
sinfect(checksh); // Flag it.
caveencshlist->newindex((void **) &parysh);
*parysh = checksh;
@@ -11012,40 +9979,26 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
sinfect(*parysh);
}
} // i
- if (b->verbose > 3) {
- printf(" %ld (%ld) cavity (interior) subfaces.\n",
- cavetetshlist->objects, caveencshlist->objects);
- }
- } // if (checksubfaceflag) {
+ } // if (checksubfaceflag)
// Create new tetrahedra to fill the cavity.
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
neightet = *cavetet;
- assert(!infected(neightet));
unmarktest(neightet); // Unmark it.
// Get the oldtet (inside the cavity).
fsym(neightet, oldtet);
if (apex(neightet) != dummypoint) {
- // Create a new tet in the cavity (see Fig. bowyerwatson 1 or 3).
+ // Create a new tet in the cavity.
maketetrahedron(&newtet);
setorg(newtet, dest(neightet));
setdest(newtet, org(neightet));
setapex(newtet, apex(neightet));
setoppo(newtet, insertpt);
- // The new tet inherits attribtes from the old tet.
- for (j = 0; j < in->numberoftetrahedronattributes; j++) {
- attrib = elemattribute(oldtet.tet, j);
- setelemattribute(newtet.tet, j, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(oldtet.tet);
- setvolumebound(newtet.tet, volume);
- }
} else {
- // Create a new hull tet (see Fig. bowyerwatson 2).
- hullsize++;
+ // Create a new hull tet.
+ hullsize++;
maketetrahedron(&newtet);
setorg(newtet, org(neightet));
setdest(newtet, dest(neightet));
@@ -11054,6 +10007,15 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// Adjust back to the cavity bounday face.
esymself(newtet);
}
+ // The new tet inherits attribtes from the old tet.
+ for (j = 0; j < numelemattrib; j++) {
+ attrib = elemattribute(oldtet.tet, j);
+ setelemattribute(newtet.tet, j, attrib);
+ }
+ if (b->varvolume) {
+ volume = volumebound(oldtet.tet);
+ setvolumebound(newtet.tet, volume);
+ }
// Connect newtet <==> neightet, this also disconnect the old bond.
bond(newtet, neightet);
// oldtet still connects to neightet.
@@ -11062,12 +10024,11 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// Set a handle for speeding point location.
recenttet = newtet;
- setpoint2tet(insertpt, encode(newtet));
+ //setpoint2tet(insertpt, encode(newtet));
+ setpoint2tet(insertpt, (tetrahedron) (newtet.tet));
- if (ivf->lawson > 1) { // if (lawson == 2 || lawson == 3) {
- // Re-use this list to save new interior cavity faces.
- cavetetlist->restart();
- }
+ // Re-use this list to save new interior cavity faces.
+ cavetetlist->restart();
// Connect adjacent new tetrahedra together.
for (i = 0; i < cavebdrylist->objects; i++) {
@@ -11089,16 +10050,15 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
fsym(spintet, newneitet);
esymself(newneitet);
- assert(newneitet.tet[newneitet.ver & 3] == NULL); // FOR DEBUG
+ assert(newneitet.tet[newneitet.ver & 3] == NULL);
bond(neightet, newneitet);
- if (ivf->lawson > 1) {
- // We are updateing a CDT. Queue the internal face.
- // See also fig/dump-cavity-case13, -case21.
+ if (ivf->lawson > 1) {
cavetetlist->newindex((void **) &parytet);
*parytet = neightet;
}
}
- setpoint2tet(org(newtet), encode(newtet));
+ //setpoint2tet(org(newtet), encode(newtet));
+ setpoint2tet(org(newtet), (tetrahedron) (newtet.tet));
enextself(newtet);
enextself(oldtet);
}
@@ -11142,7 +10102,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
if (checksubfaceflag) {
- if (ivf->splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
+ if (ivf->splitbdflag) {
// Recover new subfaces in C(p).
for (i = 0; i < caveshbdlist->objects; i++) {
// Get an old subface at edge [a, b].
@@ -11187,7 +10147,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// There should be no missing interior subfaces in C(p).
assert(caveencshlist->objects == 0l);
} else {
- // bowywat = 1 or bowywat = 2.
// The Boundary reocvery phase.
// Put all new subfaces into stack for recovery.
for (i = 0; i < caveshbdlist->objects; i++) {
@@ -11196,12 +10155,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
spivot(*parysh, checksh); // The new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
- if (b->verbose > 3) {
- printf(" Queue new subface (%d, %d, %d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- //sdissolve(checksh); // It has not been connected yet.
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
@@ -11213,11 +10166,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// Some subfaces inside C(p) might be split in sinsertvertex().
// Only queue those faces which are not split.
if (!smarktested(*parysh)) {
- if (b->verbose > 3) {
- printf(" Queue a missing subface (%d, %d, %d) x%lx.\n",
- pointmark(sorg(*parysh)), pointmark(sdest(*parysh)),
- pointmark(sapex(*parysh)), (uintptr_t) parysh->sh);
- }
checksh = *parysh;
suninfect(checksh);
stdissolve(checksh); // Detach connections to old tets.
@@ -11229,7 +10177,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
} // if (checksubfaceflag)
if (checksubsegflag) {
- if (ivf->splitbdflag) { //if (bowywat > 2) { // if (bowywat == 3) {
+ if (ivf->splitbdflag) {
if (splitseg != NULL) {
// Recover the two new subsegments in C(p).
for (i = 0; i < cavesegshlist->objects; i++) {
@@ -11244,11 +10192,9 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
stpivot(checksh, neightet);
} else {
// It's a dangling segment.
- pa = sorg(checkseg);
- pb = sdest(checkseg);
- point2tetorg(pa, neightet);
- finddirection(&neightet, pb, 1);
- assert(dest(neightet) == pb);
+ point2tetorg(sorg(checkseg), neightet);
+ finddirection(&neightet, sdest(checkseg));
+ assert(dest(neightet) == sdest(checkseg));
}
assert(!infected(neightet));
sstbond1(checkseg, neightet);
@@ -11263,17 +10209,12 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// There should be no interior segment in C(p).
assert(caveencseglist->objects == 0l);
} else {
- // bowywat == 1 or bowywat == 2;
// The Boundary Recovery Phase.
// Queue missing segments in C(p) for recovery.
if (splitseg != NULL) {
// Queue two new subsegments in C(p) for recovery.
for (i = 0; i < cavesegshlist->objects; i++) {
paryseg = (face *) fastlookup(cavesegshlist, i);
- if (b->verbose > 3) {
- printf(" Queue new subseg (%d, %d)\n",
- pointmark(sorg(*paryseg)), pointmark(sdest(*paryseg)));
- }
checkseg = *paryseg;
//sstdissolve1(checkseg); // It has not been connected yet.
s = randomnation(subsegstack->objects + 1);
@@ -11287,10 +10228,6 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
paryseg = (face *) fastlookup(caveencseglist, i);
assert(sinfected(*paryseg));
if (!smarktested(*paryseg)) { // It may be split.
- if (b->verbose > 3) {
- printf(" Queue a missing segment (%d, %d).\n",
- pointmark(sorg(*paryseg)), pointmark(sdest(*paryseg)));
- }
checkseg = *paryseg;
suninfect(checkseg);
sstdissolve1(checkseg); // Detach connections to old tets.
@@ -11304,12 +10241,10 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
} // if (checksubsegflag)
- if (b->plc || b->weighted) {
+ if (b->weighted
+ ) {
// Some vertices may be completed inside the cavity. They must be
// detected and added to recovering list.
- if (b->plc) {
- tetcount = subvertstack->objects; // Re-use tetcount;
- }
// Since every "live" vertex must contain a pointer to a non-dead
// tetrahedron, we can check for each vertex this pointer.
for (i = 0; i < cavetetvertlist->objects; i++) {
@@ -11318,28 +10253,15 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
assert(searchtet->tet != NULL); // No tet has been deleted yet.
if (infected(*searchtet)) {
if (b->weighted) {
- if (b->verbose > 2) {
- printf(" Point #%d is removed from the hull.\n",
- pointmark(*pts));
- }
- setpointtype(*pts, UNUSEDVERTEX);
- } else {
- if (b->verbose > 3) {
- printf(" Queue a dangling vertex %d.\n", pointmark(*pts));
+ if (b->verbose > 1) {
+ printf(" Point #%d is non-regular after the insertion of #%d.\n",
+ pointmark(*pts), pointmark(insertpt));
}
- subvertstack->newindex((void **) &parypt);
- *parypt = *pts;
+ setpointtype(*pts, NREGULARVERTEX);
+ nonregularcount++;
}
}
}
- if (b->plc) {
- if (subvertstack->objects > tetcount) {
- // There are missing vertices after inserting the new point.
- printf("DBG: Insert %d. Found %ld interior vertices.\n",
- pointmark(insertpt), subvertstack->objects);
- assert(0); // NEED TO DEBUG.
- }
- }
}
if (ivf->chkencflag & 1) {
@@ -11348,23 +10270,14 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
paryseg = (face *) fastlookup(cavetetseglist, i);
// Skip if it is the split segment.
if (!sinfected(*paryseg)) {
- // Skip it if it has already queued.
- if (!smarktest2ed(*paryseg)) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = *paryseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(*paryseg); // An alive badface.
- }
+ enqueuesubface(badsubsegs, paryseg);
}
}
if (splitseg != NULL) {
// Queue the two new subsegments inside C(p).
for (i = 0; i < cavesegshlist->objects; i++) {
paryseg = (face *) fastlookup(cavesegshlist, i);
- bface = (badface *) badsubsegs->alloc();
- bface->ss = *paryseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(*paryseg); // An alive badface.
+ enqueuesubface(badsubsegs, paryseg);
}
}
} // if (chkencflag & 1)
@@ -11375,15 +10288,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
parysh = (face *) fastlookup(cavetetshlist, i);
// Skip if it is a split subface.
if (!sinfected(*parysh)) {
- // Skip it if it has already queued.
- if (!smarktest2ed(*parysh)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = *parysh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(*parysh); // An alive badface.
- //bface->fdest = sdest(*parysh);
- //bface->fapex = sapex(*parysh);
- }
+ enqueuesubface(badsubfacs, parysh);
}
}
// Queue all new subfaces inside C(p).
@@ -11393,11 +10298,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
spivot(*parysh, checksh); // checksh is a new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
- //assert(!smarktest2ed(checksh));
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface.
+ enqueuesubface(badsubfacs, &checksh);
}
}
} // if (chkencflag & 2)
@@ -11406,19 +10307,18 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// Queue all new tetrahedra in C(p).
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
- //assert(!marktest2ed(*cavetet));
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = *cavetet;
- marktest2(bface->tt);
- bface->forg = org(*cavetet);
+ enqueuetetrahedron(cavetet);
}
}
- // C(p) is re-meshed successfully.
+ // C(p) is re-meshed successfully.
- // Deleted the old tets in C(p).
+ // Delete the old tets in C(p).
for (i = 0; i < caveoldtetlist->objects; i++) {
searchtet = (triface *) fastlookup(caveoldtetlist, i);
+ if (ishulltet(*searchtet)) {
+ hullsize--;
+ }
tetrahedrondealloc(searchtet->tet);
}
@@ -11444,7 +10344,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
}
shellfacedealloc(subfaces, parysh->sh);
}
- if (splitseg != NULL) {
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
// Delete the old segment in sC(p).
shellfacedealloc(subsegs, splitseg->sh);
}
@@ -11453,28 +10353,25 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
if (ivf->lawson) {
for (i = 0; i < cavebdrylist->objects; i++) {
searchtet = (triface *) fastlookup(cavebdrylist, i);
- //flippush(flipstack, searchtet, insertpt);
flippush(flipstack, searchtet);
}
if (ivf->lawson > 1) {
for (i = 0; i < cavetetlist->objects; i++) {
searchtet = (triface *) fastlookup(cavetetlist, i);
- //flippush(flipstack, searchtet, oppo(*searchtet));
flippush(flipstack, searchtet);
}
}
}
- // The vertex should already have a type.
- assert(pointtype(insertpt) != UNUSEDVERTEX);
-
-#ifdef WITH_RUNTIME_COUNTERS
- tend = clock();
- t_ptinsert += (tend - tstart);
-#endif
-
- if (b->btree) {
- btree_insert(insertpt);
+ // Set the point type if it is not set yet.
+ if (pointtype(insertpt) == UNUSEDVERTEX) {
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
+ setpointtype(insertpt, FREESEGVERTEX);
+ } else if (splitsh != NULL) {
+ setpointtype(insertpt, FREEFACETVERTEX);
+ } else {
+ setpointtype(insertpt, FREEVOLVERTEX);
+ }
}
// Clean the working lists.
@@ -11493,7 +10390,7 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
caveencshlist->restart();
}
- if (b->plc || b->weighted) {
+ if (b->weighted || ivf->validflag) {
cavetetvertlist->restart();
}
@@ -11503,7 +10400,49 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
cavesegshlist->restart();
}
- return (int) loc;
+ return 1; // Point is inserted.
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// insertpoint_abort() Abort the insertion of a new vertex. //
+// //
+// The cavity will be restored. All working lists are cleared. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::insertpoint_abort(face *splitseg, insertvertexflags *ivf)
+{
+ triface *cavetet;
+ face *parysh;
+ int i;
+
+ for (i = 0; i < caveoldtetlist->objects; i++) {
+ cavetet = (triface *) fastlookup(caveoldtetlist, i);
+ uninfect(*cavetet);
+ unmarktest(*cavetet);
+ }
+ for (i = 0; i < cavebdrylist->objects; i++) {
+ cavetet = (triface *) fastlookup(cavebdrylist, i);
+ unmarktest(*cavetet);
+ }
+ cavetetlist->restart();
+ cavebdrylist->restart();
+ caveoldtetlist->restart();
+ cavetetseglist->restart();
+ cavetetshlist->restart();
+ if (ivf->splitbdflag) {
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
+ sunmarktest(*splitseg);
+ }
+ for (i = 0; i < caveshlist->objects; i++) {
+ parysh = (face *) fastlookup(caveshlist, i);
+ assert(smarktested(*parysh));
+ sunmarktest(*parysh);
+ }
+ caveshlist->restart();
+ cavesegshlist->restart();
+ }
}
//// ////
@@ -11518,10 +10457,10 @@ int tetgenmesh::insertvertex(point insertpt, triface *searchtet, face *splitsh,
// //
// transfernodes() Read the vertices from the input (tetgenio). //
// //
-// Initializing 'this->points'. Transferring all points from 'in->pointlist'//
-// into it. All points are indexed (start from in->firstnumber). Each point //
-// is initialized be UNUSEDVERTEX. The bounding box (xmin, xmax, ymin, ymax,//
-// zmin, zmax) and the diameter (longest) of the point set are calculated. //
+// Transferring all points from input ('in->pointlist') to TetGen's 'points'.//
+// All points are indexed (the first point index is 'in->firstnumber'). Each //
+// point's type is initialized as UNUSEDVERTEX. The bounding box (xmax, xmin,//
+// ...) and the diameter (longest) of the point set are calculated. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -11534,9 +10473,6 @@ void tetgenmesh::transfernodes()
int mtrindex;
int i, j;
- if (b->psc) {
- assert(in->pointparamlist != NULL);
- }
// Read the points.
coordindex = 0;
@@ -11547,30 +10483,32 @@ void tetgenmesh::transfernodes()
// Read the point coordinates.
x = pointloop[0] = in->pointlist[coordindex++];
y = pointloop[1] = in->pointlist[coordindex++];
- z = pointloop[2] = in->pointlist[coordindex++];
+ z = pointloop[2] = in->pointlist[coordindex++];
+ // Read the point attributes. (Including point weights.)
+ for (j = 0; j < in->numberofpointattributes; j++) {
+ pointloop[3 + j] = in->pointattributelist[attribindex++];
+ }
+ // Read the point metric tensor.
+ for (j = 0; j < in->numberofpointmtrs; j++) {
+ pointloop[pointmtrindex + j] = in->pointmtrlist[mtrindex++];
+ }
if (b->weighted) { // -w option
if (in->numberofpointattributes > 0) {
- // The first point attribute is weight.
- w = in->pointattributelist[in->numberofpointattributes * i];
+ // The first point attribute is its weight.
+ //w = in->pointattributelist[in->numberofpointattributes * i];
+ w = pointloop[3];
} else {
- // No given weight available.
- w = 0;
+ // No given weight available. Default choose the maximum
+ // absolute value among its coordinates.
+ w = fabs(x);
+ if (w < fabs(y)) w = fabs(y);
+ if (w < fabs(z)) w = fabs(z);
}
if (b->weighted_param == 0) {
pointloop[3] = x * x + y * y + z * z - w; // Weighted DT.
} else { // -w1 option
pointloop[3] = w; // Regular tetrahedralization.
}
- } else {
- pointloop[3] = 0;
- }
- // Read the point attributes.
- for (j = 0; j < in->numberofpointattributes; j++) {
- pointloop[4 + j] = in->pointattributelist[attribindex++];
- }
- // Read the point metric tensor.
- for (j = 0; j < in->numberofpointmtrs; j++) {
- pointloop[pointmtrindex + j] = in->pointmtrlist[mtrindex++];
}
// Determine the smallest and largests x, y and z coordinates.
if (i == 0) {
@@ -11620,293 +10558,256 @@ void tetgenmesh::transfernodes()
///////////////////////////////////////////////////////////////////////////////
// //
-// btree_sort() Sort vertices using a binary space partition (bsp) tree. //
+// hilbert_init() Initialize the Gray code permutation table. //
+// //
+// The table 'transgc' has 8 x 3 x 8 entries. It contains all possible Gray //
+// code sequences traveled by the 1st order Hilbert curve in 3 dimensions. //
+// The first column is the Gray code of the entry point of the curve, and //
+// the second column is the direction (0, 1, or 2, 0 means the x-axis) where //
+// the exit point of curve lies. //
+// //
+// The table 'tsb1mod3' contains the numbers of trailing set '1' bits of the //
+// indices from 0 to 7, modulo by '3'. The code for generating this table is //
+// from: http://graphics.stanford.edu/~seander/bithacks.html. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::btree_sort(point* vertexarray, int arraysize, int axis,
- REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
- REAL bzmin, REAL bzmax, int depth)
+void tetgenmesh::hilbert_init(int n)
{
- point *leftarray, *rightarray;
- point **pptary, swapvert;
- REAL split;
- bool lflag, rflag;
- int i, j, k; // *iptr,
+ int gc[8], N, mask, travel_bit;
+ int e, d, f, k, g;
+ int v, c;
+ int i;
- if (b->verbose > 3) {
- printf(" Depth %d, %d verts. Bbox (%g, %g, %g),(%g, %g, %g). %s-axis\n",
- depth, arraysize, bxmin, bymin, bzmin, bxmax, bymax, bzmax,
- axis == 0 ? "x" : (axis == 1 ? "y" : "z"));
+ N = (n == 2) ? 4 : 8;
+ mask = (n == 2) ? 3 : 7;
+
+ // Generate the Gray code sequence.
+ for (i = 0; i < N; i++) {
+ gc[i] = i ^ (i >> 1);
+ }
+
+ for (e = 0; e < N; e++) {
+ for (d = 0; d < n; d++) {
+ // Calculate the end point (f).
+ f = e ^ (1 << d); // Toggle the d-th bit of 'e'.
+ // travel_bit = 2**p, the bit we want to travel.
+ travel_bit = e ^ f;
+ for (i = 0; i < N; i++) {
+ // // Rotate gc[i] left by (p + 1) % n bits.
+ k = gc[i] * (travel_bit * 2);
+ g = ((k | (k / N)) & mask);
+ // Calculate the permuted Gray code by xor with the start point (e).
+ transgc[e][d][i] = (g ^ e);
+ }
+ assert(transgc[e][d][0] == e);
+ assert(transgc[e][d][N - 1] == f);
+ } // d
+ } // e
+
+ // Count the consecutive '1' bits (trailing) on the right.
+ tsb1mod3[0] = 0;
+ for (i = 1; i < N; i++) {
+ v = ~i; // Count the 0s.
+ v = (v ^ (v - 1)) >> 1; // Set v's trailing 0s to 1s and zero rest
+ for (c = 0; v; c++) {
+ v >>= 1;
+ }
+ tsb1mod3[i] = c % n;
}
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// hilbert_sort3() Sort points using the 3d Hilbert curve. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+int tetgenmesh::hilbert_split(point* vertexarray,int arraysize,int gc0,int gc1,
+ REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
+ REAL bzmin, REAL bzmax)
+{
+ point swapvert;
+ int axis, d;
+ REAL split;
+ int i, j;
- if (depth > max_btree_depth) {
- max_btree_depth = depth;
- }
+ // Find the current splitting axis. 'axis' is a value 0, or 1, or 2, which
+ // correspoding to x-, or y- or z-axis.
+ axis = (gc0 ^ gc1) >> 1;
+
+ // Calulate the split position along the axis.
if (axis == 0) {
- // Split along x-axis.
split = 0.5 * (bxmin + bxmax);
} else if (axis == 1) {
- // Split along y-axis.
split = 0.5 * (bymin + bymax);
- } else {
- // Split along z-axis.
+ } else { // == 2
split = 0.5 * (bzmin + bzmax);
}
+ // Find the direction (+1 or -1) of the axis. If 'd' is +1, the direction
+ // of the axis is to the positive of the axis, otherwise, it is -1.
+ d = ((gc0 & (1<<axis)) == 0) ? 1 : -1;
+
+ // Partition the vertices into left- and right-arraies such that left points
+ // have Hilbert indices lower than the right points.
i = 0;
j = arraysize - 1;
// Partition the vertices into left- and right-arraies.
- do {
- for (; i < arraysize; i++) {
- if (vertexarray[i][axis] >= split) {
- break;
- }
- }
- for (; j >= 0; j--) {
- if (vertexarray[j][axis] < split) {
- break;
- }
- }
- // Is the partition finished?
- if (i == (j + 1)) {
- break;
- }
- // Swap i-th and j-th vertices.
- swapvert = vertexarray[i];
- vertexarray[i] = vertexarray[j];
- vertexarray[j] = swapvert;
- // Continue patitioning the array;
- } while (true);
-
- if (b->verbose > 3) {
- printf(" leftsize = %d, rightsize = %d\n", i, arraysize - i);
- }
- lflag = rflag = false;
-
- // Do not continue the partition if one of the array sizes is 0.
- // if (depth < max_tree_depth) {
- if (!((i == 0) || (i == arraysize))) {
- if (i > b->max_btreenode_size) {
- // Recursively partition the left array (length = i).
- if (axis == 0) { // x
- btree_sort(vertexarray, i, (axis + 1) % 3, bxmin, split, bymin,
- bymax, bzmin, bzmax, depth + 1);
- } else if (axis == 1) { // y
- btree_sort(vertexarray, i, (axis + 1) % 3, bxmin, bxmax, bymin,
- split, bzmin, bzmax, depth + 1);
- } else { // z
- btree_sort(vertexarray, i, (axis + 1) % 3, bxmin, bxmax, bymin,
- bymax, bzmin, split, depth + 1);
+ if (d > 0) {
+ do {
+ for (; i < arraysize; i++) {
+ if (vertexarray[i][axis] >= split) break;
+ }
+ for (; j >= 0; j--) {
+ if (vertexarray[j][axis] < split) break;
+ }
+ // Is the partition finished?
+ if (i == (j + 1)) break;
+ // Swap i-th and j-th vertices.
+ swapvert = vertexarray[i];
+ vertexarray[i] = vertexarray[j];
+ vertexarray[j] = swapvert;
+ // Continue patitioning the array;
+ } while (true);
+ } else {
+ do {
+ for (; i < arraysize; i++) {
+ if (vertexarray[i][axis] <= split) break;
}
- } else {
- lflag = true;
- }
- if ((arraysize - i) > b->max_btreenode_size) {
- // Recursively partition the right array (length = arraysize - i).
- if (axis == 0) { // x
- btree_sort(&(vertexarray[i]), arraysize - i, (axis + 1) % 3, split,
- bxmax, bymin, bymax, bzmin, bzmax, depth + 1);
- } else if (axis == 1) { // y
- btree_sort(&(vertexarray[i]), arraysize - i, (axis + 1) % 3, bxmin,
- bxmax, split, bymax, bzmin, bzmax, depth + 1);
- } else { // z
- btree_sort(&(vertexarray[i]), arraysize - i, (axis + 1) % 3, bxmin,
- bxmax, bymin, bymax, split, bzmax, depth + 1);
+ for (; j >= 0; j--) {
+ if (vertexarray[j][axis] > split) break;
}
- } else {
- rflag = true;
- }
- } else {
- // Both left and right are done.
- lflag = rflag = true;
- }
-
- if (lflag && (i > 0)) {
- // Remember the maximal length of the partitions.
- if (i > max_btreenode_size) {
- max_btreenode_size = i;
- }
- // Allocate space for the left array (use the first entry to save
- // the length of this array).
- leftarray = new point[i + 1];
- leftarray[0] = (point) i; // The array lenth.
- //iptr = (int *) &(leftarray[0]);
- //*iptr = i; // Save the array lenth in the first entry.
- // Put all points in this array.
- for (k = 0; k < i; k++) {
- leftarray[k + 1] = vertexarray[k];
- setpoint2ppt(leftarray[k + 1], (point) leftarray);
- }
- // Save this array in list.
- btreenode_list->newindex((void **) &pptary);
- *pptary = leftarray;
- }
-
- // Get the length of the right array.
- j = arraysize - i;
- if (rflag && (j > 0)) {
- if (j > max_btreenode_size) {
- max_btreenode_size = j;
- }
- // Allocate space for the right array (use the first entry to save
- // the length of this array).
- rightarray = new point[j + 1];
- rightarray[0] = (point) j; // The array lenth.
- //iptr = (int *) &(rightarray[0]);
- //*iptr = j; // Save the array length in the first entry.
- // Put all points in this array.
- for (k = 0; k < j; k++) {
- rightarray[k + 1] = vertexarray[i + k];
- setpoint2ppt(rightarray[k + 1], (point) rightarray);
- }
- // Save this array in list.
- btreenode_list->newindex((void **) &pptary);
- *pptary = rightarray;
+ // Is the partition finished?
+ if (i == (j + 1)) break;
+ // Swap i-th and j-th vertices.
+ swapvert = vertexarray[i];
+ vertexarray[i] = vertexarray[j];
+ vertexarray[j] = swapvert;
+ // Continue patitioning the array;
+ } while (true);
}
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// btree_insert() Add a vertex into a tree node. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::btree_insert(point insertpt)
-{
- point *ptary;
- long arylen; // The array lenhgth is saved in ptary[0].
-
- // Get the tree node (save in this point).
- ptary = (point *) point2ppt(insertpt);
- // Get the current array length.
- arylen = (long long) ptary[0];
- // Insert the point into the node.
- ptary[arylen + 1] = insertpt;
- // Increase the array length by 1.
- ptary[0] = (point) (arylen + 1);
+ return i;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// btree_search() Search a near point for an inserting point. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::btree_search(point insertpt, triface* searchtet)
+void tetgenmesh::hilbert_sort3(point* vertexarray, int arraysize, int e, int d,
+ REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
+ REAL bzmin, REAL bzmax, int depth)
{
- point *ptary;
- point nearpt, candpt;
- REAL dist2, mindist2;
- int ptsamples, ptidx;
- long arylen;
- int i;
-
- // Get the tree node (save in this point).
- ptary = (point *) point2ppt(insertpt);
- // Get the current array length.
- arylen = (long long) ptary[0];
-
- if (arylen == 0) {
- searchtet->tet = NULL;
- return;
- }
-
- if (1) {
-
- if (arylen < 5) { //if (arylen < 10) {
- ptsamples = arylen;
- } else {
- ptsamples = 5; // Take at least 10 samples.
- // The number of random samples taken is proportional to the third root
- // of the number of points in the cell.
- while (ptsamples * ptsamples * ptsamples < arylen) {
- ptsamples++;
+ REAL x1, x2, y1, y2, z1, z2;
+ int p[9], w, e_w, d_w, k, ei, di;
+ int n = 3, mask = 7;
+
+ p[0] = 0;
+ p[8] = arraysize;
+
+ // Sort the points according to the 1st order Hilbert curve in 3d.
+ p[4] = hilbert_split(vertexarray, p[8], transgc[e][d][3], transgc[e][d][4],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax);
+ p[2] = hilbert_split(vertexarray, p[4], transgc[e][d][1], transgc[e][d][2],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax);
+ p[1] = hilbert_split(vertexarray, p[2], transgc[e][d][0], transgc[e][d][1],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax);
+ p[3] = hilbert_split(&(vertexarray[p[2]]), p[4] - p[2],
+ transgc[e][d][2], transgc[e][d][3],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[2];
+ p[6] = hilbert_split(&(vertexarray[p[4]]), p[8] - p[4],
+ transgc[e][d][5], transgc[e][d][6],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[4];
+ p[5] = hilbert_split(&(vertexarray[p[4]]), p[6] - p[4],
+ transgc[e][d][4], transgc[e][d][5],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[4];
+ p[7] = hilbert_split(&(vertexarray[p[6]]), p[8] - p[6],
+ transgc[e][d][6], transgc[e][d][7],
+ bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[6];
+
+ if (b->hilbert_order > 0) {
+ // A maximum order is prescribed.
+ if ((depth + 1) == b->hilbert_order) {
+ // The maximum prescribed order is reached.
+ return;
+ }
+ }
+
+ // Recursivly sort the points in sub-boxes.
+ for (w = 0; w < 8; w++) {
+ // w is the local Hilbert index (NOT Gray code).
+ // Sort into the sub-box either there are more than 2 points in it, or
+ // the prescribed order of the curve is not reached yet.
+ //if ((p[w+1] - p[w] > b->hilbert_limit) || (b->hilbert_order > 0)) {
+ if ((p[w+1] - p[w]) > b->hilbert_limit) {
+ // Calulcate the start point (ei) of the curve in this sub-box.
+ // update e = e ^ (e(w) left_rotate (d+1)).
+ if (w == 0) {
+ e_w = 0;
+ } else {
+ // calculate e(w) = gc(2 * floor((w - 1) / 2)).
+ k = 2 * ((w - 1) / 2);
+ e_w = k ^ (k >> 1); // = gc(k).
+ }
+ k = e_w;
+ e_w = ((k << (d+1)) & mask) | ((k >> (n-d-1)) & mask);
+ ei = e ^ e_w;
+ // Calulcate the direction (di) of the curve in this sub-box.
+ // update d = (d + d(w) + 1) % n
+ if (w == 0) {
+ d_w = 0;
+ } else {
+ d_w = ((w % 2) == 0) ? tsb1mod3[w - 1] : tsb1mod3[w];
}
- }
-
- // Select "good" candidate using k random samples, taking the closest one.
- mindist2 = 1.79769E+308; // The largest double value (8 byte).
- nearpt = NULL;
-
- for (i = 0; i < ptsamples; i++) {
- ptidx = randomnation((unsigned long) arylen);
- candpt = ptary[ptidx + 1];
- dist2 = (candpt[0] - insertpt[0]) * (candpt[0] - insertpt[0])
- + (candpt[1] - insertpt[1]) * (candpt[1] - insertpt[1])
- + (candpt[2] - insertpt[2]) * (candpt[2] - insertpt[2]);
- if (dist2 < mindist2) {
- mindist2 = dist2;
- nearpt = candpt;
+ di = (d + d_w + 1) % n;
+ // Calculate the bounding box of the sub-box.
+ if (transgc[e][d][w] & 1) { // x-axis
+ x1 = 0.5 * (bxmin + bxmax);
+ x2 = bxmax;
+ } else {
+ x1 = bxmin;
+ x2 = 0.5 * (bxmin + bxmax);
}
- }
-
- } else {
-
- // TEST, randomly select a point.
- ptidx = randomnation((unsigned long) arylen);
- nearpt = ptary[ptidx + 1];
-
- }
-
- if (b->verbose > 2) {
- printf(" Get point %d (cell size %ld).\n", pointmark(nearpt), arylen);
- }
-
- decode(point2tet(nearpt), *searchtet);
+ if (transgc[e][d][w] & 2) { // y-axis
+ y1 = 0.5 * (bymin + bymax);
+ y2 = bymax;
+ } else {
+ y1 = bymin;
+ y2 = 0.5 * (bymin + bymax);
+ }
+ if (transgc[e][d][w] & 4) { // z-axis
+ z1 = 0.5 * (bzmin + bzmax);
+ z2 = bzmax;
+ } else {
+ z1 = bzmin;
+ z2 = 0.5 * (bzmin + bzmax);
+ }
+ hilbert_sort3(&(vertexarray[p[w]]), p[w+1] - p[w], ei, di,
+ x1, x2, y1, y2, z1, z2, depth+1);
+ } // if (p[w+1] - p[w] > 1)
+ } // w
}
///////////////////////////////////////////////////////////////////////////////
// //
-// ordervertices() Order the vertices for incremental inserting. //
-// //
-// We assume the vertices have been sorted by a binary tree. //
+// brio_multiscale_sort() Sort the points using BRIO and Hilbert curve. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::ordervertices(point* vertexarray, int arraysize)
+void tetgenmesh::brio_multiscale_sort(point* vertexarray, int arraysize,
+ int threshold, REAL ratio, int *depth)
{
- point **ipptary, **jpptary, *swappptary;
- point *ptary;
- long arylen;
- int index, i, j;
-
- // First pick one vertex from each tree node.
- for (i = 0; i < (int) btreenode_list->objects; i++) {
- ipptary = (point **) fastlookup(btreenode_list, i);
- ptary = *ipptary;
- vertexarray[i] = ptary[1]; // Skip the first entry.
- }
-
- index = i;
- // Then put all other points in the array node by node.
- for (i = (int) btreenode_list->objects - 1; i >= 0; i--) {
- // Randomly pick a tree node.
- j = randomnation(i + 1);
- // Save the i-th node.
- ipptary = (point **) fastlookup(btreenode_list, i);
- // Get the j-th node.
- jpptary = (point **) fastlookup(btreenode_list, j);
- // Order the points in the node.
- ptary = *jpptary;
- arylen = (long long) ptary[0];
- for (j = 2; j <= arylen; j++) { // Skip the first point.
- vertexarray[index] = ptary[j];
- index++;
- }
- // Clear this tree node.
- ptary[0] = (point) 0;
- // Swap i-th node to j-th node.
- swappptary = *ipptary;
- *ipptary = *jpptary; // [i] <= [j]
- *jpptary = swappptary; // [j] <= [i]
- }
-
- // Make sure we've done correctly.
- assert(index == arraysize);
+ int middle;
+
+ middle = 0;
+ if (arraysize >= threshold) {
+ (*depth)++;
+ middle = arraysize * ratio;
+ brio_multiscale_sort(vertexarray, middle, threshold, ratio, depth);
+ }
+ // Sort the right-array (rnd-th round) using the Hilbert curve.
+ hilbert_sort3(&(vertexarray[middle]), arraysize - middle, 0, 0, // e, d
+ xmin, xmax, ymin, ymax, zmin, zmax, 0); // depth.
}
///////////////////////////////////////////////////////////////////////////////
@@ -11938,17 +10839,14 @@ unsigned long tetgenmesh::randomnation(unsigned int choices)
// //
// randomsample() Randomly sample the tetrahedra for point loation. //
// //
-// This routine implements Muecke's Jump-and-walk point location algorithm. //
-// It improves the simple walk-through by "jumping" to a good starting point //
-// via random sampling. Searching begins from one of handles: the input //
-// 'searchtet', a recently encountered tetrahedron 'recenttet', or from one //
-// chosen from a random sample. The choice is made by determining which one //
-// 's origin is closest to the point we are searcing for. Having chosen the //
-// starting tetrahedron, the simple Walk-through algorithm is executed. //
+// Searching begins from one of handles: the input 'searchtet', a recently //
+// encountered tetrahedron 'recenttet', or from one chosen from a random //
+// sample. The choice is made by determining which one's origin is closest //
+// to the point we are searcing for. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::randomsample(point searchpt, triface *searchtet)
+void tetgenmesh::randomsample(point searchpt,triface *searchtet)
{
tetrahedron *firsttet, *tetptr;
point torg;
@@ -11963,44 +10861,50 @@ void tetgenmesh::randomsample(point searchpt, triface *searchtet)
pointmark(searchpt));
}
- if (searchtet->tet == NULL) {
- // A null tet. Choose the recenttet as the starting tet.
- *searchtet = recenttet;
- // Recenttet should not be dead.
- assert(recenttet.tet[4] != NULL);
- }
-
- // 'searchtet' should be a valid tetrahedron. Choose the base face
- // whose vertices must not be 'dummypoint'.
- searchtet->ver = 3;
- // Record the distance from its origin to the searching point.
- torg = org(*searchtet);
- searchdist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) +
- (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
- (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
- if (b->verbose > 3) {
- printf(" Dist %g from tet (%d, %d, %d, %d).\n", searchdist,
- pointmark(torg), pointmark(dest(*searchtet)),
- pointmark(apex(*searchtet)), pointmark(oppo(*searchtet)));
- }
-
- // If a recently encountered tetrahedron has been recorded and has not
- // been deallocated, test it as a good starting point.
- if (recenttet.tet != searchtet->tet) {
- recenttet.ver = 3;
- torg = org(recenttet);
- dist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) +
- (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
- (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
- if (dist < searchdist) {
+ if (!nonconvex) {
+ if (searchtet->tet == NULL) {
+ // A null tet. Choose the recenttet as the starting tet.
*searchtet = recenttet;
- searchdist = dist;
- if (b->verbose > 3) {
- printf(" Dist %g from recent tet (%d, %d, %d, %d).\n",
- searchdist, pointmark(torg), pointmark(dest(*searchtet)),
- pointmark(apex(*searchtet)), pointmark(oppo(*searchtet)));
+ // Recenttet should not be dead.
+ assert(recenttet.tet[4] != NULL);
+ }
+
+ // 'searchtet' should be a valid tetrahedron. Choose the base face
+ // whose vertices must not be 'dummypoint'.
+ searchtet->ver = 3;
+ // Record the distance from its origin to the searching point.
+ torg = org(*searchtet);
+ searchdist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) +
+ (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
+ (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
+ if (b->verbose > 3) {
+ printf(" Dist %g from tet (%d, %d, %d, %d).\n", searchdist,
+ pointmark(torg), pointmark(dest(*searchtet)),
+ pointmark(apex(*searchtet)), pointmark(oppo(*searchtet)));
+ }
+
+ // If a recently encountered tetrahedron has been recorded and has not
+ // been deallocated, test it as a good starting point.
+ if (recenttet.tet != searchtet->tet) {
+ recenttet.ver = 3;
+ torg = org(recenttet);
+ dist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) +
+ (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
+ (searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
+ if (dist < searchdist) {
+ *searchtet = recenttet;
+ searchdist = dist;
+ if (b->verbose > 3) {
+ printf(" Dist %g from recent tet (%d, %d, %d, %d).\n",
+ searchdist, pointmark(torg), pointmark(dest(*searchtet)),
+ pointmark(apex(*searchtet)), pointmark(oppo(*searchtet)));
+ }
}
}
+ } else {
+ // The mesh is non-convex. Do not use 'recenttet'.
+ assert(samples >= 1l); // Make sure at least 1 sample.
+ searchdist = longest;
}
// Select "good" candidate using k random samples, taking the closest one.
@@ -12040,11 +10944,6 @@ void tetgenmesh::randomsample(point searchpt, triface *searchtet)
searchtet->tet = tetptr;
searchtet->ver = 11; // torg = org(t);
searchdist = dist;
- if (b->verbose > 3) {
- printf(" Dist %g from tet (%d, %d, %d, %d).\n", searchdist,
- pointmark(torg), pointmark(dest(*searchtet)),
- pointmark(apex(*searchtet)), pointmark(oppo(*searchtet)));
- }
}
} else {
// A dead tet. Re-sample it.
@@ -12059,7 +10958,6 @@ void tetgenmesh::randomsample(point searchpt, triface *searchtet)
// //
// locate() Find a tetrahedron containing a given point. //
// //
-// This routine implements the simple Walk-through point location algorithm. //
// Begins its search from 'searchtet', assume there is a line segment L from //
// a vertex of 'searchtet' to the query point 'searchpt', and simply walk //
// towards 'searchpt' by traversing all faces intersected by L. //
@@ -12071,34 +10969,26 @@ void tetgenmesh::randomsample(point searchpt, triface *searchtet)
// - ONFACE, the search point lies on a face of 'searchtet'. //
// - INTET, the search point lies in the interior of 'searchtet'. //
// - OUTSIDE, the search point lies outside the mesh. 'searchtet' is a //
-// hull tetrahedron whose base face is visible by the search point. //
+// hull face which is visible by the search point. //
// //
// WARNING: This routine is designed for convex triangulations, and will not //
// generally work after the holes and concavities have been carved. //
// //
-// If 'randflag' is set (> 0). Randomly choose a tetrahedron when there are //
-// multiple choices in the path. //
-// //
///////////////////////////////////////////////////////////////////////////////
enum tetgenmesh::locateresult
- tetgenmesh::locate(point searchpt, triface* searchtet, int chkencflag,
- int randflag)
+ tetgenmesh::locate(point searchpt, triface* searchtet, int chkencflag)
{
- triface neightet;
- face checksh;
point torg, tdest, tapex, toppo;
enum {ORGMOVE, DESTMOVE, APEXMOVE} nextmove;
REAL ori, oriorg, oridest, oriapex;
- enum locateresult loc;
- int s; // i;
-
+ enum locateresult loc = OUTSIDE;
+ int t1ver;
+ int s;
if (searchtet->tet == NULL) {
// A null tet. Choose the recenttet as the starting tet.
- *searchtet = recenttet;
- // Recenttet should not be dead.
- assert(recenttet.tet[4] != NULL);
+ searchtet->tet = recenttet.tet;
}
// Check if we are in the outside of the convex hull.
@@ -12106,7 +10996,6 @@ enum tetgenmesh::locateresult
// Get its adjacent tet (inside the hull).
searchtet->ver = 3;
fsymself(*searchtet);
- assert(!ishulltet(*searchtet));
}
// Let searchtet be the face such that 'searchpt' lies above to it.
@@ -12114,22 +11003,14 @@ enum tetgenmesh::locateresult
torg = org(*searchtet);
tdest = dest(*searchtet);
tapex = apex(*searchtet);
- ori = orient3d(torg, tdest, tapex, searchpt); orient3dcount++;
+ ori = orient3d(torg, tdest, tapex, searchpt);
if (ori < 0.0) break;
}
- if (searchtet->ver == 4) {
- // Either 'searchtet' is a very flat tet, or the 'searchpt' lies in
- // infinity, or both of them. Return OUTSIDE.
- assert(0); // return OUTSIDE;
- }
-
- loc = OUTSIDE; // Set a default return value.
+ assert(searchtet->ver != 4);
// Walk through tetrahedra to locate the point.
while (true) {
- ptloc_count++; // Algorithimic count.
-
toppo = oppo(*searchtet);
// Check if the vertex is we seek.
@@ -12141,58 +11022,43 @@ enum tetgenmesh::locateresult
break;
}
- // We enter from serarchtet's base face. There are three other faces in
- // searchtet (all connecting to toppo), which one is the exit?
+ // We enter from one of serarchtet's faces, which face do we exit?
oriorg = orient3d(tdest, tapex, toppo, searchpt);
oridest = orient3d(tapex, torg, toppo, searchpt);
oriapex = orient3d(torg, tdest, toppo, searchpt);
- orient3dcount+=3;
// Now decide which face to move. It is possible there are more than one
- // faces are viable moves. Use the opposite points of thier neighbors
- // to discriminate, i.e., we choose the face whose opposite point has
- // the shortest distance to searchpt.
+ // faces are viable moves. If so, randomly choose one.
if (oriorg < 0) {
if (oridest < 0) {
if (oriapex < 0) {
- if (0) { //if (!randflag) {
+ // All three faces are possible.
+ s = randomnation(3); // 's' is in {0,1,2}.
+ if (s == 0) {
+ nextmove = ORGMOVE;
+ } else if (s == 1) {
+ nextmove = DESTMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(3); // 's' is in {0,1,2}.
- if (s == 0) {
- nextmove = ORGMOVE;
- } else if (s == 1) {
- nextmove = DESTMOVE;
- } else {
- nextmove = APEXMOVE;
- }
- } // if (randflag)
+ nextmove = APEXMOVE;
+ }
} else {
// Two faces, opposite to origin and destination, are viable.
- if (0) { // if (!randflag) {
+ //s = randomnation(2); // 's' is in {0,1}.
+ if (randomnation(2)) {
+ nextmove = ORGMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(2); // 's' is in {0,1}.
- if (s == 0) {
- nextmove = ORGMOVE;
- } else {
- nextmove = DESTMOVE;
- }
- } // if (randflag)
+ nextmove = DESTMOVE;
+ }
}
} else {
if (oriapex < 0) {
// Two faces, opposite to origin and apex, are viable.
- if (0) { // if (!randflag) {
+ //s = randomnation(2); // 's' is in {0,1}.
+ if (randomnation(2)) {
+ nextmove = ORGMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(2); // 's' is in {0,1}.
- if (s == 0) {
- nextmove = ORGMOVE;
- } else {
- nextmove = APEXMOVE;
- }
- } // if (randflag)
+ nextmove = APEXMOVE;
+ }
} else {
// Only the face opposite to origin is viable.
nextmove = ORGMOVE;
@@ -12202,16 +11068,12 @@ enum tetgenmesh::locateresult
if (oridest < 0) {
if (oriapex < 0) {
// Two faces, opposite to destination and apex, are viable.
- if (0) { // if (!randflag) {
+ //s = randomnation(2); // 's' is in {0,1}.
+ if (randomnation(2)) {
+ nextmove = DESTMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(2); // 's' is in {0,1}.
- if (s == 0) {
- nextmove = DESTMOVE;
- } else {
- nextmove = APEXMOVE;
- }
- } // if (randflag)
+ nextmove = APEXMOVE;
+ }
} else {
// Only the face opposite to destination is viable.
nextmove = DESTMOVE;
@@ -12225,10 +11087,8 @@ enum tetgenmesh::locateresult
// tetrahedron. Check for boundary cases.
if (oriorg == 0) {
// Go to the face opposite to origin.
- //enextfnextself(*searchtet);
enextesymself(*searchtet);
if (oridest == 0) {
- //enextself(*searchtet); // edge apex->oppo
eprevself(*searchtet); // edge oppo->apex
if (oriapex == 0) {
// oppo is duplicated with p.
@@ -12239,7 +11099,6 @@ enum tetgenmesh::locateresult
break;
}
if (oriapex == 0) {
- //enext2self(*searchtet);
enextself(*searchtet); // edge dest->oppo
loc = ONEDGE; // return ONEDGE;
break;
@@ -12249,63 +11108,284 @@ enum tetgenmesh::locateresult
}
if (oridest == 0) {
// Go to the face opposite to destination.
- //enext2fnextself(*searchtet);
eprevesymself(*searchtet);
if (oriapex == 0) {
- //enextself(*searchtet);
eprevself(*searchtet); // edge oppo->org
loc = ONEDGE; // return ONEDGE;
break;
}
- loc = ONFACE; // return ONFACE;
- break;
- }
- if (oriapex == 0) {
- // Go to the face opposite to apex
- //fnextself(*searchtet);
- esymself(*searchtet);
- loc = ONFACE; // return ONFACE;
- break;
+ loc = ONFACE; // return ONFACE;
+ break;
+ }
+ if (oriapex == 0) {
+ // Go to the face opposite to apex
+ esymself(*searchtet);
+ loc = ONFACE; // return ONFACE;
+ break;
+ }
+ loc = INTETRAHEDRON; // return INTETRAHEDRON;
+ break;
+ }
+ }
+ }
+
+ // Move to the selected face.
+ if (nextmove == ORGMOVE) {
+ enextesymself(*searchtet);
+ } else if (nextmove == DESTMOVE) {
+ eprevesymself(*searchtet);
+ } else {
+ esymself(*searchtet);
+ }
+ if (chkencflag) {
+ // Check if we are walking across a subface.
+ if (issubface(*searchtet)) {
+ loc = ENCSUBFACE;
+ break;
+ }
+ }
+ // Move to the adjacent tetrahedron (maybe a hull tetrahedron).
+ fsymself(*searchtet);
+ if (oppo(*searchtet) == dummypoint) {
+ loc = OUTSIDE; // return OUTSIDE;
+ break;
+ }
+
+ // Retreat the three vertices of the base face.
+ torg = org(*searchtet);
+ tdest = dest(*searchtet);
+ tapex = apex(*searchtet);
+
+ } // while (true)
+
+ return loc;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// flippush() Push a face (possibly will be flipped) into flipstack. //
+// //
+// The face is marked. The flag is used to check the validity of the face on //
+// its popup. Some other flips may change it already. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::flippush(badface*& fstack, triface* flipface)
+{
+ badface *newflipface;
+
+ if (!facemarked(*flipface)) {
+ newflipface = (badface *) flippool->alloc();
+ newflipface->tt = *flipface;
+ markface(newflipface->tt);
+ // Push this face into stack.
+ newflipface->nextitem = fstack;
+ fstack = newflipface;
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// incrementalflip() Incrementally flipping to construct DT. //
+// //
+// Faces need to be checked for flipping are already queued in 'flipstack'. //
+// Return the total number of performed flips. //
+// //
+// Comment: This routine should be only used in the incremental Delaunay //
+// construction. In other cases, lawsonflip3d() should be used. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+int tetgenmesh::incrementalflip(point newpt, flipconstraints *fc)
+{
+ badface *popface;
+ triface fliptets[5], *parytet;
+ point *pts;
+ REAL sign, ori;
+ int flipcount = 0;
+ int i;
+
+ if (b->verbose > 2) {
+ printf(" Lawson flip (%ld faces).\n", flippool->items);
+ }
+
+ // Loop until the queue is empty.
+ while (flipstack != NULL) {
+
+ // Pop a face from the stack.
+ popface = flipstack;
+ fliptets[0] = popface->tt;
+ flipstack = flipstack->nextitem; // The next top item in stack.
+ flippool->dealloc((void *) popface);
+
+ // Skip it if it is a dead tet (destroyed by previous flips).
+ if (isdeadtet(fliptets[0])) continue;
+ // Skip it if it is not the same tet as we saved.
+ if (!facemarked(fliptets[0])) continue;
+
+ unmarkface(fliptets[0]);
+
+ if ((point) fliptets[0].tet[7] == dummypoint) {
+ // It must be a hull edge.
+ fliptets[0].ver = epivot[fliptets[0].ver];
+ // A hull edge. The current convex hull may be enlarged.
+ fsym(fliptets[0], fliptets[1]);
+ pts = (point *) fliptets[1].tet;
+ ori = orient3d(pts[4], pts[5], pts[6], newpt);
+ if (ori < 0) {
+ // Perform a 2-to-3 flip. Replace face [a,b,c] by edge [e,d].
+ // [0] [a,b,c,d], d = newpt.
+ // [1] [b,a,c,e], c = dummypoint.
+ flip23(fliptets, 1, fc);
+ flipcount++;
+ } else if (ori == 0) {
+ if (oppo(fliptets[1]) != newpt) {
+ // A coplanar convex hull face!
+ // Treat it as unflippable.
+ } else {
+ // Two identical hull faces were bonded together!
+ triface fliptet = fliptets[0];
+ triface neightet = fliptets[1];
+ // First infect the two hull tets (they will be deleted).
+ infect(fliptet);
+ infect(neightet);
+ // Connect the actual adjacent tets.
+ for (i = 0; i < 3; i++) {
+ fnext(fliptet, fliptets[0]);
+ fnext(neightet, fliptets[1]);
+ if (!infected(fliptets[0])) {
+ assert(!infected(fliptets[1]));
+ bond(fliptets[0], fliptets[1]);
+ // Update the point-to-tet map.
+ setpoint2tet(org(fliptet), encode(fliptets[0]));
+ setpoint2tet(dest(fliptet), encode(fliptets[0]));
+ // Remeber a recent tet for point location.
+ recenttet = fliptets[0];
+ // apex(fliptets[0]) is the new point. The opposite face may
+ // be not locally Delaunay. Put it in flip stack.
+ assert(apex(fliptets[0]) == newpt); // SELF_CHECK
+ esymself(fliptets[0]);
+ flippush(flipstack, &(fliptets[0]));
+ assert(apex(fliptets[1]) == newpt); // SELF_CHECK
+ esymself(fliptets[1]);
+ flippush(flipstack, &(fliptets[1]));
+ }
+ enextself(fliptet);
+ eprevself(neightet);
}
- loc = INTETRAHEDRON; // return INTETRAHEDRON;
- break;
+ // Delete the two tets.
+ tetrahedrondealloc(fliptet.tet);
+ tetrahedrondealloc(neightet.tet);
+ // Update the hull size.
+ hullsize -= 2;
+ flipcount++;
}
- }
+ } // ori
+ continue;
+ } // if (dummypoint)
+
+ fsym(fliptets[0], fliptets[1]);
+ if ((point) fliptets[1].tet[7] == dummypoint) {
+ // A hull face is locally Delaunay.
+ continue;
}
-
- // Move to the selected face.
- if (nextmove == ORGMOVE) {
- enextesymself(*searchtet);
- } else if (nextmove == DESTMOVE) {
- eprevesymself(*searchtet);
+ // Check if the adjacent tet has already been tested.
+ if (marktested(fliptets[1])) {
+ // It has been tested and it is Delaunay.
+ continue;
+ }
+
+ // Test whether the face is locally Delaunay or not.
+ pts = (point *) fliptets[1].tet;
+ if (b->weighted) {
+ sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], newpt,
+ pts[4][3], pts[5][3], pts[6][3], pts[7][3],
+ newpt[3]);
} else {
- esymself(*searchtet);
+ sign = insphere_s(pts[4], pts[5], pts[6], pts[7], newpt);
}
- if (chkencflag) {
- // Check if we are walking across a subface.
- tspivot(*searchtet, checksh);
- if (checksh.sh != NULL) {
- loc = ENCSUBFACE;
- break;
+
+
+ if (sign < 0) {
+ point pd = newpt;
+ point pe = oppo(fliptets[1]);
+ // Check the convexity of its three edges. Stop checking either a
+ // locally non-convex edge (ori < 0) or a flat edge (ori = 0) is
+ // encountered, and 'fliptet' represents that edge.
+ for (i = 0; i < 3; i++) {
+ ori = orient3d(org(fliptets[0]), dest(fliptets[0]), pd, pe);
+ if (ori <= 0) break;
+ enextself(fliptets[0]);
}
- }
- // Move to the adjacent tetrahedron (maybe a hull tetrahedron).
- fsymself(*searchtet);
- if (oppo(*searchtet) == dummypoint) {
- loc = OUTSIDE; // return OUTSIDE;
- break;
+ if (ori > 0) {
+ // A 2-to-3 flip is found.
+ // [0] [a,b,c,d],
+ // [1] [b,a,c,e]. no dummypoint.
+ flip23(fliptets, 0, fc);
+ flipcount++;
+ } else { // ori <= 0
+ // The edge ('fliptets[0]' = [a',b',c',d]) is non-convex or flat,
+ // where the edge [a',b'] is one of [a,b], [b,c], and [c,a].
+ // Check if there are three or four tets sharing at this edge.
+ esymself(fliptets[0]); // [b,a,d,c]
+ for (i = 0; i < 3; i++) {
+ fnext(fliptets[i], fliptets[i+1]);
+ }
+ if (fliptets[3].tet == fliptets[0].tet) {
+ // A 3-to-2 flip is found. (No hull tet.)
+ flip32(fliptets, 0, fc);
+ flipcount++;
+ } else {
+ // There are more than 3 tets at this edge.
+ fnext(fliptets[3], fliptets[4]);
+ if (fliptets[4].tet == fliptets[0].tet) {
+ if (ori == 0) {
+ // A 4-to-4 flip is found. (Two hull tets may be involved.)
+ // Current tets in 'fliptets':
+ // [0] [b,a,d,c] (d may be newpt)
+ // [1] [b,a,c,e]
+ // [2] [b,a,e,f] (f may be dummypoint)
+ // [3] [b,a,f,d]
+ esymself(fliptets[0]); // [a,b,c,d]
+ // A 2-to-3 flip replaces face [a,b,c] by edge [e,d].
+ // This creates a degenerate tet [e,d,a,b] (tmpfliptets[0]).
+ // It will be removed by the followed 3-to-2 flip.
+ flip23(fliptets, 0, fc); // No hull tet.
+ fnext(fliptets[3], fliptets[1]);
+ fnext(fliptets[1], fliptets[2]);
+ // Current tets in 'fliptets':
+ // [0] [...]
+ // [1] [b,a,d,e] (degenerated, d may be new point).
+ // [2] [b,a,e,f] (f may be dummypoint)
+ // [3] [b,a,f,d]
+ // A 3-to-2 flip replaces edge [b,a] by face [d,e,f].
+ // Hull tets may be involved (f may be dummypoint).
+ flip32(&(fliptets[1]), (apex(fliptets[3]) == dummypoint), fc);
+ flipcount++;
+ }
+ }
+ }
+ } // ori
+ } else {
+ // The adjacent tet is Delaunay. Mark it to avoid testing it again.
+ marktest(fliptets[1]);
+ // Save it for unmarking it later.
+ cavebdrylist->newindex((void **) &parytet);
+ *parytet = fliptets[1];
}
- // Retreat the three vertices of the base face.
- torg = org(*searchtet);
- tdest = dest(*searchtet);
- tapex = apex(*searchtet);
+ } // while (flipstack)
- } // while (true)
+ // Unmark saved tetrahedra.
+ for (i = 0; i < cavebdrylist->objects; i++) {
+ parytet = (triface *) fastlookup(cavebdrylist, i);
+ unmarktest(*parytet);
+ }
+ cavebdrylist->restart();
- return loc;
-}
+ return flipcount;
+}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -12383,13 +11463,6 @@ void tetgenmesh::initialdelaunay(point pa, point pb, point pc, point pd)
setpointtype(pd, VOLVERTEX);
}
- if (b->btree) {
- btree_insert(pa);
- btree_insert(pb);
- btree_insert(pc);
- btree_insert(pd);
- }
-
setpoint2tet(pa, encode(firsttet));
setpoint2tet(pb, encode(firsttet));
setpoint2tet(pc, encode(firsttet));
@@ -12406,53 +11479,29 @@ void tetgenmesh::initialdelaunay(point pa, point pb, point pc, point pd)
// //
///////////////////////////////////////////////////////////////////////////////
+
void tetgenmesh::incrementaldelaunay(clock_t& tv)
{
triface searchtet;
point *permutarray, swapvertex;
- insertvertexflags ivf;
REAL v1[3], v2[3], n[3];
REAL bboxsize, bboxsize2, bboxsize3, ori;
- int randindex, loc;
+ int randindex;
+ int ngroup = 0;
int i, j;
if (!b->quiet) {
printf("Delaunizing vertices...\n");
}
- if (b->max_btreenode_size > 0) { // not -u0.
- b->btree = 1;
- btreenode_list = new arraypool(sizeof(point*), 10);
- max_btreenode_size = 0;
- max_btree_depth = 0;
- }
-
-
// Form a random permuation (uniformly at random) of the set of vertices.
permutarray = new point[in->numberofpoints];
points->traversalinit();
- if (b->btree) { // -u option
- for (i = 0; i < in->numberofpoints; i++) {
- permutarray[i] = (point) points->traverse();
- }
- if (b->verbose) {
- printf(" Sorting vertices by a bsp-tree.\n");
- }
- // Sort the points using a binary tree recursively.
- btree_sort(permutarray, in->numberofpoints, 0, xmin, xmax, ymin, ymax,
- zmin, zmax, 0);
- if (b->verbose) {
- printf(" Number of tree nodes: %ld.\n", btreenode_list->objects);
- printf(" Maximum tree node size: %d.\n", max_btreenode_size);
- printf(" Maximum tree depth: %d.\n", max_btree_depth);
- }
- // Order the sorted points.
- ordervertices(permutarray, in->numberofpoints);
- } else if (b->hilbertcurve) {
+
+ if (b->no_sort) {
if (b->verbose) {
- printf(" Sorting vertices by hilbert curve.\n");
+ printf(" Using the input order.\n");
}
- // To be done...
for (i = 0; i < in->numberofpoints; i++) {
permutarray[i] = (point) points->traverse();
}
@@ -12460,23 +11509,32 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
if (b->verbose) {
printf(" Permuting vertices.\n");
}
+ srand(in->numberofpoints);
for (i = 0; i < in->numberofpoints; i++) {
- randindex = randomnation(i + 1);
+ randindex = rand() % (i + 1); // randomnation(i + 1);
permutarray[i] = permutarray[randindex];
permutarray[randindex] = (point) points->traverse();
}
+ if (b->brio_hilbert) { // -b option
+ if (b->verbose) {
+ printf(" Sort vertices using BRIO and Hilbert curve.\n");
+ }
+ hilbert_init(in->mesh_dim);
+ brio_multiscale_sort(permutarray, in->numberofpoints, b->brio_threshold,
+ b->brio_ratio, &ngroup);
+ }
}
tv = clock(); // Remember the time for sorting points.
// Calculate the diagonal size of its bounding box.
- bboxsize = sqrt(NORM2(xmax - xmin, ymax - ymin, zmax - zmin));
+ bboxsize = sqrt(norm2(xmax - xmin, ymax - ymin, zmax - zmin));
bboxsize2 = bboxsize * bboxsize;
bboxsize3 = bboxsize2 * bboxsize;
// Make sure the second vertex is not identical with the first one.
i = 1;
- while ((DIST(permutarray[0], permutarray[i]) / bboxsize) < b->epsilon) {
+ while ((distance(permutarray[0],permutarray[i])/bboxsize)<b->epsilon) {
i++;
if (i == in->numberofpoints - 1) {
printf("Exception: All vertices are (nearly) identical (Tol = %g).\n",
@@ -12497,8 +11555,8 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
v1[j] = permutarray[1][j] - permutarray[0][j];
v2[j] = permutarray[i][j] - permutarray[0][j];
}
- CROSS(v1, v2, n);
- while ((sqrt(NORM2(n[0], n[1], n[2])) / bboxsize2) < b->epsilon) {
+ cross(v1, v2, n);
+ while ((sqrt(norm2(n[0], n[1], n[2])) / bboxsize2) < b->epsilon) {
i++;
if (i == in->numberofpoints - 1) {
printf("Exception: All vertices are (nearly) collinear (Tol = %g).\n",
@@ -12508,7 +11566,7 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
for (j = 0; j < 3; j++) {
v2[j] = permutarray[i][j] - permutarray[0][j];
}
- CROSS(v1, v2, n);
+ cross(v1, v2, n);
}
if (i > 2) {
// Swap to move the non-indetical vertex from index i to index 1.
@@ -12519,8 +11577,8 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
// Make sure the fourth vertex is not coplanar with the first three.
i = 3;
- ori = orient3d(permutarray[0], permutarray[1], permutarray[2],
- permutarray[i]);
+ ori = orient3dfast(permutarray[0], permutarray[1], permutarray[2],
+ permutarray[i]);
while ((fabs(ori) / bboxsize3) < b->epsilon) {
i++;
if (i == in->numberofpoints) {
@@ -12528,8 +11586,8 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
b->epsilon);
terminatetetgen(10);
}
- ori = orient3d(permutarray[0], permutarray[1], permutarray[2],
- permutarray[i]);
+ ori = orient3dfast(permutarray[0], permutarray[1], permutarray[2],
+ permutarray[i]);
}
if (i > 3) {
// Swap to move the non-indetical vertex from index i to index 1.
@@ -12554,57 +11612,73 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
if (b->verbose) {
printf(" Incrementally inserting vertices.\n");
}
+ insertvertexflags ivf;
+ flipconstraints fc;
+ // int loc;
- // Choose algorithm: Bowyer-Watson (default) or Incremental Flip (-l).
+ // Choose algorithm: Bowyer-Watson (default) or Incremental Flip
if (b->incrflip) {
ivf.bowywat = 0;
ivf.lawson = 1;
+ fc.enqflag = 1;
} else {
ivf.bowywat = 1;
ivf.lawson = 0;
}
+
for (i = 4; i < in->numberofpoints; i++) {
- if (b->verbose > 2) printf(" #%d", i);
if (pointtype(permutarray[i]) == UNUSEDVERTEX) {
setpointtype(permutarray[i], VOLVERTEX);
}
- // Auto choose the starting tet for point location.
- searchtet.tet = NULL;
+ if (b->brio_hilbert || b->no_sort) { // -b or -b/1
+ // Start the last updated tet.
+ searchtet.tet = recenttet.tet;
+ } else { // -b0
+ // Randomly choose the starting tet for point location.
+ searchtet.tet = NULL;
+ }
ivf.iloc = (int) OUTSIDE;
// Insert the vertex.
- loc = insertvertex(permutarray[i], &searchtet, NULL, NULL, &ivf);
- if (loc == (int) ONVERTEX) {
- // The point already exists. Mark it and do nothing on it.
- swapvertex = org(searchtet);
- assert(swapvertex != permutarray[i]); // SELF_CHECK
- if (b->object != tetgenbehavior::STL) {
+ if (insertpoint(permutarray[i], &searchtet, NULL, NULL, &ivf)) {
+ if (flipstack != NULL) {
+ // Perform flip to recover Delaunayness.
+ incrementalflip(permutarray[i], &fc);
+ }
+ } else {
+ if (ivf.iloc == (int) ONVERTEX) {
+ // The point already exists. Mark it and do nothing on it.
+ swapvertex = org(searchtet);
+ assert(swapvertex != permutarray[i]); // SELF_CHECK
+ if (b->object != tetgenbehavior::STL) {
+ if (!b->quiet) {
+ printf("Warning: Point #%d is coincident with #%d. Ignored!\n",
+ pointmark(permutarray[i]), pointmark(swapvertex));
+ }
+ }
+ setpoint2ppt(permutarray[i], swapvertex);
+ setpointtype(permutarray[i], DUPLICATEDVERTEX);
+ dupverts++;
+ } else if (ivf.iloc == (int) NEARVERTEX) {
+ swapvertex = point2ppt(permutarray[i]);
if (!b->quiet) {
- printf("Warning: Point #%d is coincident with #%d. Ignored!\n",
+ printf("Warning: Point %d is replaced by point %d.\n",
pointmark(permutarray[i]), pointmark(swapvertex));
+ printf(" Avoid creating a very short edge (len = %g) (< %g).\n",
+ permutarray[i][3], b->minedgelength);
+ printf(" You may try a smaller tolerance (-T) (current is %g)\n",
+ b->epsilon);
+ printf(" or use the option -M0/1 to avoid such replacement.\n");
}
+ // Remember it is a duplicated point.
+ setpointtype(permutarray[i], DUPLICATEDVERTEX);
+ // Count the number of duplicated points.
+ dupverts++;
}
- setpoint2ppt(permutarray[i], swapvertex);
- setpointtype(permutarray[i], DUPLICATEDVERTEX);
- dupverts++;
- continue;
- }
- if (ivf.lawson) {
- // If -l option. Perform flip to recover Delaunayness.
- lawsonflip3d(permutarray[i], ivf.lawson, 0, 0, 0);
}
}
- if (b->btree) {
- // Bsp-tree is used only in DT construction.
- point **pptary;
- for (i = 0; i < (int) btreenode_list->objects; i++) {
- pptary = (point **) fastlookup(btreenode_list, i);
- delete [] *pptary;
- }
- delete btreenode_list;
- b->btree = 0; // Disable it.
- }
+
delete [] permutarray;
}
@@ -12617,123 +11691,6 @@ void tetgenmesh::incrementaldelaunay(clock_t& tv)
//// ////
//// ////
-///////////////////////////////////////////////////////////////////////////////
-// //
-// calculateabovepoint() Calculate a point above a facet in 'dummypoint'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::calculateabovepoint(arraypool *facpoints, point *ppa,
- point *ppb, point *ppc)
-{
- point *ppt, pa, pb, pc;
- REAL v1[3], v2[3], n[3];
- REAL lab, len, A, area;
- REAL x, y, z;
- int i;
-
- ppt = (point *) fastlookup(facpoints, 0);
- pa = *ppt; // a is the first point.
- pb = pc = NULL; // Avoid compiler warnings.
-
- // Get a point b s.t. the length of [a, b] is maximal.
- lab = 0;
- for (i = 1; i < facpoints->objects; i++) {
- ppt = (point *) fastlookup(facpoints, i);
- x = (*ppt)[0] - pa[0];
- y = (*ppt)[1] - pa[1];
- z = (*ppt)[2] - pa[2];
- len = x * x + y * y + z * z;
- if (len > lab) {
- lab = len;
- pb = *ppt;
- }
- }
- lab = sqrt(lab);
- if (lab == 0) {
- if (!b->quiet) {
- printf("Warning: All points of a facet are coincident with %d.\n",
- pointmark(pa));
- }
- return false;
- }
-
- // Get a point c s.t. the area of [a, b, c] is maximal.
- v1[0] = pb[0] - pa[0];
- v1[1] = pb[1] - pa[1];
- v1[2] = pb[2] - pa[2];
- A = 0;
- for (i = 1; i < facpoints->objects; i++) {
- ppt = (point *) fastlookup(facpoints, i);
- v2[0] = (*ppt)[0] - pa[0];
- v2[1] = (*ppt)[1] - pa[1];
- v2[2] = (*ppt)[2] - pa[2];
- CROSS(v1, v2, n);
- area = DOT(n, n);
- if (area > A) {
- A = area;
- pc = *ppt;
- }
- }
- if (A == 0) {
- // All points are collinear. No above point.
- if (!b->quiet) {
- printf("Warning: All points of a facet are collinaer with [%d, %d].\n",
- pointmark(pa), pointmark(pb));
- }
- return false;
- }
-
- // Calculate an above point of this facet.
- facenormal(pa, pb, pc, n, 1, NULL);
- len = sqrt(DOT(n, n));
- n[0] /= len;
- n[1] /= len;
- n[2] /= len;
- lab /= 2.0; // Half the maximal length.
- dummypoint[0] = pa[0] + lab * n[0];
- dummypoint[1] = pa[1] + lab * n[1];
- dummypoint[2] = pa[2] + lab * n[2];
-
- if (ppa != NULL) {
- // Return the three points.
- *ppa = pa;
- *ppb = pb;
- *ppc = pc;
- }
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Calculate an above point. It lies above the plane containing the subface //
-// [a,b,c], and save it in dummypoint. Moreover, the vector pa->dummypoint //
-// is the normal of the plane. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::calculateabovepoint4(point pa, point pb, point pc, point pd)
-{
- arraypool *ptarray;
- point *parypt;
-
- ptarray = new arraypool(sizeof(point), 4);
-
- ptarray->newindex((void **) &parypt);
- *parypt = pa;
- ptarray->newindex((void **) &parypt);
- *parypt = pb;
- ptarray->newindex((void **) &parypt);
- *parypt = pc;
- ptarray->newindex((void **) &parypt);
- *parypt = pd;
-
- calculateabovepoint(ptarray, NULL, NULL, NULL);
-
- delete ptarray;
-}
-
///////////////////////////////////////////////////////////////////////////////
// //
// flipshpush() Push a facet edge into flip stack. //
@@ -12754,19 +11711,20 @@ void tetgenmesh::flipshpush(face* flipedge)
///////////////////////////////////////////////////////////////////////////////
// //
-// flip22() Remove an edge by transforming 2-to-2 subfaces. //
+// flip22() Perform a 2-to-2 flip in surface mesh. //
// //
-// 'flipfaces' contains two faces: abc and bad. This routine removes these 2 //
-// faces and replaces them by two new faces: cdb and dca. //
+// 'flipfaces' is an array of two subfaces. On input, they are [a,b,c] and //
+// [b,a,d]. On output, they are [c,d,b] and [d,c,a]. As a result, edge [a,b] //
+// is replaced by edge [c,d]. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
{
- face bdedges[4], outfaces[4], infaces[4], bdsegs[4];
- face checkface, checkseg;
+ face bdedges[4], outfaces[4], infaces[4];
+ face bdsegs[4];
+ face checkface;
point pa, pb, pc, pd;
- badface *bface;
int i;
pa = sorg(flipfaces[0]);
@@ -12778,10 +11736,6 @@ void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
sesymself(flipfaces[1]);
}
- if (b->verbose > 3) {
- printf(" flip 2-to-2: (%d, %d, %d, %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd));
- }
flip22count++;
// Collect the four boundary edges.
@@ -12796,8 +11750,7 @@ void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
infaces[i] = outfaces[i];
sspivot(bdedges[i], bdsegs[i]);
if (outfaces[i].sh != NULL) {
- sspivot(bdedges[i], checkseg);
- if (checkseg.sh != NULL) {
+ if (isshsubseg(bdedges[i])) {
spivot(infaces[i], checkface);
while (checkface.sh != bdedges[i].sh) {
infaces[i] = checkface;
@@ -12811,9 +11764,9 @@ void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
// Shellmark does not change.
// area constraint does not change.
- // Transform abc -> cdb.
+ // Transform [a,b,c] -> [c,d,b].
setshvertices(flipfaces[0], pc, pd, pb);
- // Transform bad -> dca.
+ // Transform [b,a,d] -> [d,c,a].
setshvertices(flipfaces[1], pd, pc, pa);
// Update the point-to-subface map.
@@ -12849,12 +11802,7 @@ void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
ssbond(bdedges[i], bdsegs[(3 + i) % 4]);
if (chkencflag & 1) {
// Queue this segment for encroaching check.
- if (!smarktest2ed(bdsegs[(3 + i) % 4])) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = bdsegs[(3 + i) % 4];
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(bface->ss); // An alive badface.
- }
+ enqueuesubface(badsubsegs, &(bdsegs[(3 + i) % 4]));
}
} else {
ssdissolve(bdedges[i]);
@@ -12864,12 +11812,7 @@ void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
if (chkencflag & 2) {
// Queue the flipped subfaces for quality/encroaching checks.
for (i = 0; i < 2; i++) {
- if (!smarktest2ed(flipfaces[i])) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = flipfaces[i];
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(bface->ss); // An alive badface.
- }
+ enqueuesubface(badsubfacs, &(flipfaces[i]));
}
}
@@ -12900,22 +11843,17 @@ void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
void tetgenmesh::flip31(face* flipfaces, int flipflag)
{
- face bdedges[3], outfaces[3], infaces[3], bdsegs[3];
- face checkface, checkseg;
- point pa, pb, pc, delpt;
- REAL area;
+ face bdedges[3], outfaces[3], infaces[3];
+ face bdsegs[3];
+ face checkface;
+ point pa, pb, pc;
int i;
- delpt = sorg(flipfaces[0]);
pa = sdest(flipfaces[0]);
pb = sdest(flipfaces[1]);
pc = sdest(flipfaces[2]);
- if (b->verbose > 3) {
- printf(" flip 3-to-1: (%d, %d, %d) - %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(delpt));
- }
- // flip31count++;
+ flip31count++;
// Collect all infos at the three boundary edges.
for (i = 0; i < 3; i++) {
@@ -12924,8 +11862,7 @@ void tetgenmesh::flip31(face* flipfaces, int flipflag)
infaces[i] = outfaces[i];
sspivot(bdedges[i], bdsegs[i]);
if (outfaces[i].sh != NULL) {
- sspivot(bdedges[i], checkseg);
- if (checkseg.sh != NULL) {
+ if (isshsubseg(bdedges[i])) {
spivot(infaces[i], checkface);
while (checkface.sh != bdedges[i].sh) {
infaces[i] = checkface;
@@ -12940,8 +11877,8 @@ void tetgenmesh::flip31(face* flipfaces, int flipflag)
setshvertices(flipfaces[3], pa, pb,pc);
setshellmark(flipfaces[3], shellmark(flipfaces[0]));
if (checkconstraints) {
- area = areabound(flipfaces[0]);
- setareabound(flipfaces[3], area);
+ //area = areabound(flipfaces[0]);
+ setareabound(flipfaces[3], areabound(flipfaces[0]));
}
// Update the point-to-subface map.
@@ -12998,15 +11935,13 @@ long tetgenmesh::lawsonflip()
{
badface *popface;
face flipfaces[2];
- face checkseg;
point pa, pb, pc, pd;
REAL sign;
- long flipcount;
+ long flipcount = 0;
if (b->verbose > 2) {
printf(" Lawson flip %ld edges.\n", flippool->items);
}
- flipcount = flip22count;
while (flipstack != (badface *) NULL) {
@@ -13023,8 +11958,7 @@ long tetgenmesh::lawsonflip()
// Skip it if it is not the same edge as we saved.
if ((sorg(flipfaces[0]) != pa) || (sdest(flipfaces[0]) != pb)) continue;
// Skip it if it is a subsegment.
- sspivot(flipfaces[0], checkseg);
- if (checkseg.sh != NULL) continue;
+ if (isshsubseg(flipfaces[0])) continue;
// Get the adjacent face.
spivot(flipfaces[0], flipfaces[1]);
@@ -13037,16 +11971,15 @@ long tetgenmesh::lawsonflip()
if (sign < 0) {
// It is non-locally Delaunay. Flip it.
flip22(flipfaces, 1, 0);
+ flipcount++;
}
}
if (b->verbose > 2) {
- printf(" %ld edges stacked, %ld flips.\n", flippool->items,
- flip22count - flipcount);
+ printf(" Performed %ld flips.\n", flipcount);
}
- assert(flippool->items == 0l); // SELF_CHECK
- return flip22count - flipcount;
+ return flipcount;
}
///////////////////////////////////////////////////////////////////////////////
@@ -13058,6 +11991,19 @@ long tetgenmesh::lawsonflip()
// 'caveshbdlist' contains new subfaces in C(p). If the new point lies on a //
// segment, 'cavesegshlist' returns the two new subsegments. //
// //
+// 'iloc' suggests the location of the point. If it is OUTSIDE, this routine //
+// will first locate the point. It starts searching from 'searchsh' or 'rec- //
+// entsh' if 'searchsh' is NULL. //
+// //
+// If 'bowywat' is set (1), the Bowyer-Watson algorithm is used to insert //
+// the vertex. Otherwise, only insert the vertex in the initial cavity. //
+// //
+// If 'iloc' is 'INSTAR', this means the cavity of this vertex was already //
+// provided in the list 'caveshlist'. //
+// //
+// If 'splitseg' is not NULL, the new vertex lies on the segment and it will //
+// be split. 'iloc' must be either 'ONEDGE' or 'INSTAR'.
+// //
// NOTE: the old subfaces in C(p) are not deleted. Theyare needed in case we //
// want to remove the new point immedately. //
// //
@@ -13066,67 +12012,47 @@ long tetgenmesh::lawsonflip()
int tetgenmesh::sinsertvertex(point insertpt, face *searchsh, face *splitseg,
int iloc, int bowywat)
{
- triface adjtet;
face cavesh, neighsh, *parysh;
face newsh, casout, casin;
- face aseg, bseg, aoutseg, boutseg;
face checkseg;
- point pa, pb, pc;
- enum locateresult loc;
- REAL sign, ori, area;
+ point pa, pb;
+ enum locateresult loc = OUTSIDE;
+ REAL sign, ori;
int i, j;
if (b->verbose > 2) {
printf(" Insert facet point %d.\n", pointmark(insertpt));
}
- if (splitseg != NULL) {
- // A segment is going to be split, no point location.
- spivot(*splitseg, *searchsh);
- loc = ONEDGE;
- } else {
- loc = (enum locateresult) iloc;
- if (loc == OUTSIDE) {
- // Do point location in surface mesh.
- if (searchsh->sh == NULL) {
- *searchsh = recentsh;
- }
- // Start searching from 'searchsh'.
- loc = slocate(insertpt, searchsh, 1, 1, 0);
- }
+ if (bowywat == 3) {
+ loc = INSTAR;
}
- if (b->verbose > 2) {
- if (searchsh->sh != NULL) {
- pa = sorg(*searchsh);
- pb = sdest(*searchsh);
- pc = sapex(*searchsh);
- printf(" Located subface (%d, %d, %d).\n", pointmark(pa),
- pointmark(pb), pointmark(pc));
- } else {
- assert(splitseg != NULL);
- pa = sorg(*splitseg);
- pb = sdest(*splitseg);
- printf(" Located segment (%d, %d).\n", pointmark(pa),pointmark(pb));
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
+ // A segment is going to be split, no point location.
+ spivot(*splitseg, *searchsh);
+ if (loc != INSTAR) loc = ONEDGE;
+ } else {
+ if (loc != INSTAR) loc = (enum locateresult) iloc;
+ if (loc == OUTSIDE) {
+ // Do point location in surface mesh.
+ if (searchsh->sh == NULL) {
+ *searchsh = recentsh;
+ }
+ // Search the vertex. An above point must be provided ('aflag' = 1).
+ loc = slocate(insertpt, searchsh, 1, 1, 0);
}
}
-if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
// Form the initial sC(p).
if (loc == ONFACE) {
- if (b->verbose > 2) {
- printf(" Inside face.\n");
- }
// Add the face into list (in B-W cavity).
smarktest(*searchsh);
caveshlist->newindex((void **) &parysh);
*parysh = *searchsh;
} else if (loc == ONEDGE) {
- if (b->verbose > 2) {
- printf(" On edge.\n");
- }
- if (splitseg != NULL) {
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
splitseg->shver = 0;
pa = sorg(*splitseg);
} else {
@@ -13137,9 +12063,7 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
neighsh = *searchsh;
while (1) {
// Adjust the origin of its edge to be 'pa'.
- if (sorg(neighsh) != pa) {
- sesymself(neighsh);
- }
+ if (sorg(neighsh) != pa) sesymself(neighsh);
// Add this face into list (in B-W cavity).
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
@@ -13155,18 +12079,12 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
}
} // If (not a non-dangling segment).
} else if (loc == ONVERTEX) {
- if (b->verbose > 2) {
- printf(" On vertex.\n");
- }
return (int) loc;
} else if (loc == OUTSIDE) {
// Comment: This should only happen during the surface meshing step.
// Enlarge the convex hull of the triangulation by including p.
// An above point of the facet is set in 'dummypoint' to replace
// orient2d tests by orient3d tests.
- if (b->verbose > 2) {
- printf(" Outside face.\n");
- }
// Imagine that the current edge a->b (in 'searchsh') is horizontal in a
// plane, and a->b is directed from left to right, p lies above a->b.
// Find the right-most edge of the triangulation which is visible by p.
@@ -13176,9 +12094,7 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
spivot(neighsh, casout);
if (casout.sh == NULL) {
// A convex hull edge. Is it visible by p.
- pa = sorg(neighsh);
- pb = sdest(neighsh);
- ori = orient3d(pa, pb, dummypoint, insertpt);
+ ori = orient3d(sorg(neighsh), sdest(neighsh), dummypoint, insertpt);
if (ori < 0) {
*searchsh = neighsh; // Visible, update 'searchsh'.
} else {
@@ -13199,8 +12115,8 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
setshvertices(newsh, pb, pa, insertpt);
setshellmark(newsh, shellmark(*searchsh));
if (checkconstraints) {
- area = areabound(*searchsh);
- setareabound(newsh, area);
+ //area = areabound(*searchsh);
+ setareabound(newsh, areabound(*searchsh));
}
// Connect the new subface to the bottom subfaces.
sbond1(newsh, *searchsh);
@@ -13236,47 +12152,30 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
// Finish the process if p is not visible by the hull edge.
if (ori >= 0) break;
}
+ } else if (loc == INSTAR) {
+ // Under this case, the sub-cavity sC(p) has already been formed in
+ // insertvertex().
}
-} else {
-
- // Under this case, the sub-cavity sC(p) has already been formed in
- // insertvertex(). Check it.
- // FOR DEBUG ONLY.
- for (i = 0; i < caveshlist->objects; i++) {
- cavesh = * (face *) fastlookup(caveshlist, i);
- assert(smarktested(cavesh));
- }
- if (splitseg != NULL) {
- assert(smarktested(*splitseg));
- }
-
-
-}// if (bowywat < 3)
-
// Form the Bowyer-Watson cavity sC(p).
for (i = 0; i < caveshlist->objects; i++) {
cavesh = * (face *) fastlookup(caveshlist, i);
for (j = 0; j < 3; j++) {
- sspivot(cavesh, checkseg);
- if (checkseg.sh == NULL) {
+ if (!isshsubseg(cavesh)) {
spivot(cavesh, neighsh);
if (neighsh.sh != NULL) {
// The adjacent face exists.
if (!smarktested(neighsh)) {
if (bowywat) {
- if (bowywat > 2) {
+ if (loc == INSTAR) { // if (bowywat > 2) {
// It must be a boundary edge.
sign = 1;
} else {
// Check if this subface is connected to adjacent tet(s).
- stpivot(neighsh, adjtet);
- if (adjtet.tet == NULL) {
+ if (!isshtet(neighsh)) {
// Check if the subface is non-Delaunay wrt. the new pt.
- pa = sorg(neighsh);
- pb = sdest(neighsh);
- pc = sapex(neighsh);
- sign = incircle3d(pa, pb, pc, insertpt);
+ sign = incircle3d(sorg(neighsh), sdest(neighsh),
+ sapex(neighsh), insertpt);
} else {
// It is connected to an adjacent tet. A boundary edge.
sign = 1;
@@ -13320,10 +12219,6 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
} // j
} // i
- if (b->verbose > 3) {
- printf(" Size of cavity: %ld faces, %ld bdry edges.\n",
- caveshlist->objects, caveshbdlist->objects);
- }
// Creating new subfaces.
for (i = 0; i < caveshbdlist->objects; i++) {
@@ -13338,8 +12233,8 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
setshellmark(newsh, shellmark(*parysh));
setshelltype(newsh, shelltype(*parysh));
if (checkconstraints) {
- area = areabound(*parysh);
- setareabound(newsh, area);
+ //area = areabound(*parysh);
+ setareabound(newsh, areabound(*parysh));
}
// Update the point-to-subface map.
if (pointtype(pa) == FREEFACETVERTEX) {
@@ -13376,8 +12271,10 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
sbond1(*parysh, newsh);
}
- // Set a handle for searching.
- recentsh = newsh;
+ if (newsh.sh != NULL) {
+ // Set a handle for searching.
+ recentsh = newsh;
+ }
// Update the point-to-subface map.
if (pointtype(insertpt) == FREEFACETVERTEX) {
@@ -13405,8 +12302,6 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
if (neighsh.sh != NULL) {
// Now 'neighsh' is a new subface at edge [b, #].
if (sorg(neighsh) != pb) sesymself(neighsh);
- assert(sorg(neighsh) == pb); // SELF_CHECK
- assert(sapex(neighsh) == insertpt); // SELF_CHECK
senext2self(neighsh); // Go to the open edge [p, b].
sbond(newsh, neighsh);
} else {
@@ -13431,8 +12326,6 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
if (neighsh.sh != NULL) {
// Now 'neighsh' is a new subface at edge [#, a].
if (sdest(neighsh) != pa) sesymself(neighsh);
- assert(sdest(neighsh) == pa); // SELF_CHECK
- assert(sapex(neighsh) == insertpt); // SELF_CHECK
senextself(neighsh); // Go to the open edge [a, p].
sbond(newsh, neighsh);
} else {
@@ -13442,13 +12335,15 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
}
}
- if (loc == ONEDGE) {
-
+ if ((loc == ONEDGE) || ((splitseg != NULL) && (splitseg->sh != NULL))
+ || (cavesegshlist->objects > 0l)) {
// An edge is being split. We distinguish two cases:
// (1) the edge is not on the boundary of the cavity;
// (2) the edge is on the boundary of the cavity.
// In case (2), the edge is either a segment or a hull edge. There are
// degenerated new faces in the cavity. They must be removed.
+ face aseg, bseg, aoutseg, boutseg;
+
for (i = 0; i < cavesegshlist->objects; i++) {
// Get the saved old subface.
parysh = (face *) fastlookup(cavesegshlist, i);
@@ -13490,7 +12385,7 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
sdissolve(newsh);
}
}
- recentsh = newsh;
+ //recentsh = newsh;
// Update the point-to-subface map.
if (pointtype(insertpt) == FREEFACETVERTEX) {
setpoint2sh(insertpt, sencode(newsh));
@@ -13498,18 +12393,14 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
}
}
- if (splitseg != NULL) {
- if (bowywat < 3) {
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
+ if (loc != INSTAR) { // if (bowywat < 3) {
smarktest(*splitseg); // Mark it as being processed.
}
aseg = *splitseg;
pa = sorg(*splitseg);
pb = sdest(*splitseg);
- if (b->verbose > 2) {
- printf(" Split seg (%d, %d) by %d.\n", pointmark(pa),
- pointmark(pb), pointmark(insertpt));
- }
// Insert the new point p.
makeshellface(subsegs, &aseg);
@@ -13522,7 +12413,7 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
setshelltype(aseg, shelltype(*splitseg));
setshelltype(bseg, shelltype(*splitseg));
if (checkconstraints) {
- setareabound(bseg, areabound(*splitseg));
+ setareabound(aseg, areabound(*splitseg));
setareabound(bseg, areabound(*splitseg));
}
@@ -13565,11 +12456,17 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
// Let the point remember the segment it lies on.
- setpoint2sh(insertpt, sencode(aseg));
+ if (pointtype(insertpt) == FREESEGVERTEX) {
+ setpoint2sh(insertpt, sencode(aseg));
+ }
// Update the point-to-seg map.
- setpoint2sh(pa, sencode(aseg));
- setpoint2sh(pb, sencode(bseg));
- } // if (splitseg != NULL)
+ if (pointtype(pa) == FREESEGVERTEX) {
+ setpoint2sh(pa, sencode(aseg));
+ }
+ if (pointtype(pb) == FREESEGVERTEX) {
+ setpoint2sh(pb, sencode(bseg));
+ }
+ } // if ((splitseg != NULL) && (splitseg->sh != NULL))
// Delete all degenerated new faces.
for (i = 0; i < cavesegshlist->objects; i++) {
@@ -13581,7 +12478,7 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
}
cavesegshlist->restart();
- if (splitseg != NULL) {
+ if ((splitseg != NULL) && (splitseg->sh != NULL)) {
// Return the two new subsegments (for further process).
// Re-use 'cavesegshlist'.
cavesegshlist->newindex((void **) &parysh);
@@ -13589,7 +12486,6 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
cavesegshlist->newindex((void **) &parysh);
*parysh = bseg;
}
-
} // if (loc == ONEDGE)
@@ -13604,39 +12500,34 @@ if (bowywat < 3) { // if (bowywat == 1 || bowywat == 2) {
// a segment vertex, and the origin of 'parentseg' is p. Otherwise, p is a //
// facet vertex, and the origin of 'parentsh' is p. //
// //
-// If 'lawson' > 0, the Lawson flip algorithm is used to recover Delaunay- //
-// ness after p is removed. //
-// //
// Within each facet, we first use a sequence of 2-to-2 flips to flip any //
// edge at p, finally use a 3-to-1 flip to remove p. //
// //
// All new created subfaces are returned in the global array 'caveshbdlist'. //
// The new segment (when p is on segment) is returned in 'parentseg'. //
// //
+// If 'lawson' > 0, the Lawson flip algorithm is used to recover Delaunay- //
+// ness after p is removed. //
+// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
int lawson)
{
- face flipfaces[4], *parysh;
- face spinsh, startsh, neighsh, nextsh, fakesh;
- face abseg, prevseg, checkseg;
- face adjseg1, adjseg2;
+ face flipfaces[4], spinsh, *parysh;
point pa, pb, pc, pd;
- int it, i, j;
-
- REAL *norm, n1[3], n2[3];
- REAL len, len1, len2;
REAL ori1, ori2;
+ int it, i, j;
if (parentseg != NULL) {
- assert(sorg(*parentseg) == delpt);
- assert(parentseg->shver == 0);
// 'delpt' (p) should be a Steiner point inserted in a segment [a,b],
// where 'parentseg' should be [p,b]. Find the segment [a,p].
+ face startsh, neighsh, nextsh;
+ face abseg, prevseg, checkseg;
+ face adjseg1, adjseg2;
+ face fakesh;
senext2(*parentseg, prevseg);
spivotself(prevseg);
- assert(prevseg.sh != NULL);
prevseg.shver = 0;
assert(sdest(prevseg) == delpt);
// Restore the original segment [a,b].
@@ -13741,12 +12632,7 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
// Since we will re-connect the face ring using the faked subfaces.
// We put the adjacent face of [a,b,p] to the list.
spivot(neighsh, startsh); // The original adjacent subface.
- if (sorg(startsh) != pa) {
- sesymself(startsh);
- }
- assert(sorg(startsh) == pa);
- assert(sdest(startsh) == pb);
- assert(sapex(startsh) != delpt);
+ if (sorg(startsh) != pa) sesymself(startsh);
sdissolve(startsh);
// Connect fakesh to the segment [a,b].
ssbond(startsh, abseg);
@@ -13797,9 +12683,7 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
parentsh = (face *) fastlookup(cavesegshlist, it); // [a,b,p]
senextself(*parentsh); // [b,p,a].
spivotself(*parentsh);
- if (sorg(*parentsh) != delpt) {
- sesymself(*parentsh);
- }
+ if (sorg(*parentsh) != delpt) sesymself(*parentsh);
// now parentsh is [p,b,#].
if (sorg(*parentsh) != delpt) {
// The vertex has already been removed in above special case.
@@ -13817,10 +12701,8 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
spivotself(spinsh);
assert(spinsh.sh != NULL);
if (spinsh.sh == parentsh->sh) break;
- if (sorg(spinsh) != delpt) {
- sesymself(spinsh);
- assert(sorg(spinsh) == delpt);
- }
+ if (sorg(spinsh) != delpt) sesymself(spinsh);
+ assert(sorg(spinsh) == delpt);
} // while (1)
if (caveshlist->objects == 3) {
@@ -13839,9 +12721,6 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
*parysh = flipfaces[3];
// The vertex is removed.
break;
- } else {
- // There should be more than 3 subfaces in list.
- assert(caveshlist->objects > 3);
}
// Search an edge to flip.
@@ -13849,35 +12728,15 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
parysh = (face *) fastlookup(caveshlist, i);
flipfaces[0] = *parysh;
spivot(flipfaces[0], flipfaces[1]);
- if (sorg(flipfaces[0]) != sdest(flipfaces[1])) {
+ if (sorg(flipfaces[0]) != sdest(flipfaces[1]))
sesymself(flipfaces[1]);
- }
// Skip this edge if it belongs to a faked subface.
if (!smarktested(flipfaces[0]) && !smarktested(flipfaces[1])) {
pa = sorg(flipfaces[0]);
pb = sdest(flipfaces[0]);
pc = sapex(flipfaces[0]);
pd = sapex(flipfaces[1]);
- // Select a base.
- facenormal(pa, pb, pc, n1, 1, NULL);
- len1 = sqrt(DOT(n1, n1));
- facenormal(pa, pb, pd, n2, 1, NULL);
- len2 = sqrt(DOT(n2, n2));
- if (len1 > len2) {
- norm = n1;
- len = len1;
- } else {
- norm = n2;
- len = len2;
- }
- assert(len > 0);
- norm[0] /= len;
- norm[1] /= len;
- norm[2] /= len;
- len = DIST(pa, pb);
- dummypoint[0] = pa[0] + len * norm[0];
- dummypoint[1] = pa[1] + len * norm[1];
- dummypoint[2] = pa[2] + len * norm[2];
+ calculateabovepoint4(pa, pb, pc, pd);
// Check if a 2-to-2 flip is possible.
ori1 = orient3d(pc, pd, dummypoint, pa);
ori2 = orient3d(pc, pd, dummypoint, pb);
@@ -13894,6 +12753,7 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
}
} //
} // i
+
if (i == caveshlist->objects) {
// This can happen only if there are 4 edges at p, and they are
// orthogonal to each other, see Fig. 2010-11-01.
@@ -13911,6 +12771,7 @@ int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
caveshbdlist->newindex((void **) &parysh);
*parysh = flipfaces[0];
}
+
// The edge list at p are changed.
caveshlist->restart();
} // while (1)
@@ -13962,35 +12823,19 @@ enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt,
face* searchsh, int aflag, int cflag, int rflag)
{
face neighsh;
- face checkseg;
- point pa, pb, pc, pd, *parypt;
+ point pa, pb, pc;
enum locateresult loc;
enum {MOVE_BC, MOVE_CA} nextmove;
REAL ori, ori_bc, ori_ca;
- REAL dist_bc, dist_ca;
int i;
- // For finding an approximate location.
- //REAL n[3], len, len3;
- REAL n[3], area_abc, area_abp, area_bcp, area_cap;
-
pa = sorg(*searchsh);
pb = sdest(*searchsh);
pc = sapex(*searchsh);
if (!aflag) {
// No above point is given. Calculate an above point for this facet.
- // Re-use the 'cavetetvertlist'.
- cavetetvertlist->newindex((void **) &parypt);
- *parypt = pa;
- cavetetvertlist->newindex((void **) &parypt);
- *parypt = pb;
- cavetetvertlist->newindex((void **) &parypt);
- *parypt = pc;
- cavetetvertlist->newindex((void **) &parypt);
- *parypt = searchpt;
- calculateabovepoint(cavetetvertlist, NULL, NULL, NULL);
- cavetetvertlist->restart();
+ calculateabovepoint4(pa, pb, pc, searchpt);
}
// 'dummypoint' is given. Make sure it is above [a,b,c]
@@ -14025,25 +12870,7 @@ enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt,
if (ori_bc < 0) {
if (ori_ca < 0) { // (--)
// Any of the edges is a viable move.
- senext(*searchsh, neighsh); // At edge [b, c].
- spivotself(neighsh);
- if (neighsh.sh != NULL) {
- pd = sapex(neighsh);
- dist_bc = NORM2(searchpt[0] - pd[0], searchpt[1] - pd[1],
- searchpt[2] - pd[2]);
- } else {
- dist_bc = NORM2(xmax - xmin, ymax - ymin, zmax - zmin);
- }
- senext2(*searchsh, neighsh); // At edge [c, a].
- spivotself(neighsh);
- if (neighsh.sh != NULL) {
- pd = sapex(neighsh);
- dist_ca = NORM2(searchpt[0] - pd[0], searchpt[1] - pd[1],
- searchpt[2] - pd[2]);
- } else {
- dist_ca = dist_bc;
- }
- if (dist_ca < dist_bc) {
+ if (randomnation(2)) {
nextmove = MOVE_CA;
} else {
nextmove = MOVE_BC;
@@ -14088,8 +12915,7 @@ enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt,
}
if (!cflag) {
// NON-convex case. Check if we will cross a boundary.
- sspivot(*searchsh, checkseg);
- if (checkseg.sh != NULL) {
+ if (isshsubseg(*searchsh)) {
return ENCSEGMENT;
}
}
@@ -14121,6 +12947,8 @@ enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt,
if (rflag) {
// Round the locate result before return.
+ REAL n[3], area_abc, area_abp, area_bcp, area_cap;
+
pa = sorg(*searchsh);
pb = sdest(*searchsh);
pc = sapex(*searchsh);
@@ -14194,17 +13022,15 @@ enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt,
// //
///////////////////////////////////////////////////////////////////////////////
-enum tetgenmesh::interresult
- tetgenmesh::sscoutsegment(face *searchsh, point endpt)
+enum tetgenmesh::interresult tetgenmesh::sscoutsegment(face *searchsh,
+ point endpt)
{
face flipshs[2], neighsh;
- face newseg, checkseg;
+ face newseg;
point startpt, pa, pb, pc, pd;
enum interresult dir;
enum {MOVE_AB, MOVE_CA} nextmove;
REAL ori_ab, ori_ca;
- REAL dist_b, dist_c;
- int shmark = 0;
// The origin of 'searchsh' is fixed.
startpt = sorg(*searchsh); // pa = startpt;
@@ -14238,16 +13064,7 @@ enum tetgenmesh::interresult
if (ori_ab < 0) {
if (ori_ca < 0) { // (--)
// Both sides are viable moves.
- spivot(*searchsh, neighsh); // At edge [a, b].
- assert(neighsh.sh != NULL); // SELF_CHECK
- pd = sapex(neighsh);
- dist_b = NORM2(endpt[0] - pd[0], endpt[1] - pd[1], endpt[2] - pd[2]);
- senext2(*searchsh, neighsh); // At edge [c, a].
- spivotself(neighsh);
- assert(neighsh.sh != NULL); // SELF_CHECK
- pd = sapex(neighsh);
- dist_c = NORM2(endpt[0] - pd[0], endpt[1] - pd[1], endpt[2] - pd[2]);
- if (dist_c < dist_b) {
+ if (randomnation(2)) {
nextmove = MOVE_CA;
} else {
nextmove = MOVE_AB;
@@ -14303,11 +13120,8 @@ enum tetgenmesh::interresult
// Insert the segment into the triangulation.
makeshellface(subsegs, &newseg);
setshvertices(newseg, startpt, endpt, NULL);
- // Set the actual segment marker.
- if (in->facetmarkerlist != NULL) {
- shmark = shellmark(*searchsh);
- setshellmark(newseg, in->facetmarkerlist[shmark - 1]);
- }
+ // Set the default segment marker.
+ setshellmark(newseg, 1);
ssbond(*searchsh, newseg);
spivot(*searchsh, neighsh);
if (neighsh.sh != NULL) {
@@ -14324,8 +13138,7 @@ enum tetgenmesh::interresult
if (dir == ACROSSEDGE) {
// Edge [b, c] intersects with the segment.
senext(*searchsh, flipshs[0]);
- sspivot(flipshs[0], checkseg);
- if (checkseg.sh != NULL) {
+ if (isshsubseg(flipshs[0])) {
printf("Error: Invalid PLC.\n");
pb = sorg(flipshs[0]);
pc = sdest(flipshs[0]);
@@ -14349,16 +13162,8 @@ enum tetgenmesh::interresult
ori_ca = orient3d(pd, pc, dummypoint, pa);
//assert(ori_ab * ori_ca != 0); // SELF_CHECK
if (ori_ab < 0) {
- if (b->verbose > 2) {
- printf(" Queue an inversed triangle (%d, %d, %d) %d\n",
- pointmark(pc), pointmark(pd), pointmark(pb), pointmark(pa));
- }
flipshpush(&(flipshs[0])); // push it to 'flipstack'
} else if (ori_ca < 0) {
- if (b->verbose > 2) {
- printf(" Queue an inversed triangle (%d, %d, %d) %d\n",
- pointmark(pd), pointmark(pc), pointmark(pa), pointmark(pb));
- }
flipshpush(&(flipshs[1])); // // push it to 'flipstack'
}
// Set 'searchsh' s.t. its origin is 'startpt'.
@@ -14380,7 +13185,6 @@ enum tetgenmesh::interresult
void tetgenmesh::scarveholes(int holes, REAL* holelist)
{
face *parysh, searchsh, neighsh;
- face checkseg;
enum locateresult loc;
int i, j;
@@ -14403,8 +13207,7 @@ void tetgenmesh::scarveholes(int holes, REAL* holelist)
}
} else {
// A hull side. Check if it is protected by a segment.
- sspivot(searchsh, checkseg);
- if (checkseg.sh == NULL) {
+ if (!isshsubseg(searchsh)) {
// Not protected. Save this face.
if (!sinfected(searchsh)) {
sinfect(searchsh);
@@ -14436,8 +13239,7 @@ void tetgenmesh::scarveholes(int holes, REAL* holelist)
for (j = 0; j < 3; j++) {
spivot(searchsh, neighsh);
if (neighsh.sh != NULL) {
- sspivot(searchsh, checkseg);
- if (checkseg.sh == NULL) {
+ if (!isshsubseg(searchsh)) {
if (!sinfected(neighsh)) {
sinfect(neighsh);
caveshbdlist->newindex((void **) &parysh);
@@ -14469,6 +13271,9 @@ void tetgenmesh::scarveholes(int holes, REAL* holelist)
// //
// triangulate() Create a CDT for the facet. //
// //
+// All vertices of the triangulation have type FACETVERTEX. The actual type //
+// of boundary vertices are set by the routine unifysements(). //
+// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
@@ -14477,7 +13282,6 @@ void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
face searchsh, newsh, *parysh;
face newseg;
point pa, pb, pc, *ppt, *cons;
- enum locateresult loc;
int iloc;
int i, j;
@@ -14493,57 +13297,27 @@ void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
if (ptlist->objects < 2l) {
// Not a segment or a facet.
return;
- } if (ptlist->objects == 2l) {
+ }
+
+ if (ptlist->objects == 2l) {
pa = * (point *) fastlookup(ptlist, 0);
pb = * (point *) fastlookup(ptlist, 1);
if (distance(pa, pb) > 0) {
// It is a single segment.
makeshellface(subsegs, &newseg);
setshvertices(newseg, pa, pb, NULL);
- // Set the actual segment marker.
- if (in->facetmarkerlist != NULL) {
- setshellmark(newseg, in->facetmarkerlist[shmark - 1]);
- }
+ // Set the default segment marker '1'.
+ setshellmark(newseg, 1);
}
if (pointtype(pa) == VOLVERTEX) {
- setpointtype(pa, RIDGEVERTEX);
+ setpointtype(pa, FACETVERTEX);
}
if (pointtype(pb) == VOLVERTEX) {
- setpointtype(pb, RIDGEVERTEX);
- }
- return;
- } if (ptlist->objects == 3l) {
- // The facet has only one triangle.
- pa = * (point *) fastlookup(ptlist, 0);
- pb = * (point *) fastlookup(ptlist, 1);
- pc = * (point *) fastlookup(ptlist, 2);
- if (triarea(pa, pb, pc) > 0) {
- makeshellface(subfaces, &newsh);
- setshvertices(newsh, pa, pb, pc);
- setshellmark(newsh, shmark);
- // Create three new segments.
- for (i = 0; i < 3; i++) {
- makeshellface(subsegs, &newseg);
- setshvertices(newseg, sorg(newsh), sdest(newsh), NULL);
- // Set the actual segment marker.
- if (in->facetmarkerlist != NULL) {
- setshellmark(newseg, in->facetmarkerlist[shmark - 1]);
- }
- ssbond(newsh, newseg);
- senextself(newsh);
- }
- if (pointtype(pa) == VOLVERTEX) {
- setpointtype(pa, FACETVERTEX);
- }
- if (pointtype(pb) == VOLVERTEX) {
- setpointtype(pb, FACETVERTEX);
- }
- if (pointtype(pc) == VOLVERTEX) {
- setpointtype(pc, FACETVERTEX);
- }
+ setpointtype(pb, FACETVERTEX);
}
return;
- }
+ }
+
// Calulcate an above point of this facet.
if (!calculateabovepoint(ptlist, &pa, &pb, &pc)) {
@@ -14566,6 +13340,34 @@ void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
setpointtype(pc, FACETVERTEX);
}
+ // Are there area constraints?
+ if (b->quality && (in->facetconstraintlist != (REAL *) NULL)) {
+ int idx, fmarker;
+ REAL area;
+ idx = in->facetmarkerlist[shmark - 1]; // The actual facet marker.
+ for (i = 0; i < in->numberoffacetconstraints; i++) {
+ fmarker = (int) in->facetconstraintlist[i * 2];
+ if (fmarker == idx) {
+ area = in->facetconstraintlist[i * 2 + 1];
+ setareabound(newsh, area);
+ break;
+ }
+ }
+ }
+
+ if (ptlist->objects == 3) {
+ // The triangulation only has one element.
+ for (i = 0; i < 3; i++) {
+ makeshellface(subsegs, &newseg);
+ setshvertices(newseg, sorg(newsh), sdest(newsh), NULL);
+ // Set the default segment marker '1'.
+ setshellmark(newseg, 1);
+ ssbond(newsh, newseg);
+ senextself(newsh);
+ }
+ return;
+ }
+
// Incrementally build the triangulation.
pinfect(pa);
pinfect(pb);
@@ -14576,8 +13378,8 @@ void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
searchsh = recentsh; // Start from 'recentsh'.
iloc = (int) OUTSIDE;
if (b->verbose > 2) printf(" # %d", i);
- loc = (enum locateresult) sinsertvertex(*ppt, &searchsh, NULL, iloc, 1);
- assert(loc != ONVERTEX); // SELF_CHECK
+ iloc = sinsertvertex(*ppt, &searchsh, NULL, iloc, 1);
+ assert(iloc != (enum locateresult) ONVERTEX); // SELF_CHECK
if (pointtype(*ppt) == VOLVERTEX) {
setpointtype(*ppt, FACETVERTEX);
}
@@ -14599,8 +13401,8 @@ void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
for (i = 0; i < conlist->objects; i++) {
cons = (point *) fastlookup(conlist, i);
searchsh = recentsh;
- loc = slocate(cons[0], &searchsh, 1, 1, 0);
- assert(loc == ONVERTEX); // SELF_CHECK
+ iloc = (int) slocate(cons[0], &searchsh, 1, 1, 0);
+ assert(iloc == (enum locateresult) ONVERTEX); // SELF_CHECK
// Recover the segment. Some edges may be flipped.
sscoutsegment(&searchsh, cons[1]);
if (flipstack != NULL) {
@@ -14629,18 +13431,13 @@ void tetgenmesh::triangulate(int shmark, arraypool* ptlist, arraypool* conlist,
void tetgenmesh::unifysubfaces(face *f1, face *f2)
{
face casout, casin, neighsh;
- face sseg, checkseg;
+ face sseg;
point pa, pb, pc, pd;
int i;
- assert(f1->sh != f2->sh); // SELF_CHECK
-
pa = sorg(*f1);
pb = sdest(*f1);
pc = sapex(*f1);
-
- assert(sorg(*f2) == pa); // SELF_CHECK
- assert(sdest(*f2) == pb); // SELF_CHECK
pd = sapex(*f2);
if (pc != pd) {
@@ -14687,10 +13484,6 @@ void tetgenmesh::unifysubfaces(face *f1, face *f2)
sspivot(*f2, sseg);
if (sseg.sh != NULL) {
// f2 has a segment. It must be different to f1's.
- sspivot(*f1, checkseg); // SELF_CHECK
- if (checkseg.sh != NULL) { // SELF_CHECK
- assert(checkseg.sh != sseg.sh); // SELF_CHECK
- }
// Disconnect bonds of subfaces to this segment.
spivot(*f2, casout);
if (casout.sh != NULL) {
@@ -14730,6 +13523,9 @@ void tetgenmesh::unifysubfaces(face *f1, face *f2)
// //
// unifysegments() Remove redundant segments and create face links. //
// //
+// After this routine, although segments are unique, but some of them may be //
+// removed later by mergefacet(). All vertices still have type FACETVERTEX. //
+// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::unifysegments()
@@ -14852,7 +13648,7 @@ void tetgenmesh::unifysegments()
// f is either codirection with f1 or is codirection with f2.
facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL);
facenormal(torg, tdest, sapex(sface), n2, 1, NULL);
- if (DOT(n1, n2) > 0) {
+ if (dot(n1, n2) > 0) {
unifysubfaces(&(f1->ss), &sface);
} else {
unifysubfaces(&(f2->ss), &sface);
@@ -14878,7 +13674,7 @@ void tetgenmesh::unifysegments()
// f is coplanar with f1 (see Fig. 8).
facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL);
facenormal(torg, tdest, sapex(sface), n2, 1, NULL);
- if (DOT(n1, n2) > 0) {
+ if (dot(n1, n2) > 0) {
// The two faces are codirectional as well.
unifysubfaces(&(f1->ss), &sface);
}
@@ -14900,16 +13696,10 @@ void tetgenmesh::unifysegments()
}
} // for (k = idx2faclist[idx]; ...)
- if (b->verbose > 2) {
- printf(" Found %ld segments at (%d %d).\n", flippool->items,
- pointmark(torg), pointmark(tdest));
- }
- //if (b->nobisect || b->nomerge) { // -Y or -M
- // Set the vertex types of the endpoints of the segment.
- setpointtype(torg, RIDGEVERTEX);
- setpointtype(tdest, RIDGEVERTEX);
- //}
+ // Set the vertex types of the endpoints of the segment.
+ //setpointtype(torg, RIDGEVERTEX);
+ //setpointtype(tdest, RIDGEVERTEX);
// Set the connection between this segment and faces containing it,
// at the same time, remove redundant segments.
@@ -14930,21 +13720,30 @@ void tetgenmesh::unifysegments()
f1 = facelink;
for (k = 1; k <= flippool->items; k++) {
k < flippool->items ? f2 = f1->nextitem : f2 = facelink;
- if (b->verbose > 3) {
- printf(" Bond subfaces (%d, %d, %d) and (%d, %d, %d).\n",
- pointmark(torg), pointmark(tdest), pointmark(sapex(f1->ss)),
- pointmark(torg), pointmark(tdest), pointmark(sapex(f2->ss)));
- }
sbond1(f1->ss, f2->ss);
f1 = f2;
}
}
- // // All identified segments has a marker "-1".
- //setshellmark(subsegloop, -1);
// All identified segments has an init marker "0".
flippool->restart();
+ // Are there length constraints?
+ if (b->quality && (in->segmentconstraintlist != (REAL *) NULL)) {
+ int e1, e2;
+ REAL len;
+ for (k = 0; k < in->numberofsegmentconstraints; k++) {
+ e1 = (int) in->segmentconstraintlist[k * 3];
+ e2 = (int) in->segmentconstraintlist[k * 3 + 1];
+ if (((pointmark(torg) == e1) && (pointmark(tdest) == e2)) ||
+ ((pointmark(torg) == e2) && (pointmark(tdest) == e1))) {
+ len = in->segmentconstraintlist[k * 3 + 2];
+ setareabound(subsegloop, len);
+ break;
+ }
+ }
+ }
+
subsegloop.sh = shellfacetraverse(subsegs);
}
@@ -15009,11 +13808,6 @@ void tetgenmesh::mergefacets()
ang = facedihedral(pa, pb, pc, pd);
if (ang > PI) ang = (2 * PI - ang);
if (ang > ang_tol) {
- if (b->verbose > 2) {
- printf(" Merge at segment (%d, %d)-(%d, %d) ang = %g\n",
- pointmark(pa), pointmark(pb), pointmark(pc),
- pointmark(pd), ang / PI * 180.0);
- }
remsegcount++;
ssdissolve(parentsh);
ssdissolve(neighsh);
@@ -15033,7 +13827,6 @@ void tetgenmesh::mergefacets()
lawsonflip(); // Recover Delaunayness.
}
-
if (b->verbose > 1) {
printf(" %d segments are removed.\n", remsegcount);
}
@@ -15063,12 +13856,13 @@ void tetgenmesh::identifypscedges(point *idx2verlist)
int edgemarker;
int idx, i, j;
+ int e1, e2;
+ REAL len;
+
if (!b->quiet) {
printf("Inserting edges ...\n");
}
- //assert(in->numberofedges > 0); // SELF_CHECK
- //assert(in->edgemarkerlist != NULL); // SELF_CHECK
// All identified segments have the initial marker '0'.
// All segments inserted here should have a non-zero marker.
@@ -15079,6 +13873,7 @@ void tetgenmesh::identifypscedges(point *idx2verlist)
for (i = 0; i < in->numberofedges; i++) {
endpts = &(in->edgelist[(i << 1)]);
// Find a face contains the edge.
+ newseg.sh = NULL;
searchsh.sh = NULL;
idx = endpts[0] - in->firstnumber;
for (j = idx2shlist[idx]; j < idx2shlist[idx + 1]; j++) {
@@ -15102,7 +13897,7 @@ void tetgenmesh::identifypscedges(point *idx2verlist)
if (edgemarker == 0) {
edgemarker = 1;
}
- // We should find a subface having this edge.
+
if (searchsh.sh != NULL) {
// Check if this edge is already a segment of the mesh.
sspivot(searchsh, checkseg);
@@ -15114,10 +13909,6 @@ void tetgenmesh::identifypscedges(point *idx2verlist)
// Create a new segment at this edge.
pa = sorg(searchsh);
pb = sdest(searchsh);
- if (b->verbose > 2) {
- printf(" Create a new segment (%d, %d).\n",
- pointmark(pa), pointmark(pb));
- }
makeshellface(subsegs, &newseg);
setshvertices(newseg, pa, pb, NULL);
setshellmark(newseg, edgemarker);
@@ -15129,27 +13920,30 @@ void tetgenmesh::identifypscedges(point *idx2verlist)
spivotself(neighsh); // SELF_CHECK
assert(neighsh.sh == searchsh.sh);
}
- if (!b->psc) {
- setpointtype(pa, RIDGEVERTEX);
- setpointtype(pb, RIDGEVERTEX);
- }
}
} else {
// It is a dangling segment (not belong to any facets).
// Get the two endpoints of this segment.
pa = idx2verlist[endpts[0]];
pb = idx2verlist[endpts[1]];
- if (b->verbose > 2) {
- printf(" Create a new segment (%d, %d) - dangling.\n",
- pointmark(pa), pointmark(pb));
- }
makeshellface(subsegs, &newseg);
setshvertices(newseg, pa, pb, NULL);
setshellmark(newseg, edgemarker);
- //if (!b->psc) {
- setpointtype(pa, RIDGEVERTEX);
- setpointtype(pb, RIDGEVERTEX);
- //}
+ }
+
+ if (newseg.sh != NULL) {
+ if (b->quality && (in->segmentconstraintlist != (REAL *) NULL)) {
+ for (i = 0; i < in->numberofsegmentconstraints; i++) {
+ e1 = (int) in->segmentconstraintlist[i * 3];
+ e2 = (int) in->segmentconstraintlist[i * 3 + 1];
+ if (((pointmark(pa) == e1) && (pointmark(pb) == e2)) ||
+ ((pointmark(pa) == e2) && (pointmark(pb) == e1))) {
+ len = in->segmentconstraintlist[i * 3 + 2];
+ setareabound(newseg, len);
+ break;
+ }
+ }
+ }
}
} // i
@@ -15159,10 +13953,6 @@ void tetgenmesh::identifypscedges(point *idx2verlist)
segloop.sh = shellfacetraverse(subsegs);
while (segloop.sh != NULL) {
if (shellmark(segloop) == 0) {
- if (b->verbose > 2) {
- printf(" Remove a segment (%d, %d).\n",
- pointmark(sorg(segloop)), pointmark(sdest(segloop)));
- }
spivot(segloop, searchsh);
if (searchsh.sh != NULL) {
ssdissolve(searchsh);
@@ -15326,7 +14116,7 @@ void tetgenmesh::meshsurface()
unifysegments();
}
- if (!b->nomerge && !b->nobisect && !b->diagnose) {
+ if (!b->nomergefacet && !b->nobisect && !b->diagnose) {
// Merge adjacent coplanar facets.
mergefacets();
}
@@ -15354,6 +14144,7 @@ void tetgenmesh::meshsurface()
delete conlist;
}
+
///////////////////////////////////////////////////////////////////////////////
// //
// interecursive() Recursively do intersection test on a set of triangles.//
@@ -15442,9 +14233,7 @@ void tetgenmesh::interecursive(shellface** subfacearray, int arraysize,
toright = true;
}
// At least one is true;
-#ifdef SELF_CHECK
assert(!(toleft == false && toright == false));
-#endif
if (toleft) {
leftarray[leftsize] = sface1.sh;
leftsize++;
@@ -15619,7 +14408,7 @@ void tetgenmesh::detectinterfaces()
// //
// markacutevertices() Classify vertices as ACUTEVERTEXs or RIDGEVERTEXs. //
// //
-// Initially all segment vertices have type RIDGEVERTEX. A segment is acute //
+// Initialize all segment vertices's type be RIDGEVERTEX. A segment is acute //
// if there are at least two segments incident at it form an angle less than //
// theta (= 60 degree). //
// //
@@ -15632,19 +14421,16 @@ void tetgenmesh::markacutevertices()
face* segperverlist;
int* idx2seglist;
point pa, pb, pc;
- REAL anglimit, ang;
+ REAL anglimit, sharpanglimit, ang;
bool acuteflag;
- int acutecount;
+ int acutecount, sharpsegcount;
int idx, i, j;
- REAL sharpanglimit;
- int sharpsegcount;
-
if (b->verbose) {
printf(" Marking acute vertices.\n");
}
anglimit = PI / 3.0; // 60 degree.
- sharpanglimit = 10.0 / 180.0 * PI; // 10 degree.
+ sharpanglimit = 5.0 / 180.0 * PI; // 5 degree.
minfaceang = PI; // 180 degree.
acutecount = sharpsegcount = 0;
@@ -15658,22 +14444,15 @@ void tetgenmesh::markacutevertices()
idx = pointmark(pa) - in->firstnumber;
// Mark it if it is an endpoint of some segments.
if (idx2seglist[idx + 1] > idx2seglist[idx]) {
- if (b->psc) {
- // Only test it if it is an input vertex.
- if (pointtype(pa) == FREESEGVERTEX) {
- pa = pointtraverse();
- continue;
- }
- }
+ // It is an endpoint of some segments.
+ setpointtype(pa, RIDGEVERTEX);
acuteflag = false;
// Do a brute-force pair-pair check.
for (i=idx2seglist[idx]; i<idx2seglist[idx + 1]; i++) {
pb = sdest(segperverlist[i]);
- //for (j = i + 1; j < idx2seglist[idx + 1] && !acuteflag; j++) {
for (j = i + 1; j < idx2seglist[idx + 1]; j++) {
pc = sdest(segperverlist[j]);
ang = interiorangle(pa, pb, pc, NULL);
- //acuteflag = ang < anglimit;
if (!acuteflag) {
acuteflag = ang < anglimit;
}
@@ -15688,20 +14467,11 @@ void tetgenmesh::markacutevertices()
if (shelltype(segperverlist[j]) != SHARP) {
setshelltype(segperverlist[j], SHARP);
sharpsegcount++;
- }
+ }
}
} // j
} // i
- if (!acuteflag) {
- if ((idx2seglist[idx + 1] - idx2seglist[idx]) > 4) {
- // There are at least 5 segments shared at this vertices.
- acuteflag = true;
- }
- }
if (acuteflag) {
- if (b->verbose > 2) {
- printf(" Mark %d as ACUTEVERTEX.\n", pointmark(pa));
- }
setpointtype(pa, ACUTEVERTEX);
acutecount++;
}
@@ -15723,34 +14493,6 @@ void tetgenmesh::markacutevertices()
delete [] segperverlist;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// reportselfintersect() Report a self-intersection. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::reportselfintersect(face *checkseg, face *checksh)
-{
- face parentsh;
- point pa, pb, pc, pd, pe;
- point fa, fb;
-
- pa = sorg(*checkseg);
- pb = sdest(*checkseg);
- fa = farsorg(*checkseg);
- fb = farsdest(*checkseg);
-
- pc = sorg(*checksh);
- pd = sdest(*checksh);
- pe = sapex(*checksh);
-
- printf(" !! Detected a self-intersection between:\n");
- printf(" A segment [%d,%d] < [%d,%d], \n", pointmark(pa), pointmark(pb),
- pointmark(fa), pointmark(fb));
- printf(" a subface [%d,%d,%d] in facet #%d.\n", pointmark(pc),
- pointmark(pd), pointmark(pe), shellmark(*checksh));
-
-}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -15771,21 +14513,20 @@ void tetgenmesh::reportselfintersect(face *checkseg, face *checksh)
///////////////////////////////////////////////////////////////////////////////
enum tetgenmesh::interresult
- tetgenmesh::finddirection(triface* searchtet, point endpt, int randflag)
+ tetgenmesh::finddirection(triface* searchtet, point endpt)
{
triface neightet;
point pa, pb, pc, pd;
enum {HMOVE, RMOVE, LMOVE} nextmove;
REAL hori, rori, lori;
+ int t1ver;
int s;
-
// The origin is fixed.
pa = org(*searchtet);
if ((point) searchtet->tet[7] == dummypoint) {
// A hull tet. Choose the neighbor of its base face.
- searchtet->ver = 11;
- fsymself(*searchtet);
+ decode(searchtet->tet[3], *searchtet);
// Reset the origin to be pa.
if ((point) searchtet->tet[4] == pa) {
searchtet->ver = 11;
@@ -15794,7 +14535,7 @@ enum tetgenmesh::interresult
} else if ((point) searchtet->tet[6] == pa) {
searchtet->ver = 7;
} else {
- assert((point) searchtet->tet[7] == pa); // SELF_CHECK
+ assert((point) searchtet->tet[7] == pa);
searchtet->ver = 0;
}
}
@@ -15809,8 +14550,7 @@ enum tetgenmesh::interresult
pc = apex(*searchtet);
if (pc == endpt) {
// pa->pc is the search edge.
- eprevself(*searchtet);
- esymself(*searchtet);
+ eprevesymself(*searchtet);
return ACROSSVERT;
}
@@ -15818,12 +14558,6 @@ enum tetgenmesh::interresult
while (1) {
pd = oppo(*searchtet);
-
- if (b->verbose > 3) {
- printf(" From tet (%d, %d, %d, %d) to %d.\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd), pointmark(endpt));
- }
-
// Check whether the opposite vertex is 'endpt'.
if (pd == endpt) {
// pa->pd is the search edge.
@@ -15846,54 +14580,39 @@ enum tetgenmesh::interresult
hori = orient3d(pa, pb, pc, endpt);
rori = orient3d(pb, pa, pd, endpt);
lori = orient3d(pa, pc, pd, endpt);
- orient3dcount += 3;
// Now decide the tet to move. It is possible there are more than one
- // tet are viable moves. Use the opposite points of thier neighbors
- // to discriminate, i.e., we choose the tet whose opposite point has
- // the shortest distance to 'endpt'.
+ // tets are viable moves. Is so, randomly choose one.
if (hori > 0) {
if (rori > 0) {
if (lori > 0) {
// Any of the three neighbors is a viable move.
- if (0) { // if (!randflag) {
+ s = randomnation(3);
+ if (s == 0) {
+ nextmove = HMOVE;
+ } else if (s == 1) {
+ nextmove = RMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(3); // 's' is in {0,1,2}.
- if (s == 0) {
- nextmove = HMOVE;
- } else if (s == 1) {
- nextmove = RMOVE;
- } else {
- nextmove = LMOVE;
- }
- } // if (randflag)
+ nextmove = LMOVE;
+ }
} else {
// Two tets, below horizon and below right, are viable.
- if (0) { // if (!randflag) {
+ //s = randomnation(2);
+ if (randomnation(2)) {
+ nextmove = HMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(2); // 's' is in {0,1}.
- if (s == 0) {
- nextmove = HMOVE;
- } else {
- nextmove = RMOVE;
- }
- } // if (randflag)
+ nextmove = RMOVE;
+ }
}
} else {
if (lori > 0) {
// Two tets, below horizon and below left, are viable.
- if (0) { // if (!randflag) {
+ //s = randomnation(2);
+ if (randomnation(2)) {
+ nextmove = HMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(2); // 's' is in {0,1}.
- if (s == 0) {
- nextmove = HMOVE;
- } else {
- nextmove = LMOVE;
- }
- } // if (randflag)
+ nextmove = LMOVE;
+ }
} else {
// The tet below horizon is chosen.
nextmove = HMOVE;
@@ -15903,16 +14622,12 @@ enum tetgenmesh::interresult
if (rori > 0) {
if (lori > 0) {
// Two tets, below right and below left, are viable.
- if (0) { // if (!randflag) {
+ //s = randomnation(2);
+ if (randomnation(2)) {
+ nextmove = RMOVE;
} else {
- // Randomly choose a direction.
- s = randomnation(2); // 's' is in {0,1}.
- if (s == 0) {
- nextmove = RMOVE;
- } else {
- nextmove = LMOVE;
- }
- } // if (randflag)
+ nextmove = LMOVE;
+ }
} else {
// The tet below right is chosen.
nextmove = RMOVE;
@@ -15930,8 +14645,7 @@ enum tetgenmesh::interresult
}
if (lori == 0) {
// pa->'endpt' is COLLINEAR with pa->pc.
- eprevself(*searchtet);
- esymself(*searchtet); // [a,c,d]
+ eprevesymself(*searchtet); // // [a,c,d]
return ACROSSVERT;
}
// pa->'endpt' crosses the edge pb->pc.
@@ -15951,8 +14665,7 @@ enum tetgenmesh::interresult
}
if (lori == 0) {
// pa->'endpt' crosses the edge pc->pd.
- eprevself(*searchtet);
- esymself(*searchtet); // face acd
+ eprevesymself(*searchtet); // [a,c,d]
return ACROSSEDGE;
}
// pa->'endpt' crosses the face bcd.
@@ -15972,7 +14685,7 @@ enum tetgenmesh::interresult
fsymself(*searchtet);
enextself(*searchtet);
}
- assert(org(*searchtet) == pa); // SELF_CHECK
+ assert(org(*searchtet) == pa);
pb = dest(*searchtet);
pc = apex(*searchtet);
@@ -15982,25 +14695,22 @@ enum tetgenmesh::interresult
///////////////////////////////////////////////////////////////////////////////
// //
-// scoutsegment() Look for a given segment in the tetrahedralization T. //
+// scoutsegment() Search an edge in the tetrahedralization. //
// //
-// Search an edge in the tetrahedralization that matches the given segmment. //
-// If such an edge exists, the segment is 'locked' at the edge. 'searchtet' //
-// returns this (constrained) edge. Otherwise, the segment is missing. //
+// If the edge is found, it returns SHAREEDGE, and 'searchtet' returns the //
+// edge from startpt to endpt. //
// //
-// The returned value indicates one of the following cases: //
-// - SHAREEDGE, the segment exists and is inserted in T; //
-// - ACROSSEDGE, the segment intersects an edge (in 'searchtet'). //
-// - ACROSSFACE, the segment crosses a face (in 'searchtet'). //
+// If the edge is missing, it returns either ACROSSEDGE or ACROSSFACE, which //
+// indicates that the edge intersects an edge or a face. If 'refpt' is NULL,//
+// 'searchtet' returns the edge or face. If 'refpt' is not NULL, it returns //
+// a vertex which encroaches upon this edge, and 'searchtet' returns a tet //
+// which containing 'refpt'. //
// //
// The following cases can happen when the input PLC is not valid. //
-// - ACROSSVERT, the segment intersects a vertex ('refpt'). //
-// - ACROSSSEG, the segment intersects a segment(returned by 'searchtet'). //
-// - ACROSSSUB, the segment intersects a subface(returned by 'searchtet'). //
-// //
-// If the returned value is ACROSSEDGE or ACROSSFACE, i.e., the segment is //
-// missing, 'refpt' returns the reference point for splitting thus segment, //
-// 'searchtet' returns a tet containing the 'refpt'. //
+// - ACROSSVERT, the edge intersects a vertex return by the origin of //
+// 'searchtet'. //
+// - ACROSSSEG, the edge intersects a segment returned by 'searchtet'. //
+// - ACROSSSUB, the edge intersects a subface returned by 'searchtet'. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -16008,22 +14718,16 @@ enum tetgenmesh::interresult
tetgenmesh::scoutsegment(point startpt, point endpt, triface* searchtet,
point* refpt, arraypool* intfacelist)
{
- triface neightet, reftet;
- face checkseg, checksh;
- point pa, pb, pc, pd;
- badface *bface;
+ point pd;
enum interresult dir;
- REAL angmax, ang;
- long facecount;
- int types[2], poss[4];
- int pos, i, j;
+ int t1ver;
if (b->verbose > 2) {
- printf(" Scout seg (%d, %d).\n", pointmark(startpt), pointmark(endpt));
+ printf(" Scout seg (%d, %d).\n",pointmark(startpt),pointmark(endpt));
}
point2tetorg(startpt, *searchtet);
- dir = finddirection(searchtet, endpt, 0);
+ dir = finddirection(searchtet, endpt);
if (dir == ACROSSVERT) {
pd = dest(*searchtet);
@@ -16032,14 +14736,13 @@ enum tetgenmesh::interresult
return SHAREEDGE;
} else {
// A point is on the path.
- *refpt = pd;
+ // Let the origin of the searchtet be the vertex.
+ enextself(*searchtet);
+ if (refpt) *refpt = pd;
return ACROSSVERT;
}
} // if (dir == ACROSSVERT)
- if (b->verbose > 2) {
- printf(" Seg is missing.\n");
- }
// dir is either ACROSSEDGE or ACROSSFACE.
enextesymself(*searchtet); // Go to the opposite face.
@@ -16047,29 +14750,28 @@ enum tetgenmesh::interresult
if (dir == ACROSSEDGE) {
// Check whether two segments are intersecting.
- tsspivot1(*searchtet, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(*searchtet)) {
return ACROSSSEG;
}
- across_edge_count++;
} else if (dir == ACROSSFACE) {
if (checksubfaceflag) {
// Check whether a segment and a subface are intersecting.
- tspivot(*searchtet, checksh);
- if (checksh.sh != NULL) {
+ if (issubface(*searchtet)) {
return ACROSSSUB;
}
}
}
if (refpt == NULL) {
+ // Do not need a reference point. Return.
return dir;
}
- if (b->verbose > 2) {
- printf(" Scout a ref-point for it.\n");
- }
- facecount = across_face_count;
+ triface neightet, reftet;
+ point pa, pb, pc;
+ REAL angmax, ang;
+ int types[2], poss[4];
+ int pos, i, j;
pa = org(*searchtet);
angmax = interiorangle(pa, startpt, endpt, NULL);
@@ -16091,53 +14793,10 @@ enum tetgenmesh::interresult
// Search intersecting faces along the segment.
while (1) {
- if (intfacelist != NULL) {
- if (dir == ACROSSFACE) {
- // Save the intersecting face.
- intfacelist->newindex((void **) &bface);
- bface->tt = *searchtet;
- bface->forg = org(*searchtet);
- bface->fdest = dest(*searchtet);
- bface->fapex = apex(*searchtet);
- // Save the intersection type (ACROSSFACE or ACROSSEDGE).
- bface->key = (REAL) dir;
- } else { // dir == ACROSSEDGE
- i = 0;
- if (intfacelist->objects > 0l) {
- // Get the last saved one.
- bface = (badface *) fastlookup(intfacelist, intfacelist->objects - 1);
- if (((enum interresult) (int) bface->key) == ACROSSEDGE) {
- // Skip this edge if it is the same as the last saved one.
- if (((bface->forg == org(*searchtet)) &&
- (bface->fdest == dest(*searchtet))) ||
- ((bface->forg == dest(*searchtet)) &&
- (bface->fdest == org(*searchtet)))) {
- i = 1; // Skip this edge.
- }
- }
- }
- if (i == 0) {
- // Save this crossing edge.
- intfacelist->newindex((void **) &bface);
- bface->tt = *searchtet;
- bface->forg = org(*searchtet);
- bface->fdest = dest(*searchtet);
- // bface->fapex = apex(*searchtet);
- // Save the intersection type (ACROSSFACE or ACROSSEDGE).
- bface->key = (REAL) dir;
- }
- }
- }
pd = oppo(*searchtet);
assert(pd != dummypoint); // SELF_CHECK
- if (b->verbose > 3) {
- printf(" Passing face (%d, %d, %d, %d), dir(%d).\n",
- pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd),
- (int) dir);
- }
- across_face_count++;
// Stop if we meet 'endpt'.
if (pd == endpt) break;
@@ -16205,9 +14864,6 @@ enum tetgenmesh::interresult
enextself(neightet);
}
pd = org(neightet);
- if (b->verbose > 2) {
- angmax = interiorangle(pd, startpt, endpt, NULL);
- }
*refpt = pd;
// break;
return ACROSSVERT;
@@ -16222,16 +14878,13 @@ enum tetgenmesh::interresult
if (dir == ACROSSEDGE) {
// Check whether two segments are intersecting.
- tsspivot1(*searchtet, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(*searchtet)) {
return ACROSSSEG;
}
- across_edge_count++;
} else if (dir == ACROSSFACE) {
if (checksubfaceflag) {
// Check whether a segment and a subface are intersecting.
- tspivot(*searchtet, checksh);
- if (checksh.sh != NULL) {
+ if (issubface(*searchtet)) {
return ACROSSSUB;
}
}
@@ -16245,19 +14898,6 @@ enum tetgenmesh::interresult
*refpt = NULL;
}
- // dir is either ACROSSVERT, or ACROSSEDGE, or ACROSSFACE.
- if (b->verbose > 2) {
- if (*refpt != NULL) {
- printf(" Refpt %d (%g), visited %ld faces.\n", pointmark(*refpt),
- angmax / PI * 180.0, across_face_count - facecount);
- } else {
- printf(" No refpt (%g) is found, visited %ld faces.\n",
- angmax / PI * 180.0, across_face_count - facecount);
- }
- }
- if (across_face_count - facecount > across_max_count) {
- across_max_count = across_face_count - facecount;
- }
*searchtet = reftet;
return dir;
@@ -16272,175 +14912,71 @@ enum tetgenmesh::interresult
void tetgenmesh::getsteinerptonsegment(face* seg, point refpt, point steinpt)
{
point ei, ej;
- REAL Li, Lj, L, dj, dr;
- REAL ti = 0.0, tj = 0.0, t;
- int type, eid = 0, i;
-
- REAL diff, stept = 0.0, L1;
- int iter;
-
- ei = sorg(*seg);
- ej = sdest(*seg);
-
-
- if (b->verbose > 2) {
- printf(" Get Steiner point on seg [%d (%c), %d (%c)].\n",
- pointmark(ei), pointtype(ei) == ACUTEVERTEX ? 'A' : 'N',
- pointmark(ej), pointtype(ej) == ACUTEVERTEX ? 'A' : 'N');
- }
-
- if (b->psc) {
- eid = shellmark(*seg);
- if (pointtype(ei) != FREESEGVERTEX) {
- ti = in->getvertexparamonedge(in->geomhandle, pointmark(ei), eid);
- } else {
- ti = pointgeomuv(ei, 0);
- }
- if (pointtype(ej) != FREESEGVERTEX) {
- tj = in->getvertexparamonedge(in->geomhandle, pointmark(ej), eid);
- } else {
- tj = pointgeomuv(ej, 0);
- }
- }
+ REAL Li, Lj, L;
+ REAL t;
+ int i;
- if (refpt != NULL) {
- if (pointtype(ei) == ACUTEVERTEX) {
- if (pointtype(ej) == ACUTEVERTEX) {
- // Choose the vertex which is closer to refpt.
- Li = distance(ei, refpt);
- Lj = distance(ej, refpt);
- if (Li > Lj) {
- // Swap ei and ej;
- sesymself(*seg);
- ei = sorg(*seg);
- ej = sdest(*seg);
- t = ti;
- ti = tj;
- tj = t;
- }
- type = 1;
- } else {
- type = 1;
- }
- } else {
- if (pointtype(ej) == ACUTEVERTEX) {
- type = 1;
- // Swap ei and ej;
- sesymself(*seg);
- ei = sorg(*seg);
- ej = sdest(*seg);
- t = ti;
- ti = tj;
- tj = t;
- } else {
- type = 0;
- }
- }
- } else {
- type = 0;
- }
+ ei = sorg(*seg);
+ ej = sdest(*seg);
- if (type == 1) {
- L = distance(ei, ej);
+
+ if (refpt != NULL) {
+ // Let ei be the closer one to refpt.
Li = distance(ei, refpt);
- // Cut the segment by a sphere centered at ei with radius Li.
- if (b->psc) {
- stept = (tj - ti) / 100.0;
- iter = 0;
- t = ti + (Li / L) * (tj - ti);
- while (1) {
- in->getsteineronedge(in->geomhandle, eid, t, steinpt);
- L1 = distance(steinpt, ei);
- diff = L1 - Li;
- if ((fabs(diff) / L) < 1e-3) {
- break;
- }
- if (diff > 0) {
- t -= stept; // Move it towards ei.
- } else {
- t += stept; // Move it towards ej.
- }
- iter++;
- if (iter > 10) {
- printf("Warning: Get the right Steiner point failed.\n");
- break;
- }
- } // while (1)
- } else {
- t = Li / L;
+ Lj = distance(ej, refpt);
+ if (Li > Lj) {
+ // Swap ei and ej;
+ sesymself(*seg);
+ ei = sorg(*seg);
+ ej = sdest(*seg);
+ L = Li;
+ Li = Lj;
+ Lj = L;
+ }
+ if (pointtype(ei) == ACUTEVERTEX) {
+ // Cut the segment by a sphere centered at ei with radius Li.
+ L = distance(ei, ej);
+ t = Li / L; // t \in (0, 1).
for (i = 0; i < 3; i++) {
steinpt[i] = ei[i] + t * (ej[i] - ei[i]);
}
- }
- // Avoid creating a too short edge.
- dj = distance(steinpt, ej);
- dr = distance(steinpt, refpt);
- if (dj < dr) {
- // Cut the segment by the radius equal to Li / 2.
- if (b->psc) {
- iter = 0;
- t = ti + ((Li / 2.0) / L) * (tj - ti);
- while (1) {
- in->getsteineronedge(in->geomhandle, eid, t, steinpt);
- L1 = distance(steinpt, ei);
- diff = L1 - (Li / 2.0);
- if ((fabs(diff) / L) < 1e-3) {
- break;
- }
- if (diff > 0) {
- t -= stept; // Move it towards ei.
- } else {
- t += stept; // Move it towards ej.
- }
- iter++;
- if (iter > 10) {
- printf("Warning: Get the right Steiner point failed.\n");
- break;
- }
- } // while (1)
- } else {
- t = (Li / 2.0) / L;
+ // Re-use Li and Lj;
+ Li = distance(steinpt, refpt);
+ Lj = distance(steinpt, ej);
+ if (Li > Lj) {
+ // Avoid to create a very short edge at ej.
+ t = 0.5;
for (i = 0; i < 3; i++) {
steinpt[i] = ei[i] + t * (ej[i] - ei[i]);
}
}
- r3count++;
} else {
- r2count++;
+ // Cut the segment by the projection point of refpt.
+ projpt2edge(refpt, ei, ej, steinpt);
+ L = distance(steinpt, refpt);
+ if ((L > distance(steinpt, ei)) || (L > distance(steinpt, ej))) {
+ // Avoid creating a very short edge.
+ t = 0.5;
+ for (i = 0; i < 3; i++) {
+ steinpt[i] = ei[i] + t * (ej[i] - ei[i]);
+ }
+ }
}
} else {
// Split the point at the middle.
- if (b->psc) {
- t = 0.5 * (ti + tj);
- in->getsteineronedge(in->geomhandle, eid, t, steinpt);
- } else {
- t = 0.5;
- for (i = 0; i < 3; i++) {
- steinpt[i] = ei[i] + t * (ej[i] - ei[i]);
- }
+ t = 0.5;
+ for (i = 0; i < 3; i++) {
+ steinpt[i] = ei[i] + t * (ej[i] - ei[i]);
}
- r1count++;
- }
-
- if (b->psc) {
- setpointgeomuv(steinpt, 0, t);
- setpointgeomtag(steinpt, eid);
- }
+ } // if (refpt == NULL)
if (pointtype(steinpt) == UNUSEDVERTEX) {
setpointtype(steinpt, FREESEGVERTEX);
}
-
- if (b->verbose > 2) {
- printf(" Split at t(%g)", t);
- if (b->psc) {
- printf(", ti(%g), tj(%g)", ti, tj);
- }
- printf(".\n");
- }
}
+
///////////////////////////////////////////////////////////////////////////////
// //
// delaunizesegments() Recover segments in a DT. //
@@ -16458,29 +14994,18 @@ void tetgenmesh::getsteinerptonsegment(face* seg, point refpt, point steinpt)
void tetgenmesh::delaunizesegments()
{
triface searchtet, spintet;
- face searchsh, checksh;
- face sseg, checkseg, *psseg;
+ face searchsh;
+ face sseg, *psseg;
point refpt, newpt;
enum interresult dir;
insertvertexflags ivf;
- int loc;
+ int t1ver;
- // For reporting PLC problems.
- point forg1, fdest1; // The 1st segment.
- point forg2, fdest2, fapex2; // The 2nd segment.
-
- // Does this mesh containing subfaces?
- if (checksubfaceflag) {
- ivf.bowywat = 2; // The mesh is a CDT.
- ivf.lawson = 2; // Do flip to recover Delaunayness.
- ivf.validflag = 1; // Validation is needed.
- } else {
- ivf.bowywat = 1; // The mesh is a DT.
- ivf.lawson = 0; // No need to do flip.
- ivf.validflag = 0; // No need to valid the B-W cavity.
- }
- searchsh.sh = NULL;
+ ivf.bowywat = 1; // Use Bowyer-Watson insertion.
+ ivf.assignmeshsize = b->metric;
+ ivf.sloc = (int) ONEDGE; // on 'sseg'.
+ ivf.sbowywat = 1; // Use Bowyer-Watson insertion.
// Loop until 'subsegstack' is empty.
while (subsegstack->objects > 0l) {
@@ -16489,14 +15014,9 @@ void tetgenmesh::delaunizesegments()
psseg = (face *) fastlookup(subsegstack, subsegstack->objects);
sseg = *psseg;
- assert(!sinfected(sseg)); // FOR DEBUG
// Check if this segment has been recovered.
sstpivot1(sseg, searchtet);
if (searchtet.tet != NULL) {
- // FOR DEBUG
- // Check if the tet contains the same segment.
- tsspivot1(searchtet, checkseg);
- assert(checkseg.sh == sseg.sh);
continue; // Not a missing segment.
}
@@ -16505,8 +15025,7 @@ void tetgenmesh::delaunizesegments()
if (dir == SHAREEDGE) {
// Found this segment, insert it.
- tsspivot1(searchtet, checkseg); // SELF_CHECK
- if (checkseg.sh == NULL) {
+ if (!issubseg(searchtet)) {
// Let the segment remember an adjacent tet.
sstbond1(sseg, searchtet);
// Bond the segment to all tets containing it.
@@ -16516,7 +15035,7 @@ void tetgenmesh::delaunizesegments()
fnextself(spintet);
} while (spintet.tet != searchtet.tet);
} else {
- // Collision! Should not happen.
+ // Collision! Maybe a bug.
assert(0);
}
} else {
@@ -16527,145 +15046,30 @@ void tetgenmesh::delaunizesegments()
//setpointtype(newpt, FREESEGVERTEX);
getsteinerptonsegment(&sseg, refpt, newpt);
- // Start searching from the 'searchtet'.
+ // Start searching from 'searchtet'.
ivf.iloc = (int) OUTSIDE;
- //ivf.bowywat;
- //ivf.lawson;
- ivf.rejflag = 0;
- ivf.chkencflag = 0;
- ivf.sloc = ivf.iloc;
- ivf.sbowywat = ivf.bowywat;
- ivf.splitbdflag = 0;
- // ivf.validflag
- ivf.respectbdflag = 0;
- ivf.assignmeshsize = 0;
// Insert the new point into the tetrahedralization T.
// Missing segments and subfaces are queued for recovery.
// Note that T is convex (nonconvex = 0).
- loc = insertvertex(newpt, &searchtet, &searchsh, &sseg, &ivf);
-
- assert(loc != (int) ONVERTEX);
- if (loc != (int) NEARVERTEX) {
+ if (insertpoint(newpt, &searchtet, &searchsh, &sseg, &ivf)) {
// The new point has been inserted.
- if (ivf.lawson > 0) {
- // For CDT, use flips to reocver Delaunayness.
- lawsonflip3d(newpt, ivf.lawson, 0, 0, 0);
- }
- st_segref_count++; //st_segpro_count++;
+ st_segref_count++;
if (steinerleft > 0) steinerleft--;
} else {
- // The new point is either ON or VERY CLOSE to an existing point.
- refpt = point2ppt(newpt);
- printf(" !! Avoid to create a short edge (length = %g)\n",
- distance(newpt, refpt));
-
- // It is probably an input problem. Two possible cases are:
- // (1) An input vertex is very close an input segment; or
- // (2) Two input segments are nearly intersect each other.
- forg1 = farsorg(sseg);
- fdest1 = farsdest(sseg);
-
- if ((pointtype(refpt) == RIDGEVERTEX) ||
- (pointtype(refpt) == ACUTEVERTEX) ||
- (pointtype(refpt) == VOLVERTEX)) {
- // Case (1)
- printf(" !! Point %d is very close to segment (%d, %d).\n",
- pointmark(refpt), pointmark(forg1), pointmark(fdest1));
- } else if (pointtype(refpt) == FREESEGVERTEX) {
- // Case (2). Find a subsegment contain 'refpt'.
- subsegs->traversalinit();
- checkseg.sh = shellfacetraverse(subsegs);
- while (checkseg.sh != NULL) {
- if (((point) checkseg.sh[3] == refpt) ||
- ((point) checkseg.sh[4] == refpt)) break;
- checkseg.sh = shellfacetraverse(subsegs);
- }
- assert(checkseg.sh != NULL);
- checkseg.shver = 0;
- forg2 = farsorg(checkseg);
- fdest2 = farsdest(checkseg);
- printf(" !! Two segments are very close to each other.\n");
- printf(" 1st: (%d, %d), 2nd: (%d, %d)\n", pointmark(forg1),
- pointmark(fdest1), pointmark(forg2), pointmark(fdest2));
- } else {
- // Unknown case
- assert(0);
- }
- // Indicate it may be an input problem.
- printf(" Short edge length bound is: %g. Tolerance is %g.\n",
- b->minedgelength, b->epsilon);
+ assert (ivf.iloc == (enum locateresult) NEARVERTEX);
terminatetetgen(4);
}
} else {
- // The input PLC contains self-intersections.
- if (dir == ACROSSVERT) {
- // refpt is the vertex intersecting the segment.
- forg1 = farsorg(sseg);
- fdest1 = farsdest(sseg);
- if ((pointtype(refpt) == RIDGEVERTEX) ||
- (pointtype(refpt) == ACUTEVERTEX) ||
- (pointtype(refpt) == FACETVERTEX) ||
- (pointtype(refpt) == VOLVERTEX)) {
- printf("Point %d is on segment (%d, %d).\n",
- pointmark(refpt), pointmark(forg1), pointmark(fdest1));
- } else if (pointtype(refpt) == FREESEGVERTEX) {
- // Case (2). Find a subsegment contain 'refpt'.
- subsegs->traversalinit();
- checkseg.sh = shellfacetraverse(subsegs);
- while (checkseg.sh != NULL) {
- if (((point) checkseg.sh[3] == refpt) ||
- ((point) checkseg.sh[4] == refpt)) break;
- checkseg.sh = shellfacetraverse(subsegs);
- }
- assert(checkseg.sh != NULL);
- checkseg.shver = 0;
- forg2 = farsorg(checkseg);
- fdest2 = farsdest(checkseg);
- printf("Two segments intersect.\n");
- printf(" 1st: (%d, %d), 2nd: (%d, %d)", pointmark(forg1),
- pointmark(fdest1), pointmark(forg2), pointmark(fdest2));
- } else if (pointtype(refpt) == FREEFACETVERTEX) {
- assert(0); // Report this case.
- }
- } else if (dir == ACROSSSEG) {
- tsspivot1(searchtet, checkseg);
- if (!b->quiet) {
- printf("Two segments intersect.\n");
- forg1 = farsorg(sseg);
- fdest1 = farsdest(sseg);
- forg2 = farsorg(checkseg);
- fdest2 = farsdest(checkseg);
- printf(" 1st: (%d, %d), 2nd: (%d, %d).\n", pointmark(forg1),
- pointmark(fdest1), pointmark(forg2), pointmark(fdest2));
- }
- } else if (dir == ACROSSSUB) {
- tspivot(searchtet, checksh);
- if (!b->quiet) {
- printf("A segment and a subface intersect.\n");
- forg1 = farsorg(sseg);
- fdest1 = farsdest(sseg);
- forg2 = sorg(checksh);
- fdest2 = sdest(checksh);
- fapex2 = sapex(checksh);
- printf(" Seg: (%d, %d), Sub: (%d, %d, %d).\n",
- pointmark(forg1), pointmark(fdest1),
- pointmark(forg2), pointmark(fdest2), pointmark(fapex2));
- }
- } else {
- // Unknown cases.
- assert(0);
- }
// Indicate it is an input problem.
terminatetetgen(3);
}
}
} // while
-
}
///////////////////////////////////////////////////////////////////////////////
// //
-// scoutsubface() Look for a given subface in the tetrahedralization T. //
+// scoutsubface() Search subface in the tetrahedralization. //
// //
// 'searchsh' is searched in T. If it exists, it is 'locked' at the face in //
// T. 'searchtet' refers to the face. Otherwise, it is missing. //
@@ -16681,27 +15085,25 @@ enum tetgenmesh::interresult
tetgenmesh::scoutsubface(face* searchsh, triface* searchtet)
{
triface spintet;
- face checksh;
point pa, pb, pc;
enum interresult dir;
+ int t1ver;
pa = sorg(*searchsh);
pb = sdest(*searchsh);
- if (b->verbose > 2) {
- printf(" Scout subface (%d, %d, %d).\n", pointmark(pa), pointmark(pb),
- pointmark(sapex(*searchsh)));
- }
// Get a tet whose origin is a.
point2tetorg(pa, *searchtet);
// Search the edge [a,b].
- dir = finddirection(searchtet, pb, 0);
+ dir = finddirection(searchtet, pb);
if (dir == ACROSSVERT) {
// Check validity of a PLC.
if (dest(*searchtet) != pb) {
- // A vertex lies on the search edge. Return it.
+ // A vertex lies on the search edge.
enextself(*searchtet);
+ // It is possible a PLC self-intersection problem.
+ terminatetetgen(3);
return TOUCHEDGE;
}
// The edge exists. Check if the face exists.
@@ -16711,8 +15113,7 @@ enum tetgenmesh::interresult
while (1) {
if (apex(spintet) == pc) {
// Found a face matching to 'searchsh'!
- tspivot(spintet, checksh);
- if (checksh.sh == NULL) {
+ if (!issubface(spintet)) {
// Insert 'searchsh'.
tsbond(spintet, *searchsh);
fsymself(spintet);
@@ -16722,6 +15123,8 @@ enum tetgenmesh::interresult
return SHAREFACE;
} else {
// Another subface is already inserted.
+ face checksh;
+ tspivot(spintet, checksh);
assert(checksh.sh != searchsh->sh); // SELF_CHECK
// This is possibly an input problem, i.e., two facets overlap.
// Report this problem and exit.
@@ -16738,47 +15141,39 @@ enum tetgenmesh::interresult
}
// dir is either ACROSSEDGE or ACROSSFACE.
- return dir; //ACROSSTET;
+ return dir;
}
///////////////////////////////////////////////////////////////////////////////
// //
-// formmissingregion() Form the missing region of a missing subface. //
+// formregion() Form the missing region of a missing subface. //
// //
// 'missh' is a missing subface. From it we form a missing region R which is //
-// a collection of missing subfaces connected through adjacent edges. //
-// //
-// The missing region R is returned in the array 'missingshs'. All subfaces //
-// in R are oriented as 'missh'. The array 'missingshverts' returns all ver- //
-// tices of R. All subfaces and vertices of R are marktested. //
+// a connected region formed by a set of missing subfaces of a facet. //
+// Comment: There should be no segment inside R. //
// //
-// 'adjtets' returns a list of tetrahedra adjacent to R. They are used to //
-// search a crossing tetrahedron of R. //
-// //
-// Many ways are possible to form the missing region. The method used here //
-// is to search missing edges in R. Starting from 'missh', its three edges //
-// are checked. If one of the edges is missing, then the adjacent subface at //
-// this edge is also missing. It is added to the array. By an incrementally //
-// broad-first searching, we can find all subfaces of R. //
+// 'missingshs' returns the list of subfaces in R. All subfaces in this list //
+// are oriented as the 'missh'. 'missingshbds' returns the list of boundary //
+// edges (tetrahedral handles) of R. 'missingshverts' returns all vertices //
+// of R. They are all pmarktested. //
// //
+// Except the first one (which is 'missh') in 'missingshs', each subface in //
+// this list represents an internal edge of R, i.e., it is missing in the //
+// tetrahedralization. Since R may contain interior vertices, not all miss- //
+// ing edges can be found by this way. //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::formmissingregion(face* missh, arraypool* missingshs,
- arraypool* missingshbds,
- arraypool* missingshverts,
- arraypool* adjtets)
+void tetgenmesh::formregion(face* missh, arraypool* missingshs,
+ arraypool* missingshbds, arraypool* missingshverts)
{
- triface searchtet, *parytet;
+ triface searchtet, spintet;
face neighsh, *parysh;
+ face neighseg, fakeseg;
point pa, pb, *parypt;
enum interresult dir;
+ int t1ver;
int i, j;
- if (b->verbose > 2) {
- printf(" Form missing region from subface (%d, %d, %d)\n",
- pointmark(sorg(*missh)), pointmark(sdest(*missh)),
- pointmark(sapex(*missh)));
- }
smarktest(*missh);
missingshs->newindex((void **) &parysh);
*parysh = *missh;
@@ -16789,43 +15184,22 @@ void tetgenmesh::formmissingregion(face* missh, arraypool* missingshs,
for (j = 0; j < 3; j++) {
pa = sorg(*missh);
pb = sdest(*missh);
- // Get a tet whose origin is a.
point2tetorg(pa, searchtet);
- // Search the edge [a,b].
- dir = finddirection(&searchtet, pb, 0);
+ dir = finddirection(&searchtet, pb);
if (dir != ACROSSVERT) {
// This edge is missing. Its neighbor is a missing subface.
spivot(*missh, neighsh);
- assert(neighsh.sh != NULL);
if (!smarktested(neighsh)) {
// Adjust the face orientation.
- if (sorg(neighsh) != pb) {
- sesymself(neighsh);
- }
- if (b->verbose > 3) {
- printf(" Add a missing subface (%d, %d, %d)\n",
- pointmark(pb), pointmark(pa), pointmark(sapex(neighsh)));
- }
+ if (sorg(neighsh) != pb) sesymself(neighsh);
smarktest(neighsh);
missingshs->newindex((void **) &parysh);
*parysh = neighsh;
}
} else {
- if (dest(searchtet) == pb) {
- // Remember an existing edge for searching the first crossing tet.
- adjtets->newindex((void **) &parytet);
- *parytet = searchtet;
- // Found an existing edge, it must be a boundary edge of R.
- if (b->verbose > 3) {
- printf(" -- A boundary edge (%d, %d)\n", pointmark(pa),
- pointmark(pb));
- }
- missingshbds->newindex((void **) &parysh);
- *parysh = *missh; // It is only queued once.
- } else {
- // The input PLC has problem.
- //assert(0);
- terminatetetgen(3);
+ if (dest(searchtet) != pb) {
+ // This might be a self-intersection problem.
+ terminatetetgen(3);
}
}
// Collect the vertices of R.
@@ -16838,57 +15212,86 @@ void tetgenmesh::formmissingregion(face* missh, arraypool* missingshs,
} // j
} // i
- if (b->verbose > 2) {
- printf(" Region has: %ld subfaces, %ld vertices\n",
- missingshs->objects, missingshverts->objects);
- }
+ // Get the boundary edges of R.
+ for (i = 0; i < missingshs->objects; i++) {
+ missh = (face *) fastlookup(missingshs, i);
+ for (j = 0; j < 3; j++) {
+ spivot(*missh, neighsh);
+ if ((neighsh.sh == NULL) || !smarktested(neighsh)) {
+ // A boundary edge of R.
+ // Let the segment point to the adjacent tet.
+ point2tetorg(sorg(*missh), searchtet);
+ finddirection(&searchtet, sdest(*missh));
+ missingshbds->newindex((void **) &parysh);
+ *parysh = *missh;
+ // Check if this edge is a segment.
+ sspivot(*missh, neighseg);
+ if (neighseg.sh == NULL) {
+ // Temporarily create a segment at this edge.
+ makeshellface(subsegs, &fakeseg);
+ setsorg(fakeseg, sorg(*missh));
+ setsdest(fakeseg, sdest(*missh));
+ sinfect(fakeseg); // Mark it as faked.
+ // Connect it to all tets at this edge.
+ spintet = searchtet;
+ while (1) {
+ tssbond1(spintet, fakeseg);
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) break;
+ }
+ neighseg = fakeseg;
+ }
+ // Let the segment and the boundary edge point to each other.
+ ssbond(*missh, neighseg);
+ sstbond1(neighseg, searchtet);
+ }
+ senextself(*missh);
+ } // j
+ } // i
- if (missingshs->objects > maxregionsize) {
- maxregionsize = missingshs->objects;
- }
// Unmarktest collected missing subfaces.
for (i = 0; i < missingshs->objects; i++) {
- missh = (face *) fastlookup(missingshs, i);
- sunmarktest(*missh);
+ parysh = (face *) fastlookup(missingshs, i);
+ sunmarktest(*parysh);
}
-
- // Comment: All vertices in R are pmarktested.
}
-
-
///////////////////////////////////////////////////////////////////////////////
// //
// scoutcrossedge() Search an edge that crosses the missing region. //
// //
+// Return 1 if a crossing edge is found. It is returned by 'crosstet'. More- //
+// over, the edge is oriented such that its origin lies below R. Return 0 //
+// if no such edge is found. //
+// //
// Assumption: All vertices of the missing region are marktested. //
// //
///////////////////////////////////////////////////////////////////////////////
-int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
+int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* missingshbds,
arraypool* missingshs)
{
- triface *searchtet, spintet;
+ triface searchtet, spintet;
face *parysh;
- face checkseg;
+ face neighseg;
point pa, pb, pc, pd, pe;
enum interresult dir;
REAL ori;
int types[2], poss[4];
int searchflag, interflag;
+ int t1ver;
int i, j;
- if (b->verbose > 2) {
- printf(" Search a crossing edge.\n");
- }
searchflag = 0;
- for (j = 0; j < adjtets->objects && !searchflag; j++) {
- searchtet = (triface *) fastlookup(adjtets, j);
+ for (j = 0; j < missingshbds->objects && !searchflag; j++) {
+ parysh = (face *) fastlookup(missingshbds, j);
+ sspivot(*parysh, neighseg);
+ sstpivot1(neighseg, searchtet);
interflag = 0;
// Let 'spintet' be [#,#,d,e] where [#,#] is the boundary edge of R.
- spintet = *searchtet;
+ spintet = searchtet;
while (1) {
pd = apex(spintet);
pe = oppo(spintet);
@@ -16902,7 +15305,7 @@ int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
pa = sorg(*parysh);
pb = sdest(*parysh);
pc = sapex(*parysh);
- interflag = tri_edge_test(pa, pb, pc, pd, pe, NULL, 1, types, poss);
+ interflag=tri_edge_test(pa, pb, pc, pd, pe, NULL, 1, types, poss);
if (interflag > 0) {
if (interflag == 2) {
// They intersect at a single point.
@@ -16910,13 +15313,12 @@ int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
if ((dir == ACROSSFACE) || (dir == ACROSSEDGE)) {
//pos = poss[0];
// Go to the crossing edge [d,e,#,#].
- eprev(spintet, crosstet);
- esymself(crosstet);
- enextself(crosstet); // [d,e,#,#].
+ edestoppo(spintet, crosstet); // // [d,e,#,#].
// Check if it is a segment.
- tsspivot1(crosstet, checkseg);
- if (checkseg.sh != NULL) {
- reportselfintersect(&checkseg, parysh);
+ if (issubseg(crosstet)) {
+ //face checkseg;
+ //tsspivot1(crosstet, checkseg);
+ //reportselfintersect(&checkseg, parysh);
terminatetetgen(3);
}
// Adjust the edge such that d lies below [a,b,c].
@@ -16925,21 +15327,7 @@ int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
if (ori < 0) {
esymself(crosstet);
}
- if (b->verbose > 2) {
- printf(" Found edge (%d, %d) intersect", pointmark(pd),
- pointmark(pe));
- printf(" face (%d, %d, %d)\n", pointmark(pa), pointmark(pb),
- pointmark(pc));
- }
- // Save the corners of this subface.
- plane_pa = pa;
- plane_pb = pb;
- plane_pc = pc;
searchflag = 1;
- } else {
- // An improper intersection type.
- // Maybe it is a PLC problem.
- // At the moment, just ignore it.
}
}
break;
@@ -16951,11 +15339,10 @@ int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
if (interflag > 0) break;
// Go to the next tetrahedron.
fnextself(spintet);
- if (spintet.tet == searchtet->tet) break;
+ if (spintet.tet == searchtet.tet) break;
} // while (1)
} // j
- adjtets->restart();
return searchflag;
}
@@ -16969,23 +15356,6 @@ int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
// #] which intersects R in its interior, where the edge [d,e] intersects R, //
// and d lies below R. //
// //
-// By knowing a crossing edge [d,e], all tetrahedra sharing at [d,e] must //
-// cross R. They are added into the list 'crosstets'. From this set of tets, //
-// new crossing edges (if there exist) can be detected. The key is how to //
-// detect them correctly. The approach used here is described as follows: //
-// Suppose [d,e,a,b] is a crossing tet, where [d,e] intersects R and d lies //
-// below R. We look at the face [d,e,a]. If the apex a is not pmarktested, //
-// i.e., it is not a vertex of R, then either edge [e,a] or [a,d] intersects //
-// R. A simple way is to perform above/below test between [a] and R. But it //
-// is not clear which subface of R is the best for this test. Also, this is //
-// not safe when R is not strictly planar. A second way is to test if [e,a] //
-// intersects one of the subfaces of R. If an intersection is found, then [e,//
-// a] is a crossing edge. Otherwise, the edge [a,d] must be a crossing edge //
-// of R. NOTE: This statement is correct if the input PLC is correct. We can //
-// also detect the incorrectness of the input, e.g., if [a] only touches a //
-// subface of R. The second approach is implemented here. It is slow, but is //
-// more robust. //
-// //
// 'crosstets' returns the set of crossing tets. Every tet in it has the //
// form [d,e,#,#] where [d,e] is a crossing edge, and d lies below R. The //
// set of tets form the cavity C, which is divided into two parts by R, one //
@@ -16994,13 +15364,6 @@ int tetgenmesh::scoutcrossedge(triface& crosstet, arraypool* adjtets,
// in the top part of C, and so does 'botpoints'. Both 'toppoints' and //
// 'botpoints' contain vertices of R. //
// //
-// NOTE: 'toppoints' may contain points which are not vertices of any top //
-// faces, and so may 'botpoints'. Such points may belong to other facets and //
-// need to be present after the recovery of this cavity (P1029.poly). //
-// //
-// A pair of boundary faces: 'firsttopface' and 'firstbotface', are saved. //
-// They share the same edge in the boundary of the missing region. //
-// //
// Important: This routine assumes all vertices of the facet containing this //
// subface are marked, i.e., pmarktested(p) returns true. //
// //
@@ -17011,27 +15374,22 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
arraypool* botfaces, arraypool* toppoints,
arraypool* botpoints)
{
- arraypool *crossedges, *testededges;
+ arraypool *crossedges;
triface spintet, neightet, *parytet;
- face checksh, *parysh = NULL;
- face checkseg; // *paryseg;
+ face *parysh = NULL;
point pa, pd, pe, *parypt;
enum interresult dir;
- //REAL ori;
- //REAL elen[3];
bool testflag, invalidflag;
int types[2], poss[4];
+ int t1ver;
int i, j, k;
// Temporarily re-use 'topfaces' for all crossing edges.
crossedges = topfaces;
- // Temporarily re-use 'botfaces' for all tested edges.
- testededges = botfaces; // Only used by 'b->psc'.
if (b->verbose > 2) {
- printf(" Form the cavity of missing region.\n");
+ printf(" Form the cavity of a missing region.\n");
}
- missingsubfacecount += missingshs->objects;
// Mark this edge to avoid testing it later.
markedge(*searchtet);
crossedges->newindex((void **) &parytet);
@@ -17042,22 +15400,18 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
// Collect all crossing tets. Each cross tet is saved in the standard
// form [d,e,#,#], where [d,e] is a corossing edge, d lies below R.
// NEITHER d NOR e is a vertex of R (!pmarktested).
- // NOTE: hull tets may be collected. See fig/dump-cavity-case2a(b).lua.
- // Make sure that neither d nor e is dummypoint.
for (i = 0; i < crossedges->objects; i++) {
// Get a crossing edge [d,e,#,#].
searchtet = (triface *) fastlookup(crossedges, i);
// Sort vertices into the bottom and top arrays.
pd = org(*searchtet);
- assert(!pmarktested(pd)); // pd is not on R.
if (!pinfected(pd)) {
pinfect(pd);
botpoints->newindex((void **) &parypt);
*parypt = pd;
}
pe = dest(*searchtet);
- assert(!pmarktested(pe)); // pe is not on R.
if (!pinfected(pe)) {
pinfect(pe);
toppoints->newindex((void **) &parypt);
@@ -17068,11 +15422,6 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
spintet = *searchtet;
while (1) {
if (!infected(spintet)) {
- if (b->verbose > 3) {
- printf(" Add a crossing tet (%d, %d, %d, %d)\n",
- pointmark(org(spintet)), pointmark(dest(spintet)),
- pointmark(apex(spintet)), pointmark(oppo(spintet)));
- }
infect(spintet);
crosstets->newindex((void **) &parytet);
*parytet = spintet;
@@ -17088,10 +15437,10 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
// spintet is [d,e,a,#], where d lies below R, and e lies above R.
pa = apex(spintet);
if (pa != dummypoint) {
- if (!pmarktested(pa) || b->psc) {
- // There exists a crossing edge, either [e,a] or [a,d]. First check
- // if the crossing edge has already be added. This is to check if
- // a tetrahedron at this edge is marked.
+ if (!pmarktested(pa)) {
+ // There exists a crossing edge, either [e,a] or [a,d]. First check
+ // if the crossing edge has already be added, i.e., check if a
+ // tetrahedron at this edge is marked.
testflag = true;
for (j = 0; j < 2 && testflag; j++) {
if (j == 0) {
@@ -17117,12 +15466,8 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
pe = dest(spintet);
for (k = 0; k < missingshs->objects; k++) {
parysh = (face *) fastlookup(missingshs, k);
- plane_pa = sorg(*parysh);
- plane_pb = sdest(*parysh);
- plane_pc = sapex(*parysh);
- // Test if this face intersects [e,a].
- if (tri_edge_test(plane_pa, plane_pb, plane_pc, pe, pa,
- NULL, 1, types, poss)) {
+ if (tri_edge_test(sorg(*parysh), sdest(*parysh), sapex(*parysh),
+ pe, pa, NULL, 1, types, poss)) {
// Found intersection. 'a' lies below R.
enext(spintet, neightet);
dir = (enum interresult) types[0];
@@ -17134,9 +15479,8 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
}
break;
}
- // Test if this face intersects [a,d].
- if (tri_edge_test(plane_pa, plane_pb, plane_pc, pa, pd,
- NULL, 1, types, poss)) {
+ if (tri_edge_test(sorg(*parysh), sdest(*parysh), sapex(*parysh),
+ pa, pd, NULL, 1, types, poss)) {
// Found intersection. 'a' lies above R.
eprev(spintet, neightet);
dir = (enum interresult) types[0];
@@ -17152,78 +15496,56 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
if (k < missingshs->objects) {
// Found a pair of triangle - edge interseciton.
if (invalidflag) {
- if (b->verbose > 2) {
- printf(" A non-valid subface - edge intersection\n");
+ if (!b->quiet) {
+ printf("Warning: A non-valid facet - edge intersection\n");
printf(" subface: (%d, %d, %d) edge: (%d, %d)\n",
- pointmark(plane_pa), pointmark(plane_pb),
- pointmark(plane_pc), pointmark(org(neightet)),
+ pointmark(sorg(*parysh)), pointmark(sdest(*parysh)),
+ pointmark(sapex(*parysh)), pointmark(org(neightet)),
pointmark(dest(neightet)));
}
// It may be a PLC problem.
terminatetetgen(3);
- } else if (b->psc) {
- if (pmarktested(pa)) {
- // The intersection is invalid.
- if (b->verbose > 2) {
- printf(" A non-valid subface - edge intersection\n");
- printf(" subface: (%d, %d, %d) edge: (%d, %d)\n",
- pointmark(plane_pa), pointmark(plane_pb),
- pointmark(plane_pc), pointmark(org(neightet)),
- pointmark(dest(neightet)));
- }
- // Split the subface intersecting this edge.
- recentsh = *parysh;
- recenttet = neightet; // For point location.
- invalidflag = 1;
- break;
- } // if (pmarktested(pa))
- } // if (b->psc)
+ }
// Adjust the edge direction, so that its origin lies below R,
// and its destination lies above R.
esymself(neightet);
// Check if this edge is a segment.
- tsspivot1(neightet, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(neightet)) {
// Invalid PLC!
- reportselfintersect(&checkseg, parysh);
+ //face checkseg;
+ //tsspivot1(neightet, checkseg);
+ //reportselfintersect(&checkseg, parysh);
terminatetetgen(3);
}
- if (b->verbose > 3) {
- printf(" Add a crossing edge (%d, %d)\n",
- pointmark(org(neightet)), pointmark(dest(neightet)));
- }
// Mark this edge to avoid testing it again.
markedge(neightet);
crossedges->newindex((void **) &parytet);
*parytet = neightet;
} else {
// No intersection is found. It may be a PLC problem.
- //assert(b->psc);
- // Mark this edge to avoid testing it again.
- //markedge(neightet);
- //testededges->newindex((void **) &parytet);
- //*parytet = neightet;
invalidflag = 1;
// Split the subface intersecting [d,e].
for (k = 0; k < missingshs->objects; k++) {
parysh = (face *) fastlookup(missingshs, k);
- plane_pa = sorg(*parysh);
- plane_pb = sdest(*parysh);
- plane_pc = sapex(*parysh);
// Test if this face intersects [e,a].
- if (tri_edge_test(plane_pa, plane_pb, plane_pc, pd, pe,
- NULL, 1, types, poss)) {
+ if (tri_edge_test(sorg(*parysh),sdest(*parysh),sapex(*parysh),
+ pd, pe, NULL, 1, types, poss)) {
break;
}
} // k
- assert(k < missingshs->objects);
+ if (k == missingshs->objects) {
+ // Not found such an edge.
+ // Arbitrarily choose an edge (except the first) to split.
+ k = randomnation(missingshs->objects - 1);
+ parysh = (face *) fastlookup(missingshs, k + 1);
+ }
recentsh = *parysh;
recenttet = spintet; // For point location.
break; // the while (1) loop
} // if (k == missingshs->objects)
} // if (testflag)
- } // if (!pmarktested(pa) || b->psc)
- }
+ } // if (!pmarktested(pa) || b->psc)
+ } // if (pa != dummypoint)
// Go to the next crossing tet.
fnextself(spintet);
if (spintet.tet == searchtet->tet) break;
@@ -17238,7 +15560,6 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
printf(" Formed cavity: %ld (%ld) cross tets (edges).\n",
crosstets->objects, crossedges->objects);
}
- crossingtetcount += crosstets->objects;
// Unmark all marked edges.
for (i = 0; i < crossedges->objects; i++) {
@@ -17248,17 +15569,6 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
}
crossedges->restart();
- if (b->psc) {
- // Unmark all marked edges.
- for (i = 0; i < testededges->objects; i++) {
- searchtet = (triface *) fastlookup(testededges, i);
- assert(edgemarked(*searchtet)); // SELF_CHECK
- unmarkedge(*searchtet);
- }
- testededges->restart();
- } else { // only p->plc
- assert(testededges->objects == 0l);
- }
if (invalidflag) {
// Unmark all collected tets.
@@ -17278,37 +15588,13 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
crosstets->restart();
botpoints->restart();
toppoints->restart();
+
+ // Randomly split an interior edge of R.
+ i = randomnation(missingshs->objects - 1);
+ recentsh = * (face *) fastlookup(missingshs, i);
return false;
}
- // Find a pair of cavity boundary faces from the top and bottom sides of
- // the facet each, and they share the same edge. Save them in the
- // global variables: firsttopface, firstbotface. They will be used in
- // fillcavity() for gluing top and bottom new tets.
- for (i = 0; i < crosstets->objects; i++) {
- searchtet = (triface *) fastlookup(crosstets, i);
- // Crosstet is [d,e,a,b].
- enextesym(*searchtet, spintet);
- eprevself(spintet); // spintet is [b,a,e,d]
- fsym(spintet, neightet); // neightet is [a,b,e,#]
- if (!infected(neightet)) {
- // A top face.
- firsttopface = neightet;
- } else {
- continue; // Go to the next cross tet.
- }
- eprevesym(*searchtet, spintet);
- enextself(spintet); // spintet is [a,b,d,e]
- fsym(spintet, neightet); // neightet is [b,a,d,#]
- if (!infected(neightet)) {
- // A bottom face.
- firstbotface = neightet;
- } else {
- continue;
- }
- break;
- } // i
- assert(i < crosstets->objects); // SELF_CHECK
// Collect the top and bottom faces and the middle vertices. Since all top
// and bottom vertices have been infected. Uninfected vertices must be
@@ -17325,16 +15611,14 @@ bool tetgenmesh::formcavity(triface* searchtet, arraypool* missingshs,
for (i = 0; i < crosstets->objects; i++) {
searchtet = (triface *) fastlookup(crosstets, i);
// searchtet is [d,e,a,b].
- enextesym(*searchtet, spintet);
- eprevself(spintet); // spintet is [b,a,e,d]
+ eorgoppo(*searchtet, spintet);
fsym(spintet, neightet); // neightet is [a,b,e,#]
if (!infected(neightet)) {
// A top face.
topfaces->newindex((void **) &parytet);
*parytet = neightet;
- }
- eprevesym(*searchtet, spintet);
- enextself(spintet); // spintet is [a,b,d,e]
+ }
+ edestoppo(*searchtet, spintet);
fsym(spintet, neightet); // neightet is [b,a,d,#]
if (!infected(neightet)) {
// A bottom face.
@@ -17399,19 +15683,17 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
arraypool *cavshells, arraypool *newtets,
arraypool *crosstets, arraypool *misfaces)
{
- triface searchtet, neightet, spintet, *parytet, *parytet1;
- face checksh, tmpsh, *parysh;
- face checkseg;
+ triface searchtet, neightet, *parytet, *parytet1;
+ face tmpsh, *parysh;
point pa, pb, pc, pd, pt[3], *parypt;
enum interresult dir;
insertvertexflags ivf;
- REAL ori; //, ang, len;
+ REAL ori;
long baknum, bakhullsize;
int bakchecksubsegflag, bakchecksubfaceflag;
- //int iloc;
+ int t1ver;
int i, j;
-
if (b->verbose > 2) {
printf(" Delaunizing cavity: %ld points, %ld faces.\n",
cavpoints->objects, cavfaces->objects);
@@ -17425,31 +15707,38 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
checksubsegflag = 0;
checksubfaceflag = 0;
b->verbose--; // Suppress informations for creating Delaunay tetra.
- b->plc = 0; // Do not do unifypoint();
+ b->plc = 0; // Do not check near vertices.
+
+ ivf.bowywat = 1; // Use Bowyer-Watson algorithm.
// Get four non-coplanar points (no dummypoint).
- parytet = (triface *) fastlookup(cavfaces, 0);
- pa = org(*parytet);
- pb = dest(*parytet);
- pc = apex(*parytet);
+ pa = pb = pc = NULL;
+ for (i = 0; i < cavfaces->objects; i++) {
+ parytet = (triface *) fastlookup(cavfaces, i);
+ parytet->ver = epivot[parytet->ver];
+ if (apex(*parytet) != dummypoint) {
+ pa = org(*parytet);
+ pb = dest(*parytet);
+ pc = apex(*parytet);
+ break;
+ }
+ }
pd = NULL;
- for (i = 1; i < cavfaces->objects; i++) {
+ for (; i < cavfaces->objects; i++) {
parytet = (triface *) fastlookup(cavfaces, i);
pt[0] = org(*parytet);
pt[1] = dest(*parytet);
pt[2] = apex(*parytet);
for (j = 0; j < 3; j++) {
if (pt[j] != dummypoint) { // Do not include a hull point.
- // if (!pinfected(pt[j])) {
- ori = orient3d(pa, pb, pc, pt[j]);
- if (ori != 0) {
- pd = pt[j];
- if (ori > 0) { // Swap pa and pb.
- pt[j] = pa; pa = pb; pb = pt[j];
- }
- break;
+ ori = orient3d(pa, pb, pc, pt[j]);
+ if (ori != 0) {
+ pd = pt[j];
+ if (ori > 0) { // Swap pa and pb.
+ pt[j] = pa; pa = pb; pb = pt[j];
}
- // }
+ break;
+ }
}
}
if (pd != NULL) break;
@@ -17462,11 +15751,9 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
// Incrementally insert the vertices (duplicated vertices are ignored).
for (i = 0; i < cavpoints->objects; i++) {
pt[0] = * (point *) fastlookup(cavpoints, i);
- assert(pt[0] != dummypoint); // SELF_CHECK
searchtet = recenttet;
ivf.iloc = (int) OUTSIDE;
- ivf.bowywat = 1;
- insertvertex(pt[0], &searchtet, NULL, NULL, &ivf);
+ insertpoint(pt[0], &searchtet, NULL, NULL, &ivf);
}
if (b->verbose > 2) {
@@ -17481,10 +15768,7 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
parytet = (triface *) fastlookup(cavfaces, i);
// Skip an interior face (due to the enlargement of the cavity).
if (infected(*parytet)) continue;
- // This face may contain dummypoint (See fig/dum-cavity-case2).
- // If so, dummypoint must be its apex.
- j = (parytet->ver & 3); // j is the face number.
- parytet->ver = epivot[j]; // [4,5,2,11]
+ parytet->ver = epivot[parytet->ver];
pt[0] = org(*parytet);
pt[1] = dest(*parytet);
pt[2] = apex(*parytet);
@@ -17495,38 +15779,21 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
searchtet.tet = NULL;
dir = scoutsubface(&tmpsh, &searchtet);
if (dir == SHAREFACE) {
- // Inserted. Make sure that tmpsh connects an interior tet of C.
- stpivot(tmpsh, neightet);
- // neightet and tmpsh refer to the same edge [pt[0], pt[1]].
- // If the origin of neightet is pt[1], it is inside.
- if (org(neightet) != pt[1]) {
- fsymself(neightet);
- assert(org(neightet) == pt[1]); // SELF_CHECK
- // Make sure that tmpsh is connected with an interior tet.
- sesymself(tmpsh);
- tsbond(neightet, tmpsh);
- }
- assert(dest(neightet) == pt[0]); // SELF_CHECK
- } else if (dir == COLLISIONFACE) {
- // This case is not possible anymore. 2010-02-01
- assert(0);
- } else {
- if (b->verbose > 2) {
- printf(" bdry face (%d, %d, %d) -- %d is missing\n",
- pointmark(pt[0]), pointmark(pt[1]), pointmark(pt[2]), i);
- }
+ // Inserted! 'tmpsh' must face toward the inside of the cavity.
+ // Remember the boundary tet (outside the cavity) in tmpsh
+ // (use the adjacent tet slot).
+ tmpsh.sh[0] = (shellface) encode(*parytet);
+ // Save this subface.
+ cavshells->newindex((void **) &parysh);
+ *parysh = tmpsh;
+ }
+ else {
+ // This boundary face is missing.
shellfacedealloc(subfaces, tmpsh.sh);
// Save this face in list.
misfaces->newindex((void **) &parytet1);
*parytet1 = *parytet;
- continue;
}
- // Remember the boundary tet (outside the cavity) in tmpsh
- // (use the adjacent tet slot).
- tmpsh.sh[0] = (shellface) encode(*parytet);
- // Save this subface.
- cavshells->newindex((void **) &parysh);
- *parysh = tmpsh;
} // i
if (misfaces->objects > 0) {
@@ -17566,11 +15833,7 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
if (!pinfected(pd)) {
searchtet = recenttet;
ivf.iloc = (int) OUTSIDE;
- ivf.bowywat = 1;
- insertvertex(pd, &searchtet, NULL, NULL, &ivf);
- if (b->verbose > 2) {
- printf(" Add point %d into list.\n", pointmark(pd));
- }
+ insertpoint(pd, &searchtet, NULL, NULL, &ivf);
pinfect(pd);
cavpoints->newindex((void **) &parypt);
*parypt = pd;
@@ -17580,15 +15843,9 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
esym(*parytet, neightet);
fsymself(neightet);
if (!infected(neightet)) {
- if (b->verbose > 2) {
- printf(" Add a cavface (%d, %d, %d).\n",
- pointmark(org(neightet)), pointmark(dest(neightet)),
- pointmark(apex(neightet)));
- }
cavfaces->newindex((void **) &parytet1);
*parytet1 = neightet;
- } else {
- }
+ }
enextself(*parytet);
} // j
} // if (!infected(parytet))
@@ -17614,8 +15871,8 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
*parytet = recenttet;
for (i = 0; i < newtets->objects; i++) {
searchtet = * (triface *) fastlookup(newtets, i);
- for (searchtet.ver = 0; searchtet.ver < 4; searchtet.ver++) {
- fsym(searchtet, neightet);
+ for (j = 0; j < 4; j++) {
+ decode(searchtet.tet[j], neightet);
if (!marktested(neightet)) {
marktest(neightet);
newtets->newindex((void **) &parytet);
@@ -17627,9 +15884,6 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
cavpoints->restart();
cavfaces->restart();
- if (cavshells->objects > maxcavsize) {
- maxcavsize = cavshells->objects;
- }
if (crosstets->objects > baknum) {
// The cavity has been enlarged.
cavityexpcount++;
@@ -17657,112 +15911,131 @@ void tetgenmesh::delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells,
- arraypool* midfaces, arraypool* missingshs)
+ arraypool* midfaces, arraypool* missingshs,
+ arraypool* topnewtets, arraypool* botnewtets,
+ triface* crossedge)
{
arraypool *cavshells;
- triface *parytet, bdrytet, toptet, bottet, midface;
- triface neightet, spintet;
- face checksh, *parysh;
+ triface bdrytet, neightet, *parytet;
+ triface searchtet, spintet;
+ face *parysh;
face checkseg;
- point pa, pb, pc, pf, pg; //, *pts;
- int types[2], poss[4];
- //REAL elen[3]; //ori, len, n[3];
- bool mflag, bflag;
- int i, j, k;
+ point pa, pb, pc;
+ bool mflag;
+ int t1ver;
+ int i, j;
// Connect newtets to tets outside the cavity. These connections are needed
// for identifying the middle faces (which belong to R).
- for (k = 0; k < 2; k++) {
- cavshells = (k == 0 ? topshells : botshells);
+ for (j = 0; j < 2; j++) {
+ cavshells = (j == 0 ? topshells : botshells);
if (cavshells != NULL) {
for (i = 0; i < cavshells->objects; i++) {
// Get a temp subface.
parysh = (face *) fastlookup(cavshells, i);
- // Get the boundary tet outside the cavity.
+ // Get the boundary tet outside the cavity (saved in sh[0]).
decode(parysh->sh[0], bdrytet);
pa = org(bdrytet);
pb = dest(bdrytet);
pc = apex(bdrytet);
- // Get the adjacent new tet.
+ // Get the adjacent new tet inside the cavity.
stpivot(*parysh, neightet);
- assert(org(neightet) == pb); // SELF_CHECK
- assert(dest(neightet) == pa); // SELF_CHECK
- // Mark neightet as an interior tet of this cavity, 2009-04-24.
- // Comment: We know neightet is an interior tet.
- if (!infected(neightet)) {
- infect(neightet);
- }
- assert(oppo(bdrytet) != NULL); // No faked tet.
- // if (oppo(bdrytet) != NULL) {
- // Bond the two tets.
- bond(bdrytet, neightet); // Also cleared the pointer to tmpsh.
- // }
+ // Mark neightet as an interior tet of this cavity.
+ infect(neightet);
+ // Connect the two tets (the old connections are replaced).
+ bond(bdrytet, neightet);
tsdissolve(neightet); // Clear the pointer to tmpsh.
// Update the point-to-tets map.
- setpoint2tet(pa, encode(neightet));
- setpoint2tet(pb, encode(neightet));
- setpoint2tet(pc, encode(neightet));
- // Delete the temp subface.
- // shellfacedealloc(subfacepool, parysh->sh);
+ setpoint2tet(pa, (tetrahedron) neightet.tet);
+ setpoint2tet(pb, (tetrahedron) neightet.tet);
+ setpoint2tet(pc, (tetrahedron) neightet.tet);
} // i
} // if (cavshells != NULL)
- } // k
-
- mflag = true; // Initialize it.
+ } // j
- if (midfaces != NULL) {
+ if (crossedge != NULL) {
+ // Glue top and bottom tets at their common facet.
+ triface toptet, bottet, spintet, *midface;
+ point pd, pe;
+ REAL ori;
+ int types[2], poss[4];
+ int interflag;
+ int bflag;
+
+ mflag = false;
+ pd = org(*crossedge);
+ pe = dest(*crossedge);
+
+ // Search the first (middle) face in R.
+ // Since R may be non-convex, we must make sure that the face is in the
+ // interior of R. We search a face in 'topnewtets' whose three vertices
+ // are on R and it intersects 'crossedge' in its interior. Then search
+ // a matching face in 'botnewtets'.
+ for (i = 0; i < topnewtets->objects && !mflag; i++) {
+ searchtet = * (triface *) fastlookup(topnewtets, i);
+ for (searchtet.ver = 0; searchtet.ver < 4 && !mflag; searchtet.ver++) {
+ pa = org(searchtet);
+ if (pmarktested(pa)) {
+ pb = dest(searchtet);
+ if (pmarktested(pb)) {
+ pc = apex(searchtet);
+ if (pmarktested(pc)) {
+ // Check if this face intersects [d,e].
+ interflag = tri_edge_test(pa,pb,pc,pd,pe,NULL,1,types,poss);
+ if (interflag == 2) {
+ // They intersect at a single point. Found.
+ toptet = searchtet;
+ // The face lies in the interior of R.
+ // Get the tet (in topnewtets) which lies above R.
+ ori = orient3d(pa, pb, pc, pd);
+ assert(ori != 0);
+ if (ori < 0) {
+ fsymself(toptet);
+ pa = org(toptet);
+ pb = dest(toptet);
+ }
+ // Search the face [b,a,c] in 'botnewtets'.
+ for (j = 0; j < botnewtets->objects; j++) {
+ neightet = * (triface *) fastlookup(botnewtets, j);
+ // Is neightet contains 'b'.
+ if ((point) neightet.tet[4] == pb) {
+ neightet.ver = 11;
+ } else if ((point) neightet.tet[5] == pb) {
+ neightet.ver = 3;
+ } else if ((point) neightet.tet[6] == pb) {
+ neightet.ver = 7;
+ } else if ((point) neightet.tet[7] == pb) {
+ neightet.ver = 0;
+ } else {
+ continue;
+ }
+ // Is the 'neightet' contains edge [b,a].
+ if (dest(neightet) == pa) {
+ // 'neightet' is just the edge.
+ } else if (apex(neightet) == pa) {
+ eprevesymself(neightet);
+ } else if (oppo(neightet) == pa) {
+ esymself(neightet);
+ enextself(neightet);
+ } else {
+ continue;
+ }
+ // Is 'neightet' the face [b,a,c].
+ if (apex(neightet) == pc) {
+ bottet = neightet;
+ mflag = true;
+ break;
+ }
+ } // j
+ } // if (interflag == 2)
+ } // pc
+ } // pb
+ } // pa
+ } // toptet.ver
+ } // i
- // The first pair of top and bottom tets share the same edge [a, b].
- // toptet = * (triface *) fastlookup(topfaces, 0);
- if (infected(firsttopface)) {
- // This is due to he enlargement of the cavity. Find the updated top
- // boundary face at edge [a,b].
- // Comment: An uninfected tet at [a,b] should be found since [a,b] is a
- // boundary edge of the missing region R. It should not be enclosed
- // by the enlarged cavity.
- pa = apex(firsttopface); // SELF_CHECK
- while (1) {
- fnextself(firsttopface);
- if (!infected(firsttopface)) break;
- assert(apex(firsttopface) != pa); // SELF_CHECK
- }
- }
- toptet = firsttopface;
- pa = apex(toptet);
- fsymself(toptet);
- // Search a subface from the top mesh.
- while (1) {
- esymself(toptet); // The next face in the same tet.
- pc = apex(toptet);
- assert(pc != pa); // We should not return to the starting point.
- if (pmarktested(pc)) break; // [a,b,c] is a subface.
- fsymself(toptet); // Go to the adjacent tet.
- }
- // Search the subface [a,b,c] in the bottom mesh.
- // bottet = * (triface *) fastlookup(botfaces, 0);
- if (infected(firstbotface)) {
- pa = apex(firstbotface); // SELF_CHECK
- while (1) {
- fnextself(firstbotface);
- if (!infected(firstbotface)) break;
- assert(apex(firstbotface) != pa); // SELF_CHECK
- }
- }
- bottet = firstbotface;
- pa = apex(bottet);
- fsymself(bottet);
- while (1) {
- esymself(bottet); // The next face in the same tet.
- pf = apex(bottet);
- assert(pf != pa); // We should not return to the starting point.
- if (pf == pc) break; // Face matched.
- if (pmarktested(pf)) {
- mflag = false; break; // Not matched.
- }
- fsymself(bottet);
- }
if (mflag) {
- // Connect the two tets together.
+ // Found a pair of matched faces in 'toptet' and 'bottet'.
bond(toptet, bottet);
// Both are interior tets.
infect(toptet);
@@ -17771,20 +16044,23 @@ bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells,
markface(toptet);
midfaces->newindex((void **) &parytet);
*parytet = toptet;
+ } else {
+ // No pair of 'toptet' and 'bottet'.
+ toptet.tet = NULL;
+ // Randomly split an interior edge of R.
+ i = randomnation(missingshs->objects - 1);
+ recentsh = * (face *) fastlookup(missingshs, i);
}
- // Match pairs of subfaces (middle faces), connect top and bottom tets.
+ // Find other middle faces, connect top and bottom tets.
for (i = 0; i < midfaces->objects && mflag; i++) {
// Get a matched middle face [a, b, c]
- midface = * (triface *) fastlookup(midfaces, i);
+ midface = (triface *) fastlookup(midfaces, i);
// The tet must be a new created tet (marktested).
- assert(marktested(midface)); // SELF_CHECK
-
- // Check the neighbors at edges [b, c] and [c, a].
- for (j = 0; j < 2 && mflag; j++) {
- enextself(midface); // [b, c] or [c, a].
- pg = apex(midface);
- toptet = midface;
+ assert(marktested(*midface)); // SELF_CHECK
+ // Check the neighbors at the edges of this face.
+ for (j = 0; j < 3 && mflag; j++) {
+ toptet = *midface;
bflag = false;
while (1) {
// Go to the next face in the same tet.
@@ -17794,6 +16070,7 @@ bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells,
break; // Find a subface.
}
if (pc == dummypoint) {
+ assert(0); // Check this case.
break; // Find a subface.
}
// Go to the adjacent tet.
@@ -17807,16 +16084,19 @@ bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells,
if (!bflag) {
// assert(marktested(toptet)); // SELF_CHECK
if (!facemarked(toptet)) {
- fsym(midface, bottet);
+ fsym(*midface, bottet);
+ spintet = bottet;
while (1) {
esymself(bottet);
- pf = apex(bottet);
- if (pf == pc) break; // Face matched.
- if (pmarktested(pf)) {
- mflag = false; break; // Not matched
- }
+ pd = apex(bottet);
+ if (pd == pc) break; // Face matched.
fsymself(bottet);
- }
+ if (bottet.tet == spintet.tet) {
+ // Not found a matched bottom face.
+ mflag = false;
+ break;
+ }
+ } // while (1)
if (mflag) {
if (marktested(bottet)) {
// Connect two tets together.
@@ -17828,79 +16108,185 @@ bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells,
markface(toptet);
midfaces->newindex((void **) &parytet);
*parytet = toptet;
- } else {
- // The 'bottet' is not inside the cavity!
- // This case can happen when the cavity was enlarged, and the
- // 'toptet' is a co-facet (sub)face adjacent to the missing
- // region, and it is a boundary face of the top cavity.
- // So the toptet and bottet should be bonded already through
- // a temp subface. See fig/dump-cavity-case18. Check it.
- fsym(toptet, neightet);
- assert(neightet.tet == bottet.tet); // SELF_CHECK
- assert(neightet.ver == bottet.ver); // SELF_CHECK
- // Do not add this face into 'midfaces'.
}
- }
+ } else { // mflag == false
+ // Adjust 'toptet' and 'bottet' to be the crossing edges.
+ fsym(*midface, bottet);
+ spintet = bottet;
+ while (1) {
+ esymself(bottet);
+ pd = apex(bottet);
+ if (pmarktested(pd)) {
+ // assert(pd != pc);
+ // Let 'toptet' be [a,b,c,#], and 'bottet' be [b,a,d,*].
+ // Adjust 'toptet' and 'bottet' to be the crossing edges.
+ // Test orient3d(b,c,#,d).
+ ori = orient3d(dest(toptet), pc, oppo(toptet), pd);
+ if (ori < 0) {
+ // Edges [a,d] and [b,c] cross each other.
+ enextself(toptet); // [b,c]
+ enextself(bottet); // [a,d]
+ } else if (ori > 0) {
+ // Edges [a,c] and [b,d] cross each other.
+ eprevself(toptet); // [c,a]
+ eprevself(bottet); // [d,b]
+ } else {
+ // b,c,#,and d are coplanar!.
+ assert(0);
+ }
+ break; // Not matched
+ }
+ fsymself(bottet);
+ assert (bottet.tet != spintet.tet);
+ }
+ } // if (!mflag)
} // if (!facemarked(toptet))
- }
+ } // if (!bflag)
+ enextself(*midface);
} // j
} // i
- } // if (midfaces != NULL)
-
- if (mflag) {
- if (midfaces != NULL) {
+ if (mflag) {
if (b->verbose > 2) {
printf(" Found %ld middle subfaces.\n", midfaces->objects);
}
- if (midfaces->objects > maxregionsize) {
- maxregionsize = midfaces->objects;
- }
- // Unmark middle faces.
+ face oldsh, newsh, casout, casin, neighsh;
+
+ oldsh = * (face *) fastlookup(missingshs, 0);
+
+ // Create new subfaces to fill the region R.
for (i = 0; i < midfaces->objects; i++) {
// Get a matched middle face [a, b, c]
- midface = * (triface *) fastlookup(midfaces, i);
- assert(facemarked(midface)); // SELF_CHECK
- unmarkface(midface);
- }
- }
- } else {
- // Faces at top and bottom are not matched. There exists non-Delaunay
- // subedges. See fig/dump-cavity-case5.lua.
- pa = org(toptet);
- pb = dest(toptet);
- pc = apex(toptet);
- pf = apex(bottet);
-
- pf = oppo(toptet);
- pg = oppo(bottet);
- // Find a subface in R which intersects the edge [f,g].
- for (i = 0; i < missingshs->objects; i++) {
- parysh = (face *) fastlookup(missingshs, i);
- pa = sorg(*parysh);
- pb = sdest(*parysh);
- pc = sapex(*parysh);
- if (tri_edge_test(pa, pb, pc, pf, pg, NULL, 1, types, poss)) {
- // Found a subface.
- break;
+ midface = (triface *) fastlookup(midfaces, i);
+ unmarkface(*midface);
+ makeshellface(subfaces, &newsh);
+ setsorg(newsh, org(*midface));
+ setsdest(newsh, dest(*midface));
+ setsapex(newsh, apex(*midface));
+ // The new subface gets its markers from the old one.
+ setshellmark(newsh, shellmark(oldsh));
+ if (checkconstraints) {
+ setareabound(newsh, areabound(oldsh));
+ }
+ // Connect the new subface to adjacent tets.
+ tsbond(*midface, newsh);
+ fsym(*midface, neightet);
+ sesymself(newsh);
+ tsbond(neightet, newsh);
}
- }
- if (i < missingshs->objects) {
- // Such subface exist.
- recentsh = *parysh;
+ // Connect new subfaces together and to the bdry of R.
+ // Delete faked segments.
+ for (i = 0; i < midfaces->objects; i++) {
+ // Get a matched middle face [a, b, c]
+ midface = (triface *) fastlookup(midfaces, i);
+ for (j = 0; j < 3; j++) {
+ tspivot(*midface, newsh);
+ spivot(newsh, casout);
+ if (casout.sh == NULL) {
+ // Search its neighbor.
+ fnext(*midface, searchtet);
+ while (1) {
+ // (1) First check if this side is a bdry edge of R.
+ tsspivot1(searchtet, checkseg);
+ if (checkseg.sh != NULL) {
+ // It's a bdry edge of R.
+ assert(!infected(searchtet)); // It must not be a cavity tet.
+ // Get the old subface.
+ checkseg.shver = 0;
+ spivot(checkseg, oldsh);
+ if (sinfected(checkseg)) {
+ // It's a faked segment. Delete it.
+ spintet = searchtet;
+ while (1) {
+ tssdissolve1(spintet);
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) break;
+ }
+ shellfacedealloc(subsegs, checkseg.sh);
+ ssdissolve(oldsh);
+ checkseg.sh = NULL;
+ }
+ spivot(oldsh, casout);
+ if (casout.sh != NULL) {
+ casin = casout;
+ if (checkseg.sh != NULL) {
+ // Make sure that the subface has the right ori at the
+ // segment.
+ checkseg.shver = 0;
+ if (sorg(newsh) != sorg(checkseg)) {
+ sesymself(newsh);
+ }
+ spivot(casin, neighsh);
+ while (neighsh.sh != oldsh.sh) {
+ casin = neighsh;
+ spivot(casin, neighsh);
+ }
+ }
+ sbond1(newsh, casout);
+ sbond1(casin, newsh);
+ }
+ if (checkseg.sh != NULL) {
+ ssbond(newsh, checkseg);
+ }
+ break;
+ } // if (checkseg.sh != NULL)
+ // (2) Second check if this side is an interior edge of R.
+ tspivot(searchtet, neighsh);
+ if (neighsh.sh != NULL) {
+ // Found an adjacent subface of newsh (an interior edge).
+ sbond(newsh, neighsh);
+ break;
+ }
+ fnextself(searchtet);
+ assert(searchtet.tet != midface->tet);
+ } // while (1)
+ } // if (casout.sh == NULL)
+ enextself(*midface);
+ } // j
+ } // i
+
+ // Delete old subfaces.
+ for (i = 0; i < missingshs->objects; i++) {
+ parysh = (face *) fastlookup(missingshs, i);
+ shellfacedealloc(subfaces, parysh->sh);
+ }
} else {
- assert(0); // Debug this case.
+ if (toptet.tet != NULL) {
+ // Faces at top and bottom are not matched.
+ // Choose a Steiner point in R.
+ // Split one of the crossing edges.
+ pa = org(toptet);
+ pb = dest(toptet);
+ pc = org(bottet);
+ pd = dest(bottet);
+ // Search an edge in R which is either [a,b] or [c,d].
+ // Reminder: Subfaces in this list 'missingshs', except the first
+ // one, represents an interior edge of R.
+ for (i = 1; i < missingshs->objects; i++) {
+ parysh = (face *) fastlookup(missingshs, i);
+ if (((sorg(*parysh) == pa) && (sdest(*parysh) == pb)) ||
+ ((sorg(*parysh) == pb) && (sdest(*parysh) == pa))) break;
+ if (((sorg(*parysh) == pc) && (sdest(*parysh) == pd)) ||
+ ((sorg(*parysh) == pd) && (sdest(*parysh) == pc))) break;
+ }
+ if (i < missingshs->objects) {
+ // Found. Return it.
+ recentsh = *parysh;
+ } else {
+ assert(0);
+ }
+ }
}
-
- // Set a tet for searching the new point.
- recenttet = firsttopface;
- }
+ midfaces->restart();
+ } else {
+ mflag = true;
+ }
// Delete the temp subfaces.
- for (k = 0; k < 2; k++) {
- cavshells = (k == 0 ? topshells : botshells);
+ for (j = 0; j < 2; j++) {
+ cavshells = (j == 0 ? topshells : botshells);
if (cavshells != NULL) {
for (i = 0; i < cavshells->objects; i++) {
parysh = (face *) fastlookup(cavshells, i);
@@ -17913,9 +16299,6 @@ bool tetgenmesh::fillcavity(arraypool* topshells, arraypool* botshells,
if (botshells != NULL) {
botshells->restart();
}
- if (midfaces != NULL) {
- midfaces->restart();
- }
return mflag;
}
@@ -17930,10 +16313,12 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
arraypool *botnewtets)
{
arraypool *newtets;
+ shellface *sptr, *ssptr;
triface *parytet, *pnewtet, newtet, neightet, spintet;
face checksh, *parysh;
face checkseg, *paryseg;
- int i, j, k;
+ int t1ver;
+ int i, j;
if (b->verbose > 2) {
printf(" Carve cavity: %ld old tets.\n", crosstets->objects);
@@ -17949,38 +16334,44 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
// Collect all subfaces and segments which attached to the old tets.
for (i = 0; i < crosstets->objects; i++) {
parytet = (triface *) fastlookup(crosstets, i);
- assert(infected(*parytet)); // SELF_CHECK
- for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) {
- tspivot(*parytet, checksh);
- if (checksh.sh != NULL) {
- if (!sinfected(checksh)) {
- sinfect(checksh);
- cavetetshlist->newindex((void **) &parysh);
- *parysh = checksh;
+ if ((sptr = (shellface*) parytet->tet[9]) != NULL) {
+ for (j = 0; j < 4; j++) {
+ if (sptr[j]) {
+ sdecode(sptr[j], checksh);
+ if (!sinfected(checksh)) {
+ sinfect(checksh);
+ cavetetshlist->newindex((void **) &parysh);
+ *parysh = checksh;
+ }
}
- }
+ } // j
}
- for (j = 0; j < 6; j++) {
- parytet->ver = edge2ver[j];
- tsspivot1(*parytet, checkseg);
- if (checkseg.sh != NULL) {
- if (!sinfected(checkseg)) {
- sinfect(checkseg);
- cavetetseglist->newindex((void **) &paryseg);
- *paryseg = checkseg;
+ if ((ssptr = (shellface*) parytet->tet[8]) != NULL) {
+ for (j = 0; j < 6; j++) {
+ if (ssptr[j]) {
+ sdecode(ssptr[j], checkseg);
+ // Skip a deleted segment (was a faked segment)
+ if (checkseg.sh[3] != NULL) {
+ if (!sinfected(checkseg)) {
+ sinfect(checkseg);
+ cavetetseglist->newindex((void **) &paryseg);
+ *paryseg = checkseg;
+ }
+ }
}
- }
+ } // j
}
} // i
+
// Uninfect collected subfaces.
for (i = 0; i < cavetetshlist->objects; i++) {
- checksh = * (face *) fastlookup(cavetetshlist, i);
- suninfect(checksh);
+ parysh = (face *) fastlookup(cavetetshlist, i);
+ suninfect(*parysh);
}
// Uninfect collected segments.
for (i = 0; i < cavetetseglist->objects; i++) {
- checkseg = * (face *) fastlookup(cavetetseglist, i);
- suninfect(checkseg);
+ paryseg = (face *) fastlookup(cavetetseglist, i);
+ suninfect(*paryseg);
}
// Connect subfaces to new tets.
@@ -17996,11 +16387,6 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
// Does this tet lie inside the cavity.
if (infected(neightet)) {
checksh = *parysh;
- if (b->verbose > 2) {
- printf(" Found an interior subface (%d, %d, %d)\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
stdissolve(checksh);
caveencshlist->newindex((void **) &parysh);
*parysh = checksh;
@@ -18014,10 +16400,7 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
tsbond(newtet, *parysh);
}
} // i
- if (b->verbose > 2) {
- printf(" %ld (%ld) cavity (interior) subfaces.\n",
- cavetetshlist->objects, caveencshlist->objects);
- }
+
for (i = 0; i < cavetetseglist->objects; i++) {
checkseg = * (face *) fastlookup(cavetetseglist, i);
@@ -18031,10 +16414,6 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
}
fnextself(spintet);
if (spintet.tet == neightet.tet) {
- if (b->verbose > 2) {
- printf(" Found an interior seg (%d, %d)\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
sstdissolve1(checkseg);
caveencseglist->newindex((void **) &paryseg);
*paryseg = checkseg;
@@ -18052,10 +16431,7 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
}
}
} // i
- if (b->verbose > 2) {
- printf(" %ld (%ld) cavity (interior) segments.\n",
- cavetetseglist->objects, caveencseglist->objects);
- }
+
cavetetshlist->restart();
cavetetseglist->restart();
@@ -18063,6 +16439,9 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
// Delete the old tets in cavity.
for (i = 0; i < crosstets->objects; i++) {
parytet = (triface *) fastlookup(crosstets, i);
+ if (ishulltet(*parytet)) {
+ hullsize--;
+ }
tetrahedrondealloc(parytet->tet);
}
@@ -18070,8 +16449,8 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
// Collect new tets in cavity. Some new tets have already been found
// (and infected) in the fillcavity(). We first collect them.
- for (k = 0; k < 2; k++) {
- newtets = (k == 0 ? topnewtets : botnewtets);
+ for (j = 0; j < 2; j++) {
+ newtets = (j == 0 ? topnewtets : botnewtets);
if (newtets != NULL) {
for (i = 0; i < newtets->objects; i++) {
parytet = (triface *) fastlookup(newtets, i);
@@ -18081,20 +16460,17 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
}
} // i
}
- } // k
+ } // j
// Now we collect all new tets in cavity.
for (i = 0; i < crosstets->objects; i++) {
parytet = (triface *) fastlookup(crosstets, i);
- if (i == 0) {
- recenttet = *parytet; // Remember a live handle.
- }
for (j = 0; j < 4; j++) {
decode(parytet->tet[j], neightet);
if (marktested(neightet)) { // Is it a new tet?
if (!infected(neightet)) {
// Find an interior tet.
- assert((point) neightet.tet[7] != dummypoint); // SELF_CHECK
+ //assert((point) neightet.tet[7] != dummypoint); // SELF_CHECK
infect(neightet);
crosstets->newindex((void **) &pnewtet);
*pnewtet = neightet;
@@ -18103,9 +16479,12 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
} // j
} // i
+ parytet = (triface *) fastlookup(crosstets, 0);
+ recenttet = *parytet; // Remember a live handle.
+
// Delete outer new tets.
- for (k = 0; k < 2; k++) {
- newtets = (k == 0 ? topnewtets : botnewtets);
+ for (j = 0; j < 2; j++) {
+ newtets = (j == 0 ? topnewtets : botnewtets);
if (newtets != NULL) {
for (i = 0; i < newtets->objects; i++) {
parytet = (triface *) fastlookup(newtets, i);
@@ -18113,6 +16492,9 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
// This is an interior tet.
uninfect(*parytet);
unmarktest(*parytet);
+ if (ishulltet(*parytet)) {
+ hullsize++;
+ }
} else {
// An outer tet. Delete it.
tetrahedrondealloc(parytet->tet);
@@ -18135,21 +16517,19 @@ void tetgenmesh::carvecavity(arraypool *crosstets, arraypool *topnewtets,
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::restorecavity(arraypool *crosstets, arraypool *topnewtets,
- arraypool *botnewtets)
+ arraypool *botnewtets, arraypool *missingshbds)
{
- triface *parytet, neightet;
- face checksh;
+ triface *parytet, neightet, spintet;
+ face *parysh;
face checkseg;
point *ppt;
+ int t1ver;
int i, j;
// Reconnect crossing tets to cavity boundary.
for (i = 0; i < crosstets->objects; i++) {
parytet = (triface *) fastlookup(crosstets, i);
assert(infected(*parytet)); // SELF_CHECK
- if (i == 0) {
- recenttet = *parytet; // Remember a live handle.
- }
parytet->ver = 0;
for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) {
fsym(*parytet, neightet);
@@ -18172,6 +16552,31 @@ void tetgenmesh::restorecavity(arraypool *crosstets, arraypool *topnewtets,
uninfect(*parytet);
}
+ // Remember a live handle.
+ recenttet = * (triface *) fastlookup(crosstets, 0);
+
+ // Delete faked segments.
+ for (i = 0; i < missingshbds->objects; i++) {
+ parysh = (face *) fastlookup(missingshbds, i);
+ sspivot(*parysh, checkseg);
+ assert(checkseg.sh != NULL);
+ if (checkseg.sh[3] != NULL) {
+ if (sinfected(checkseg)) {
+ // It's a faked segment. Delete it.
+ sstpivot1(checkseg, neightet);
+ spintet = neightet;
+ while (1) {
+ tssdissolve1(spintet);
+ fnextself(spintet);
+ if (spintet.tet == neightet.tet) break;
+ }
+ shellfacedealloc(subsegs, checkseg.sh);
+ ssdissolve(*parysh);
+ //checkseg.sh = NULL;
+ }
+ }
+ } // i
+
// Delete new tets.
for (i = 0; i < topnewtets->objects; i++) {
parytet = (triface *) fastlookup(topnewtets, i);
@@ -18201,7 +16606,8 @@ void tetgenmesh::restorecavity(arraypool *crosstets, arraypool *topnewtets,
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::flipcertify(triface *chkface, badface **pqueue)
+void tetgenmesh::flipcertify(triface *chkface,badface **pqueue,point plane_pa,
+ point plane_pb, point plane_pc)
{
badface *parybf, *prevbf, *nextbf;
triface neightet;
@@ -18278,7 +16684,7 @@ void tetgenmesh::flipcertify(triface *chkface, badface **pqueue)
for (i = 0; i < 5; i++) {
if (pmarktest2ed(p[i])) {
// A top point has a positive weight.
- w[i] = orient3d(plane_pa, plane_pb, plane_pc, p[i]);
+ w[i] = orient3dfast(plane_pa, plane_pb, plane_pc, p[i]);
if (w[i] < 0) w[i] = -w[i];
assert(w[i] != 0);
} else {
@@ -18294,12 +16700,7 @@ void tetgenmesh::flipcertify(triface *chkface, badface **pqueue)
// p[1], p[0], p[2], p[3].
insph = insphere(p[1], p[0], p[2], p[3], p[4]);
-
- if (b->flipinsert_ori4dexact) {
- ori4 = orient4dexact(p[1], p[0], p[2], p[3], p[4],w[1],w[0],w[2],w[3],w[4]);
- } else {
- ori4 = orient4d(p[1], p[0], p[2], p[3], p[4], w[1], w[0], w[2], w[3], w[4]);
- }
+ ori4 = orient4d(p[1], p[0], p[2], p[3], p[4], w[1], w[0], w[2], w[3], w[4]);
if (b->verbose > 2) {
printf(" Heights: (%g, %g, %g, %g, %g)\n", w[0],w[1],w[2],w[3],w[4]);
@@ -18332,7 +16733,7 @@ void tetgenmesh::flipcertify(triface *chkface, badface **pqueue)
// Search an item whose key is larger or equal to current key.
prevbf = NULL;
nextbf = *pqueue;
- if (!b->flipinsert_random) { // Default use a priority queue.
+ //if (!b->flipinsert_random) { // Default use a priority queue.
// Insert the item into priority queue.
while (nextbf != NULL) {
if (nextbf->key < parybf->key) {
@@ -18342,7 +16743,7 @@ void tetgenmesh::flipcertify(triface *chkface, badface **pqueue)
break;
}
}
- } // if (!b->flipinsert_random) // -L1
+ //} // if (!b->flipinsert_random)
// Insert the new item between prev and next items.
if (prevbf == NULL) {
*pqueue = parybf;
@@ -18374,19 +16775,20 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
arraypool *botpoints, arraypool *midpoints)
{
arraypool *crossfaces, *bfacearray;
- triface fliptets[5], baktets[2], fliptet, newface;
+ triface fliptets[6], baktets[2], fliptet, newface;
triface neightet, *parytet;
face checksh;
face checkseg;
badface *pqueue;
badface *popbf, bface;
+ point plane_pa, plane_pb, plane_pc;
point p1, p2, pd, pe;
point *parypt;
+ flipconstraints fc;
REAL ori[3];
int convcount, copcount;
int flipflag, fcount;
int n, i;
-
long f23count, f32count, f44count;
long totalfcount;
@@ -18434,9 +16836,6 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
if (b->verbose > 1) {
printf(" Found %ld crossing faces.\n", crossfaces->objects);
}
- if (crossfaces->objects > maxcrossfacecount) {
- maxcrossfacecount = crossfaces->objects;
- }
for (i = 0; i < crosstets->objects; i++) {
parytet = (triface *) fastlookup(crosstets, i);
@@ -18449,14 +16848,13 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
for (i = 0; i < crossfaces->objects; i++) {
parytet = (triface *) fastlookup(crossfaces, i);
- flipcertify(parytet, &pqueue);
+ flipcertify(parytet, &pqueue, plane_pa, plane_pb, plane_pc);
}
crossfaces->restart();
// The list for temporarily storing unflipable faces.
bfacearray = new arraypool(sizeof(triface), 4);
- fliploop:
fcount = 0; // Count the number of flips.
@@ -18518,7 +16916,7 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
fliptets[0] = fliptet; // abcd, d may be the new vertex.
fliptets[1] = neightet; // bace.
- flip23(fliptets, 1, 0, 0);
+ flip23(fliptets, 1, &fc);
// Put the link faces into check list.
for (i = 0; i < 3; i++) {
eprevesym(fliptets[i], newface);
@@ -18545,16 +16943,26 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
assert(checkseg.sh == NULL);
// Collect tets sharing at this edge.
+ // NOTE: This operation may collect tets which lie outside the
+ // cavity, e.g., when the edge lies on the boundary of the
+ // cavity. Do not flip if there are outside tets at this edge.
+ // 2012-07-27.
esym(fliptet, fliptets[0]); // [b,a,d,c]
n = 0;
do {
+ p1 = apex(fliptets[n]);
+ if (!(pmarktested(p1) || pmarktest2ed(p1) || pmarktest3ed(p1))) {
+ // This apex is not on the cavity. Hence the face does not
+ // lie inside the cavity. Do not flip this edge.
+ n = 1000; break;
+ }
fnext(fliptets[n], fliptets[n + 1]);
n++;
} while ((fliptets[n].tet != fliptet.tet) && (n < 5));
if (n == 3) {
// Found a 3-to-2 flip.
- flip32(fliptets, 1, 0, 0);
+ flip32(fliptets, 1, &fc);
// Put the link faces into check list.
for (i = 0; i < 3; i++) {
esym(fliptets[0], newface);
@@ -18588,7 +16996,7 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
baktets[0] = fliptets[2]; // = [b,a,e,f]
baktets[1] = fliptets[3]; // = [b,a,f,d]
// The flip may involve hull tets.
- flip23(fliptets, 1, 0, 0);
+ flip23(fliptets, 1, &fc);
// Put the "outer" link faces into check list.
// fliptets[0] = [e,d,a,b] => will be flipped, so
// [a,b,d] and [a,b,e] are not "outer" link faces.
@@ -18607,7 +17015,7 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
eprevself(fliptets[0]); // = [b,a,d,c], d is the new vertex.
fliptets[1] = baktets[0]; // = [b,a,e,f]
fliptets[2] = baktets[1]; // = [b,a,f,d]
- flip32(fliptets, 1, 0, 0);
+ flip32(fliptets, 1, &fc);
// Put the "outer" link faces into check list.
// fliptets[0] = [d,e,f,a]
// fliptets[1] = [e,d,f,b]
@@ -18645,23 +17053,22 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
pointmark(bface.fapex), pointmark(bface.foppo),
pointmark(bface.noppo), bface.key);
}
- dbg_ignore_facecount++;
} // if (convcount == 1)
if (flipflag == 1) {
// Update the priority queue.
for (i = 0; i < crossfaces->objects; i++) {
parytet = (triface *) fastlookup(crossfaces, i);
- flipcertify(parytet, &pqueue);
+ flipcertify(parytet, &pqueue, plane_pa, plane_pb, plane_pc);
}
crossfaces->restart();
- if (!b->flipinsert_random) {
+ if (1) { // if (!b->flipinsert_random) {
// Insert all queued unflipped faces.
for (i = 0; i < bfacearray->objects; i++) {
parytet = (triface *) fastlookup(bfacearray, i);
// This face may be changed.
if (!isdeadtet(*parytet)) {
- flipcertify(parytet, &pqueue);
+ flipcertify(parytet, &pqueue, plane_pa, plane_pb, plane_pc);
}
}
bfacearray->restart();
@@ -18683,22 +17090,10 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
printf("!! No flip is found in %ld faces.\n", bfacearray->objects);
assert(0);
}
- if (b->flipinsert_random) {
- // Insert all queued unflipped faces.
- for (i = 0; i < bfacearray->objects; i++) {
- parytet = (triface *) fastlookup(bfacearray, i);
- // This face may be changed.
- if (!isdeadtet(*parytet)) {
- flipcertify(parytet, &pqueue);
- }
- }
- bfacearray->restart();
- goto fliploop;
- }
}
// 'bfacearray' may be not empty (for what reason ??).
- dbg_unflip_facecount += bfacearray->objects;
+ //dbg_unflip_facecount += bfacearray->objects;
assert(flippool->items == 0l);
delete bfacearray;
@@ -18717,11 +17112,6 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
f32count = flip32count - f32count;
f44count = flip44count - f44count;
totalfcount = f23count + f32count + f44count;
-
- if (totalfcount > maxflipsequence) {
- maxflipsequence = totalfcount;
- }
-
if (b->verbose > 2) {
printf(" Total %ld flips. f23(%ld), f32(%ld), f44(%ld).\n",
totalfcount, f23count, f32count, f44count);
@@ -18734,156 +17124,85 @@ void tetgenmesh::flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
// //
// 'missingshs' contains the list of subfaces in R. Moreover, each subface //
// (except the first one) in this list represents an interior edge of R. //
-// Note: All subfaces in R are smarktested. //
// //
// Note: We assume that all vertices of R are marktested so we can detect //
// new subface by checking the flag in apexes. //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::fillregion(arraypool* missingshs, arraypool* missingshbds,
+bool tetgenmesh::fillregion(arraypool* missingshs, arraypool* missingshbds,
arraypool* newshs)
{
badface *newflipface, *popface;
- triface searchtet, spintet;
+ triface searchtet, spintet, neightet;
face oldsh, newsh, opensh, *parysh;
face casout, casin, neighsh, checksh;
- face checkseg, fakeseg;
- point pc, pd, pe, pf, ppt[2];
- enum interresult dir;
- REAL n[3], len; // elen[3];
- bool insideflag;
- int types[2], poss[4];
- int i, j, k;
+ face neighseg, checkseg;
+ point pc;
+ int success;
+ int t1ver;
+ int i, j;
- if (b->verbose > 2) {
- printf(" Fill region: %ld old subfaces (%ld).\n", missingshs->objects,
- fillregioncount);
- }
-
- // Search the first constrained face of R. It is found from the set of
- // faces sharing at a boundary edge [a,b]. Such face must be found.
- // The search takes the following two steps:
- // - First, finds a candidate face [a,b,c] where c is also a vertex of R;
- // Note that [a,b,c] may not be the right face to fill R. For instance,
- // when R is concave at b.
- // - Second, check if [a,b,c] can fill R. This can be checked if an
- // adjacent tet of [a,b,c] intersects R. This is a tetrahedron-triangle
- // intersection test. It can be reduced to two triangle-edge intersect
- // tests, i.e., intersect the two faces not containing the edge [a,b] in
- // this tet with all interior edges of R.
-
- // We start from the first boundary edge of R.
- oldsh = * (face *) fastlookup(missingshbds, 0);
- ppt[0] = sorg(oldsh);
- ppt[1] = sdest(oldsh);
- point2tetorg(ppt[0], searchtet);
- dir = finddirection(&searchtet, ppt[1], 0);
- assert(dir == ACROSSVERT); // SELF_CHECK
-
- insideflag = false;
-
- // Each face has two adjacent tets.
- for (k = 0; k < 2; k++) {
- if (b->verbose > 2) {
- printf(" Search an interior face from edge (%d, %d).\n",
- pointmark(ppt[0]), pointmark(ppt[1]));
- }
+
+ // Search the first new subface to fill the region.
+ for (i = 0; i < missingshbds->objects; i++) {
+ parysh = (face *) fastlookup(missingshbds, i);
+ sspivot(*parysh, neighseg);
+ sstpivot1(neighseg, searchtet);
+ j = 0; // Count the number of passes of R.
spintet = searchtet;
while (1) {
pc = apex(spintet);
if (pmarktested(pc)) {
- // Found a candidate face. Check if it is inside R.
- if (missingshs->objects > 2l) {
- // pd = oppo(spintet);
- // if (pd == dummypoint) {
- // Calculate an above point for this subface.
- facenormal(ppt[0], ppt[1], pc, n, 1, NULL);
- len = sqrt(DOT(n, n));
- n[0] /= len;
- n[1] /= len;
- n[2] /= len;
- len = DIST(ppt[0], ppt[1]);
- len += DIST(ppt[1], pc);
- len += DIST(pc, ppt[0]);
- len /= 3.0;
- dummypoint[0] = ppt[0][0] + len * n[0];
- dummypoint[1] = ppt[0][1] + len * n[1];
- dummypoint[2] = ppt[0][2] + len * n[2];
- pd = dummypoint;
- // }
- //if (pd != dummypoint) {
- for (j = 0; j < 2 && !insideflag; j++) {
- for (i = 1; i < missingshs->objects && !insideflag; i++) {
- parysh = (face *) fastlookup(missingshs, i);
- // Get an interior edge of R.
- pe = sorg(*parysh);
- pf = sdest(*parysh);
- if (tri_edge_test(ppt[j],pc,pd,pe,pf,NULL,1,types,poss)) {
- dir = (enum interresult) types[0];
- if (dir == ACROSSFACE) {
- searchtet = spintet;
- insideflag = true;
- } else if (dir == ACROSSEDGE) {
- searchtet = spintet;
- insideflag = true;
- }
- }
- } // i
- } // j
- // }
- // if (pd == dummypoint) {
- dummypoint[0] = 0;
- dummypoint[1] = 0;
- dummypoint[2] = 0;
- // }
- } else {
- // It is a simple 2-to-2 flip.
- searchtet = spintet;
- insideflag = true;
- }
- } // if (pmarktested(pc))
- if (insideflag) break;
+ neightet = spintet;
+ j++;
+ }
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
- } // while (1)
- if (insideflag) break;
- esymself(searchtet);
- ppt[0] = org(searchtet);
- ppt[1] = dest(searchtet);
- } // k
-
- if (!insideflag) {
- // Something strange is happening.
- // Refine the missing region by adding a Steiner point.
- recentsh = oldsh;
- recenttet = searchtet; // For point location.
+ }
+ assert(j >= 1);
+ if (j == 1) {
+ // Found an interior new subface.
+ searchtet = neightet;
+ oldsh = *parysh;
+ break;
+ }
+ } // i
+
+ if (i == missingshbds->objects) {
+ // Failed to find any interior subface.
+ // Need Steiner points.
return false;
}
- // Create a new subface at the boundary edge.
- if (b->verbose > 2) {
- printf(" Create a new subface (%d, %d, %d)\n", pointmark(ppt[0]),
- pointmark(ppt[1]), pointmark(pc));
- }
makeshellface(subfaces, &newsh);
- setsorg(newsh, ppt[0]);
- setsdest(newsh, ppt[1]);
- setsapex(newsh, pc);
+ setsorg(newsh, org(searchtet));
+ setsdest(newsh, dest(searchtet));
+ setsapex(newsh, apex(searchtet));
// The new subface gets its markers from the old one.
setshellmark(newsh, shellmark(oldsh));
if (checkconstraints) {
setareabound(newsh, areabound(oldsh));
}
// Connect the new subface to adjacent tets.
- tspivot(searchtet, checksh); // SELF_CHECK
- assert(checksh.sh == NULL); // SELF_CHECK
tsbond(searchtet, newsh);
fsymself(searchtet);
sesymself(newsh);
tsbond(searchtet, newsh);
// Connect newsh to outer subfaces.
sspivot(oldsh, checkseg);
+ if (sinfected(checkseg)) {
+ // It's a faked segment. Delete it.
+ spintet = searchtet;
+ while (1) {
+ tssdissolve1(spintet);
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) break;
+ }
+ shellfacedealloc(subsegs, checkseg.sh);
+ ssdissolve(oldsh);
+ checkseg.sh = NULL;
+ }
spivot(oldsh, casout);
if (casout.sh != NULL) {
casin = casout;
@@ -18902,384 +17221,491 @@ bool tetgenmesh::fillregion(arraypool* missingshs, arraypool* missingshbds,
sbond1(newsh, casout);
sbond1(casin, newsh);
}
- if (checkseg.sh != NULL) {
- ssbond(newsh, checkseg);
+ if (checkseg.sh != NULL) {
+ ssbond(newsh, checkseg);
+ }
+ // Add this new subface into list.
+ sinfect(newsh);
+ newshs->newindex((void **) &parysh);
+ *parysh = newsh;
+
+ // Push two "open" side of the new subface into stack.
+ for (i = 0; i < 2; i++) {
+ senextself(newsh);
+ newflipface = (badface *) flippool->alloc();
+ newflipface->ss = newsh;
+ newflipface->nextitem = flipstack;
+ flipstack = newflipface;
+ }
+
+ success = 1;
+
+ // Loop until 'flipstack' is empty.
+ while ((flipstack != NULL) && success) {
+ // Pop an "open" side from the stack.
+ popface = flipstack;
+ opensh = popface->ss;
+ flipstack = popface->nextitem; // The next top item in stack.
+ flippool->dealloc((void *) popface);
+
+ // opensh is either (1) an interior edge or (2) a bdry edge.
+ stpivot(opensh, searchtet);
+ tsspivot1(searchtet, checkseg);
+ if (checkseg.sh == NULL) {
+ // No segment. It is an interior edge of R.
+ // Search for a new face in R.
+ spintet = searchtet;
+ fnextself(spintet); // Skip the current face.
+ while (1) {
+ pc = apex(spintet);
+ if (pmarktested(pc)) {
+ // 'opensh' is an interior edge.
+ if (!issubface(spintet)) {
+ // Create a new subface.
+ makeshellface(subfaces, &newsh);
+ setsorg(newsh, org(spintet));
+ setsdest(newsh, dest(spintet));
+ setsapex(newsh, pc);
+ // The new subface gets its markers from its neighbor.
+ setshellmark(newsh, shellmark(opensh));
+ if (checkconstraints) {
+ setareabound(newsh, areabound(opensh));
+ }
+ // Connect the new subface to adjacent tets.
+ tsbond(spintet, newsh);
+ fsymself(spintet);
+ sesymself(newsh);
+ tsbond(spintet, newsh);
+ // Connect newsh to its adjacent subface.
+ sbond(newsh, opensh);
+ // Add this new subface into list.
+ sinfect(newsh);
+ newshs->newindex((void **) &parysh);
+ *parysh = newsh;
+ // Push two "open" side of the new subface into stack.
+ for (i = 0; i < 2; i++) {
+ senextself(newsh);
+ newflipface = (badface *) flippool->alloc();
+ newflipface->ss = newsh;
+ newflipface->nextitem = flipstack;
+ flipstack = newflipface;
+ }
+ } else {
+ // Connect to another open edge.
+ tspivot(spintet, checksh);
+ sbond(opensh, checksh);
+ }
+ break;
+ } // if (pmarktested(pc))
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) {
+ // Not find any face to fill in R at this side.
+ // Suggest a point to split the edge.
+ success = 0;
+ break;
+ }
+ } // while (1)
+ } else {
+ // This side coincident with a boundary edge of R.
+ checkseg.shver = 0;
+ spivot(checkseg, oldsh);
+ if (sinfected(checkseg)) {
+ // It's a faked segment. Delete it.
+ spintet = searchtet;
+ while (1) {
+ tssdissolve1(spintet);
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) break;
+ }
+ shellfacedealloc(subsegs, checkseg.sh);
+ ssdissolve(oldsh);
+ checkseg.sh = NULL;
+ }
+ spivot(oldsh, casout);
+ if (casout.sh != NULL) {
+ casin = casout;
+ if (checkseg.sh != NULL) {
+ // Make sure that the subface has the right ori at the segment.
+ checkseg.shver = 0;
+ if (sorg(opensh) != sorg(checkseg)) {
+ sesymself(opensh);
+ }
+ spivot(casin, neighsh);
+ while (neighsh.sh != oldsh.sh) {
+ casin = neighsh;
+ spivot(casin, neighsh);
+ }
+ }
+ sbond1(opensh, casout);
+ sbond1(casin, opensh);
+ }
+ if (checkseg.sh != NULL) {
+ ssbond(opensh, checkseg);
+ }
+ } // if (checkseg.sh != NULL)
+ } // while ((flipstack != NULL) && success)
+
+ if (success) {
+ // Uninfect all new subfaces.
+ for (i = 0; i < newshs->objects; i++) {
+ parysh = (face *) fastlookup(newshs, i);
+ suninfect(*parysh);
+ }
+ // Delete old subfaces.
+ for (i = 0; i < missingshs->objects; i++) {
+ parysh = (face *) fastlookup(missingshs, i);
+ shellfacedealloc(subfaces, parysh->sh);
+ }
+ fillregioncount++;
+ } else {
+ // Failed to fill the region.
+ // Re-connect old subfaces at boundaries of R.
+ // Also delete fake segments.
+ for (i = 0; i < missingshbds->objects; i++) {
+ parysh = (face *) fastlookup(missingshbds, i);
+ // It still connect to 'casout'.
+ // Re-connect 'casin' to it.
+ spivot(*parysh, casout);
+ casin = casout;
+ spivot(casin, neighsh);
+ while (1) {
+ if (sinfected(neighsh)) break;
+ if (neighsh.sh == parysh->sh) break;
+ casin = neighsh;
+ spivot(casin, neighsh);
+ }
+ if (sinfected(neighsh)) {
+ sbond1(casin, *parysh);
+ }
+ sspivot(*parysh, checkseg);
+ if (checkseg.sh != NULL) {
+ if (checkseg.sh[3] != NULL) {
+ if (sinfected(checkseg)) {
+ sstpivot1(checkseg, searchtet);
+ spintet = searchtet;
+ while (1) {
+ tssdissolve1(spintet);
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) break;
+ }
+ ssdissolve(*parysh);
+ shellfacedealloc(subsegs, checkseg.sh);
+ }
+ }
+ }
+ }
+ // Delete all new subfaces.
+ for (i = 0; i < newshs->objects; i++) {
+ parysh = (face *) fastlookup(newshs, i);
+ shellfacedealloc(subfaces, parysh->sh);
+ }
+ // Clear the flip pool.
+ flippool->restart();
+ flipstack = NULL;
+
+ // Choose an interior edge of R to split.
+ assert(missingshs->objects > 1);
+ // Skip the first subface in 'missingshs'.
+ i = randomnation(missingshs->objects - 1) + 1;
+ parysh = (face *) fastlookup(missingshs, i);
+ recentsh = *parysh;
+ }
+
+ newshs->restart();
+
+ return success;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// insertpoint_cdt() Insert a new point into a CDT. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+int tetgenmesh::insertpoint_cdt(point newpt, triface *searchtet, face *splitsh,
+ face *splitseg, insertvertexflags *ivf,
+ arraypool *cavpoints, arraypool *cavfaces,
+ arraypool *cavshells, arraypool *newtets,
+ arraypool *crosstets, arraypool *misfaces)
+{
+ triface neightet, *parytet;
+ face checksh, *parysh, *parysh1;
+ face *paryseg, *paryseg1;
+ point *parypt;
+ int t1ver;
+ int i;
+
+ if (b->verbose > 2) {
+ printf(" Insert point %d into CDT\n", pointmark(newpt));
+ }
+
+ if (!insertpoint(newpt, searchtet, NULL, NULL, ivf)) {
+ // Point is not inserted. Check ivf->iloc for reason.
+ return 0;
}
- // Add this new subface into list.
- sinfect(newsh);
- newshs->newindex((void **) &parysh);
- *parysh = newsh;
- // Push two "open" side of the new subface into stack.
- for (i = 0; i < 2; i++) {
- senextself(newsh);
- newflipface = (badface *) flippool->alloc();
- newflipface->ss = newsh;
- newflipface->nextitem = flipstack;
- flipstack = newflipface;
+
+ for (i = 0; i < cavetetvertlist->objects; i++) {
+ cavpoints->newindex((void **) &parypt);
+ *parypt = * (point *) fastlookup(cavetetvertlist, i);
}
+ // Add the new point into the point list.
+ cavpoints->newindex((void **) &parypt);
+ *parypt = newpt;
- // Every other boundary edge of R is identified as a segment. Insert a faked
- // segments at the place if it is not a segment.
- for (i = 1; i < missingshbds->objects; i++) {
- parysh = (face *) fastlookup(missingshbds, i);
- ppt[0] = sorg(*parysh);
- ppt[1] = sdest(*parysh);
- point2tetorg(ppt[0], searchtet);
- dir = finddirection(&searchtet, ppt[1], 0);
- assert(dir == ACROSSVERT); // SELF_CHECK
- tsspivot1(searchtet, checkseg);
- if (checkseg.sh == NULL) {
- // Insert a fake segment at this tet.
- if (b->verbose > 2) {
- printf(" Insert a fake segment (%d, %d)\n", pointmark(ppt[0]),
- pointmark(ppt[1]));
- }
- makeshellface(subsegs, &fakeseg);
- setsorg(fakeseg, ppt[0]);
- setsdest(fakeseg, ppt[1]);
- sinfect(fakeseg); // Mark it as faked.
- // Connect it to all tets at this edge.
- spintet = searchtet;
- while (1) {
- tssbond1(spintet, fakeseg);
- fnextself(spintet);
- if (spintet.tet == searchtet.tet) break;
- }
- checkseg = fakeseg;
- }
- // Let the segment hold the old subface.
- checkseg.shver = 0;
- sbond1(checkseg, *parysh);
- // Remember it to free it later.
- *parysh = checkseg;
+ for (i = 0; i < cavebdrylist->objects; i++) {
+ cavfaces->newindex((void **) &parytet);
+ *parytet = * (triface *) fastlookup(cavebdrylist, i);
}
- // Loop until 'flipstack' is empty.
- while (flipstack != NULL) {
+ for (i = 0; i < caveoldtetlist->objects; i++) {
+ crosstets->newindex((void **) &parytet);
+ *parytet = * (triface *) fastlookup(caveoldtetlist, i);
+ }
- // Pop an "open" side from the stack.
- popface = flipstack;
- opensh = popface->ss;
- flipstack = popface->nextitem; // The next top item in stack.
- flippool->dealloc((void *) popface);
+ cavetetvertlist->restart();
+ cavebdrylist->restart();
+ caveoldtetlist->restart();
- // Process it if it is still open.
- spivot(opensh, casout);
- if (casout.sh == NULL) {
- if (b->verbose > 2) {
- printf(" Get an open side (%d, %d) - %d.\n",
- pointmark(sorg(opensh)), pointmark(sdest(opensh)),
- pointmark(sapex(opensh)));
+ // Insert the point using the cavity algorithm.
+ delaunizecavity(cavpoints, cavfaces, cavshells, newtets, crosstets,
+ misfaces);
+ fillcavity(cavshells, NULL, NULL, NULL, NULL, NULL, NULL);
+ carvecavity(crosstets, newtets, NULL);
+
+ if ((splitsh != NULL) || (splitseg != NULL)) {
+ // Insert the point into the surface mesh.
+ sinsertvertex(newpt, splitsh, splitseg, ivf->sloc, ivf->sbowywat);
+
+ // Put all new subfaces into stack.
+ for (i = 0; i < caveshbdlist->objects; i++) {
+ // Get an old subface at edge [a, b].
+ parysh = (face *) fastlookup(caveshbdlist, i);
+ spivot(*parysh, checksh); // The new subface [a, b, p].
+ // Do not recover a deleted new face (degenerated).
+ if (checksh.sh[3] != NULL) {
+ subfacstack->newindex((void **) &parysh);
+ *parysh = checksh;
}
- // Search a neighbor to close this side.
- stpivot(opensh, searchtet);
- tsspivot1(searchtet, checkseg);
- if (checkseg.sh == NULL) {
- // No segment. It is inside R. Search for a new face to fill in R.
- // Note that the face may not be found (see fig 2010-05-25-c).
- spintet = searchtet;
- fnextself(spintet); // Skip the current face.
- while (1) {
- pc = apex(spintet);
- if (pmarktested(pc)) {
- // Found a place for a new subface inside R -- Case (i).
- tspivot(spintet, checksh);
- if (checksh.sh == NULL) {
- // Create a new subface.
- if (b->verbose > 2) {
- printf(" Create a new subface (%d, %d, %d)\n",
- pointmark(org(spintet)), pointmark(dest(spintet)),
- pointmark(pc));
- }
- makeshellface(subfaces, &newsh);
- setsorg(newsh, org(spintet));
- setsdest(newsh, dest(spintet));
- setsapex(newsh, pc);
- // The new subface gets its markers from its neighbor.
- setshellmark(newsh, shellmark(opensh));
- if (checkconstraints) {
- setareabound(newsh, areabound(opensh));
- }
- // Connect the new subface to adjacent tets.
- tsbond(spintet, newsh);
- fsymself(spintet);
- sesymself(newsh);
- tsbond(spintet, newsh);
- // Connect newsh to its adjacent subface.
- sbond(newsh, opensh);
- // Add this new subface into list.
- sinfect(newsh);
- newshs->newindex((void **) &parysh);
- *parysh = newsh;
- // Push two "open" side of the new subface into stack.
- for (i = 0; i < 2; i++) {
- senextself(newsh);
- newflipface = (badface *) flippool->alloc();
- newflipface->ss = newsh;
- newflipface->nextitem = flipstack;
- flipstack = newflipface;
- }
- } else {
- // A new subface has already been created.
- assert(sinfected(checksh)); // It must be in stack.
- spivot(checksh, neighsh); // SELF_CHECK
- assert(neighsh.sh == NULL); // Its side must be open.
- if (b->verbose > 2) {
- printf(" Connect to another open side (%d, %d, %d)\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- sbond(opensh, checksh); // Simply connect them.
- }
- break; // -- Case (i)
- }
- fnextself(spintet);
- if (spintet.tet == searchtet.tet) {
- // Not find any face to fill in R at this side.
- // TO DO: suggest a point to split the edge.
- assert(0);
- }
- } // while (1)
- } else {
- // This side coincident with a boundary edge of R.
- checkseg.shver = 0;
- spivot(checkseg, oldsh);
- if (sinfected(checkseg)) {
- // It's a faked segment. Delete it.
- if (b->verbose > 2) {
- printf(" Delete a fake segment (%d, %d)\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
- spintet = searchtet;
- while (1) {
- tssdissolve1(spintet);
- fnextself(spintet);
- if (spintet.tet == searchtet.tet) break;
- }
- shellfacedealloc(subsegs, checkseg.sh);
- }
- if (b->verbose > 2) {
- printf(" Connect to a boundary edge (%d, %d, %d)\n",
- pointmark(sorg(oldsh)), pointmark(sdest(oldsh)),
- pointmark(sapex(oldsh)));
- }
- sspivot(oldsh, checkseg);
- spivot(oldsh, casout);
- if (casout.sh != NULL) {
- casin = casout;
- if (checkseg.sh != NULL) {
- // Make sure that the subface has the right ori at the segment.
- checkseg.shver = 0;
- if (sorg(opensh) != sorg(checkseg)) {
- sesymself(opensh);
- }
- spivot(casin, neighsh);
- while (neighsh.sh != oldsh.sh) {
- casin = neighsh;
- spivot(casin, neighsh);
- }
+ }
+
+ if (splitseg != NULL) {
+ // Queue two new subsegments in C(p) for recovery.
+ for (i = 0; i < cavesegshlist->objects; i++) {
+ paryseg = (face *) fastlookup(cavesegshlist, i);
+ subsegstack->newindex((void **) &paryseg1);
+ *paryseg1 = *paryseg;
+ }
+ } // if (splitseg != NULL)
+
+ // Delete the old subfaces in sC(p).
+ for (i = 0; i < caveshlist->objects; i++) {
+ parysh = (face *) fastlookup(caveshlist, i);
+ if (checksubfaceflag) {
+ // It is possible that this subface still connects to adjacent
+ // tets which are not in C(p). If so, clear connections in the
+ // adjacent tets at this subface.
+ stpivot(*parysh, neightet);
+ if (neightet.tet != NULL) {
+ if (neightet.tet[4] != NULL) {
+ // Found an adjacent tet. It must be not in C(p).
+ assert(!infected(neightet));
+ tsdissolve(neightet);
+ fsymself(neightet);
+ assert(!infected(neightet));
+ tsdissolve(neightet);
}
- sbond1(opensh, casout);
- sbond1(casin, opensh);
- }
- if (checkseg.sh != NULL) {
- ssbond(opensh, checkseg);
}
}
+ shellfacedealloc(subfaces, parysh->sh);
+ }
+ if (splitseg != NULL) {
+ // Delete the old segment in sC(p).
+ shellfacedealloc(subsegs, splitseg->sh);
+ }
- } // if (casout.sh == NULL)
-
- } // while (flipstack != NULL)
-
- // Uninfect all new subfaces.
- for (i = 0; i < newshs->objects; i++) {
- parysh = (face *) fastlookup(newshs, i);
- suninfect(*parysh);
+ // Clear working lists.
+ caveshlist->restart();
+ caveshbdlist->restart();
+ cavesegshlist->restart();
+ } // if ((splitsh != NULL) || (splitseg != NULL))
+
+ // Put all interior subfaces into stack for recovery.
+ // They were collected in carvecavity().
+ // Note: Some collected subfaces may be deleted by sinsertvertex().
+ for (i = 0; i < caveencshlist->objects; i++) {
+ parysh = (face *) fastlookup(caveencshlist, i);
+ if (parysh->sh[3] != NULL) {
+ subfacstack->newindex((void **) &parysh1);
+ *parysh1 = *parysh;
+ }
}
- if (b->verbose > 2) {
- printf(" Created %ld new subfaces.\n", newshs->objects);
+ // Put all interior segments into stack for recovery.
+ // They were collected in carvecavity().
+ // Note: Some collected segments may be deleted by sinsertvertex().
+ for (i = 0; i < caveencseglist->objects; i++) {
+ paryseg = (face *) fastlookup(caveencseglist, i);
+ if (paryseg->sh[3] != NULL) {
+ subsegstack->newindex((void **) &paryseg1);
+ *paryseg1 = *paryseg;
+ }
}
- fillregioncount++;
- return true;
+ caveencshlist->restart();
+ caveencseglist->restart();
+
+ return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// refineregion() Refine a missing region by inserting points. //
// //
+// 'splitsh' represents an edge of the facet to be split. It must be not a //
+// segment.
+// //
+// Assumption: The current mesh is a CDT and is convex. //
+// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::refineregion()
+void tetgenmesh::refineregion(face &splitsh, arraypool *cavpoints,
+ arraypool *cavfaces, arraypool *cavshells,
+ arraypool *newtets, arraypool *crosstets,
+ arraypool *misfaces)
{
- triface searchtet;
- face splitsh;
- face *paryseg, sseg;
- point steinpt, pa, pb, pc;
+ triface searchtet, spintet;
+ face splitseg, *paryseg;
+ point steinpt, pa, pb, refpt;
insertvertexflags ivf;
- REAL auv[2], buv[2], newuv[2], t;
- int fmark, fid, eid;
- int loc; // iloc, sloc;
- int s, i;
-
- // The mesh is a CDT.
- assert(subsegstack->objects == 0l); // SELF_CHECK
+ enum interresult dir;
+ long baknum = points->items;
+ int t1ver;
+ int i;
- // Create a new point.
- makepoint(&steinpt, FREEFACETVERTEX);
+ if (b->verbose > 2) {
+ printf(" Refining region at edge (%d, %d, %d).\n",
+ pointmark(sorg(splitsh)), pointmark(sdest(splitsh)),
+ pointmark(sapex(splitsh)));
+ }
- // The 'recentsh' saved an edge to be split.
- splitsh = recentsh;
// Add the Steiner point at the barycenter of the face.
pa = sorg(splitsh);
pb = sdest(splitsh);
- pc = sapex(splitsh);
-
- if (b->psc) {
- assert(in->facetmarkerlist != NULL);
- fmark = shellmark(splitsh) - 1;
- fid = in->facetmarkerlist[fmark];
- if (pointtype(pa) == RIDGEVERTEX) {
- in->getvertexparamonface(in->geomhandle, pointmark(pa), fid, auv);
- } else if (pointtype(pa) == FREESEGVERTEX) {
- eid = pointgeomtag(pa); // The Edge containing this Steiner point.
- t = pointgeomuv(pa, 0); // The Steiner point's parameter on Edge.
- in->getedgesteinerparamonface(in->geomhandle, eid, t, fid, auv);
- } else if (pointtype(pa) == FREEFACETVERTEX) {
- auv[0] = pointgeomuv(pa, 0);
- auv[1] = pointgeomuv(pa, 1);
- } else {
- assert(0);
- }
- if (pointtype(pb) == RIDGEVERTEX) {
- in->getvertexparamonface(in->geomhandle, pointmark(pb), fid, buv);
- } else if (pointtype(pb) == FREESEGVERTEX) {
- eid = pointgeomtag(pb); // The Edge containing this Steiner point.
- t = pointgeomuv(pb, 0); // The Steiner point's parameter on Edge.
- in->getedgesteinerparamonface(in->geomhandle, eid, t, fid, buv);
- } else if (pointtype(pb) == FREEFACETVERTEX) {
- buv[0] = pointgeomuv(pb, 0);
- buv[1] = pointgeomuv(pb, 1);
- } else {
- assert(0);
- }
- newuv[0] = 0.5 * (auv[0] + buv[0]);
- newuv[1] = 0.5 * (auv[1] + buv[1]);
- in->getsteineronface(in->geomhandle, fid, newuv, steinpt);
- setpointgeomuv(steinpt, 0, newuv[0]);
- setpointgeomuv(steinpt, 1, newuv[1]);
- setpointgeomtag(steinpt, fid);
- } else {
- for (i = 0; i < 3; i++) {
- steinpt[i] = (pa[i] + pb[i] + pc[i]) / 3.0;
- }
+ // Create a new point.
+ makepoint(&steinpt, FREEFACETVERTEX);
+ for (i = 0; i < 3; i++) {
+ steinpt[i] = 0.5 * (pa[i] + pb[i]);
}
- // Start searching it from 'recentet'.
- searchtet = recenttet;
- // Now insert the point p. The flags are chosen as follows:
- // - boywat = 2, the current T is a CDT,
- // - lawson = 2, do flip after inserting p, some existing segments
- // and subfaces may be flipped, they are queued and
- // and will be recovered.
- // - rejflag = 1, reject p if it encroaches upon at least one segment,
- // queue encroached segments.
- ivf.iloc = (int) OUTSIDE;
- ivf.bowywat = 2;
- ivf.lawson = 2;
- ivf.rejflag = 1;
- ivf.chkencflag = 0;
- ivf.sloc = (int) ONFACE;
- ivf.sbowywat = 2;
- ivf.splitbdflag = 0;
- ivf.validflag = 1;
- ivf.respectbdflag = 0;
- ivf.assignmeshsize = 0;
- loc = insertvertex(steinpt, &searchtet, &splitsh, NULL, &ivf);
-
- assert((loc != OUTSIDE) && (loc != ONVERTEX));
- if (loc == NEARVERTEX) {
- // The new point is either ON or VERY CLOSE to an existing point.
- pa = point2ppt(steinpt);
- printf(" !! Avoid to create a short edge (length = %g)\n",
- distance(steinpt, pa));
- // Indicate it may be an input problem.
- printf(" Short edge length bound is: %g. Tolerance is %g.\n",
- b->minedgelength, b->epsilon);
- terminatetetgen(4);
- }
-
- if (loc == ENCSEGMENT) {
- // Some segments are encroached and queued.
- assert(encseglist->objects > 0l);
- // Randomly pick one encroached segment to split.
- s = randomnation(encseglist->objects);
- paryseg = (face *) fastlookup(encseglist, s);
- sseg = *paryseg;
- // The new point p is the midpoint of this segment.
- getsteinerptonsegment(&sseg, NULL, steinpt);
- setpointtype(steinpt, FREESEGVERTEX);
- encseglist->restart(); // Clear the queue.
+ ivf.bowywat = 1; // Use the Bowyer-Watson algorrithm.
+ ivf.cdtflag = 1; // Only create the initial cavity.
+ ivf.sloc = (int) ONEDGE;
+ ivf.sbowywat = 1;
+ ivf.assignmeshsize = b->metric;
- // Start searching from an adjacent tetrahedron (containing the segment).
- sstpivot1(sseg, searchtet);
- spivot(sseg, splitsh);
- // Insert the point p. The flags are chosen as follows:
- // - boywat = 2, the current T is a CDT,
- // - lawson = 2, do flip after inserting p, some existing segments
- // and subfaces may be flipped, they are queued and
- // and will be recovered.
- // - rejflag = 0, always insert p, even it will cause some segments
- // or subfaces missing, queue missing boundaries.
- ivf.iloc = (int) ONEDGE;
- ivf.bowywat = 2;
- ivf.lawson = 2;
- ivf.rejflag = 0;
- ivf.chkencflag = 0;
- ivf.sloc = (int) ONEDGE;
- ivf.sbowywat = 2;
- ivf.splitbdflag = 0;
- ivf.validflag = 1;
- ivf.respectbdflag = 0;
- ivf.assignmeshsize = 0;
- loc = insertvertex(steinpt, &searchtet, &splitsh, &sseg, &ivf);
+ point2tetorg(pa, searchtet); // Start location from it.
+ ivf.iloc = (int) OUTSIDE;
- if (loc == NEARVERTEX) {
- // The new point is either ON or VERY CLOSE to an existing point.
- pa = point2ppt(steinpt);
- printf(" !! Avoid to create a short edge (length = %g)\n",
- distance(steinpt, pa));
- // Indicate it may be an input problem.
- printf(" Short edge length bound is: %g. Tolerance is %g.\n",
- b->minedgelength, b->epsilon);
- terminatetetgen(4);
+ ivf.rejflag = 1; // Reject it if it encroaches upon any segment.
+ if (!insertpoint_cdt(steinpt, &searchtet, &splitsh, NULL, &ivf, cavpoints,
+ cavfaces, cavshells, newtets, crosstets, misfaces)) {
+ if (ivf.iloc == (int) ENCSEGMENT) {
+ pointdealloc(steinpt);
+ // Split an encroached segment.
+ assert(encseglist->objects > 0);
+ i = randomnation(encseglist->objects);
+ paryseg = (face *) fastlookup(encseglist, i);
+ splitseg = *paryseg;
+ encseglist->restart();
+
+ // Split the segment.
+ pa = sorg(splitseg);
+ pb = sdest(splitseg);
+ // Create a new point.
+ makepoint(&steinpt, FREESEGVERTEX);
+ for (i = 0; i < 3; i++) {
+ steinpt[i] = 0.5 * (pa[i] + pb[i]);
+ }
+ point2tetorg(pa, searchtet);
+ ivf.iloc = (int) OUTSIDE;
+ ivf.rejflag = 0;
+ if (!insertpoint_cdt(steinpt, &searchtet, &splitsh, &splitseg, &ivf,
+ cavpoints, cavfaces, cavshells, newtets,
+ crosstets, misfaces)) {
+ assert(0);
+ }
+ st_segref_count++;
+ if (steinerleft > 0) steinerleft--;
+ } else {
+ assert(0);
}
-
- st_segref_count++;
} else {
st_facref_count++;
+ if (steinerleft > 0) steinerleft--;
}
- if (steinerleft > 0) steinerleft--;
- // Do flip to recover Delaunayniess.
- lawsonflip3d(steinpt, 2, 0, 0, 0);
+ while (subsegstack->objects > 0l) {
+ // seglist is used as a stack.
+ subsegstack->objects--;
+ paryseg = (face *) fastlookup(subsegstack, subsegstack->objects);
+ splitseg = *paryseg;
- // Some vertices may be queued, recover them.
- if (subvertstack->objects > 0l) {
- assert(0); //delaunizevertices();
- }
+ // Check if this segment has been recovered.
+ sstpivot1(splitseg, searchtet);
+ if (searchtet.tet != NULL) continue;
+
+ // Search the segment.
+ dir = scoutsegment(sorg(splitseg), sdest(splitseg), &searchtet, &refpt,
+ NULL);
+ if (dir == SHAREEDGE) {
+ // Found this segment, insert it.
+ if (!issubseg(searchtet)) {
+ // Let the segment remember an adjacent tet.
+ sstbond1(splitseg, searchtet);
+ // Bond the segment to all tets containing it.
+ spintet = searchtet;
+ do {
+ tssbond1(spintet, splitseg);
+ fnextself(spintet);
+ } while (spintet.tet != searchtet.tet);
+ } else {
+ // Collision! Should not happen.
+ assert(0);
+ }
+ } else {
+ if ((dir == ACROSSFACE) || (dir == ACROSSEDGE)) {
+ // Split the segment.
+ // Create a new point.
+ makepoint(&steinpt, FREESEGVERTEX);
+ //setpointtype(newpt, FREESEGVERTEX);
+ getsteinerptonsegment(&splitseg, refpt, steinpt);
+ ivf.iloc = (int) OUTSIDE;
+ ivf.rejflag = 0;
+ if (!insertpoint_cdt(steinpt, &searchtet, &splitsh, &splitseg, &ivf,
+ cavpoints, cavfaces, cavshells, newtets,
+ crosstets, misfaces)) {
+ assert(0);
+ }
+ st_segref_count++;
+ if (steinerleft > 0) steinerleft--;
+ } else {
+ // Maybe a PLC problem.
+ assert(0);
+ }
+ }
+ } // while
- // Some subsegments may be queued, recover them.
- if (subsegstack->objects > 0l) {
- delaunizesegments();
+ if (b->verbose > 2) {
+ printf(" Added %ld Steiner points.\n", points->items - baknum);
}
}
///////////////////////////////////////////////////////////////////////////////
// //
-// constrainedfacets() Recover subfaces saved in 'subfacestack'. //
+// constrainedfacets() Recover constrained facets in a CDT. //
+// //
+// All unrecovered subfaces are queued in 'subfacestack'. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -19290,16 +17716,14 @@ void tetgenmesh::constrainedfacets()
arraypool *tg_topshells, *tg_botshells, *tg_facfaces;
arraypool *tg_toppoints, *tg_botpoints;
arraypool *tg_missingshs, *tg_missingshbds, *tg_missingshverts;
-
- triface searchtet, neightet;
- face searchsh, neighsh, *parysh;
- face checkseg, *paryseg;
- point refpt, *parypt;
+ triface searchtet, neightet, crossedge;
+ face searchsh, *parysh, *parysh1;
+ face *paryseg;
+ point *parypt;
enum interresult dir;
- bool success;
int facetcount;
- //int bakhullsize;
- int crossflag;
+ int success;
+ int t1ver;
int i, j;
// Initialize arrays.
@@ -19317,245 +17741,184 @@ void tetgenmesh::constrainedfacets()
tg_missingshs = new arraypool(sizeof(face), 10);
tg_missingshbds = new arraypool(sizeof(face), 10);
tg_missingshverts = new arraypool(sizeof(point), 8);
-
// This is a global array used by refineregion().
- encseglist = new arraypool(sizeof(face), 4);
+ encseglist = new arraypool(sizeof(face), 4);
facetcount = 0;
- // Loop until 'subfacstack' is empty.
while (subfacstack->objects > 0l) {
+
subfacstack->objects--;
parysh = (face *) fastlookup(subfacstack, subfacstack->objects);
searchsh = *parysh;
- if (searchsh.sh[3] == NULL) continue; // Skip a dead subface.
+ if (searchsh.sh[3] == NULL) continue; // It is dead.
+ if (isshtet(searchsh)) continue; // It is recovered.
- stpivot(searchsh, neightet);
- if (neightet.tet == NULL) {
- // Find an unrecovered subface.
- smarktest(searchsh);
- tg_facfaces->newindex((void **) &parysh);
- *parysh = searchsh;
- // Collect all non-recovered subfaces of the same facet.
- for (i = 0; i < tg_facfaces->objects; i++) {
- searchsh = * (face *) fastlookup(tg_facfaces, i);
- for (j = 0; j < 3; j++) {
- sspivot(searchsh, checkseg);
- if (checkseg.sh == NULL) {
- spivot(searchsh, neighsh);
- assert(neighsh.sh != NULL); // SELF_CHECK
- if (!smarktested(neighsh)) {
- // It may be already recovered.
- stpivot(neighsh, neightet);
- if (neightet.tet == NULL) {
- smarktest(neighsh);
- tg_facfaces->newindex((void **) &parysh);
- *parysh = neighsh;
- }
+ // Collect all unrecovered subfaces which are co-facet.
+ smarktest(searchsh);
+ tg_facfaces->newindex((void **) &parysh);
+ *parysh = searchsh;
+ for (i = 0; i < tg_facfaces->objects; i++) {
+ parysh = (face *) fastlookup(tg_facfaces, i);
+ for (j = 0; j < 3; j++) {
+ if (!isshsubseg(*parysh)) {
+ spivot(*parysh, searchsh);
+ assert(searchsh.sh != NULL); // SELF_CHECK
+ if (!smarktested(searchsh)) {
+ if (!isshtet(searchsh)) {
+ smarktest(searchsh);
+ tg_facfaces->newindex((void **) &parysh1);
+ *parysh1 = searchsh;
}
}
- senextself(searchsh);
- } // j
- } // i
- // Have found all facet subfaces (vertices). Uninfect them.
- for (i = 0; i < tg_facfaces->objects; i++) {
- parysh = (face *) fastlookup(tg_facfaces, i);
- sunmarktest(*parysh);
- }
+ }
+ senextself(*parysh);
+ } // j
+ } // i
+ // Have found all facet subfaces. Unmark them.
+ for (i = 0; i < tg_facfaces->objects; i++) {
+ parysh = (face *) fastlookup(tg_facfaces, i);
+ sunmarktest(*parysh);
+ }
- if (b->verbose > 2) {
- printf(" Recover facet #%d: %ld subfaces.\n", facetcount + 1,
- tg_facfaces->objects);
- }
- facetcount++;
-
- // Loop until 'tg_facfaces' is empty.
- while (tg_facfaces->objects > 0l) {
- // Get the last subface of this array.
- tg_facfaces->objects--;
- parysh = (face *) fastlookup(tg_facfaces, tg_facfaces->objects);
- searchsh = *parysh;
-
- if (searchsh.sh[3] == NULL) continue; // Skip a dead subface.
-
- stpivot(searchsh, neightet);
- if (neightet.tet != NULL) continue; // Not a missing subface.
-
- // Insert the subface.
- searchtet.tet = NULL;
- dir = scoutsubface(&searchsh, &searchtet);
- if (dir == SHAREFACE) continue; // The subface is inserted.
- if (dir == COLLISIONFACE) continue; // The subface is removed.
-
- // The subface is missing. Form the missing region.
- // Re-use 'tg_crosstets' for 'adjtets'.
- formmissingregion(&searchsh, tg_missingshs, tg_missingshbds,
- tg_missingshverts, tg_crosstets);
-
- // Search for a crossing edge (tg_crosstets is cleared).
- crossflag = scoutcrossedge(searchtet, tg_crosstets, tg_missingshs);
-
- if (crossflag == 1) {
- // Recover subfaces by local retetrahedralization.
- // Form a cavity of crossing tets.
- if (formcavity(&searchtet, tg_missingshs, tg_crosstets, tg_topfaces,
- tg_botfaces, tg_toppoints, tg_botpoints)) {
- if (!b->flipinsert) {
- // Tetrahedralize the top part. Re-use 'tg_midfaces'.
- delaunizecavity(tg_toppoints, tg_topfaces, tg_topshells,
- tg_topnewtets, tg_crosstets, tg_midfaces);
- // Tetrahedralize the bottom part. Re-use 'tg_midfaces'.
- delaunizecavity(tg_botpoints, tg_botfaces, tg_botshells,
- tg_botnewtets, tg_crosstets, tg_midfaces);
- // Fill the cavity with new tets.
- success = fillcavity(tg_topshells, tg_botshells, tg_midfaces,
- tg_missingshs);
- if (success) {
- // Cavity is remeshed. Delete old tets and outer new tets.
- carvecavity(tg_crosstets, tg_topnewtets, tg_botnewtets);
- // Insert the missing region into cavity.
- j = 0; // FOR DEBUG! Count the number of non-recovered faces.
- for (i = 0; i < tg_missingshs->objects; i++) {
- searchsh = * (face *) fastlookup(tg_missingshs, i);
- searchtet.tet = NULL;
- dir = scoutsubface(&searchsh, &searchtet);
- assert(dir != COLLISIONFACE); // SELF_CHECK
- if (dir != SHAREFACE) {
- // A subface is missing. This is possible that the subface
- // is not actually a constrained Delaunay face in T.
- // Add this face at the end of the list, so it will be
- // processed immediately. This is necessary because we
- // have created some non-locally Delaunay face (by the
- // remesh of the cavity). We have to insert the subfaces
- // to make these face constrained Delaunay.
- tg_facfaces->newindex((void **) &parysh);
- *parysh = searchsh;
- j++; // FOR DEBUG!
- }
- } // i
- // Recover interior subfaces.
- for (i = 0; i < caveencshlist->objects; i++) {
- searchsh = * (face *) fastlookup(caveencshlist, i);
- searchtet.tet = NULL;
- dir = scoutsubface(&searchsh, &searchtet);
- assert(dir != COLLISIONFACE); // SELF_CHECK
- if (dir != SHAREFACE) {
- // The subface is missing. This is possible that the subface
- // is removed by the enlargement of the cavity. It has to
- // be recovered.
- // Add this face at the end of the list, so it will be
- // processed immediately. We have to insert the subfaces
- // to make these face constrained Delaunay.
- tg_facfaces->newindex((void **) &parysh);
- *parysh = searchsh;
- j++; // FOR DEBUG!
- }
- } // i
- // Recover interior segments. This should always be recovered.
- for (i = 0; i < caveencseglist->objects; i++) {
- paryseg = (face *) fastlookup(caveencseglist, i);
- searchtet.tet = NULL;
- refpt = NULL;
- dir = scoutsegment(sorg(*paryseg),sdest(*paryseg),&searchtet,
- &refpt, NULL);
- assert(dir == SHAREEDGE);
- // Insert this segment.
- tsspivot1(searchtet, checkseg); // SELF_CHECK
- if (checkseg.sh == NULL) {
- // Let the segment remember an adjacent tet.
- sstbond1(*paryseg, searchtet);
- // Bond the segment to all tets containing it.
- neightet = searchtet;
- do {
- tssbond1(neightet, *paryseg);
- fnextself(neightet);
- } while (neightet.tet != searchtet.tet);
- } else {
- // Collision! Should not happen.
- assert(0);
- }
- } // i
- caveencshlist->restart();
- caveencseglist->restart();
- } else {
- // Restore old tets and delete new tets.
- restorecavity(tg_crosstets, tg_topnewtets, tg_botnewtets);
- // Set a handle for searching subface.
- //recentsh = searchsh;
- }
+ if (b->verbose > 2) {
+ printf(" Recovering facet #%d: %ld subfaces.\n", facetcount + 1,
+ tg_facfaces->objects);
+ }
+ facetcount++;
+
+ while (tg_facfaces->objects > 0l) {
+
+ tg_facfaces->objects--;
+ parysh = (face *) fastlookup(tg_facfaces, tg_facfaces->objects);
+ searchsh = *parysh;
+
+ if (searchsh.sh[3] == NULL) continue; // It is dead.
+ if (isshtet(searchsh)) continue; // It is recovered.
+
+ searchtet.tet = NULL;
+ dir = scoutsubface(&searchsh, &searchtet);
+ if (dir == SHAREFACE) continue; // The subface is inserted.
+
+ // The subface is missing. Form the missing region.
+ // Re-use 'tg_crosstets' for 'adjtets'.
+ formregion(&searchsh, tg_missingshs, tg_missingshbds, tg_missingshverts);
+
+ if (scoutcrossedge(searchtet, tg_missingshbds, tg_missingshs)) {
+ // Save this crossing edge, will be used by fillcavity().
+ crossedge = searchtet;
+ // Form a cavity of crossing tets.
+ success = formcavity(&searchtet, tg_missingshs, tg_crosstets,
+ tg_topfaces, tg_botfaces, tg_toppoints,
+ tg_botpoints);
+ if (success) {
+ if (!b->flipinsert) {
+ // Tetrahedralize the top part. Re-use 'tg_midfaces'.
+ delaunizecavity(tg_toppoints, tg_topfaces, tg_topshells,
+ tg_topnewtets, tg_crosstets, tg_midfaces);
+ // Tetrahedralize the bottom part. Re-use 'tg_midfaces'.
+ delaunizecavity(tg_botpoints, tg_botfaces, tg_botshells,
+ tg_botnewtets, tg_crosstets, tg_midfaces);
+ // Fill the cavity with new tets.
+ success = fillcavity(tg_topshells, tg_botshells, tg_midfaces,
+ tg_missingshs, tg_topnewtets, tg_botnewtets,
+ &crossedge);
+ if (success) {
+ // Cavity is remeshed. Delete old tets and outer new tets.
+ carvecavity(tg_crosstets, tg_topnewtets, tg_botnewtets);
} else {
- // Use the flip algorithm of Shewchuk to recover the subfaces.
- flipinsertfacet(tg_crosstets, tg_toppoints, tg_botpoints,
- tg_missingshverts);
- // Check the missing subfaces again.
- j = 0; // FOR DEBUG! Count the number of non-recovered faces.
- for (i = 0; i < tg_missingshs->objects; i++) {
- searchsh = * (face *) fastlookup(tg_missingshs, i);
- searchtet.tet = NULL;
- dir = scoutsubface(&searchsh, &searchtet);
- assert(dir != COLLISIONFACE); // SELF_CHECK
- if (dir != SHAREFACE) {
- // A subface is missing. This is possible that the subface
- // is not actually a constrained Delaunay face in T.
- // Add this face at the end of the list, so it will be
- // processed immediately. This is necessary because we
- // have created some non-locally Delaunay face (by the
- // remesh of the cavity). We have to insert the subfaces
- // to make these face constrained Delaunay.
- tg_facfaces->newindex((void **) &parysh);
- *parysh = searchsh;
- j++; // FOR DEBUG!
- }
- } // i
- // Clear working lists.
- tg_crosstets->restart();
- tg_topfaces->restart();
- tg_botfaces->restart();
- tg_toppoints->restart();
- tg_botpoints->restart();
- success = true;
- } // if (b->flipinsert)
- } else {
- // Formcavity failed.
- success = false;
- }
- } else { //if (crossflag == 0) {
- // Recover subfaces by retriangulate the surface mesh.
- // Re-use tg_topshells for newshs.
- success = fillregion(tg_missingshs, tg_missingshbds, tg_topshells);
- if (success) {
- // Region is remeshed. Delete old subfaces (in tg_missingshs).
- for (i = 0; i < tg_missingshs->objects; i++) {
- parysh = (face *) fastlookup(tg_missingshs, i);
- shellfacedealloc(subfaces, parysh->sh);
+ restorecavity(tg_crosstets, tg_topnewtets, tg_botnewtets,
+ tg_missingshbds);
}
- tg_topshells->restart();
} else {
- // Search a handle for searching tetrahedron.
- recenttet = searchtet;
- }
- }
+ // Use the flip algorithm of Shewchuk to recover the subfaces.
+ flipinsertfacet(tg_crosstets, tg_toppoints, tg_botpoints,
+ tg_missingshverts);
+ // Recover the missing region.
+ success = fillregion(tg_missingshs, tg_missingshbds, tg_topshells);
+ assert(success);
+ // Clear working lists.
+ tg_crosstets->restart();
+ tg_topfaces->restart();
+ tg_botfaces->restart();
+ tg_toppoints->restart();
+ tg_botpoints->restart();
+ } // b->flipinsert
- // Unmarktest all points of the missing region.
- for (i = 0; i < tg_missingshverts->objects; i++) {
- parypt = (point *) fastlookup(tg_missingshverts, i);
- punmarktest(*parypt);
- }
- tg_missingshverts->restart();
- tg_missingshbds->restart();
- tg_missingshs->restart();
+ if (success) {
+ // Recover interior subfaces.
+ for (i = 0; i < caveencshlist->objects; i++) {
+ parysh = (face *) fastlookup(caveencshlist, i);
+ dir = scoutsubface(parysh, &searchtet);
+ if (dir != SHAREFACE) {
+ // Add this face at the end of the list, so it will be
+ // processed immediately.
+ tg_facfaces->newindex((void **) &parysh1);
+ *parysh1 = *parysh;
+ }
+ }
+ caveencshlist->restart();
+ // Recover interior segments. This should always be recovered.
+ for (i = 0; i < caveencseglist->objects; i++) {
+ paryseg = (face *) fastlookup(caveencseglist, i);
+ dir = scoutsegment(sorg(*paryseg),sdest(*paryseg),&searchtet,
+ NULL, NULL);
+ assert(dir == SHAREEDGE);
+ // Insert this segment.
+ if (!issubseg(searchtet)) {
+ // Let the segment remember an adjacent tet.
+ sstbond1(*paryseg, searchtet);
+ // Bond the segment to all tets containing it.
+ neightet = searchtet;
+ do {
+ tssbond1(neightet, *paryseg);
+ fnextself(neightet);
+ } while (neightet.tet != searchtet.tet);
+ } else {
+ // Collision! Should not happen.
+ assert(0);
+ }
+ }
+ caveencseglist->restart();
+ } // success - remesh cavity
+ } // success - form cavity
+ } else {
+ // Recover subfaces by retriangulate the surface mesh.
+ // Re-use tg_topshells for newshs.
+ success = fillregion(tg_missingshs, tg_missingshbds, tg_topshells);
+ }
- if (!success) {
- // The missing region can not be recovered. Refine it.
- refineregion();
- // Clean the current list of facet subfaces.
- //tg_facfaces->restart();
- }
- } // while (tg_facfaces->objects > 0l)
+ // Unmarktest all points of the missing region.
+ for (i = 0; i < tg_missingshverts->objects; i++) {
+ parypt = (point *) fastlookup(tg_missingshverts, i);
+ punmarktest(*parypt);
+ }
+ tg_missingshverts->restart();
+ tg_missingshbds->restart();
+ tg_missingshs->restart();
- } // if (neightet.tet == NULL)
- } // while (subfacstack->objects > 0l)
+ if (!success) {
+ // The missing region can not be recovered. Refine it.
+ refineregion(recentsh, tg_toppoints, tg_topfaces, tg_topshells,
+ tg_topnewtets, tg_crosstets, tg_midfaces);
+ // Clean the current list of facet subfaces.
+ // tg_facfaces->restart();
+ }
+ } // while (tg_facfaces->objects)
+
+ } // while ((subfacstack->objects)
+
+ // Accumulate the dynamic memory.
+ totalworkmemory += (tg_crosstets->totalmemory + tg_topnewtets->totalmemory +
+ tg_botnewtets->totalmemory + tg_topfaces->totalmemory +
+ tg_botfaces->totalmemory + tg_midfaces->totalmemory +
+ tg_toppoints->totalmemory + tg_botpoints->totalmemory +
+ tg_facfaces->totalmemory + tg_topshells->totalmemory +
+ tg_botshells->totalmemory + tg_missingshs->totalmemory +
+ tg_missingshbds->totalmemory +
+ tg_missingshverts->totalmemory +
+ encseglist->totalmemory);
// Delete arrays.
delete tg_crosstets;
@@ -19590,15 +17953,14 @@ void tetgenmesh::constraineddelaunay(clock_t& tv)
// Statistics.
long bakfillregioncount;
long bakcavitycount, bakcavityexpcount;
+ long bakseg_ref_count;
if (!b->quiet) {
printf("Constrained Delaunay...\n");
}
- //if (!b->psc) {
- // Only identify acute vertex for PLC inputs.
- markacutevertices();
- //}
+ // Identify acute vertex for PLC inputs.
+ markacutevertices();
if (b->verbose) {
printf(" Delaunizing segments.\n");
@@ -19606,37 +17968,25 @@ void tetgenmesh::constraineddelaunay(clock_t& tv)
checksubsegflag = 1;
- // Put all segments into the list.
- if (0) { //if (b->order == 4) { // '-o4' option (for debug)
- // In sequential order.
- subsegs->traversalinit();
- for (i = 0; i < subsegs->items; i++) {
- searchseg.sh = shellfacetraverse(subsegs);
- //sinfect(searchseg); // Only save it once.
- subsegstack->newindex((void **) &paryseg);
- *paryseg = searchseg;
- }
- } else {
- // In random order.
- subsegs->traversalinit();
- for (i = 0; i < subsegs->items; i++) {
- s = randomnation(i + 1);
- // Move the s-th seg to the i-th.
- subsegstack->newindex((void **) &paryseg);
- *paryseg = * (face *) fastlookup(subsegstack, s);
- // Put i-th seg to be the s-th.
- searchseg.sh = shellfacetraverse(subsegs);
- //sinfect(searchseg); // Only save it once.
- paryseg = (face *) fastlookup(subsegstack, s);
- *paryseg = searchseg;
- }
+ // Put all segments into the list (in random order).
+ subsegs->traversalinit();
+ for (i = 0; i < subsegs->items; i++) {
+ s = randomnation(i + 1);
+ // Move the s-th seg to the i-th.
+ subsegstack->newindex((void **) &paryseg);
+ *paryseg = * (face *) fastlookup(subsegstack, s);
+ // Put i-th seg to be the s-th.
+ searchseg.sh = shellfacetraverse(subsegs);
+ //sinfect(searchseg); // Only save it once.
+ paryseg = (face *) fastlookup(subsegstack, s);
+ *paryseg = searchseg;
}
// Recover non-Delaunay segments.
delaunizesegments();
if (b->verbose) {
- printf(" %ld Steiner points.\n", st_segref_count);
+ printf(" Inserted %ld Steiner points.\n", st_segref_count);
}
tv = clock();
@@ -19645,17 +17995,13 @@ void tetgenmesh::constraineddelaunay(clock_t& tv)
printf(" Constraining facets.\n");
}
- if (b->flipinsert) {
- // Clear the counters.
- flip23count = flip32count = flip44count = 0l;
- }
-
// Subfaces will be introduced.
checksubfaceflag = 1;
bakfillregioncount = fillregioncount;
bakcavitycount = cavitycount;
bakcavityexpcount = cavityexpcount;
+ bakseg_ref_count = st_segref_count;
// Randomly order the subfaces.
subfaces->traversalinit();
@@ -19684,10 +18030,10 @@ void tetgenmesh::constraineddelaunay(clock_t& tv)
}
printf(".\n");
}
- if (st_segref_count + st_facref_count > 0) {
+ if (st_segref_count + st_facref_count - bakseg_ref_count > 0) {
printf(" Inserted %ld (%ld, %ld) refine points.\n",
- st_segref_count + st_facref_count, st_segref_count,
- st_facref_count);
+ st_segref_count + st_facref_count - bakseg_ref_count,
+ st_segref_count - bakseg_ref_count, st_facref_count);
}
}
}
@@ -19711,10 +18057,6 @@ void tetgenmesh::constraineddelaunay(clock_t& tv)
// the flip face, and [d,e] is the flip edge. NOTE: 'pc' may be 'dummypoint',//
// other points must not be 'dummypoint'. //
// //
-// For avoiding mutually flipping, once a crossing face is flipped, it will //
-// never be re-created again. Also, we never create a face or edge which is //
-// intersecting the current recovering segment or subface. //
-// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
@@ -19722,45 +18064,23 @@ int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
int level, int edgepivot,
flipconstraints* fc)
{
- int rejflag;
- int i;
-
point tmppts[3];
- REAL normal[3], area, len;
- REAL ori1, ori2;
- REAL abovept[3];
-
enum interresult dir;
int types[2], poss[4];
int intflag;
-
- rejflag = 0;
+ int rejflag = 0;
+ int i;
if (fc->seg[0] != NULL) {
// A constraining edge is given (e.g., for edge recovery).
if (fliptype == 1) {
// A 2-to-3 flip: [a,b,c] => [e,d,a], [e,d,b], [e,d,c].
- if (pc != dummypoint) {
- // Do not flip if the newly created faces intersect this edge in
- // their interiors.
- tmppts[0] = pa;
- tmppts[1] = pb;
- tmppts[2] = pc;
- if (0) {
- // Make sure that the three new faces are not degenerate.
- for (i = 0; i < 3 && !rejflag; i++) {
- facenormal(pe, pd, tmppts[i], normal, 1, &len);
- area = sqrt(DOT(normal, normal));
- if (area == 0) {
- rejflag = 1; // A degenerate face.
- } else {
- if ((area / (len * len)) < b->epsilon) {
- rejflag = 1; // A nearly degenerate face.
- }
- }
- } // i
- }
- for (i = 0; i < 3 && !rejflag; i++) {
+ tmppts[0] = pa;
+ tmppts[1] = pb;
+ tmppts[2] = pc;
+ for (i = 0; i < 3 && !rejflag; i++) {
+ if (tmppts[i] != dummypoint) {
+ // Test if the face [e,d,#] intersects the edge.
intflag = tri_edge_test(pe, pd, tmppts[i], fc->seg[0], fc->seg[1],
NULL, 1, types, poss);
if (intflag == 2) {
@@ -19775,12 +18095,7 @@ int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
// Since [e,d] is the newly created edge. Reject this flip.
rejflag = 1;
}
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- } // dir
+ }
} else if (intflag == 4) {
// They may intersect at either a point or a line segment.
dir = (enum interresult) types[0];
@@ -19790,177 +18105,32 @@ int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
// Since [e,d] is the newly created edge. Reject this flip.
rejflag = 1;
}
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- }
- } // if (intflag == 4)
- } // i
- } else { // pc == dummypoint
- // Do not flip if the new hull edge [e,d] will intersect this edge
- // in its interior.
- // Comment: Here we actually need a 3D edge-edge test.
- // We only do test if the edge in 'fc' is coplanar with the plane
- // containing a,b,e,and d.
- // Choose a better triangle [a,b,e] or [a,b,d].
- facenormal(pa, pb, pe, normal, 1, &len);
- area = sqrt(DOT(normal, normal));
- facenormal(pa, pb, pd, normal, 1, &len);
- len = sqrt(DOT(normal, normal)); // Re-use len as area.
- if (area > len) {
- // Choose [a,b,e]
- ori1 = orient3d(pa, pb, pe, fc->seg[0]);
- ori2 = orient3d(pa, pb, pe, fc->seg[1]);
- } else {
- // Choose [a,b,d]
- ori1 = orient3d(pa, pb, pd, fc->seg[0]);
- ori2 = orient3d(pa, pb, pd, fc->seg[1]);
- }
- if ((ori1 == 0) && (ori2 == 0)) {
- calculateabovepoint4(pa, pb, pe, pd);
- for (i = 0; i < 3; i++) {
- abovept[i] = dummypoint[i];
- }
- intflag = tri_edge_test(pe, pd, abovept, fc->seg[0], fc->seg[1],
- NULL, 1, types, poss);
- if (intflag == 2) {
- dir = (enum interresult) types[0];
- assert(dir != ACROSSFACE);
- if (dir == ACROSSEDGE) {
- if (poss[0] == 0) {
- // The interior of [e,d] intersect the segment.
- // Since [e,d] is the newly created edge. Reject this flip.
- rejflag = 1;
- }
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- }
- } else if (intflag == 4) {
- // [e,d,abovept] is coplanar with the constraining edge 'fc'.
- // This is poissible if the edge in 'fc' is just the edge [e,d]
- // (SHAREEDGE) or they share a common vertex (SHAREVEER)
- dir = (enum interresult) types[0];
- if (dir == ACROSSEDGE) {
- // This case can only happen if [e,d] is coplanar with 'fc'.
- assert(0); // Not possible.
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
}
}
- }
- } // if (pc == dummypoint)
+ } // if (tmppts[0] != dummypoint)
+ } // i
} else if (fliptype == 2) {
// A 3-to-2 flip: [e,d,a], [e,d,b], [e,d,c] => [a,b,c]
if (pc != dummypoint) {
- if (0) {
- // Make sure that [a,b,c] is a valid face.
- facenormal(pa, pb, pc, normal, 1, &len);
- area = sqrt(DOT(normal, normal));
- if (area == 0) {
- rejflag = 1; // A degenerate face.
- } else {
- if ((area / (len * len)) < b->epsilon) {
- rejflag = 1; // A nearly degenerate face.
- }
+ // Check if the new face [a,b,c] intersect the edge in its interior.
+ intflag = tri_edge_test(pa, pb, pc, fc->seg[0], fc->seg[1], NULL,
+ 1, types, poss);
+ if (intflag == 2) {
+ // They intersect at a single point.
+ dir = (enum interresult) types[0];
+ if (dir == ACROSSFACE) {
+ // The interior of [a,b,c] intersect the segment.
+ rejflag = 1; // Do not flip.
}
- }
- if (!rejflag) {
- // Check if the new face [a,b,c] intersect the edge in its interior.
- intflag = tri_edge_test(pa, pb, pc, fc->seg[0], fc->seg[1], NULL,
- 1, types, poss);
- if (intflag == 2) {
- // They intersect at a single point.
- dir = (enum interresult) types[0];
- if (dir == ACROSSFACE) {
- // The interior of [a,b,c] intersect the segment.
- rejflag = 1; // Do not flip.
- } else if (dir == ACROSSEDGE) {
- // This case is possible since we allow a previous 2-to-3 flip
- // even it will create a degenerate tet at edge [a,b].
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- }
- } else if (intflag == 4) {
- // [a,b,c] is coplanar with the edge.
- dir = (enum interresult) types[0];
- if (dir == ACROSSEDGE) {
- // The boundary of [a,b,c] intersect the segment.
- // An example is found in case 'camila.poly', during the recovery
- // of segment [151, 161] (at linklevel = 2). See: 2011-06-10-a.
- rejflag = 1; // Do not flip.
- }
+ } else if (intflag == 4) {
+ // [a,b,c] is coplanar with the edge.
+ dir = (enum interresult) types[0];
+ if (dir == ACROSSEDGE) {
+ // The boundary of [a,b,c] intersect the segment.
+ rejflag = 1; // Do not flip.
}
- } // if (!relflag)
- } else { // pc == dummypoint
- // The flip 3-to-2 will replace [e,d] with a new hull edge [a,b].
- // Only do flip if [a,b] does not intersect the edge of 'fc'.
- // Comment: Here we acutually need a 3D edge-edge intersection test.
- // We only do test if the edge in 'fc' is coplanar with the plane
- // containing a,b,e, and d.
- // Choose a better triangle [a,b,e] or [a,b,d].
- facenormal(pa, pb, pe, normal, 1, &len);
- area = sqrt(DOT(normal, normal));
- facenormal(pa, pb, pd, normal, 1, &len);
- len = sqrt(DOT(normal, normal)); // Re-use len as area.
- if (area > len) {
- // Choose [a,b,e]
- ori1 = orient3d(pa, pb, pe, fc->seg[0]);
- ori2 = orient3d(pa, pb, pe, fc->seg[1]);
- } else {
- // Choose [a,b,d]
- ori1 = orient3d(pa, pb, pd, fc->seg[0]);
- ori2 = orient3d(pa, pb, pd, fc->seg[1]);
}
- if ((ori1 == 0) && (ori2 == 0)) {
- // The edge in 'fc' is coplanar with the plane containing [a,b,e,d].
- calculateabovepoint4(pa, pb, pe, pd);
- for (i = 0; i < 3; i++) {
- abovept[i] = dummypoint[i];
- }
- intflag = tri_edge_test(pa, pb, abovept, fc->seg[0], fc->seg[1],
- NULL, 1, types, poss);
- if (intflag == 2) {
- dir = (enum interresult) types[0];
- assert(dir != ACROSSFACE);
- if (dir == ACROSSEDGE) {
- assert(0); // Check this case.
- rejflag = 1; // Do not flip.
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- }
- } else if (intflag == 4) {
- // The edge 'fc' is coplanar with [a,b,abovept].
- // This is poissible if the edge in 'fc' is just the edge [a,b]
- // (SHAREEDGE) or they share a common vertex (SHAREVEER)
- dir = (enum interresult) types[0];
- if (dir == ACROSSEDGE) {
- // This case can only happen if [a,b] is coplanar with 'fc'.
- assert(0); // Not possible.
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) ||
- (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- }
- }
- } // if (ori1 == 0 && ori2 == 0)
- }
- } else {
- assert(0); // An unknown flip type.
+ } // if (pc != dummypoint)
}
} // if (fc->seg[0] != NULL)
@@ -19978,11 +18148,7 @@ int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
rejflag = 1;
} else if (dir == ACROSSEDGE) {
rejflag = 1;
- } else {
- if ((dir == ACROSSVERT) || (dir == TOUCHEDGE) || (dir == TOUCHFACE)) {
- assert(0); // Check this case.
- }
- }
+ }
} else if (intflag == 4) {
// The edge [e,d] is coplanar with the face.
// There may be two intersections.
@@ -20123,7 +18289,7 @@ int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
// //
// removeedgebyflips() Remove an edge by flips. //
// //
-// 'flipedge' is a non-convex or flat edge [a,b,#,#]. //
+// 'flipedge' is a non-convex or flat edge [a,b,#,#] to be removed. //
// //
// The return value is a positive integer, it indicates whether the edge is //
// removed or not. A value "2" means the edge is removed, othereise, the //
@@ -20135,77 +18301,45 @@ int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
int tetgenmesh::removeedgebyflips(triface *flipedge, flipconstraints* fc)
{
triface *abtets, spintet;
- face checkseg, *paryseg;
- int counter; // DEBUG
+ int t1ver;
int n, nn, i;
- // Bakup valuses (for free spaces in flipnm_post()).
- int bakunflip = fc->unflip;
- int bakcollectnewtets = fc->collectnewtets;
-
-
- if (b->verbose > 2) {
- printf(" Removing edge (%d, %d)\n", pointmark(org(*flipedge)),
- pointmark(dest(*flipedge)));
- }
-
- //if (fc != NULL) {
- fc->clearcounters();
- //}
-
if (checksubsegflag) {
// Do not flip a segment.
- tsspivot1(*flipedge, checkseg);
- if (checkseg.sh != NULL) {
- if (b->verbose > 2) {
- printf(" Can't flip a segment (%d, %d).\n",
- pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
- }
- //if (fc != NULL) {
- fc->encsegcount++;
- if (fc->collectencsegflag) {
- if (!sinfected(checkseg)) {
- // Queue this segment in list.
- sinfect(checkseg);
- caveencseglist->newindex((void **) &paryseg);
- *paryseg = checkseg;
- }
+ if (issubseg(*flipedge)) {
+ if (fc->collectencsegflag) {
+ face checkseg, *paryseg;
+ tsspivot1(*flipedge, checkseg);
+ if (!sinfected(checkseg)) {
+ // Queue this segment in list.
+ sinfect(checkseg);
+ caveencseglist->newindex((void **) &paryseg);
+ *paryseg = checkseg;
}
- //}
+ }
return 0;
}
}
// Count the number of tets at edge [a,b].
n = 0;
- counter = 0; // Sum of star counters;
spintet = *flipedge;
- i = 0;
while (1) {
- counter += elemcounter(spintet);
- i++;
+ n++;
fnextself(spintet);
if (spintet.tet == flipedge->tet) break;
}
- //assert(i >= 3);
- if (i < 3) {
+ //assert(n >= 3);
+ if (n < 3) {
// It is only possible when the mesh contains inverted tetrahedra.
assert(checkinverttetflag);
// Since "return 2" means success, we return 0.
return 0;
}
- assert(counter == 0); // SELF_CHECK
- n = i;
- flipstarcount++;
- // Record the maximum star size.
- if (n > maxflipstarsize) {
- maxflipstarsize = n;
- }
if ((b->flipstarsize > 0) && (n > b->flipstarsize)) {
- // The star size exceeds the given limit (-YY__).
- skpflipstarcount++;
+ // The star size exceeds the limit.
return 0; // Do not flip it.
}
@@ -20216,8 +18350,7 @@ int tetgenmesh::removeedgebyflips(triface *flipedge, flipconstraints* fc)
i = 0;
while (1) {
abtets[i] = spintet;
- //marktest(abtets[i]); // Marktest it (in Star(ab)).
- setelemcounter(abtets[i], 1);
+ setelemcounter(abtets[i], 1);
i++;
fnextself(spintet);
if (spintet.tet == flipedge->tet) break;
@@ -20228,45 +18361,33 @@ int tetgenmesh::removeedgebyflips(triface *flipedge, flipconstraints* fc)
nn = flipnm(abtets, n, 0, 0, fc);
- if (nn == 2) {
- // Edge is flipped.
- if (b->verbose > 2) {
- printf(" Edge is removed.\n");
- }
- } else {
+ if (nn > 2) {
// Edge is not flipped. Unmarktest the remaining tets in Star(ab).
for (i = 0; i < nn; i++) {
- //assert(marktested(abtets[i]));
- //unmarktest(abtets[i]);
- assert(elemcounter(abtets[i]) == 1);
setelemcounter(abtets[i], 0);
}
- if (b->verbose > 2) {
- printf(" Edge is not removed. n(%d), nn(%d).\n", n, nn);
- }
// Restore the input edge (needed by Lawson's flip).
*flipedge = abtets[0];
}
// Release the temporary allocated spaces.
// NOTE: fc->unflip must be 0.
+ int bakunflip = fc->unflip;
fc->unflip = 0;
- fc->collectnewtets = 0;
-
flipnm_post(abtets, n, nn, 0, fc);
-
fc->unflip = bakunflip;
- fc->collectnewtets = bakcollectnewtets;
delete [] abtets;
- return nn; //return nn == 2;
+ return nn;
}
///////////////////////////////////////////////////////////////////////////////
// //
// removefacebyflips() Remove a face by flips. //
// //
+// Return 1 if the face is removed. Otherwise, return 0. //
+// //
// ASSUMPTIONS: //
// - 'flipface' must not be a hull face. //
// //
@@ -20274,45 +18395,25 @@ int tetgenmesh::removeedgebyflips(triface *flipedge, flipconstraints* fc)
int tetgenmesh::removefacebyflips(triface *flipface, flipconstraints* fc)
{
- triface fliptets[3], flipedge;
- face checksh;
- point pa, pb, pc, pd, pe;
- point pts[3];
- enum interresult dir;
- int types[2], poss[4], pos;
- REAL ori;
- int reducflag, rejflag;
- int i, j;
-
if (checksubfaceflag) {
- tspivot(*flipface, checksh);
- if (checksh.sh != NULL) {
- if (b->verbose > 2) {
- printf(" Can't flip a subface.\n");
- }
+ if (issubface(*flipface)) {
return 0;
}
}
+ triface fliptets[3], flipedge;
+ point pa, pb, pc, pd, pe;
+ REAL ori;
+ int reducflag = 0;
+
fliptets[0] = *flipface;
fsym(*flipface, fliptets[1]);
-
- assert(!ishulltet(fliptets[0]));
- assert(!ishulltet(fliptets[1]));
-
pa = org(fliptets[0]);
pb = dest(fliptets[0]);
pc = apex(fliptets[0]);
pd = oppo(fliptets[0]);
pe = oppo(fliptets[1]);
- if (b->verbose > 2) {
- printf(" Removing face (%d, %d, %d) -- %d, %d\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pe));
- }
-
- reducflag = 0;
-
ori = orient3d(pa, pb, pd, pe);
if (ori > 0) {
ori = orient3d(pb, pc, pd, pe);
@@ -20333,109 +18434,12 @@ int tetgenmesh::removefacebyflips(triface *flipface, flipconstraints* fc)
if (reducflag) {
// A 2-to-3 flip is found.
- rejflag = 0;
- if (fc != NULL) {
- //rejflag = checkflipeligibility(1, pa, pb, pc, pd, pe, fc);
- }
- if (!rejflag) {
- flip23(fliptets, 0, 0, 0);
- if (b->verbose > 2) {
- printf(" Face is removed by a 2-to-3 flip.\n");
- }
- return 1;
- } else {
- if (b->verbose > 2) {
- printf(" -- Reject a 2-to-3 flip at face (%d, %d, %d)\n",
- pointmark(pa), pointmark(pb), pointmark(pc));
- }
- if (fc != NULL) {
- fc->rejf23count++;
- }
- }
+ flip23(fliptets, 0, fc);
+ return 1;
} else {
- if (0) {
- // Try to flip one of the edges of this face.
- pts[0] = org(flipedge);
- pts[1] = dest(flipedge);
- pts[2] = apex(flipedge);
- // Start from the recorded locally non-convex edge 'flipedge'.
- for (i = 0; i < 3; i++) {
- if (removeedgebyflips(&flipedge, fc) == 2) {
- if (b->verbose > 2) {
- printf(" Face is removed by removing edge (%d, %d).\n",
- pointmark(pts[i]), pointmark(pts[(i+1)%3]));
- }
- return 1;
- }
- // The 'flipedge' may be dead in above call.
- point2tetorg(pts[i], flipedge);
- finddirection(&flipedge, pts[(i+1)%3], 1);
- if (dest(flipedge) != pts[(i+1)%3]) {
- if (b->verbose > 2) {
- printf(" Face is removed during removing edge (%d, %d).\n",
- pointmark(pts[i]), pointmark(pts[(i+1)%3]));
- }
- return 1;
- }
- } // i
- } else {
- if (0) { //if (fc->seg[0] != NULL) {
- // The face is intersecting a segment.
- // Find the edge shared by three corssing faces.
- // We assume that the 'flipface' is facing to 'fc->seg[0]'. It is the
- // case when the function is called from 'recoveredgebyflips()'.
- // DEBUG BEGIN
- pa = org(*flipface);
- pb = dest(*flipface);
- pc = apex(*flipface);
- ori = orient3d(pa, pb, pc, fc->seg[0]);
- assert(ori < 0);
- // DEBUG END
- fsym(*flipface, flipedge);
- pc = oppo(flipedge);
- for (i = 0; i < 3; i++) {
- pa = org(flipedge);
- pb = dest(flipedge);
- if (tri_edge_test(pa, pb, pc, fc->seg[0], fc->seg[1], NULL, 1,
- types, poss)) {
- dir = (enum interresult) types[0];
- if (dir == ACROSSFACE) {
- break; // Found the crossing face.
- } else if (dir == ACROSSEDGE) {
- // Found an edge intersects the segment.
- esymself(flipedge);
- pos = poss[0];
- for (j = 0; j < pos; j++) {
- eprevself(flipedge);
- }
- // Flip this edge.
- break;
- } else if (dir == SHAREVERT) {
- // We have reached the endpoint of the segment.
- assert(pc == fc->seg[1]);
- // The face is not flippable.
- return 0;
- } else {
- assert(0); // Not possible.
- }
- }
- enextself(flipedge);
- }
- assert(i < 3);
- } else {
- if (b->verbose > 2) {
- pa = org(flipedge);
- pb = dest(flipedge);
- }
- }
- // Try to flip the selected edge of this face.
- if (removeedgebyflips(&flipedge, fc) == 2) {
- if (b->verbose > 2) {
- printf(" Face is removed by removing edge (%d, %d).\n",
- pointmark(pa), pointmark(pb));
- }
- return 1;
- }
+ // Try to flip the selected edge of this face.
+ if (removeedgebyflips(&flipedge, fc) == 2) {
+ return 1;
}
}
@@ -20450,7 +18454,7 @@ int tetgenmesh::removefacebyflips(triface *flipface, flipconstraints* fc)
// If the edge is recovered, 'searchtet' returns a tet containing the edge. //
// //
// This edge may intersect a set of faces and edges in the mesh. All these //
-// faces or edges are needed to be flipped. //
+// faces or edges are needed to be removed. //
// //
// If the parameter 'fullsearch' is set, it tries to flip any face or edge //
// that intersects the recovering edge. Otherwise, only the face or edge //
@@ -20461,38 +18465,24 @@ int tetgenmesh::removefacebyflips(triface *flipface, flipconstraints* fc)
int tetgenmesh::recoveredgebyflips(point startpt, point endpt,
triface* searchtet, int fullsearch)
{
- triface neightet, spintet; // *abtets;
- point pa, pb, pc, pd;
- badface bakface;
- enum interresult dir, dir1;
flipconstraints fc;
- int types[2], poss[4], pos = 0;
- int success;
- //int n, endi;
- int i, j; //, k;
-
- if (b->verbose > 2) {
- printf(" Recovering edge (%d, %d)\n", pointmark(startpt),
- pointmark(endpt));
- }
-
+ enum interresult dir;
fc.seg[0] = startpt;
fc.seg[1] = endpt;
+ fc.checkflipeligibility = 1;
// The mainloop of the edge reocvery.
while (1) { // Loop I
// Search the edge from 'startpt'.
point2tetorg(startpt, *searchtet);
- assert(org(*searchtet) == startpt); // SELF_CHECK
- dir = finddirection(searchtet, endpt, 1);
+ dir = finddirection(searchtet, endpt);
if (dir == ACROSSVERT) {
if (dest(*searchtet) == endpt) {
return 1; // Edge is recovered.
} else {
- // A PLC problem, or there is a Steiner point.
- terminatetetgen(3); //assert(0); // Debug
+ terminatetetgen(3); // // It may be a PLC problem.
}
}
@@ -20511,175 +18501,178 @@ int tetgenmesh::recoveredgebyflips(point startpt, point endpt,
continue;
}
} else {
- terminatetetgen(3); //assert(0); // A PLC problem.
+ terminatetetgen(3); // It may be a PLC problem.
}
// The edge is missing.
if (fullsearch) {
-
- if (1) {
- // Try to flip one of the faces/edges which intersects the edge.
- success = 0;
-
- // Loop through the sequence of intersecting faces/edges from
- // 'startpt' to 'endpt'.
- point2tetorg(startpt, *searchtet);
- assert(org(*searchtet) == startpt); // SELF_CHECK
- dir = finddirection(searchtet, endpt, 1);
- assert(dir != ACROSSVERT);
-
- // Go to the face/edge intersecting the searching edge.
- enextesymself(*searchtet); // Go to the opposite face.
- // This face/edge has been tried in previous step.
-
- while (1) { // Loop I-I
-
- // Find the next intersecting face/edge.
- fsymself(*searchtet);
- if (dir == ACROSSFACE) {
- neightet = *searchtet;
- j = (neightet.ver & 3); // j is the current face number.
- for (i = j + 1; i < j + 4; i++) {
- neightet.ver = (i % 4);
+ // Try to flip one of the faces/edges which intersects the edge.
+ triface neightet, spintet;
+ point pa, pb, pc, pd;
+ badface bakface;
+ enum interresult dir1;
+ int types[2], poss[4], pos = 0;
+ int success = 0;
+ int t1ver;
+ int i, j;
+
+ // Loop through the sequence of intersecting faces/edges from
+ // 'startpt' to 'endpt'.
+ point2tetorg(startpt, *searchtet);
+ dir = finddirection(searchtet, endpt);
+ //assert(dir != ACROSSVERT);
+
+ // Go to the face/edge intersecting the searching edge.
+ enextesymself(*searchtet); // Go to the opposite face.
+ // This face/edge has been tried in previous step.
+
+ while (1) { // Loop I-I
+
+ // Find the next intersecting face/edge.
+ fsymself(*searchtet);
+ if (dir == ACROSSFACE) {
+ neightet = *searchtet;
+ j = (neightet.ver & 3); // j is the current face number.
+ for (i = j + 1; i < j + 4; i++) {
+ neightet.ver = (i % 4);
+ pa = org(neightet);
+ pb = dest(neightet);
+ pc = apex(neightet);
+ pd = oppo(neightet); // The above point.
+ if (tri_edge_test(pa,pb,pc,startpt,endpt, pd, 1, types, poss)) {
+ dir = (enum interresult) types[0];
+ pos = poss[0];
+ break;
+ } else {
+ dir = DISJOINT;
+ pos = 0;
+ }
+ } // i
+ // There must be an intersection face/edge.
+ assert(dir != DISJOINT); // SELF_CHECK
+ } else {
+ assert(dir == ACROSSEDGE);
+ while (1) { // Loop I-I-I
+ // Check the two opposite faces (of the edge) in 'searchtet'.
+ for (i = 0; i < 2; i++) {
+ if (i == 0) {
+ enextesym(*searchtet, neightet);
+ } else {
+ eprevesym(*searchtet, neightet);
+ }
pa = org(neightet);
pb = dest(neightet);
pc = apex(neightet);
pd = oppo(neightet); // The above point.
- if (tri_edge_test(pa,pb,pc,startpt,endpt, pd, 1, types, poss)) {
+ if (tri_edge_test(pa,pb,pc,startpt,endpt,pd,1, types, poss)) {
dir = (enum interresult) types[0];
pos = poss[0];
- break;
- } else {
- dir = DISJOINT;
- pos = 0;
- }
- } // i
- // There must be an intersection face/edge.
- assert(dir != DISJOINT); // SELF_CHECK
- } else {
- assert(dir == ACROSSEDGE);
- while (1) { // Loop I-I-I
- // Check the two opposite faces (of the edge) in 'searchtet'.
- for (i = 0; i < 2; i++) {
- if (i == 0) {
- enextesym(*searchtet, neightet);
- } else {
- eprevesym(*searchtet, neightet);
- }
- pa = org(neightet);
- pb = dest(neightet);
- pc = apex(neightet);
- pd = oppo(neightet); // The above point.
- if (tri_edge_test(pa,pb,pc,startpt,endpt,pd,1, types, poss)) {
- dir = (enum interresult) types[0];
- pos = poss[0];
- break; // for loop
- } else {
- dir = DISJOINT;
- pos = 0;
- }
- } // i
- if (dir != DISJOINT) {
- // Find an intersection face/edge.
- break; // Loop I-I-I
+ break; // for loop
+ } else {
+ dir = DISJOINT;
+ pos = 0;
}
- // No intersection. Rotate to the next tet at the edge.
- fnextself(*searchtet);
- } // while (1) // Loop I-I-I
- }
+ } // i
+ if (dir != DISJOINT) {
+ // Find an intersection face/edge.
+ break; // Loop I-I-I
+ }
+ // No intersection. Rotate to the next tet at the edge.
+ fnextself(*searchtet);
+ } // while (1) // Loop I-I-I
+ }
- // Adjust to the intersecting edge/vertex.
- for (i = 0; i < pos; i++) {
- enextself(neightet);
- }
+ // Adjust to the intersecting edge/vertex.
+ for (i = 0; i < pos; i++) {
+ enextself(neightet);
+ }
- if (dir == SHAREVERT) {
- // Check if we have reached the 'endpt'.
- pd = org(neightet);
- if (pd == endpt) {
- // Failed to recover the edge.
- break; // Loop I-I
- } else {
- // We need to further check this case. It might be a PLC problem
- // or a Steiner point that was added at a bad location.
- assert(0);
- }
+ if (dir == SHAREVERT) {
+ // Check if we have reached the 'endpt'.
+ pd = org(neightet);
+ if (pd == endpt) {
+ // Failed to recover the edge.
+ break; // Loop I-I
+ } else {
+ // We need to further check this case. It might be a PLC problem
+ // or a Steiner point that was added at a bad location.
+ assert(0);
}
+ }
- // The next to be flipped face/edge.
- *searchtet = neightet;
+ // The next to be flipped face/edge.
+ *searchtet = neightet;
- // Bakup this face (tetrahedron).
- bakface.forg = org(*searchtet);
- bakface.fdest = dest(*searchtet);
- bakface.fapex = apex(*searchtet);
- bakface.foppo = oppo(*searchtet);
+ // Bakup this face (tetrahedron).
+ bakface.forg = org(*searchtet);
+ bakface.fdest = dest(*searchtet);
+ bakface.fapex = apex(*searchtet);
+ bakface.foppo = oppo(*searchtet);
- // Try to flip this intersecting face/edge.
- if (dir == ACROSSFACE) {
- if (removefacebyflips(searchtet, &fc)) {
- success = 1;
- break; // Loop I-I
- }
- } else if (dir == ACROSSEDGE) {
- if (removeedgebyflips(searchtet, &fc) == 2) {
- success = 1;
- break; // Loop I-I
- }
- } else {
- assert(0); // A PLC problem.
- }
-
- // The face/edge is not flipped.
- if ((searchtet->tet == NULL) ||
- (org(*searchtet) != bakface.forg) ||
- (dest(*searchtet) != bakface.fdest) ||
- (apex(*searchtet) != bakface.fapex) ||
- (oppo(*searchtet) != bakface.foppo)) {
- // 'searchtet' was flipped. We must restore it.
- point2tetorg(bakface.forg, *searchtet);
- dir1 = finddirection(searchtet, bakface.fdest, 1);
- if (dir1 == ACROSSVERT) {
- assert(dest(*searchtet) == bakface.fdest);
- spintet = *searchtet;
- while (1) {
- if (apex(spintet) == bakface.fapex) {
- // Found the face.
- *searchtet = spintet;
- break;
- }
- fnextself(spintet);
- if (spintet.tet == searchtet->tet) {
+ // Try to flip this intersecting face/edge.
+ if (dir == ACROSSFACE) {
+ if (removefacebyflips(searchtet, &fc)) {
+ success = 1;
+ break; // Loop I-I
+ }
+ } else if (dir == ACROSSEDGE) {
+ if (removeedgebyflips(searchtet, &fc) == 2) {
+ success = 1;
+ break; // Loop I-I
+ }
+ } else {
+ assert(0); // A PLC problem.
+ }
+
+ // The face/edge is not flipped.
+ if ((searchtet->tet == NULL) ||
+ (org(*searchtet) != bakface.forg) ||
+ (dest(*searchtet) != bakface.fdest) ||
+ (apex(*searchtet) != bakface.fapex) ||
+ (oppo(*searchtet) != bakface.foppo)) {
+ // 'searchtet' was flipped. We must restore it.
+ point2tetorg(bakface.forg, *searchtet);
+ dir1 = finddirection(searchtet, bakface.fdest);
+ if (dir1 == ACROSSVERT) {
+ assert(dest(*searchtet) == bakface.fdest);
+ spintet = *searchtet;
+ while (1) {
+ if (apex(spintet) == bakface.fapex) {
+ // Found the face.
+ *searchtet = spintet;
+ break;
+ }
+ fnextself(spintet);
+ if (spintet.tet == searchtet->tet) {
+ searchtet->tet = NULL;
+ break; // Not find.
+ }
+ } // while (1)
+ if (searchtet->tet != NULL) {
+ if (oppo(*searchtet) != bakface.foppo) {
+ fsymself(*searchtet);
+ if (oppo(*searchtet) != bakface.foppo) {
+ assert(0); // Check this case.
searchtet->tet = NULL;
break; // Not find.
}
- } // while (1)
- if (searchtet->tet != NULL) {
- if (oppo(*searchtet) != bakface.foppo) {
- fsymself(*searchtet);
- if (oppo(*searchtet) != bakface.foppo) {
- assert(0); // Check this case.
- searchtet->tet = NULL;
- break; // Not find.
- }
- }
}
- } else {
- searchtet->tet = NULL; // Not find.
- }
- if (searchtet->tet == NULL) {
- success = 0; // This face/edge has been destroed.
- break; // Loop I-I
}
+ } else {
+ searchtet->tet = NULL; // Not find.
+ }
+ if (searchtet->tet == NULL) {
+ success = 0; // This face/edge has been destroed.
+ break; // Loop I-I
}
- } // while (1) // Loop I-I
-
- if (success) {
- // One of intersecting faces/edges is flipped.
- continue;
}
- } // if (0)
+ } // while (1) // Loop I-I
+
+ if (success) {
+ // One of intersecting faces/edges is flipped.
+ continue;
+ }
} // if (fullsearch)
@@ -20688,7 +18681,6 @@ int tetgenmesh::recoveredgebyflips(point startpt, point endpt,
} // while (1) // Loop I
- // The edge is not recovered.
return 0;
}
@@ -20701,24 +18693,8 @@ int tetgenmesh::recoveredgebyflips(point startpt, point endpt,
// tets are [a,b,p0,p1], [a,b,p1,p2], ..., [a,b,p_(n-2),p_(n-1)]. Moreover, //
// the edge [p0,p_(n-1)] intersects all of the tets in 'abtets'. A special //
// case is that the edge [p0,p_(n-1)] is coplanar with the edge [a,b]. //
-// //
-// These set of tets arises when we want to recover an edge from 'p0' to 'p_ //
-// (n-1)', and the recoveredgenbyflips() routine fails. Note that the outer //
-// faces of these tets defines a polyhedron P, and the set of tets gives the //
-// ONLY tetrahedralization of P. If we replace the two boundary faces [a,b, //
-// p0] and [a,b,p_(n-1)] by [p0,p_(n-1),a] and [p0,p_(n-1),b], and call the //
-// new polyhedron P'. In this routine, we think P' is not tetrahedralizable //
-// (since the routine recoveredgenbyflips() fails!! AND no flip is possible //
-// on any of these edges: [a,p1], [b,p1], [a,p2], [b,p2], ..., [a,p_(n-2)], //
-// and [b,p_(n-1)]). If n = 3, P' is just the famous Schoenhardt polyhedron. //
-// For n > 3, we call P' the generalized Schoenhardt polyhedron, it includes //
-// the Bagemihl's polyhedron as a special case. //
-// //
-// It is obvious that P is a Star-shaped polyhedron. The mid-point of [a,b] //
-// is visible by all boundary faces of P, push it slightly inside P does not //
-// change the visibilty. Indeed every interior point of [a,b] is visible by //
-// the boundary faces of P. //
-// //
+// Such set of tets arises when we want to recover an edge from 'p0' to 'p_ //
+// (n-1)', and the number of tets at [a,b] can not be reduced by any flip. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -20727,23 +18703,15 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
{
triface worktet, *parytet;
triface faketet1, faketet2;
- point pa, pb, pc, pd;
- point p1, p2, p3;
- point steinerpt;
+ point pc, pd, steinerpt;
insertvertexflags ivf;
optparameters opm;
REAL vcd[3], sampt[3], smtpt[3];
REAL maxminvol = 0.0, minvol = 0.0, ori;
int success, maxidx = 0;
- int loc;
int it, i;
- if (b->verbose > 2) {
- printf(" Find a Steiner in Schoenhardt polyhedron (n=%d).\n", n);
- }
- pa = org(abtets[0]);
- pb = dest(abtets[0]);
pc = apex(abtets[0]); // pc = p0
pd = oppo(abtets[n-1]); // pd = p_(n-1)
@@ -20752,12 +18720,10 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
// initialize the list of 2n boundary faces.
for (i = 0; i < n; i++) {
- eprev(abtets[i], worktet);
- esymself(worktet); // [a,p_i,p_i+1].
+ edestoppo(abtets[i], worktet); // [p_i,p_i+1,a]
cavetetlist->newindex((void **) &parytet);
*parytet = worktet;
- enext(abtets[i], worktet);
- esymself(worktet); // [p_i,b,p_i+1].
+ eorgoppo(abtets[i], worktet); // [p_i+1,p_i,b]
cavetetlist->newindex((void **) &parytet);
*parytet = worktet;
}
@@ -20772,10 +18738,7 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
}
for (i = 0; i < cavetetlist->objects; i++) {
parytet = (triface *) fastlookup(cavetetlist, i);
- p1 = org(*parytet);
- p2 = dest(*parytet);
- p3 = apex(*parytet);
- ori = orient3d(p2, p1, p3, sampt);
+ ori = orient3d(dest(*parytet), org(*parytet), apex(*parytet), sampt);
if (i == 0) {
minvol = ori;
} else {
@@ -20794,10 +18757,6 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
} // it
if (maxminvol <= 0) {
- if (b->verbose > 2) {
- printf(" Unable to find a initial point: maxminvol = %g\n",
- maxminvol);
- }
cavetetlist->restart();
return 0;
}
@@ -20809,11 +18768,11 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
// Create two faked tets to hold the two non-existing boundary faces:
// [d,c,a] and [c,d,b].
maketetrahedron(&faketet1);
- setvertices(faketet1, pd, pc, pa, dummypoint);
+ setvertices(faketet1, pd, pc, org(abtets[0]), dummypoint);
cavetetlist->newindex((void **) &parytet);
*parytet = faketet1;
maketetrahedron(&faketet2);
- setvertices(faketet2, pc, pd, pb, dummypoint);
+ setvertices(faketet2, pc, pd, dest(abtets[0]), dummypoint);
cavetetlist->newindex((void **) &parytet);
*parytet = faketet2;
@@ -20846,9 +18805,6 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
cavetetlist->restart();
if (!success) {
- if (b->verbose > 2) {
- printf(" Unable to relocate the initial point.\n");
- }
return 0;
}
@@ -20865,28 +18821,23 @@ int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
}
worktet = abtets[0]; // No need point location.
ivf.iloc = (int) INSTAR;
- ivf.bowywat = 0; // Do not use Bowyer-Watson algorithm.
- ivf.lawson = 0; // Do not flip.
- ivf.rejflag = 0;
ivf.chkencflag = chkencflag;
- ivf.sloc = 0;
- ivf.sbowywat = 0;
- ivf.splitbdflag = 0;
- ivf.validflag = 0;
- ivf.respectbdflag = 0;
- ivf.assignmeshsize = 0;
+ ivf.assignmeshsize = b->metric;
+ if (ivf.assignmeshsize) {
+ // Search the tet containing 'steinerpt' for size interpolation.
+ locate(steinerpt, &(abtets[0]), 0);
+ worktet = abtets[0];
+ }
// Insert the new point into the tetrahedralization T.
// Note that T is convex (nonconvex = 0).
- loc = insertvertex(steinerpt, &worktet, NULL, NULL, &ivf);
-
- if (loc == (int) INSTAR) {
+ if (insertpoint(steinerpt, &worktet, NULL, NULL, &ivf)) {
// The vertex has been inserted.
- st_volref_count++; //st_inpoly_count++;
+ st_volref_count++;
if (steinerleft > 0) steinerleft--;
return 1;
} else {
- // The Steiner point is too close to an existing vertex. Reject it.
+ // Not inserted.
pointdealloc(steinerpt);
return 0;
}
@@ -20902,16 +18853,14 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
{
triface *abtets, searchtet, spintet;
face splitsh;
- face checkseg;
face *paryseg;
point startpt, endpt;
point pa, pb, pd, steinerpt, *parypt;
enum interresult dir;
insertvertexflags ivf;
int types[2], poss[4];
- REAL ip[3], u;
int n, endi, success;
- int loc;
+ int t1ver;
int i;
startpt = sorg(*misseg);
@@ -20923,12 +18872,7 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
// Try to recover the edge by adding Steiner points.
point2tetorg(startpt, searchtet);
- assert(org(searchtet) == startpt); // SELF_CHECK
- dir = finddirection(&searchtet, endpt, 1);
- assert(dir != ACROSSVERT);
-
- // Get the first intersecting face/edge.
- assert(!ishulltet(searchtet));
+ dir = finddirection(&searchtet, endpt);
enextself(searchtet);
//assert(apex(searchtet) == startpt);
@@ -20936,13 +18880,8 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
// The segment is crossing at least 3 faces. Find the common edge of
// the first 3 crossing faces.
esymself(searchtet);
- assert(oppo(searchtet) == startpt);
fsym(searchtet, spintet);
pd = oppo(spintet);
- if (pd == endpt) {
- // This should be possible.
- assert(0); // Debug this case.
- }
for (i = 0; i < 3; i++) {
pa = org(spintet);
pb = dest(spintet);
@@ -20958,8 +18897,9 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
} else {
assert(dir == ACROSSEDGE);
// PLC check.
- tsspivot1(searchtet, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(searchtet)) {
+ face checkseg;
+ tsspivot1(searchtet, checkseg);
printf("Found two segments intersect each other.\n");
pa = farsorg(*misseg);
pb = farsdest(*misseg);
@@ -20996,8 +18936,6 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
abtets[i] = spintet;
fnextself(spintet);
}
- assert(apex(abtets[0]) == startpt);
- assert(apex(abtets[endi]) == endpt);
success = 0;
@@ -21054,11 +18992,15 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
printf(" Splitting segment (%d, %d)\n", pointmark(startpt),
pointmark(endpt));
}
+ steinerpt = NULL;
- if (endi == -1) {
+ // The following code is skipped.
+ if ((endi == -1) && 0) {
// Let the missing segment be [a,b]. Let the edge [c,d] whose star contains
// a and intersects [a,b]. We choose the Steiner point at the intersection
// of the edge star of [c,d] and [a,b] (not a).
+ REAL ip[3], u;
+
if (dir == ACROSSFACE) {
pa = org(searchtet);
pb = dest(searchtet);
@@ -21078,17 +19020,6 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
}
assert(n >= 3);
assert(endi != -1);
-
- // 'abtets' is only for debug purpose.
- abtets = new triface[endi];
- spintet = searchtet;
- for (i = 0; i < endi; i++) {
- abtets[i] = spintet;
- fnextself(spintet);
- }
- searchtet = abtets[endi - 1];
- esymself(searchtet); // The exit face of [startpt, endpt].
- delete [] abtets;
} else {
assert(dir == ACROSSEDGE);
assert(apex(searchtet) == startpt);
@@ -21131,11 +19062,9 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
- ivf.assignmeshsize = 0;
- loc = insertvertex(steinerpt, &searchtet, &splitsh, misseg, &ivf);
-
- if (loc != ivf.iloc) {
- if (loc == (int) NEARVERTEX) {
+ ivf.assignmeshsize = b->metric;
+ if (!insertpoint(steinerpt, &searchtet, &splitsh, misseg, &ivf)) {
+ if (ivf.iloc == (int) NEARVERTEX) {
// The vertex is rejected. Too close to an existing vertex.
pointdealloc(steinerpt);
steinerpt = NULL;
@@ -21143,9 +19072,7 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
assert(0); // Unknown case.
}
}
- } else { // if (endi > 0)
- steinerpt = NULL;
- }
+ } // if ((endi == -1) && 0)
if (steinerpt == NULL) {
// Split the segment at its midpoint.
@@ -21167,11 +19094,10 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
- ivf.assignmeshsize = 0;
- loc = insertvertex(steinerpt, &searchtet, &splitsh, misseg, &ivf);
-
- assert(loc != (int) ONVERTEX);
- assert(loc != (int) NEARVERTEX);
+ ivf.assignmeshsize = b->metric;
+ if (!insertpoint(steinerpt, &searchtet, &splitsh, misseg, &ivf)) {
+ assert(0);
+ }
} // if (endi > 0)
// Save this Steiner point (for removal).
@@ -21189,17 +19115,11 @@ int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
// //
// recoversegments() Recover all segments. //
// //
-// All segments need to be recovered are in 'subsegstack' (Q). They will be //
-// be recovered one by one. //
-// //
-// Each segment is first tried to be recovered by a sequence of flips which //
-// removes faces intersecting this segment. However, it is not always possi- //
-// ble to recover it by only this way. Then, Steiner points will be added to //
-// help the recovery of it by flips. //
+// All segments need to be recovered are in 'subsegstack'. //
// //
-// If 'steinerflag' is set, Steiner points will be added if a segment is not //
-// able to recovered by flips. Otherwise, the segment is not recovered, and //
-// it is returned in 'misseglist'. //
+// This routine first tries to recover each segment by only using flips. If //
+// no flip is possible, and the flag 'steinerflag' is set, it then tries to //
+// insert Steiner points near or in the segment. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -21207,11 +19127,12 @@ int tetgenmesh::recoversegments(arraypool *misseglist, int fullsearch,
int steinerflag)
{
triface searchtet, spintet;
- face sseg, checkseg, *paryseg;
+ face sseg, *paryseg;
point startpt, endpt;
int success;
-
- long bak_inpoly_count = st_volref_count; //st_inpoly_count;
+ int t1ver;
+ long bak_inpoly_count = st_volref_count;
+ long bak_segref_count = st_segref_count;
if (b->verbose > 1) {
printf(" Recover segments [%s level = %2d] #: %ld.\n",
@@ -21260,8 +19181,6 @@ int tetgenmesh::recoversegments(arraypool *misseglist, int fullsearch,
if (success) {
// Segment is recovered. Insert it.
- tsspivot1(searchtet, checkseg); // SELF_CHECK
- assert(checkseg.sh == NULL);
// Let the segment remember an adjacent tet.
sstbond1(sseg, searchtet);
// Bond the segment to all tets containing it.
@@ -21300,6 +19219,10 @@ int tetgenmesh::recoversegments(arraypool *misseglist, int fullsearch,
printf(" Add %ld Steiner points in volume.\n",
st_volref_count - bak_inpoly_count);
}
+ if (st_segref_count > bak_segref_count) {
+ printf(" Add %ld Steiner points in segments.\n",
+ st_segref_count - bak_segref_count);
+ }
}
}
@@ -21319,33 +19242,26 @@ int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc,
face *searchsh, triface* searchtet)
{
triface spintet, flipedge;
- face checkseg;
point pd, pe;
enum interresult dir;
flipconstraints fc;
+ int types[2], poss[4], intflag;
int success, success1;
+ int t1ver;
int i, j;
- int intflag;
- int types[2], poss[4];
-
- if (b->verbose > 2) {
- printf(" Recovering face (%d, %d, %d) by flips\n", pointmark(pa),
- pointmark(pb), pointmark(pc));
- }
-
fc.fac[0] = pa;
fc.fac[1] = pb;
fc.fac[2] = pc;
+ fc.checkflipeligibility = 1;
success = 0;
for (i = 0; i < 3 && !success; i++) {
while (1) {
// Get a tet containing the edge [a,b].
point2tetorg(fc.fac[i], *searchtet);
- assert(org(*searchtet) == fc.fac[i]); // SELF_CHECK
- dir = finddirection(searchtet, fc.fac[(i+1)%3], 1);
+ dir = finddirection(searchtet, fc.fac[(i+1)%3]);
//assert(dir == ACROSSVERT);
assert(dest(*searchtet) == fc.fac[(i+1)%3]);
// Search the face [a,b,c]
@@ -21382,14 +19298,13 @@ int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc,
dir = (enum interresult) types[0];
if ((dir == ACROSSFACE) || (dir == ACROSSEDGE)) {
// Go to the edge [d,e].
- eprev(spintet, flipedge);
- esymself(flipedge);
- enextself(flipedge); // [d,e,a,b].
+ edestoppo(spintet, flipedge); // [d,e,a,b]
if (searchsh != NULL) {
// Check if [e,d] is a segment.
- tsspivot1(flipedge, checkseg);
- if (checkseg.sh != NULL) {
- if (!b->quiet) {
+ if (issubseg(flipedge)) {
+ if (!b->quiet) {
+ face checkseg;
+ tsspivot1(flipedge, checkseg);
printf("Found a segment and a subface intersect.\n");
pd = farsorg(checkseg);
pe = farsdest(checkseg);
@@ -21397,16 +19312,16 @@ int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc,
pointmark(pe), shellmark(checkseg));
printf(" 2nd: [%d,%d,%d] %d\n", pointmark(pa),
pointmark(pb), pointmark(pc), shellmark(*searchsh));
- }
+ }
terminatetetgen(3);
- }
+ }
}
// Try to flip the edge [d,e].
success1 = (removeedgebyflips(&flipedge, &fc) == 2);
} else {
if (dir == TOUCHFACE) {
point touchpt, *parypt;
- if (poss[0] == 0) {
+ if (poss[1] == 0) {
touchpt = pd; // pd is a coplanar vertex.
} else {
touchpt = pe; // pe is a coplanar vertex.
@@ -21414,17 +19329,11 @@ int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc,
if (pointtype(touchpt) == FREEVOLVERTEX) {
// A volume Steiner point was added in this subface.
// Split this subface by this point.
- if (b->verbose > 2) {
- printf(" Shift volume Steiner point %d to facet.\n",
- pointmark(touchpt));
- }
face checksh, *parysh;
int siloc = (int) ONFACE;
int sbowat = 0; // Only split this subface.
-
- sinsertvertex(touchpt, searchsh, NULL, siloc, sbowat);
-
setpointtype(touchpt, FREEFACETVERTEX);
+ sinsertvertex(touchpt, searchsh, NULL, siloc, sbowat);
st_volref_count--;
st_facref_count++;
// Queue this vertex for removal.
@@ -21438,12 +19347,6 @@ int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc,
spivot(*parysh, checksh); // The new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
- if (b->verbose > 3) {
- printf(" Queue new subface (%d, %d, %d).\n",
- pointmark(sorg(checksh)), pointmark(sdest(checksh)),
- pointmark(sapex(checksh)));
- }
- //sdissolve(checksh); // It has not been connected yet.
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
@@ -21502,13 +19405,13 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
{
triface searchtet, neightet, spintet;
face searchsh, neighsh, neineish, *parysh;
- face bdsegs[3], checkseg;
+ face bdsegs[3];
point startpt, endpt, apexpt, *parypt;
point steinerpt;
enum interresult dir;
insertvertexflags ivf;
int success;
- int loc;
+ int t1ver;
int i, j;
if (b->verbose > 1) {
@@ -21532,7 +19435,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
if (b->verbose > 2) {
- printf(" Recover subface (%d, %d, %d).\n", pointmark(sorg(searchsh)),
+ printf(" Recover subface (%d, %d, %d).\n",pointmark(sorg(searchsh)),
pointmark(sdest(searchsh)), pointmark(sapex(searchsh)));
}
@@ -21552,8 +19455,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
startpt = sorg(searchsh);
endpt = sdest(searchsh);
point2tetorg(startpt, searchtet);
- assert(org(searchtet) == startpt); // SELF_CHECK
- dir = finddirection(&searchtet, endpt, 1);
+ dir = finddirection(&searchtet, endpt);
if (dir == ACROSSVERT) {
if (dest(searchtet) == endpt) {
success = 1;
@@ -21573,13 +19475,8 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
}
if (success) {
// Insert a temporary segment to protect this edge.
- if (b->verbose > 2) {
- printf(" Insert a temp segment to protect edge [%d, %d].\n",
- pointmark(startpt), pointmark(endpt));
- }
makeshellface(subsegs, &(bdsegs[i]));
setshvertices(bdsegs[i], startpt, endpt, NULL);
- //setshellmark(bdsegs[i], -2); // It's a temporary segment.
smarktest2(bdsegs[i]); // It's a temporary segment.
// Insert this segment into surface mesh.
ssbond(searchsh, bdsegs[i]);
@@ -21588,8 +19485,6 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
ssbond(neighsh, bdsegs[i]);
}
// Insert this segment into tetrahedralization.
- tsspivot1(searchtet, checkseg); // SELF_CHECK
- assert(checkseg.sh == NULL);
sstbond1(bdsegs[i], searchtet);
// Bond the segment to all tets containing it.
spintet = searchtet;
@@ -21601,11 +19496,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
// An edge of this subface is missing. Can't recover this subface.
// Delete any temporary segment that has been created.
for (j = (i - 1); j >= 0; j--) {
- if (smarktest2ed(bdsegs[j])) { // if (shellmark(bdsegs[j]) == -2) {
- if (b->verbose > 2) {
- printf(" Remove a temp segment (%d, %d).\n",
- pointmark(sorg(bdsegs[j])), pointmark(sdest(bdsegs[j])));
- }
+ if (smarktest2ed(bdsegs[j])) {
spivot(bdsegs[j], neineish);
assert(neineish.sh != NULL);
//if (neineish.sh != NULL) {
@@ -21617,7 +19508,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
spivotself(neighsh); // SELF_CHECK
assert(neighsh.sh == neineish.sh);
}
- //}
+ //}
sstpivot1(bdsegs[j], searchtet);
assert(searchtet.tet != NULL);
//if (searchtet.tet != NULL) {
@@ -21627,7 +19518,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
- //}
+ //}
shellfacedealloc(subsegs, bdsegs[j].sh);
}
} // j
@@ -21653,10 +19544,10 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
- ivf.assignmeshsize = 0;
- loc = insertvertex(steinerpt, &searchtet, &searchsh, NULL, &ivf);
- assert(loc != (int) OUTSIDE);
-
+ ivf.assignmeshsize = b->metric;
+ if (!insertpoint(steinerpt, &searchtet, &searchsh, NULL, &ivf)) {
+ assert(0);
+ }
// Save this Steiner point (for removal).
// Re-use the array 'subvertstack'.
subvertstack->newindex((void **) &parypt);
@@ -21681,11 +19572,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
// Delete any temporary segment that has been created.
for (j = 0; j < 3; j++) {
- if (smarktest2ed(bdsegs[j])) { //if (shellmark(bdsegs[j]) == -2) {
- if (b->verbose > 2) {
- printf(" Remove a temp segment (%d, %d).\n",
- pointmark(sorg(bdsegs[j])), pointmark(sdest(bdsegs[j])));
- }
+ if (smarktest2ed(bdsegs[j])) {
spivot(bdsegs[j], neineish);
assert(neineish.sh != NULL);
//if (neineish.sh != NULL) {
@@ -21697,7 +19584,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
spivotself(neighsh); // SELF_CHECK
assert(neighsh.sh == neineish.sh);
}
- //}
+ //}
sstpivot1(bdsegs[j], neightet);
assert(neightet.tet != NULL);
//if (neightet.tet != NULL) {
@@ -21707,7 +19594,7 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
- //}
+ //}
shellfacedealloc(subsegs, bdsegs[j].sh);
}
} // j
@@ -21743,10 +19630,10 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
- ivf.assignmeshsize = 0;
- loc = insertvertex(steinerpt, &searchtet, &searchsh, NULL, &ivf);
- assert(loc != (int) OUTSIDE);
-
+ ivf.assignmeshsize = b->metric;
+ if (!insertpoint(steinerpt, &searchtet, &searchsh, NULL, &ivf)) {
+ assert(0);
+ }
// Save this Steiner point (for removal).
// Re-use the array 'subvertstack'.
subvertstack->newindex((void **) &parypt);
@@ -21762,11 +19649,6 @@ int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
if (!success) {
if (misshlist != NULL) {
- if (b->verbose > 2) {
- printf(" Subface (%d, %d, %d) is missing.\n",
- pointmark(sorg(searchsh)), pointmark(sdest(searchsh)),
- pointmark(sapex(searchsh)));
- }
// Save this subface.
misshlist->newindex((void **) &parysh);
*parysh = searchsh;
@@ -21800,32 +19682,27 @@ int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist,
{
triface searchtet, neightet, *parytet;
face checksh, *parysh;
- //face checkseg;
point pt, *parypt;
int collectflag;
+ int t1ver;
int i, j;
- if (b->verbose > 2) {
- printf(" Form the star of vertex %d.\n", pointmark(searchpt));
- }
-
point2tetorg(searchpt, searchtet);
// Go to the opposite face (the link face) of the vertex.
- enextself(searchtet);
- esymself(searchtet);
+ enextesymself(searchtet);
//assert(oppo(searchtet) == searchpt);
infect(searchtet); // Collect this tet (link face).
tetlist->newindex((void **) &parytet);
*parytet = searchtet;
if (vertlist != NULL) {
// Collect three (link) vertices.
- for (i = 0; i < 3; i++) {
- pt = org(searchtet);
+ j = (searchtet.ver & 3); // The current vertex index.
+ for (i = 1; i < 4; i++) {
+ pt = (point) searchtet.tet[4 + ((j + i) % 4)];
pinfect(pt);
vertlist->newindex((void **) &parypt);
*parypt = pt;
- enextself(searchtet);
}
}
@@ -21840,14 +19717,13 @@ int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist,
shlist->newindex((void **) &parysh);
*parysh = checksh;
}
- } // if (checksh.sh != NULL)
+ }
if (!fullstar) {
collectflag = 0;
}
}
if (collectflag) {
fsymself(neightet); // Goto the adj tet of this face.
- assert(neightet.tet != NULL);
esymself(neightet); // Goto the oppo face of this vertex.
// assert(oppo(neightet) == searchpt);
infect(neightet); // Collect this tet (link face).
@@ -21871,7 +19747,6 @@ int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist,
for (j = 0; j < 2; j++) {
collectflag = 1;
enextself(searchtet);
- //fnext(searchtet, neightet);
esym(searchtet, neightet);
tspivot(neightet, checksh);
if (checksh.sh != NULL) {
@@ -21889,7 +19764,6 @@ int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist,
}
if (collectflag) {
fsymself(neightet);
- assert(neightet.tet != NULL);
if (!infected(neightet)) {
esymself(neightet); // Go to the face opposite to 'searchpt'.
infect(neightet);
@@ -21909,16 +19783,6 @@ int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist,
} // j
} // i
- if (b->verbose > 2) {
- printf(" Collected %ld tets", tetlist->objects);
- if (vertlist != NULL) {
- printf(", %ld vertices", vertlist->objects);
- }
- if (shlist != NULL) {
- printf(", %ld subfaces", shlist->objects);
- }
- printf(".\n");
- }
// Uninfect the list of tets and vertices.
for (i = 0; i < tetlist->objects; i++) {
@@ -21982,13 +19846,13 @@ int tetgenmesh::getedge(point e1, point e2, triface *tedge)
// Search for the edge [e1, e2].
point2tetorg(e1, *tedge);
- finddirection(tedge, e2, 1);
+ finddirection(tedge, e2);
if (dest(*tedge) == e2) {
return 1;
} else {
// Search for the edge [e2, e1].
point2tetorg(e2, *tedge);
- finddirection(tedge, e1, 1);
+ finddirection(tedge, e1);
if (dest(*tedge) == e1) {
esymself(*tedge);
return 1;
@@ -21998,8 +19862,7 @@ int tetgenmesh::getedge(point e1, point e2, triface *tedge)
// Go to the link face of e1.
point2tetorg(e1, searchtet);
- enextself(searchtet);
- esymself(searchtet);
+ enextesymself(searchtet);
//assert(oppo(searchtet) == e1);
assert(cavetetlist->objects == 0l); // It will re-use this list.
@@ -22009,9 +19872,7 @@ int tetgenmesh::getedge(point e1, point e2, triface *tedge)
pt = apex(searchtet);
if (pt == e2) {
// Found. 'searchtet' is [#,#,e2,e1].
- enext(searchtet, *tedge);
- esymself(*tedge);
- eprevself(*tedge); // [e1,e2,#,#].
+ eorgoppo(searchtet, *tedge); // [e1,e2,#,#].
return 1;
}
enextself(searchtet);
@@ -22024,9 +19885,7 @@ int tetgenmesh::getedge(point e1, point e2, triface *tedge)
pt = apex(neightet);
if (pt == e2) {
// Found. 'neightet' is [#,#,e2,e1].
- enext(neightet, *tedge);
- esymself(*tedge);
- eprevself(*tedge); // [e1,e2,#,#].
+ eorgoppo(neightet, *tedge); // [e1,e2,#,#].
return 1;
}
@@ -22051,9 +19910,7 @@ int tetgenmesh::getedge(point e1, point e2, triface *tedge)
pt = apex(neightet);
if (pt == e2) {
// Found. 'neightet' is [#,#,e2,e1].
- enext(neightet, *tedge);
- esymself(*tedge);
- eprevself(*tedge); // [e1,e2,#,#].
+ eorgoppo(neightet, *tedge);
done = 1;
} else {
infect(neightet);
@@ -22085,7 +19942,6 @@ int tetgenmesh::getedge(point e1, point e2, triface *tedge)
int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist)
{
triface searchtet;
- face checkseg;
point *pendpt, *parypt;
enum interresult dir;
flipconstraints fc;
@@ -22093,13 +19949,9 @@ int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist)
int count;
int n, i, j;
- if (b->verbose > 2) {
- printf(" Initial edge degree = %ld.\n", endptlist->objects);
- }
- assert(endptlist->objects >= 4l);
- // Reduce the number of edges.
fc.remvert = startpt;
+ fc.checkflipeligibility = 1;
while (1) {
@@ -22121,13 +19973,12 @@ int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist)
}
} else {
point2tetorg(startpt, searchtet);
- dir = finddirection(&searchtet, *pendpt, 1);
+ dir = finddirection(&searchtet, *pendpt);
}
if (dir == ACROSSVERT) {
if (dest(searchtet) == *pendpt) {
// Do not flip a segment.
- tsspivot1(searchtet, checkseg);
- if (checkseg.sh == NULL) {
+ if (!issubseg(searchtet)) {
n = removeedgebyflips(&searchtet, &fc);
if (n == 2) {
reduceflag = 1;
@@ -22158,10 +20009,6 @@ int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist)
} // while (1)
- if (b->verbose > 2) {
- printf(" Final edge degree = %ld.\n", endptlist->objects);
- }
-
return (int) endptlist->objects;
}
@@ -22169,28 +20016,13 @@ int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist)
// //
// removevertexbyflips() Remove a vertex by flips. //
// //
-// This routine attempts to remove the given vertex 'rempt' (p) from the cur-//
-// rent tetrahedralization (T) by a sequence of elementary flips. //
+// This routine attempts to remove the given vertex 'rempt' (p) from the //
+// tetrahedralization (T) by a sequence of flips. //
// //
// The algorithm used here is a simple edge reduce method. Suppose there are //
// n edges connected at p. We try to reduce the number of edges by flipping //
// any edge (not a segment) that is connecting at p. //
// //
-// The original location of 'p' in the tetrahedralization without 'p' is ind-//
-// icated by 'iloc'. 'searchtet' (t) is a tet in the current tetrahedralizat-//
-// ion which contains 'p'. Depending on 'iloc', it means the followig: //
-// - INTET: the origin of 't' is 'p'; //
-// - ONFACE: the origin of 't' is 'p', the face of 't' was split by 'p'; //
-// - ONEDGE: the origin of 't' is 'p', the edge of 't' was split by 'p'; //
-// //
-// If 'parentsh' (s) is given (not NULL), it indicates that 'p' is a Steiner //
-// point on a facet, and 's' was a subface created by the insertion of 'p'. //
-// 'iloc' must be either ONFACE or 'OEDGE'. The origin of 's' is 'p'. //
-// //
-// If 'parentseg' (seg) is given (not NULL), it indicated that 'p' is a //
-// Steiner point on a segment, and 'seg' was a subsegment created by 'p'. //
-// 'iloc' must be ONEDGE. The original of 'seg' is 'p'. //
-// //
// Unless T is a Delaunay tetrahedralization, there is no guarantee that 'p' //
// can be successfully removed. //
// //
@@ -22203,10 +20035,12 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
face parentsh, spinsh, checksh;
face leftseg, rightseg, checkseg;
point lpt = NULL, rpt = NULL, apexpt, *parypt;
+ flipconstraints fc;
enum verttype vt;
enum locateresult loc;
int valence, removeflag;
int slawson;
+ int t1ver;
int n, i;
vt = pointtype(steinerpt);
@@ -22232,23 +20066,6 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
}
lpt = sorg(leftseg);
rpt = sdest(rightseg);
- if (b->verbose > 2) {
- printf(" Removing Steiner point %d in segment (%d, %d).\n",
- pointmark(steinerpt), pointmark(lpt), pointmark(rpt));
-
- }
- } else if (vt == FREEFACETVERTEX) {
- if (b->verbose > 2) {
- printf(" Removing Steiner point %d in facet.\n",
- pointmark(steinerpt));
-
- }
- } else if (vt == FREEVOLVERTEX) {
- if (b->verbose > 2) {
- printf(" Removing Steiner point %d in volume.\n",
- pointmark(steinerpt));
-
- }
} else {
// It is not a Steiner point.
return 0;
@@ -22276,7 +20093,7 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
// Inverted elements.
getvertexstar(1, steinerpt, cavetetlist, NULL, NULL);
if (cavetetlist->objects == 2) {
- printf("to be continued...");
+ printf("to be continued...\n");
assert(0);
} else {
assert(0); // Unknown cases.
@@ -22399,7 +20216,7 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
if (!removeflag) {
if (vt == FREESEGVERTEX) {
- // Check if the edge [lpr, rpt] exists.
+ // Check if the edge [lpt, rpt] exists.
if (getedge(lpt, rpt, &searchtet)) {
// We have recovered this edge. Shift the vertex into the volume.
// We can recover this edge if the subfaces are not recovered yet.
@@ -22450,10 +20267,6 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
} // if (!removeflag)
if (!removeflag) {
- if (b->verbose > 2) {
- printf(" Unable to remove Steiner point %d val(%d).\n",
- pointmark(steinerpt), valence);
- }
return 0;
}
@@ -22510,7 +20323,8 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
eprevself(fliptets[3]);
esymself(fliptets[3]); // [a,b,c,p].
// Remove p by a 4-to-1 flip.
- flip41(fliptets, 1, 0, 0);
+ //flip41(fliptets, 1, 0, 0);
+ flip41(fliptets, 1, &fc);
//recenttet = fliptets[0];
} else if (loc == ONFACE) {
// Let the original two tets be [a,b,c,d] and [b,a,c,e]. And p is in
@@ -22535,18 +20349,12 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
// two new tets: [a,b,c,p] and [b,a,c,e]. The new tet [a,b,c,p] is
// degenerate (has zero volume). It will be deleted in the followed
// 4-to-1 flip.
- flip32(&(fliptets[3]), 1, 0, 0);
- // DEBUG BEGIN
- // fliptets[3] is [a,b,c,p], check it.
- assert(org(fliptets[3]) == apex(fliptets[0])); // a
- assert(dest(fliptets[3]) == apex(fliptets[1])); // b
- assert(apex(fliptets[3]) == apex(fliptets[2])); // c
- assert(oppo(fliptets[3]) == steinerpt);
- // fliptets[4] is [b,a,c,e].
- // DEBUG END
+ //flip32(&(fliptets[3]), 1, 0, 0);
+ flip32(&(fliptets[3]), 1, &fc);
// Second do a 4-to-1 flip on [p,d,a,b],[p,d,b,c],[p,d,c,a],[a,b,c,p].
// This creates a new tet [a,b,c,d].
- flip41(fliptets, 1, 0, 0);
+ //flip41(fliptets, 1, 0, 0);
+ flip41(fliptets, 1, &fc);
//recenttet = fliptets[0];
} else if (loc == ONEDGE) {
// Let the original edge be [e,d] and p is in [e,d]. Assume there are n
@@ -22590,7 +20398,8 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
enextself(wrktets[1]); // [p,p_0,e,p_1]
esymself(wrktets[1]); // [p_0,p,p_1,e]
eprevself(wrktets[1]); // [p_1,p_0,p,e] [1]
- flip23(wrktets, 1, 0, 0);
+ //flip23(wrktets, 1, 0, 0);
+ flip23(wrktets, 1, &fc);
// Save the new tet [e,d,p,p_0] (degenerated).
fliptets[n] = wrktets[2];
// Save the new tet [e,d,p_0,p_1].
@@ -22613,7 +20422,8 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
wrktets[2] = fliptets[i]; // [p,d,p_i,p_i+1]
eprevself(wrktets[2]); // [p_i,p,d,p_i+1]
esymself(wrktets[2]); // [p,p_i,p_i+1,d] [2]
- flip32(wrktets, 1, 0, 0);
+ //flip32(wrktets, 1, 0, 0);
+ flip32(wrktets, 1, &fc);
// Save the new tet [e,d,p_i,p_i+1]. // FOR DEBUG ONLY
fliptets[i] = wrktets[0]; // [d,e,p_i+1,p_i] // FOR DEBUG ONLY
esymself(fliptets[i]); // [e,d,p_i,p_i+1] // FOR DEBUG ONLY
@@ -22638,7 +20448,8 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
enextself(wrktets[2]); // [p_p_n-1,e,p_0]
esymself(wrktets[2]); // [p_n-1,p,p_0,e]
enextself(wrktets[2]); // [p,p_0,p_n-1,e] [2]
- flip41(wrktets, 1, 0, 0);
+ //flip41(wrktets, 1, 0, 0);
+ flip41(wrktets, 1, &fc);
// Save the new tet [e,d,p_n-1,p_0] // FOR DEBUG ONLY
fliptets[n-1] = wrktets[0]; // [e,d,p_n-1,p_0] // FOR DEBUG ONLY
//recenttet = fliptets[0];
@@ -22664,7 +20475,7 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
// Insert the new segment.
point2tetorg(lpt, searchtet);
- finddirection(&searchtet, rpt, 1);
+ finddirection(&searchtet, rpt);
assert(dest(searchtet) == rpt);
sstbond1(rightseg, searchtet);
spintet = searchtet;
@@ -22733,10 +20544,14 @@ int tetgenmesh::removevertexbyflips(point steinerpt)
// //
// suppresssteinerpoint() Suppress a Steiner point. //
// //
-// Remove a Steiner point 'p' from the segment it lies on. It is replaced by //
-// a set of volume Steiner points in each sector at the segment. //
+// Remove a Steiner point 'p' from the segment or facet it lies on. It is //
+// replaced by a set of volume Steiner points (which are at exactly the same //
+// location of 'p') in each sector at the segment or facet. The created //
+// volume Steiner points is returned in 'suppsteinerptlist'. //
// //
-// The list of volume Steiner points is returned in 'suppsteinerptlist'. //
+// NOTE: After this routine, the mesh contains degenerated or even inverted //
+// tets. These created volume Steiner points will be either removed or //
+// smoothed later in suppresssteinerpoints(). //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -22750,8 +20565,8 @@ int tetgenmesh::suppressssteinerpoint(point steinerpt)
point lpt = NULL, rpt = NULL, newpt, *parypt;
point pa, pb, pc;
verttype vt;
- long bak_supp_steiners;
int slawson;
+ int t1ver;
int i, j, k;
vt = pointtype(steinerpt);
@@ -22803,13 +20618,12 @@ int tetgenmesh::suppressssteinerpoint(point steinerpt)
if (vt == FREESEGVERTEX) {
// Check if this edge [lpt, rpt] already exists.
if (getedge(lpt, rpt, &searchtet)) {
- tsspivot1(searchtet, checkseg); // SELF_CHECK
- assert(checkseg.sh == NULL);
return 0;
}
}
- bak_supp_steiners = suppsteinerptlist->objects;
+ // Count the number of created Steiner points.
+ long bak_supp_steiners = suppsteinerptlist->objects;
if (vt == FREESEGVERTEX) {
// Get all subfaces at the left segment [lpt, steinerpt].
@@ -22866,6 +20680,7 @@ int tetgenmesh::suppressssteinerpoint(point steinerpt)
// Create a new vertex 'np'.
makepoint(&newpt, FREEVOLVERTEX);
st_volref_count++;
+ if (steinerleft > 0) steinerleft--;
// Init 'np' at the same location of 'p'.
for (j = 0; j < 3; j++) newpt[j] = steinerpt[j];
// Within the tet, replace 'p' by 'np'.
@@ -22873,6 +20688,9 @@ int tetgenmesh::suppressssteinerpoint(point steinerpt)
parytet = (triface *) fastlookup(cavetetlist, j);
setoppo(*parytet, newpt);
} // j
+ // Point to a parent tet.
+ parytet = (triface *) fastlookup(cavetetlist, 0);
+ setpoint2tet(newpt, (tetrahedron) (parytet->tet));
// Save the new Steiner point in list.
suppsteinerptlist->newindex((void **) &parypt);
*parypt = newpt;
@@ -22893,7 +20711,7 @@ int tetgenmesh::suppressssteinerpoint(point steinerpt)
} // i
cavesegshlist->restart();
- // Remove p from the segment.
+ // Remove p from the segment (or the facet).
slawson = 0; // Do not do flip afterword.
if (vt == FREESEGVERTEX) {
spivot(rightseg, parentsh); // 'rightseg' has p as its origin.
@@ -23061,7 +20879,7 @@ int tetgenmesh::suppressssteinerpoint(point steinerpt)
} else { // vt == FREEFACETVERTEX
st_facref_count--;
}
- if (steinerleft > 0) steinerleft++;
+ if (steinerleft > 0) steinerleft++; // We've removed a Steiner points.
if (b->verbose > 2) {
printf(" Duplicated %ld Steiner points.\n",
@@ -23086,7 +20904,7 @@ int tetgenmesh::suppresssteinerpoints()
optparameters opm;
REAL ori;
int bak_fliplinklevel;
- int remcount, smtcount;
+ int remcount, smtcount, ivcount;
int count, nt;
int i, j;
@@ -23156,6 +20974,8 @@ int tetgenmesh::suppresssteinerpoints()
if (suppsteinerptlist->objects == 0l) {
b->fliplinklevel = bak_fliplinklevel;
+ // The mesh contain no inverted (or degenerrated) tets now.
+ checkinverttetflag = 0;
return remcount;
}
@@ -23169,6 +20989,7 @@ int tetgenmesh::suppresssteinerpoints()
while (1) {
// Try to smooth volume Steiner points.
count = 0;
+ ivcount = 0; // Clear the inverted count.
for (i = 0; i < suppsteinerptlist->objects; i++) {
parypt = (point *) fastlookup(suppsteinerptlist, i);
@@ -23179,7 +21000,7 @@ int tetgenmesh::suppresssteinerpoints()
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
ppt = (point *) &(parytet->tet[4]);
- ori = orient3d(ppt[1], ppt[0], ppt[2], ppt[3]);
+ ori = orient3dfast(ppt[1], ppt[0], ppt[2], ppt[3]);
if (j == 0) {
opm.initval = ori;
} else {
@@ -23189,6 +21010,9 @@ int tetgenmesh::suppresssteinerpoints()
if (smoothpoint(rempt, cavetetlist, 1, &opm)) {
count++;
}
+ if (opm.imprval <= 0.0) {
+ ivcount++; // The mesh stll contains inverted elements.
+ }
cavetetlist->restart();
}
} // i
@@ -23206,9 +21030,6 @@ int tetgenmesh::suppresssteinerpoints()
}
} // while
- // The mesh should not contain inverted (or degenrrated) tets now.
- checkinverttetflag = 0;
-
if (b->verbose) {
if (smtcount > 0) {
printf(" Smoothed %d Steiner points.\n", smtcount);
@@ -23217,6 +21038,44 @@ int tetgenmesh::suppresssteinerpoints()
b->fliplinklevel = bak_fliplinklevel;
+ if (ivcount == 0) {
+ // The mesh should not contain inverted (or degenrrated) tets now.
+ checkinverttetflag = 0;
+ } else {
+ // Still have inserted elements.
+ for (i = 0; i < suppsteinerptlist->objects; i++) {
+ parypt = (point *) fastlookup(suppsteinerptlist, i);
+ rempt = *parypt;
+ if (pointtype(rempt) == FREEVOLVERTEX) {
+ getvertexstar(1, rempt, cavetetlist, NULL, NULL);
+ // Calculate the initial smallest volume (maybe zero or negative).
+ for (j = 0; j < cavetetlist->objects; j++) {
+ parytet = (triface *) fastlookup(cavetetlist, j);
+ ppt = (point *) &(parytet->tet[4]);
+ ori = orient3dfast(ppt[1], ppt[0], ppt[2], ppt[3]);
+ if (j == 0) {
+ opm.initval = ori;
+ } else {
+ if (opm.initval > ori) opm.initval = ori;
+ }
+ }
+ cavetetlist->restart();
+ if (opm.initval > 0) {
+ // This Steiner point is not degenerated. remove it from list.
+ // Move the last entry to fill the current one.
+ j = (int) (suppsteinerptlist->objects - 1);
+ plastpt = (point *) fastlookup(suppsteinerptlist, j);
+ *parypt = *plastpt;
+ suppsteinerptlist->objects--;
+ i--;
+ }
+ }
+ }
+ assert(suppsteinerptlist->objects > 0l);
+ printf("BUG Report! Inverted tets survived!\n");
+ assert(0);
+ }
+
return smtcount;
}
@@ -23239,17 +21098,11 @@ void tetgenmesh::recoverboundary(clock_t& tv)
// Counters.
long bak_segref_count, bak_facref_count, bak_volref_count;
- long bak_supp_count;
if (!b->quiet) {
printf("Recovering boundaries...\n");
}
- if (b->verbose) {
- printf(" Flip link level = %d\n", b->fliplinklevel);
- }
-
- //markacutevertices();
if (b->verbose) {
printf(" Recovering segments.\n");
@@ -23261,29 +21114,17 @@ void tetgenmesh::recoverboundary(clock_t& tv)
misseglist = new arraypool(sizeof(face), 8);
bdrysteinerptlist = new arraypool(sizeof(point), 8);
- if (0) { //if (b->order == 4) { // '-o4' option (for debug)
- // In sequential order.
- subsegs->traversalinit();
- for (i = 0; i < subsegs->items; i++) {
- searchseg.sh = shellfacetraverse(subsegs);
- //sinfect(searchseg); // Only save it once.
- subsegstack->newindex((void **) &paryseg);
- *paryseg = searchseg;
- }
- } else {
- // In random order.
- subsegs->traversalinit();
- for (i = 0; i < subsegs->items; i++) {
- s = randomnation(i + 1);
- // Move the s-th seg to the i-th.
- subsegstack->newindex((void **) &paryseg);
- *paryseg = * (face *) fastlookup(subsegstack, s);
- // Put i-th seg to be the s-th.
- searchseg.sh = shellfacetraverse(subsegs);
- //sinfect(searchseg); // Only save it once.
- paryseg = (face *) fastlookup(subsegstack, s);
- *paryseg = searchseg;
- }
+ // In random order.
+ subsegs->traversalinit();
+ for (i = 0; i < subsegs->items; i++) {
+ s = randomnation(i + 1);
+ // Move the s-th seg to the i-th.
+ subsegstack->newindex((void **) &paryseg);
+ *paryseg = * (face *) fastlookup(subsegstack, s);
+ // Put i-th seg to be the s-th.
+ searchseg.sh = shellfacetraverse(subsegs);
+ paryseg = (face *) fastlookup(subsegstack, s);
+ *paryseg = searchseg;
}
// The init number of missing segments.
@@ -23293,8 +21134,8 @@ void tetgenmesh::recoverboundary(clock_t& tv)
autofliplinklevel = 1; // Init value.
}
+ // First, trying to recover segments by only doing flips.
while (1) {
-
recoversegments(misseglist, 0, 0);
if (misseglist->objects > 0) {
@@ -23333,7 +21174,7 @@ void tetgenmesh::recoverboundary(clock_t& tv)
}
if (misseglist->objects > 0) {
- // There are missing segments. Increase the fliplevel.
+ // Second, trying to recover segments by doing more flips (fullsearch).
nit = 0;
while (misseglist->objects > 0) {
ms = misseglist->objects;
@@ -23343,7 +21184,6 @@ void tetgenmesh::recoverboundary(clock_t& tv)
}
misseglist->restart();
- // Recover the missing segments by doing more flips.
recoversegments(misseglist, 1, 0);
if (misseglist->objects < ms) {
@@ -23363,7 +21203,8 @@ void tetgenmesh::recoverboundary(clock_t& tv)
}
if (misseglist->objects > 0) {
- // There are missing segments. Add Steiner points in volume.
+ // Third, trying to recover segments by doing more flips (fullsearch)
+ // and adding Steiner points in the volume.
nit = 0;
while (misseglist->objects > 0) {
ms = misseglist->objects;
@@ -23373,7 +21214,6 @@ void tetgenmesh::recoverboundary(clock_t& tv)
}
misseglist->restart();
- // Recover the missing segments (with Steiner points).
recoversegments(misseglist, 1, 1);
if (misseglist->objects < ms) {
@@ -23392,7 +21232,8 @@ void tetgenmesh::recoverboundary(clock_t& tv)
}
if (misseglist->objects > 0) {
- // There are missing segments. Add Steiner points to split them.
+ // Last, trying to recover segments by doing more flips (fullsearch),
+ // and adding Steiner points in the volume, and splitting segments.
long bak_inpoly_count = st_volref_count; //st_inpoly_count;
for (i = 0; i < misseglist->objects; i++) {
subsegstack->newindex((void **) &paryseg);
@@ -23400,7 +21241,6 @@ void tetgenmesh::recoverboundary(clock_t& tv)
}
misseglist->restart();
- // Recover the missing segments (with Steiner points).
recoversegments(misseglist, 1, 2);
if (b->verbose) {
@@ -23479,6 +21319,7 @@ void tetgenmesh::recoverboundary(clock_t& tv)
while (1) {
recoversubfaces(misshlist, 0);
+
if (misshlist->objects > 0) {
if (b->fliplinklevel >= 0) {
break;
@@ -23554,7 +21395,7 @@ void tetgenmesh::recoverboundary(clock_t& tv)
if ((bdrysteinerptlist->objects > 0) && (b->nobisect_param > 0)) { // -Y1
- bak_supp_count = 0;
+ long bak_supp_count = suppsteinerptlist->objects;
b->fliplinklevel = 100000; // Unlimited flip levels.
do {
// Suppress boundary Steiner points.
@@ -23562,9 +21403,12 @@ void tetgenmesh::recoverboundary(clock_t& tv)
parypt = (point *) fastlookup(bdrysteinerptlist, i);
rempt = *parypt;
suppressssteinerpoint(rempt);
- bak_supp_count++;
}
bdrysteinerptlist->restart();
+ // The mesh may contain inverted (or degenrrated) tets now.
+ if (suppsteinerptlist->objects > bak_supp_count) {
+ checkinverttetflag = 1;
+ }
// There may be subfaces need to be recover.
if (subfacstack->objects > 0l) {
recoversubfaces(NULL, 1);
@@ -23572,13 +21416,15 @@ void tetgenmesh::recoverboundary(clock_t& tv)
} while (bdrysteinerptlist->objects > 0);
if (b->verbose) {
printf(" Suppressed %ld Steiner points from boundary.\n",
- bak_supp_count);
+ suppsteinerptlist->objects - bak_supp_count);
}
- // The mesh contains inverted (or degenrrated) tets now.
- checkinverttetflag = 1;
} // if
+ // Accumulate the dynamic memory.
+ totalworkmemory += (misseglist->totalmemory + misshlist->totalmemory +
+ bdrysteinerptlist->totalmemory);
+
delete bdrysteinerptlist;
delete misseglist;
delete misshlist;
@@ -23599,10 +21445,11 @@ void tetgenmesh::recoverboundary(clock_t& tv)
// //
///////////////////////////////////////////////////////////////////////////////
+
void tetgenmesh::carveholes()
{
- arraypool *tetarray;
- triface tetloop, neightet, hulltet, *parytet;
+ arraypool *tetarray, *hullarray;
+ triface tetloop, neightet, hulltet, *parytet, *parytet1;
triface openface, casface;
triface *regiontets;
face checksh, casingout, casingin, *parysh;
@@ -23611,12 +21458,15 @@ void tetgenmesh::carveholes()
enum locateresult loc;
REAL volume;
long delsegcount, delvertcount, delsteinercount;
+ long sliver_peel_count = 0l;
int regioncount;
int attrnum, attr, maxattr;
int remflag;
- int i, j;
+ int t1ver;
+ int i, j, k;
tetrahedron ptr;
+ shellface sptr;
if (!b->quiet) {
printf("Removing exterior tetrahedra ...\n");
@@ -23624,10 +21474,15 @@ void tetgenmesh::carveholes()
// Initialize the pool of exterior tets.
tetarray = new arraypool(sizeof(triface), 10);
- regiontets = NULL;
+ hullarray = new arraypool(sizeof(triface), 10);
+ regiontets = NULL;
+ regioncount = 0;
maxattr = 0; // Choose a small number here.
- attrnum = in->numberoftetrahedronattributes;
+ //attrnum = in->numberoftetrahedronattributes;
+ attrnum = numelemattrib - (b->regionattrib > 0);
+ // Comment: The element region marker is at the end of the list of
+ // the element attributes.
// Mark as infected any unprotected hull tets.
tetrahedrons->traversalinit();
@@ -23636,29 +21491,71 @@ void tetgenmesh::carveholes()
while (tetloop.tet != (tetrahedron *) NULL) {
if ((point) tetloop.tet[7] == dummypoint) {
// Is this side protected by a subface?
- tspivot(tetloop, checksh);
- if (checksh.sh == NULL) {
+ if (!issubface(tetloop)) {
infect(tetloop);
tetarray->newindex((void **) &parytet);
*parytet = tetloop;
+ hullsize--;
+ // Add the adjacent tet (not a hull tet) as well.
+ // tetloop's face number is 11 & 3 = 3.
+ decode(tetloop.tet[3], neightet);
+ if (!infected(neightet)) {
+ infect(neightet);
+ tetarray->newindex((void **) &parytet);
+ *parytet = neightet;
+ }
}
}
tetloop.tet = alltetrahedrontraverse();
}
- hullsize -= tetarray->objects;
-
if (in->numberofholes > 0) {
// Mark as infected any tets inside volume holes.
for (i = 0; i < 3 * in->numberofholes; i += 3) {
// Search a tet containing the i-th hole point.
neightet.tet = NULL;
randomsample(&(in->holelist[i]), &neightet);
- loc = locate(&(in->holelist[i]), &neightet, 0, 1); // randflag = 1;
+ loc = locate(&(in->holelist[i]), &neightet, 0);
if (loc != OUTSIDE) {
- infect(neightet);
- tetarray->newindex((void **) &parytet);
- *parytet = neightet;
+ // The tet 'neightet' contain this point.
+ if (!infected(neightet)) {
+ infect(neightet);
+ tetarray->newindex((void **) &parytet);
+ *parytet = neightet;
+ // Add its adjacent tet if it is not protected.
+ if (!issubface(neightet)) {
+ decode(neightet.tet[neightet.ver & 3], tetloop);
+ if (!infected(tetloop)) {
+ infect(tetloop);
+ tetarray->newindex((void **) &parytet);
+ *parytet = tetloop;
+ }
+ } else {
+ // It is protected. Check if its adjacent tet is a hull tet.
+ decode(neightet.tet[neightet.ver & 3], tetloop);
+ if (ishulltet(tetloop)) {
+ // It is hull tet, add it into the list. Moreover, the subface
+ // is dead, i.e., both sides are in exterior.
+ if (!infected(tetloop)) {
+ infect(tetloop);
+ tetarray->newindex((void **) &parytet);
+ *parytet = tetloop;
+ hullsize--;
+ }
+ }
+ if (infected(tetloop)) {
+ // Both sides of this subface are in exterior.
+ tspivot(neightet, checksh);
+ stdissolve(checksh);
+ assert(!sinfected(checksh));
+ //if (!sinfected(checksh)) {
+ sinfect(checksh); // Only queue it once.
+ subfacstack->newindex((void **) &parysh);
+ *parysh = checksh;
+ //}
+ }
+ }
+ } // if (!infected(neightet))
} else {
// A hole point locates outside of the convex hull.
if (!b->quiet) {
@@ -23666,7 +21563,7 @@ void tetgenmesh::carveholes()
printf("lies outside the convex hull.\n");
}
}
- }
+ } // i
}
if (b->regionattrib && (in->numberofregions > 0)) { // If has -A option.
@@ -23678,7 +21575,7 @@ void tetgenmesh::carveholes()
// Search a tet containing the i-th region point.
neightet.tet = NULL;
randomsample(&(in->regionlist[i]), &neightet);
- loc = locate(&(in->regionlist[i]), &neightet, 0, 1); // randflag = 1;
+ loc = locate(&(in->regionlist[i]), &neightet, 0);
if (loc != OUTSIDE) {
regiontets[i/5] = neightet;
if ((int) in->regionlist[i + 3] > maxattr) {
@@ -23694,58 +21591,61 @@ void tetgenmesh::carveholes()
}
}
+
// Find and infect all exterior tets (in concave place and in holes).
for (i = 0; i < tetarray->objects; i++) {
parytet = (triface *) fastlookup(tetarray, i);
- tetloop = *parytet;
- for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- fsym(tetloop, neightet);
- // Is this side protected by a subface?
- tspivot(tetloop, checksh);
- if (checksh.sh == NULL) {
- // Not protected. Infect it if it is not a hull tet.
- if ((point) neightet.tet[7] != dummypoint) {
- if (!infected(neightet)) {
+ // Check its three neighbors if it is not a hull tet.
+ if ((point) parytet->tet[7] != dummypoint) {
+ j = (parytet->ver & 3); // j is the current face number.
+ // Check the neighbors of the other three faces.
+ for (k = 0, j++; k < 3; k++, j++) {
+ decode(parytet->tet[j % 4], neightet); // neightet may be a hull tet.
+ if (!infected(neightet)) {
+ // Is neightet protected by a subface.
+ if (!issubface(neightet)) {
+ // Not proected. Add it into the list.
+ // It should not be a hull tet. Since all unproected hull tets
+ // should have already been added into the list.
infect(neightet);
- tetarray->newindex((void **) &parytet);
- *parytet = neightet;
- }
- }
- } else {
- // Its adjacent tet is protected.
- if ((point) neightet.tet[7] == dummypoint) {
- // A hull tet. It is dead.
- assert(!infected(neightet));
- infect(neightet);
- tetarray->newindex((void **) &parytet);
- *parytet = neightet;
- // Both sides of this subface are exterior.
- stdissolve(checksh);
- // Queue this subface (to be deleted later).
- if (!sinfected(checksh)) {
- sinfect(checksh); // Only queue it once.
- subfacstack->newindex((void **) &parysh);
- *parysh = checksh;
+ tetarray->newindex((void **) &parytet1);
+ *parytet1 = neightet;
+ } else {
+ // It is protected. However, if neightet is a hull tet, it is
+ // also an exterior tet. Moverover, the subface is dead, i.e.,
+ // both sides of it are exterior.
+ if ((point) neightet.tet[7] == dummypoint) {
+ infect(neightet);
+ tetarray->newindex((void **) &parytet1);
+ *parytet1 = neightet;
+ hullsize--;
+ // Both sides of this subface are exterior.
+ tspivot(neightet, checksh);
+ stdissolve(checksh);
+ // Queue this subface (to be deleted later).
+ assert(!sinfected(checksh));
+ //if (!sinfected(checksh)) {
+ sinfect(checksh); // Only queue it once.
+ subfacstack->newindex((void **) &parysh);
+ *parysh = checksh;
+ //}
+ }
}
- hullsize--;
} else {
- if (!infected(neightet)) {
- // The subface is still connect to a "live" tet - it survived.
- // tsbond(neightet, checksh);
- } else {
- // Both sides of this subface are exterior.
- stdissolve(checksh);
- // Queue this subface (to be deleted later).
+ // Both sides of this face are in exterior.
+ // Check if there is a subface.
+ if (issubface(neightet)) {
+ tspivot(neightet, checksh);
if (!sinfected(checksh)) {
sinfect(checksh); // Only queue it once.
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
- }
+ }
}
}
- }
+ } // j, k
}
- }
+ } // i
if (b->regionattrib && (in->numberofregions > 0)) {
// Re-check saved region tets to see if they lie outside.
@@ -23760,65 +21660,75 @@ void tetgenmesh::carveholes()
}
}
- // Remove all exterior tetrahedra (including infected hull tets).
- for (i = 0; i < tetarray->objects; i++) {
- parytet = (triface *) fastlookup(tetarray, i);
- tetloop = *parytet;
- for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- fsym(tetloop, neightet);
- if (!infected(neightet)) {
- // A "live" tet (may be a hull tet). Clear its adjacent tet.
- neightet.tet[neightet.ver & 3] = NULL;
- }
- }
- tetrahedrondealloc(parytet->tet);
- } // i
- tetarray->restart(); // Re-use it for new hull tets.
+if (!b->convex) { // no -c option
// Create new hull tets.
// Update point-to-tet map, segment-to-tet map, and subface-to-tet map.
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- if (tetloop.tet[tetloop.ver] == NULL) {
- tspivot(tetloop, checksh);
- assert(checksh.sh != NULL); // SELF_CHECK
- // Create a new hull tet.
- maketetrahedron(&hulltet);
- pa = org(tetloop);
- pb = dest(tetloop);
- pc = apex(tetloop);
- setvertices(hulltet, pb, pa, pc, dummypoint);
- bond(tetloop, hulltet);
- // Update the subface-to-tet map.
- sesymself(checksh);
- tsbond(hulltet, checksh);
- // Update the segment-to-tet map.
- for (i = 0; i < 3; i++) {
- tsspivot1(tetloop, checkseg);
- if (checkseg.sh != NULL) {
- tssbond1(hulltet, checkseg);
- sstbond1(checkseg, hulltet);
+ for (i = 0; i < tetarray->objects; i++) {
+ parytet = (triface *) fastlookup(tetarray, i);
+ if ((point) parytet->tet[7] != dummypoint) {
+ // We must check all four adjacent tets.
+ for (j = 0; j < 4; j++) {
+ decode(parytet->tet[j], tetloop);
+ if (!infected(tetloop)) {
+ // This face becomes a hull face.
+ tspivot(tetloop, checksh);
+ maketetrahedron(&hulltet);
+ pa = org(tetloop);
+ pb = dest(tetloop);
+ pc = apex(tetloop);
+ setvertices(hulltet, pb, pa, pc, dummypoint);
+ bond(tetloop, hulltet);
+ // Update the subface-to-tet map.
+ sesymself(checksh);
+ tsbond(hulltet, checksh);
+ // Update the segment-to-tet map.
+ for (k = 0; k < 3; k++) {
+ tsspivot1(tetloop, checkseg);
+ if (checkseg.sh != NULL) {
+ tssbond1(hulltet, checkseg);
+ sstbond1(checkseg, hulltet);
+ }
+ enextself(tetloop);
+ eprevself(hulltet);
+ }
+ // Update the point-to-tet map.
+ ptr = encode(tetloop);
+ setpoint2tet(pa, ptr);
+ setpoint2tet(pb, ptr);
+ setpoint2tet(pc, ptr);
+ // Save this hull tet in list.
+ hullarray->newindex((void **) &parytet1);
+ *parytet1 = hulltet;
+ }
+ } // j
+ } else {
+ // It is a hull tet. Clear the adjacent hull tets' connections to it.
+ // Our data structure ensures that the 3rd face opposites dummypoint.
+ for (j = 0; j < 3; j++) {
+ decode(parytet->tet[j], neightet);
+ if (neightet.tet != NULL) {
+ assert(ishulltet(neightet));
+ if (!infected(neightet)) {
+ neightet.tet[neightet.ver & 3] = NULL;
}
- enextself(tetloop);
- eprevself(hulltet);
}
- // Save this hull tet in list.
- tetarray->newindex((void **) &parytet);
- *parytet = hulltet;
- }
- }
- // Update the point-to-tet map.
- tetloop.ver = 0;
- ptr = encode(tetloop);
- ppt = (point *) tetloop.tet;
- for (i = 4; i < 8; i++) {
- setpoint2tet(ppt[i], ptr);
+ } // j
}
- tetloop.tet = tetrahedrontraverse();
- }
+ } // i
+
+ // Update the hull size.
+ hullsize += hullarray->objects;
+
+ // Remove all exterior tetrahedra (including infected hull tets).
+ for (i = 0; i < tetarray->objects; i++) {
+ parytet = (triface *) fastlookup(tetarray, i);
+ tetrahedrondealloc(parytet->tet);
+ } // i
+
+ tetarray->restart();
+
if (subfacstack->objects > 0) {
// Remove all subfaces which do not attach to any tetrahedron.
@@ -23883,6 +21793,7 @@ void tetgenmesh::carveholes()
subfacstack->restart();
}
+
// Some vertices may be not belong to any tet. Mark them.
delvertcount = unuverts;
delsteinercount = 0l;
@@ -23950,12 +21861,10 @@ void tetgenmesh::carveholes()
}
}
- // Update the hull size.
- hullsize += tetarray->objects;
// Connect new hull tets.
- for (i = 0; i < tetarray->objects; i++) {
- parytet = (triface *) fastlookup(tetarray, i);
+ for (i = 0; i < hullarray->objects; i++) {
+ parytet = (triface *) fastlookup(hullarray, i);
hulltet = *parytet;
for (j = 0; j < 3; j++) {
esym(hulltet, neightet);
@@ -23980,13 +21889,118 @@ void tetgenmesh::carveholes()
}
}
- // Set region attributes (when has -A and -AA options).
+} else { // '-c' option is set.
+
+
+ long bak_subface_count = subfaces->items;
+ long bak_segment_count = subsegs->items;
+
+ // In this case, we regard every hull face/edge is a subface/segment.
+ for (i = 0; i < tetarray->objects; i++) {
+ parytet = (triface *) fastlookup(tetarray, i);
+ // Only need the hull tet to find convex hull faces.
+ if ((point) parytet->tet[7] == dummypoint) {
+ hulltet.tet = parytet->tet;
+ hulltet.ver = 3; // The hull face.
+ tspivot(hulltet, checksh); // SELF_CHECK
+ if (checksh.sh == NULL) {
+ // Create a subface.
+ makeshellface(subfaces, &checksh);
+ pa = org(hulltet);
+ pb = dest(hulltet);
+ pc = apex(hulltet);
+ setsorg(checksh, pa);
+ setsdest(checksh, pb);
+ setsapex(checksh, pc);
+ // Create the point-to-subface map.
+ sptr = sencode(checksh);
+ setpoint2sh(pa, sptr);
+ setpoint2sh(pb, sptr);
+ setpoint2sh(pc, sptr);
+ }
+ // Insert this subface.
+ // Note: Even the subface is already exist, it may have been
+ // disconnected from its adjacent tets.
+ tsbond(hulltet, checksh);
+ fsym(hulltet, neightet);
+ assert(infected(neightet));
+ sesymself(checksh);
+ tsbond(neightet, checksh);
+ sesymself(checksh);
+ // Create three segments.
+ for (j = 0; j < 3; j++) {
+ tsspivot1(hulltet, checkseg);
+ if (checkseg.sh == NULL) {
+ // Create a segment.
+ makeshellface(subsegs, &checkseg);
+ pa = org(hulltet);
+ pb = dest(hulltet);
+ setshvertices(checkseg, pa, pb, NULL);
+ // Insert the segment into the mesh.
+ tetloop = hulltet;
+ pc = apex(hulltet);
+ checksh.sh = NULL;
+ while (1) {
+ tssbond1(tetloop, checkseg);
+ tspivot(tetloop, checksh);
+ if (checksh.sh != NULL) {
+ ssbond1(checksh, checkseg);
+ sbond1(checkseg, checksh);
+ }
+ fnextself(tetloop);
+ if (apex(tetloop) == pc) break;
+ }
+ sstbond1(checkseg, tetloop);
+ }
+ enextself(hulltet);
+ }
+ // Save this hull tet in list.
+ hullarray->newindex((void **) &parytet1);
+ *parytet1 = hulltet;
+ }
+ } // i
+
+ hullsize += hullarray->objects;
+
+ if (subfacstack->objects > 0) {
+ // Uninfect the collected exterior subfaces.
+ for (i = 0; i < subfacstack->objects; i++) {
+ parysh = (face *) fastlookup(subfacstack, i);
+ suninfect(*parysh);
+ }
+ }
+
if (b->regionattrib) {
+ // Only the hull tets need to be uninfected.
+ for (i = 0; i < hullarray->objects; i++) {
+ parytet = (triface *) fastlookup(hullarray, i);
+ uninfect(*parytet);
+ }
+ } else {
+ // Uninfect all collected tets.
+ for (i = 0; i < tetarray->objects; i++) {
+ parytet = (triface *) fastlookup(tetarray, i);
+ uninfect(*parytet);
+ }
+ }
+
+ tetarray->restart();
+ if (b->verbose) {
+ printf(" Created %ld convex hull boundary faces.\n",
+ subfaces->items - bak_subface_count);
+ printf(" Created %ld convex hull boundary edges.\n",
+ subsegs->items - bak_segment_count);
+ }
+
+} // if (b->convex)
+
+
+ // Set region attributes (the -A option).
+ if (b->regionattrib) {
if (!b->quiet) {
printf("Spreading region attributes.\n");
}
- regioncount = 0;
// If has user-defined region attributes.
if (in->numberofregions > 0) {
@@ -24007,81 +22021,61 @@ void tetgenmesh::carveholes()
if (b->varvolume) { // If has -a option.
setvolumebound(tetloop.tet, volume);
}
- for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- fsym(tetloop, neightet);
- // Is this side protected by a subface?
- tspivot(tetloop, checksh);
- if (checksh.sh == NULL) {
- // Not protected. It must not be a hull tet.
- // assert((point) neightet.tet[7] != dummypoint);
- if ((point) neightet.tet[7] == dummypoint) {
- assert(0);
- }
- if (!infected(neightet)) {
+ for (k = 0; k < 4; k++) {
+ decode(tetloop.tet[k], neightet);
+ // Is the adjacent already checked?
+ if (!infected(neightet)) {
+ // Is this side protected by a subface?
+ tspivot(neightet, checksh);
+ if (checksh.sh == NULL) {
infect(neightet);
tetarray->newindex((void **) &parytet);
*parytet = neightet;
}
- } else {
- // Protected. Set attribute for hull tet as well.
- if ((point) neightet.tet[7] == dummypoint) {
- setelemattribute(neightet.tet, attrnum, attr);
- if (b->varvolume) { // If has -a option.
- setvolumebound(neightet.tet, volume);
- }
- }
}
- } // ver
+ } // k
} // j
regioncount++;
} // if (regiontets[i/5].tet != NULL)
} // i
}
- if (b->regionattrib > 1) { // If has -AA option.
- // Set attributes for all tetrahedra.
- attr = maxattr + 1;
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- if (!infected(tetloop)) {
- // An unmarked region.
- tetarray->restart(); // Re-use this array.
- infect(tetloop);
- tetarray->newindex((void **) &parytet);
- *parytet = tetloop;
- // Find and mark all tets.
- for (j = 0; j < tetarray->objects; j++) {
- parytet = (triface *) fastlookup(tetarray, j);
- tetloop = *parytet;
- setelemattribute(tetloop.tet, attrnum, attr);
- for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- fsym(tetloop, neightet);
+ // Set attributes for all tetrahedra.
+ attr = maxattr + 1;
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ if (!infected(tetloop)) {
+ // An unmarked region.
+ tetarray->restart(); // Re-use this array.
+ infect(tetloop);
+ tetarray->newindex((void **) &parytet);
+ *parytet = tetloop;
+ // Find and mark all tets.
+ for (j = 0; j < tetarray->objects; j++) {
+ parytet = (triface *) fastlookup(tetarray, j);
+ tetloop = *parytet;
+ setelemattribute(tetloop.tet, attrnum, attr);
+ for (k = 0; k < 4; k++) {
+ decode(tetloop.tet[k], neightet);
+ // Is the adjacent tet already checked?
+ if (!infected(neightet)) {
// Is this side protected by a subface?
- tspivot(tetloop, checksh);
+ tspivot(neightet, checksh);
if (checksh.sh == NULL) {
- // Not protected. It must not be a hull tet.
- assert((point) neightet.tet[7] != dummypoint);
- if (!infected(neightet)) {
- infect(neightet);
- tetarray->newindex((void **) &parytet);
- *parytet = neightet;
- }
- } else {
- // Protected. Set attribute for hull tet as well.
- if ((point) neightet.tet[7] == dummypoint) {
- setelemattribute(neightet.tet, attrnum, attr);
- }
+ infect(neightet);
+ tetarray->newindex((void **) &parytet);
+ *parytet = neightet;
}
- } // loc
- }
- attr++; // Increase the attribute.
- regioncount++;
- } // if (!infected(tetloop))
- tetloop.tet = tetrahedrontraverse();
+ }
+ } // k
+ } // j
+ attr++; // Increase the attribute.
+ regioncount++;
}
- // Until here, every tet has a region attribute.
+ tetloop.tet = tetrahedrontraverse();
}
+ // Until here, every tet has a region attribute.
// Uninfect processed tets.
tetrahedrons->traversalinit();
@@ -24091,8 +22085,6 @@ void tetgenmesh::carveholes()
tetloop.tet = tetrahedrontraverse();
}
- // Mesh elements contain region attributes now.
- in->numberoftetrahedronattributes++;
if (b->verbose) {
assert(regioncount > 0);
@@ -24102,34 +22094,47 @@ void tetgenmesh::carveholes()
printf(" Found 1 domain.\n");
}
}
-
} // if (b->regionattrib)
if (b->regionattrib && (in->numberofregions > 0)) { // If has -A option.
delete [] regiontets;
}
delete tetarray;
+ delete hullarray;
+
+if (!b->convex) { // if no -c option
// The mesh is non-convex now.
nonconvex = 1;
+
// Push all hull tets into 'flipstack'.
tetrahedrons->traversalinit();
tetloop.ver = 11; // The face opposite to dummypoint.
tetloop.tet = alltetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
if ((point) tetloop.tet[7] == dummypoint) {
- flippush(flipstack, &tetloop);
+ fsym(tetloop, neightet);
+ flippush(flipstack, &neightet);
}
tetloop.tet = alltetrahedrontraverse();
}
+ flipconstraints fc;
+ fc.enqflag = 2;
+
// Peel "slivers" off the hull.
- lawsonflip3d(NULL, 4, 1, 0, 0);
+ sliver_peel_count = lawsonflip3d(&fc);
- if (b->verbose && (opt_sliver_peels > 0l)) {
- printf(" Peeled %ld hull slivers.\n", opt_sliver_peels);
+ if (b->verbose) {
+ if (sliver_peel_count > 0l) {
+ printf(" Removed %ld hull slivers.\n", sliver_peel_count);
+ }
}
+ unflipqueue->restart();
+
+} // if (!b->convex)
+
}
///////////////////////////////////////////////////////////////////////////////
@@ -24153,6 +22158,7 @@ void tetgenmesh::reconstructmesh()
REAL angtol, ang;
int eextras, marker = 0;
int bondflag;
+ int t1ver;
int idx, i, j, k;
if (!b->quiet) {
@@ -24161,12 +22167,17 @@ void tetgenmesh::reconstructmesh()
// Default assume the mesh is non-convex.
nonconvex = 1;
- // Create a map from indices to vertices.
+ // Create a map from indices to vertices.
makeindex2pointmap(idx2verlist);
+ // 'idx2verlist' has length 'in->numberofpoints + 1'.
+ if (in->firstnumber == 1) {
+ idx2verlist[0] = dummypoint; // Let 0th-entry be dummypoint.
+ }
// Allocate an array that maps each vertex to its adjacent tets.
ver2tetarray = new tetrahedron[in->numberofpoints + 1];
- for (i = 0; i < in->numberofpoints; i++) {
+ for (i = 0; i < in->numberofpoints + 1; i++) {
+ setpointtype(idx2verlist[i], VOLVERTEX); // initial type.
ver2tetarray[i] = NULL;
}
@@ -24176,7 +22187,6 @@ void tetgenmesh::reconstructmesh()
idx = i * in->numberofcorners;
for (j = 0; j < 4; j++) {
p[j] = idx2verlist[in->tetrahedronlist[idx++]];
- setpointtype(p[j], VOLVERTEX); // initial type.
}
// Check the orientation.
ori = orient3d(p[0], p[1], p[2], p[3]);
@@ -24224,7 +22234,6 @@ void tetgenmesh::reconstructmesh()
p[2] = apex(tetloop); // c
prevchktet = tetloop;
do {
- assert(checktet.ver < 4); // SELF_CHECK
q[0] = org(checktet); // a'
q[1] = dest(checktet); // b'
q[2] = apex(checktet); // c'
@@ -24410,51 +22419,51 @@ void tetgenmesh::reconstructmesh()
} // i
} // if (in->trifacelist)
- // Indentify subfaces from the mesh.
- // Create subfaces for hull faces (if they're not subface yet) and
- // interior faces which separate two different materials.
- eextras = in->numberoftetrahedronattributes;
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- while (tetloop.tet != (tetrahedron *) NULL) {
- for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- tspivot(tetloop, neighsh);
- if (neighsh.sh == NULL) {
- bondflag = 0;
- fsym(tetloop, checktet);
- if (ishulltet(checktet)) {
- bondflag = 1; // A hull face.
- } else {
- if (eextras > 0) {
- if (elemattribute(tetloop.tet, eextras - 1) !=
- elemattribute(checktet.tet, eextras - 1)) {
- bondflag = 1; // An interior interface.
- }
+ // Indentify subfaces from the mesh.
+ // Create subfaces for hull faces (if they're not subface yet) and
+ // interior faces which separate two different materials.
+ eextras = in->numberoftetrahedronattributes;
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
+ tspivot(tetloop, neighsh);
+ if (neighsh.sh == NULL) {
+ bondflag = 0;
+ fsym(tetloop, checktet);
+ if (ishulltet(checktet)) {
+ bondflag = 1; // A hull face.
+ } else {
+ if (eextras > 0) {
+ if (elemattribute(tetloop.tet, eextras - 1) !=
+ elemattribute(checktet.tet, eextras - 1)) {
+ bondflag = 1; // An interior interface.
}
}
- if (bondflag) {
- // Create a new subface.
- makeshellface(subfaces, &subloop);
- p[0] = org(tetloop);
- p[1] = dest(tetloop);
- p[2] = apex(tetloop);
- setshvertices(subloop, p[0], p[1], p[2]);
- // Create the point-to-subface map.
- sptr = sencode(subloop);
- for (j = 0; j < 3; j++) {
- setpointtype(p[j], FACETVERTEX); // initial type.
- setpoint2sh(p[j], sptr);
- }
- setshellmark(subloop, 0); // Default marker.
- // Insert the subface into the mesh.
- tsbond(tetloop, subloop);
- sesymself(subloop);
- tsbond(checktet, subloop);
- } // if (bondflag)
- } // if (neighsh.sh == NULL)
- }
- tetloop.tet = tetrahedrontraverse();
+ }
+ if (bondflag) {
+ // Create a new subface.
+ makeshellface(subfaces, &subloop);
+ p[0] = org(tetloop);
+ p[1] = dest(tetloop);
+ p[2] = apex(tetloop);
+ setshvertices(subloop, p[0], p[1], p[2]);
+ // Create the point-to-subface map.
+ sptr = sencode(subloop);
+ for (j = 0; j < 3; j++) {
+ setpointtype(p[j], FACETVERTEX); // initial type.
+ setpoint2sh(p[j], sptr);
+ }
+ setshellmark(subloop, 0); // Default marker.
+ // Insert the subface into the mesh.
+ tsbond(tetloop, subloop);
+ sesymself(subloop);
+ tsbond(checktet, subloop);
+ } // if (bondflag)
+ } // if (neighsh.sh == NULL)
}
+ tetloop.tet = tetrahedrontraverse();
+ }
// Connect subfaces together.
subfaces->traversalinit();
@@ -24488,9 +22497,6 @@ void tetgenmesh::reconstructmesh()
subloop.sh = shellfacetraverse(subfaces);
}
- //if (b->verbose) {
- // printf(" Created %ld subfaces.\n", subfaces->items);
- //}
// Segments will be introudced.
if (in->edgelist != NULL) {
@@ -24554,85 +22560,82 @@ void tetgenmesh::reconstructmesh()
} // i
} // if (in->edgelist)
- // Identify segments from the mesh.
- // Create segments for non-manifold edges (which are shared by more
- // than two subfaces), and for non-coplanar edges, i.e., two subfaces
- // form an dihedral angle > 'b->facet_ang_tol' (degree).
- angtol = b->facet_ang_tol / 180.0 * PI;
- subfaces->traversalinit();
- subloop.shver = 0;
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- for (i = 0; i < 3; i++) {
- sspivot(subloop, segloop);
- if (segloop.sh == NULL) {
- // Check if this edge is a segment.
- bondflag = 0;
- // Counter the number of subfaces at this edge.
- idx = 0;
- nextsh = subloop;
- while (1) {
- idx++;
- spivotself(nextsh);
- if (nextsh.sh == subloop.sh) break;
- }
- if (idx != 2) {
- // It's a non-manifold edge. Insert a segment.
- p[0] = sorg(subloop);
- p[1] = sdest(subloop);
+ // Identify segments from the mesh.
+ // Create segments for non-manifold edges (which are shared by more
+ // than two subfaces), and for non-coplanar edges, i.e., two subfaces
+ // form an dihedral angle > 'b->facet_ang_tol' (degree).
+ angtol = b->facet_ang_tol / 180.0 * PI;
+ subfaces->traversalinit();
+ subloop.shver = 0;
+ subloop.sh = shellfacetraverse(subfaces);
+ while (subloop.sh != (shellface *) NULL) {
+ for (i = 0; i < 3; i++) {
+ sspivot(subloop, segloop);
+ if (segloop.sh == NULL) {
+ // Check if this edge is a segment.
+ bondflag = 0;
+ // Counter the number of subfaces at this edge.
+ idx = 0;
+ nextsh = subloop;
+ while (1) {
+ idx++;
+ spivotself(nextsh);
+ if (nextsh.sh == subloop.sh) break;
+ }
+ if (idx != 2) {
+ // It's a non-manifold edge. Insert a segment.
+ p[0] = sorg(subloop);
+ p[1] = sdest(subloop);
+ bondflag = 1;
+ } else {
+ // Check the dihedral angle formed by the two subfaces.
+ spivot(subloop, neighsh);
+ p[0] = sorg(subloop);
+ p[1] = sdest(subloop);
+ p[2] = sapex(subloop);
+ p[3] = sapex(neighsh);
+ ang = facedihedral(p[0], p[1], p[2], p[3]);
+ if (ang > PI) ang = 2 * PI - ang;
+ if (ang < angtol) {
bondflag = 1;
- } else {
- // Check the dihedral angle formed by the two subfaces.
- spivot(subloop, neighsh);
- p[0] = sorg(subloop);
- p[1] = sdest(subloop);
- p[2] = sapex(subloop);
- p[3] = sapex(neighsh);
- ang = facedihedral(p[0], p[1], p[2], p[3]);
- if (ang > PI) ang = 2 * PI - ang;
- if (ang < angtol) {
- bondflag = 1;
- }
}
- if (bondflag) {
- // Create a new subface.
- makeshellface(subsegs, &segloop);
- setshvertices(segloop, p[0], p[1], NULL);
- // Create the point-to-segment map.
- sptr = sencode(segloop);
- for (j = 0; j < 2; j++) {
- setpointtype(p[j], RIDGEVERTEX); // initial type.
- setpoint2sh(p[j], sptr);
+ }
+ if (bondflag) {
+ // Create a new subface.
+ makeshellface(subsegs, &segloop);
+ setshvertices(segloop, p[0], p[1], NULL);
+ // Create the point-to-segment map.
+ sptr = sencode(segloop);
+ for (j = 0; j < 2; j++) {
+ setpointtype(p[j], RIDGEVERTEX); // initial type.
+ setpoint2sh(p[j], sptr);
+ }
+ setshellmark(segloop, marker);
+ // Insert the subface into the mesh.
+ stpivot(subloop, tetloop);
+ q[2] = apex(tetloop);
+ while (1) {
+ tssbond1(tetloop, segloop);
+ tspivot(tetloop, neighsh);
+ if (neighsh.sh != NULL) {
+ ssbond1(neighsh, segloop);
}
- setshellmark(segloop, marker);
- // Insert the subface into the mesh.
- stpivot(subloop, tetloop);
- q[2] = apex(tetloop);
- while (1) {
- tssbond1(tetloop, segloop);
- tspivot(tetloop, neighsh);
- if (neighsh.sh != NULL) {
- ssbond1(neighsh, segloop);
- }
- fnextself(tetloop);
- if (apex(tetloop) == q[2]) break;
- } // while (1)
- // Remember an adjacent tet for this segment.
- sstbond1(segloop, tetloop);
- sbond1(segloop, subloop);
- } // if (bondflag)
- } // if (neighsh.sh == NULL)
- senextself(subloop);
- }
- subloop.sh = shellfacetraverse(subfaces);
+ fnextself(tetloop);
+ if (apex(tetloop) == q[2]) break;
+ } // while (1)
+ // Remember an adjacent tet for this segment.
+ sstbond1(segloop, tetloop);
+ sbond1(segloop, subloop);
+ } // if (bondflag)
+ } // if (neighsh.sh == NULL)
+ senextself(subloop);
}
+ subloop.sh = shellfacetraverse(subfaces);
+ }
// Remember the number of input segments.
insegments = subsegs->items;
- //if (b->verbose) {
- // printf(" Created %ld segments.\n", subsegs->items);
- //}
// Set global flags.
checksubsegflag = 1;
@@ -24660,32 +22663,32 @@ int tetgenmesh::scoutpoint(point searchpt, triface *searchtet, int randflag)
point pa, pb, pc, pd;
enum locateresult loc = OUTSIDE;
REAL vol, ori1, ori2, ori3, ori4;
- int iter;
+ int t1ver;
- if (searchtet->tet == NULL) {
- *searchtet = recenttet;
- }
- iter = 0;
- while (1) {
- // Randonmly select a good starting tet.
- if (randflag) {
- randomsample(searchpt, searchtet);
- }
- loc = locate(searchpt, searchtet, 0, 1);
- if (loc == OUTSIDE) {
- // Not found. This happens when the mesh is not convex.
- if (!randflag) break;
- iter++;
- if (iter > 3) {
- searchtet->tet = NULL;
- break;
- }
- } else {
- // Found the point.
- break;
+ // Randonmly select a good starting tet.
+ if (randflag) {
+ randomsample(searchpt, searchtet);
+ } else {
+ if (searchtet->tet == NULL) {
+ *searchtet = recenttet;
}
- } // while (1)
+ }
+ loc = locate(searchpt, searchtet, 0);
+
+ if (loc == OUTSIDE) {
+ // Test if it lies nearly on the hull face.
+ // Reuse vol, ori1.
+ pa = org(*searchtet);
+ pb = dest(*searchtet);
+ pc = apex(*searchtet);
+ vol = triarea(pa, pb, pc);
+ ori1 = orient3dfast(pa, pb, pc, searchpt);
+ if (fabs(ori1 / vol) < b->epsilon) {
+ loc = ONFACE; // On face (or on edge, or on vertex).
+ fsymself(*searchtet);
+ }
+ }
if (loc != OUTSIDE) {
// Round the result of location.
@@ -24693,11 +22696,11 @@ int tetgenmesh::scoutpoint(point searchpt, triface *searchtet, int randflag)
pb = dest(*searchtet);
pc = apex(*searchtet);
pd = oppo(*searchtet);
- vol = orient3d(pa, pb, pc, pd);
- ori1 = orient3d(pa, pb, pc, searchpt);
- ori2 = orient3d(pb, pa, pd, searchpt);
- ori3 = orient3d(pc, pb, pd, searchpt);
- ori4 = orient3d(pa, pc, pd, searchpt);
+ vol = orient3dfast(pa, pb, pc, pd);
+ ori1 = orient3dfast(pa, pb, pc, searchpt);
+ ori2 = orient3dfast(pb, pa, pd, searchpt);
+ ori3 = orient3dfast(pc, pb, pd, searchpt);
+ ori4 = orient3dfast(pa, pc, pd, searchpt);
if (fabs(ori1 / vol) < b->epsilon) ori1 = 0;
if (fabs(ori2 / vol) < b->epsilon) ori2 = 0;
if (fabs(ori3 / vol) < b->epsilon) ori3 = 0;
@@ -24712,19 +22715,19 @@ int tetgenmesh::scoutpoint(point searchpt, triface *searchtet, int randflag)
pc = apex(*searchtet);
pd = oppo(*searchtet);
- vol = orient3d(pa, pb, pc, pd);
+ vol = orient3dfast(pa, pb, pc, pd);
assert(vol < 0); // vol != 0
- ori1 = orient3d(pa, pb, pc, searchpt);
+ ori1 = orient3dfast(pa, pb, pc, searchpt);
if (fabs(ori1 / vol) < b->epsilon) ori1 = 0; // Rounding.
if (ori1 <= 0) {
- ori2 = orient3d(pb, pa, pd, searchpt);
+ ori2 = orient3dfast(pb, pa, pd, searchpt);
if (fabs(ori2 / vol) < b->epsilon) ori2 = 0;
if (ori2 <= 0) {
- ori3 = orient3d(pc, pb, pd, searchpt);
+ ori3 = orient3dfast(pc, pb, pd, searchpt);
if (fabs(ori3 / vol) < b->epsilon) ori3 = 0;
if (ori3 <= 0) {
- ori4 = orient3d(pa, pc, pd, searchpt);
+ ori4 = orient3dfast(pa, pc, pd, searchpt);
if (fabs(ori4 / vol) < b->epsilon) ori4 = 0;
if (ori4 <= 0) {
// Found the tet. Return its location.
@@ -24734,8 +22737,9 @@ int tetgenmesh::scoutpoint(point searchpt, triface *searchtet, int randflag)
} // ori2
} // ori1
- searchtet->tet = bgm->tetrahedrontraverse();
+ searchtet->tet = tetrahedrontraverse();
} // while (searchtet->tet != NULL)
+ nonregularcount++; // Re-use this counter.
}
if (searchtet->tet != NULL) {
@@ -24824,13 +22828,9 @@ int tetgenmesh::scoutpoint(point searchpt, triface *searchtet, int randflag)
// 'iloc' indicates the location of the point w.r.t. 'searchtet'. The size //
// is obtained by linear interpolation on the vertices of the tet. //
// //
-// If 'posflag' is set, only do interpolation when all vertices have a posi- //
-// tive value. //
-// //
///////////////////////////////////////////////////////////////////////////////
-REAL tetgenmesh::getpointmeshsize(point searchpt, triface *searchtet, int iloc,
- int posflag)
+REAL tetgenmesh::getpointmeshsize(point searchpt, triface *searchtet, int iloc)
{
point *pts, pa, pb, pc;
REAL volume, vol[4], wei[4];
@@ -24842,15 +22842,15 @@ REAL tetgenmesh::getpointmeshsize(point searchpt, triface *searchtet, int iloc,
if (iloc == (int) INTETRAHEDRON) {
pts = (point *) &(searchtet->tet[4]);
assert(pts[3] != dummypoint);
- if (!posflag ||
- ((pts[0][pointmtrindex] > 0) && (pts[1][pointmtrindex] > 0) &&
- (pts[2][pointmtrindex] > 0) && (pts[3][pointmtrindex] > 0))) {
+ // Only do interpolation if all vertices have non-zero sizes.
+ if ((pts[0][pointmtrindex] > 0) && (pts[1][pointmtrindex] > 0) &&
+ (pts[2][pointmtrindex] > 0) && (pts[3][pointmtrindex] > 0)) {
// P1 interpolation.
- volume = orient3d(pts[0], pts[1], pts[2], pts[3]);
- vol[0] = orient3d(searchpt, pts[1], pts[2], pts[3]);
- vol[1] = orient3d(pts[0], searchpt, pts[2], pts[3]);
- vol[2] = orient3d(pts[0], pts[1], searchpt, pts[3]);
- vol[3] = orient3d(pts[0], pts[1], pts[2], searchpt);
+ volume = orient3dfast(pts[0], pts[1], pts[2], pts[3]);
+ vol[0] = orient3dfast(searchpt, pts[1], pts[2], pts[3]);
+ vol[1] = orient3dfast(pts[0], searchpt, pts[2], pts[3]);
+ vol[2] = orient3dfast(pts[0], pts[1], searchpt, pts[3]);
+ vol[3] = orient3dfast(pts[0], pts[1], pts[2], searchpt);
for (i = 0; i < 4; i++) {
wei[i] = fabs(vol[i] / volume);
size += (wei[i] * pts[i][pointmtrindex]);
@@ -24860,9 +22860,8 @@ REAL tetgenmesh::getpointmeshsize(point searchpt, triface *searchtet, int iloc,
pa = org(*searchtet);
pb = dest(*searchtet);
pc = apex(*searchtet);
- if (!posflag ||
- ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0) &&
- (pc[pointmtrindex] > 0))) {
+ if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0) &&
+ (pc[pointmtrindex] > 0)) {
volume = triarea(pa, pb, pc);
vol[0] = triarea(searchpt, pb, pc);
vol[1] = triarea(pa, searchpt, pc);
@@ -24874,7 +22873,7 @@ REAL tetgenmesh::getpointmeshsize(point searchpt, triface *searchtet, int iloc,
} else if (iloc == (int) ONEDGE) {
pa = org(*searchtet);
pb = dest(*searchtet);
- if (!posflag || ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0))) {
+ if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0)) {
volume = distance(pa, pb);
vol[0] = distance(searchpt, pb);
vol[1] = distance(pa, searchpt);
@@ -24883,7 +22882,7 @@ REAL tetgenmesh::getpointmeshsize(point searchpt, triface *searchtet, int iloc,
}
} else if (iloc == (int) ONVERTEX) {
pa = org(*searchtet);
- if (!posflag || (pa[pointmtrindex] > 0)) {
+ if (pa[pointmtrindex] > 0) {
size = pa[pointmtrindex];
}
}
@@ -24909,6 +22908,11 @@ void tetgenmesh::interpolatemeshsize()
if (!b->quiet) {
printf("Interpolating mesh size ...\n");
}
+
+ long bak_nonregularcount = nonregularcount;
+ nonregularcount = 0l; // Count the number of (slow) global searches.
+ long baksmaples = bgm->samples;
+ bgm->samples = 3l;
count = 0; // Count the number of interpolated points.
// Interpolate sizes for all points in the current mesh.
@@ -24919,8 +22923,8 @@ void tetgenmesh::interpolatemeshsize()
searchtet.tet = NULL;
iloc = bgm->scoutpoint(ploop, &searchtet, 1); // randflag = 1
if (iloc != (int) OUTSIDE) {
- // Interpolate the mesh size (posflag = 0)
- ploop[pointmtrindex] = bgm->getpointmeshsize(ploop, &searchtet, iloc, 0);
+ // Interpolate the mesh size.
+ ploop[pointmtrindex] = bgm->getpointmeshsize(ploop, &searchtet, iloc);
setpoint2bgmtet(ploop, bgm->encode(searchtet));
if (count == 0) {
// This is the first interpolated point.
@@ -24945,152 +22949,276 @@ void tetgenmesh::interpolatemeshsize()
if (b->verbose) {
printf(" Interoplated %d points.\n", count);
+ if (nonregularcount > 0l) {
+ printf(" Performed %ld brute-force searches.\n", nonregularcount);
+ }
printf(" Size rangle [%.17g, %.17g].\n", minval, maxval);
}
+
+ bgm->samples = baksmaples;
+ nonregularcount = bak_nonregularcount;
}
///////////////////////////////////////////////////////////////////////////////
// //
// insertconstrainedpoints() Insert a list of points into the mesh. //
// //
+// Assumption: The bounding box of the insert point set should be no larger //
+// than the bounding box of the mesh. (Required by point sorting). //
+// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::insertconstrainedpoints(tetgenio *addio)
+void tetgenmesh::insertconstrainedpoints(point *insertarray, int arylen)
{
triface searchtet, spintet;
- face checksh, *splitsh;
- face checkseg, *splitseg;
- point newpt;
+ face splitsh;
+ face splitseg;
insertvertexflags ivf;
- REAL *attr, x, y, z, w;
- int randflag;
- int count, index;
- int loc;
- int i, j;
+ flipconstraints fc;
+ int randflag = 0;
+ int t1ver;
+ int i;
- if (!b->quiet) {
- printf("Inserting constrained points ...\n");
+ if (b->verbose) {
+ printf(" Inserting %d constrained points\n", arylen);
}
- randflag = 1; // Randomly select start tet for point location.
- count = 0;
- index = 0;
+ if (b->no_sort) { // -b/1 option.
+ if (b->verbose) {
+ printf(" Using the input order.\n");
+ }
+ } else {
+ if (b->verbose) {
+ printf(" Permuting vertices.\n");
+ }
+ point swappoint;
+ int randindex;
+ srand(arylen);
+ for (i = 0; i < arylen; i++) {
+ randindex = rand() % (i + 1);
+ swappoint = insertarray[i];
+ insertarray[i] = insertarray[randindex];
+ insertarray[randindex] = swappoint;
+ }
+ if (b->brio_hilbert) { // -b1 option
+ if (b->verbose) {
+ printf(" Sort vertices using BRIO and Hilbert curve.\n");
+ }
+ hilbert_init(in->mesh_dim);
+ int ngroup = 0;
+ brio_multiscale_sort(insertarray, arylen, b->brio_threshold,
+ b->brio_ratio, &ngroup);
+ } else { // -b0 option.
+ randflag = 1;
+ } // if (!b->brio_hilbert)
+ } // if (!b->no_sort)
+
+ long bak_nonregularcount = nonregularcount;
+ nonregularcount = 0l;
+ long baksmaples = samples;
+ samples = 3l; // Use at least 3 samples. Updated in randomsample().
+
+ long bak_seg_count = st_segref_count;
+ long bak_fac_count = st_facref_count;
+ long bak_vol_count = st_volref_count;
+
+ // Initialize the insertion parameters.
+ if (b->incrflip) { // -l option
+ // Use incremental flip algorithm.
+ ivf.bowywat = 0;
+ ivf.lawson = 1;
+ ivf.validflag = 0; // No need to validate the cavity.
+ fc.enqflag = 2;
+ } else {
+ // Use Bowyer-Watson algorithm.
+ ivf.bowywat = 1;
+ ivf.lawson = 0;
+ ivf.validflag = 1; // Validate the B-W cavity.
+ }
+ ivf.rejflag = 0; // Do not check encroachment.
+ if (b->metric) { // -m option.
+ ivf.rejflag |= 4; // Reject it if it lies in some protecting balls.
+ }
+ ivf.chkencflag = 0;
+ ivf.sloc = (int) INSTAR;
+ ivf.sbowywat = 3;
+ ivf.splitbdflag = 1;
+ ivf.respectbdflag = 1;
+ ivf.assignmeshsize = b->metric;
- for (i = 0; i < addio->numberofpoints; i++) {
- makepoint(&newpt, VOLVERTEX);
- x = newpt[0] = addio->pointlist[index++];
- y = newpt[1] = addio->pointlist[index++];
- z = newpt[2] = addio->pointlist[index++];
- if (b->weighted) { // -w option
- if (addio->numberofpointattributes > 0) {
- // The first point attribute is weight.
- w = addio->pointattributelist[addio->numberofpointattributes * i];
+ // Insert the points.
+ for (i = 0; i < arylen; i++) {
+ // Find the location of the inserted point.
+ // Do not use 'recenttet', since the mesh may be non-convex.
+ searchtet.tet = NULL;
+ ivf.iloc = scoutpoint(insertarray[i], &searchtet, randflag);
+
+ // Decide the right type for this point.
+ setpointtype(insertarray[i], FREEVOLVERTEX); // Default.
+ splitsh.sh = NULL;
+ splitseg.sh = NULL;
+ if (ivf.iloc == (int) ONEDGE) {
+ if (issubseg(searchtet)) {
+ tsspivot1(searchtet, splitseg);
+ setpointtype(insertarray[i], FREESEGVERTEX);
+ //ivf.rejflag = 0;
} else {
- // No given weight available.
- w = 0;
- }
- if (b->weighted_param == 0) {
- newpt[3] = x * x + y * y + z * z - w; // Weighted DT.
- } else { // -w1 option
- newpt[3] = w; // Regular tetrahedralization.
- }
- } else {
- newpt[3] = 0;
- }
- // Read the add point attributes if current points have attributes.
- if ((addio->numberofpointattributes > 0) &&
- (in->numberofpointattributes > 0)) {
- attr = addio->pointattributelist + addio->numberofpointattributes * i;
- for (j = 0; j < in->numberofpointattributes; j++) {
- if (j < addio->numberofpointattributes) {
- newpt[4 + j] = attr[j];
+ // Check if it is a subface edge.
+ spintet = searchtet;
+ while (1) {
+ if (issubface(spintet)) {
+ tspivot(spintet, splitsh);
+ setpointtype(insertarray[i], FREEFACETVERTEX);
+ //ivf.rejflag |= 1;
+ break;
+ }
+ fnextself(spintet);
+ if (spintet.tet == searchtet.tet) break;
}
}
+ } else if (ivf.iloc == (int) ONFACE) {
+ if (issubface(searchtet)) {
+ tspivot(searchtet, splitsh);
+ setpointtype(insertarray[i], FREEFACETVERTEX);
+ //ivf.rejflag |= 1;
+ }
}
- // Read the point metric tensor.
- //for (j = 0; j < in->numberofpointmtrs; j++) {
- // pointloop[pointmtrindex + j] = in->pointmtrlist[mtrindex++];
- //}
- // Find the location of the inserted point.
- searchtet.tet = NULL;
- ivf.iloc = scoutpoint(newpt, &searchtet, randflag);
- if (ivf.iloc != (int) OUTSIDE) {
- // Found the point.
- // Initialize the insertion parameters.
- if (b->psc) {
- ivf.bowywat = 0; // Do not enlarge the initial cavity.
- ivf.validflag = 0; // Do not validate the initial cavity.
+ // Now insert the point.
+ if (insertpoint(insertarray[i], &searchtet, &splitsh, &splitseg, &ivf)) {
+ if (flipstack != NULL) {
+ // There are queued faces. Use flips to recover Delaunayness.
+ lawsonflip3d(&fc);
+ // There may be unflippable edges. Ignore them.
+ unflipqueue->restart();
+ }
+ // Update the Steiner counters.
+ if (pointtype(insertarray[i]) == FREESEGVERTEX) {
+ st_segref_count++;
+ } else if (pointtype(insertarray[i]) == FREEFACETVERTEX) {
+ st_facref_count++;
} else {
- ivf.bowywat = 3; // Use the "Bowyer-Watson" algorithm to form cavity.
- ivf.validflag = 1; // Validate the B-W cavity.
+ st_volref_count++;
}
- ivf.lawson = 3;
- ivf.rejflag = 0;
- ivf.chkencflag = 0;
- ivf.sloc = ivf.iloc;
- ivf.sbowywat = ivf.bowywat; // Surface mesh options.
- ivf.splitbdflag = 1;
- ivf.respectbdflag = 1;
- ivf.assignmeshsize = 1;
-
- splitsh = NULL;
- splitseg = NULL;
-
- // Set the right point type.
- if (ivf.iloc == (int) ONEDGE) {
- tsspivot1(searchtet, checkseg);
- if (checkseg.sh != NULL) {
- setpointtype(newpt, RIDGEVERTEX);
- spivot(checkseg, checksh);
- splitsh = &checksh;
- splitseg = &checkseg;
- } else {
- // Check if it is a subface edge.
- spintet = searchtet;
- while (1) {
- tspivot(spintet, checksh);
- if (checksh.sh != NULL) {
- setpointtype(newpt, FACETVERTEX);
- splitsh = &checksh;
- break;
- }
- fnextself(spintet);
- if (spintet.tet == searchtet.tet) break;
- }
+ } else {
+ // Point is not inserted.
+ if (ivf.iloc == (int) OUTSIDE) {
+ if (!b->quiet) {
+ printf("Warning: Point #%d lies outside the domain. Ignored.\n",
+ pointmark(insertarray[i]) - in->numberofpoints);
}
- } else if (ivf.iloc == (int) ONFACE) {
- tspivot(searchtet, checksh);
- if (checksh.sh != NULL) {
- setpointtype(newpt, FACETVERTEX);
- splitsh = &checksh;
+ } else if (ivf.iloc == (int) ONVERTEX) {
+ if (!b->quiet) {
+ printf("Warning: Point #%d is coincident with Point #%d. Ignored.\n",
+ pointmark(insertarray[i]) - in->numberofpoints,
+ pointmark(org(searchtet)));
+ }
+ } else if (ivf.iloc == (int) NEARVERTEX) {
+ if (!b->quiet) {
+ printf("Warning: Point #%d is too close to Point #%d. Rejected.\n",
+ pointmark(insertarray[i]) - in->numberofpoints,
+ pointmark(point2ppt(insertarray[i])));
+ }
+ } else if (ivf.iloc == (int) ENCVERTEX) {
+ if (!b->quiet) {
+ printf("Warning: Point #%d encroaches upon Point #%d. Rejected.\n",
+ pointmark(insertarray[i]) - in->numberofpoints,
+ pointmark(point2ppt(insertarray[i])));
}
- }
-
- // Insert the vertex.
- loc = insertvertex(newpt, &searchtet, splitsh, splitseg, &ivf);
-
- if (loc == ivf.iloc) {
- // The point has been inserted.
- lawsonflip3d(newpt, 4, 0, ivf.chkencflag, 0);
- count++;
} else {
if (!b->quiet) {
- printf("Warning: Failed to insert point #%d. Ignored.\n", i);
+ printf("Warning: Failed to insert Point #%d (%g,%g,%g).Ignored.\n",
+ i, insertarray[i][0], insertarray[i][1], insertarray[i][2]);
}
- pointdealloc(newpt);
}
- } else {
- if (!b->quiet) {
- printf("Warning: Can't locate add point #%d. Ignored.\n", i);
- }
- pointdealloc(newpt);
+ //pointdealloc(insertarray[i]);
+ setpointtype(insertarray[i], UNUSEDVERTEX);
+ unuverts++;
}
} // i
if (b->verbose) {
- printf(" Inserted %d of %d vertices.\n", count, addio->numberofpoints);
+ printf(" Inserted %ld (%ld, %ld, %ld) vertices.\n",
+ st_segref_count + st_facref_count + st_volref_count -
+ (bak_seg_count + bak_fac_count + bak_vol_count),
+ st_segref_count - bak_seg_count, st_facref_count - bak_fac_count,
+ st_volref_count - bak_vol_count);
+ if (nonregularcount > 0l) {
+ printf(" Performed %ld brute-force searches.\n", nonregularcount);
+ }
}
+
+ nonregularcount = bak_nonregularcount;
+ samples = baksmaples;
+}
+
+void tetgenmesh::insertconstrainedpoints(tetgenio *addio)
+{
+ point *insertarray, newpt;
+ REAL x, y, z, w;
+ int index, attribindex, mtrindex;
+ int arylen, i, j;
+
+ if (!b->quiet) {
+ printf("Inserting constrained points ...\n");
+ }
+
+ insertarray = new point[addio->numberofpoints];
+ arylen = 0;
+ index = 0;
+ attribindex = 0;
+ mtrindex = 0;
+
+ for (i = 0; i < addio->numberofpoints; i++) {
+ x = addio->pointlist[index++];
+ y = addio->pointlist[index++];
+ z = addio->pointlist[index++];
+ // Test if this point lies inside the bounding box.
+ if ((x < xmin) || (x > xmax) || (y < ymin) || (y > ymax) ||
+ (z < zmin) || (z > zmax)) {
+ if (b->verbose) {
+ printf("Warning: Point #%d lies outside the bounding box. Ignored\n",
+ i + in->firstnumber);
+ }
+ continue;
+ }
+ makepoint(&newpt, UNUSEDVERTEX);
+ newpt[0] = x;
+ newpt[1] = y;
+ newpt[2] = z;
+ // Read the point attributes. (Including point weights.)
+ for (j = 0; j < addio->numberofpointattributes; j++) {
+ newpt[3 + j] = addio->pointattributelist[attribindex++];
+ }
+ // Read the point metric tensor.
+ for (j = 0; j < addio->numberofpointmtrs; j++) {
+ newpt[pointmtrindex + j] = addio->pointmtrlist[mtrindex++];
+ }
+ if (b->weighted) { // -w option
+ if (addio->numberofpointattributes > 0) {
+ // The first point attribute is its weight.
+ w = newpt[3];
+ } else {
+ // No given weight available. Default choose the maximum
+ // absolute value among its coordinates.
+ w = fabs(x);
+ if (w < fabs(y)) w = fabs(y);
+ if (w < fabs(z)) w = fabs(z);
+ }
+ if (b->weighted_param == 0) {
+ newpt[3] = x * x + y * y + z * z - w; // Weighted DT.
+ } else { // -w1 option
+ newpt[3] = w; // Regular tetrahedralization.
+ }
+ }
+ insertarray[arylen] = newpt;
+ arylen++;
+ } // i
+
+ // Insert the points.
+ insertconstrainedpoints(insertarray, arylen);
+
+ delete [] insertarray;
}
//// ////
@@ -25105,8 +23233,6 @@ void tetgenmesh::insertconstrainedpoints(tetgenio *addio)
// //
// marksharpsegments() Mark sharp segments. //
// //
-// All segments are initialized as type NSHARP. //
-// //
// A segment is SHARP if there are two facets intersecting at it with an //
// internal dihedral angle (*) less than an angle \theta. //
// //
@@ -25139,7 +23265,7 @@ void tetgenmesh::marksharpsegments()
minfacetdihed = PI;
smallang = 65.0 * PI / 180.0; // 65 degree.
- exsmallang = 15.0 * PI / 180.0; // 15 degree.
+ exsmallang = 5.0 * PI / 180.0; // 5 degree.
sharpcount = exsharpcount = 0;
// A segment s may have been split into many subsegments. Operate the one
@@ -25297,8 +23423,8 @@ void tetgenmesh::marksharpsegments()
// (4) the square root of a maximal area constraint in a .var file; //
// (5) a maximal length constraint in a .var file; //
// //
-// If 'b->nobisect' ('-Y' option) is set, every input vertex has a feature //
-// size. //
+// If 'b->nobisect' ('-Y' option) is set, every input vertex has a size. It //
+// is used to prevent creating too close Steiner points. //
// //
// The feature size of a Steiner point is linearly interpolated from its adj-//
// acent vertices which belong to the "carrier" (the boundary of the lowrest //
@@ -25334,9 +23460,8 @@ void tetgenmesh::decidefeaturepointsizes()
maxlen = pow(6.0 * b->maxvolume, 1.0 / 3.0);
}
- // First only assign a size of p if p is not a Steiner point. The size of
- // a Steiner point will be interpolated later from the endpoints of the
- // segment on which it lies.
+ // First, assign a size of p if p is a feature point or an input point and
+ // the -Y option is used.
featurecount = 0;
points->traversalinit();
ploop = pointtraverse();
@@ -25376,9 +23501,7 @@ void tetgenmesh::decidefeaturepointsizes()
sdecode(point2sh(adjpt), checkseg);
assert(checkseg.sh != NULL);
checkseg.shver = 0;
- if (sdest(checkseg) != adjpt) {
- sesymself(checkseg);
- }
+ if (sdest(checkseg) != adjpt) sesymself(checkseg);
assert(sdest(checkseg) == adjpt);
// It is possible that the original segment of 'adjpt' does not
// have 'ploop' as an endpoint.
@@ -25393,14 +23516,12 @@ void tetgenmesh::decidefeaturepointsizes()
nextseg = testseg;
// Adjust the direction of the nextseg.
nextseg.shver = 0;
- if (sorg(nextseg) != adjpt) {
- sesymself(nextseg);
- }
+ if (sorg(nextseg) != adjpt) sesymself(nextseg);
assert(sorg(nextseg) == adjpt);
adjpt = sdest(nextseg);
}
}
- } else if (pointtype(adjpt) == FREEFACETVERTEX) {
+ } else if (pointtype(adjpt) == FREEFACETVERTEX) {
// Ignore a Steiner point on facet.
continue;
} else if (pointtype(adjpt) == FREEVOLVERTEX) {
@@ -25418,8 +23539,8 @@ void tetgenmesh::decidefeaturepointsizes()
for (i = 0; i < tetlist->objects; i++) {
parytet = (triface *) fastlookup(tetlist, i);
for (j = 0; j < 3; j++) {
- tsspivot1(*parytet, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(*parytet)) {
+ tsspivot1(*parytet, checkseg);
e1 = sorg(checkseg);
e2 = sdest(checkseg);
// Only do calculation if the projeciton of 'p' lies inside the
@@ -25444,8 +23565,8 @@ void tetgenmesh::decidefeaturepointsizes()
lfs_2 = lfs_0;
for (i = 0; i < tetlist->objects; i++) {
parytet = (triface *) fastlookup(tetlist, i);
- tspivot(*parytet, checksh);
- if (checksh.sh != NULL) {
+ if (issubface(*parytet)) {
+ tspivot(*parytet, checksh);
adjpt = sorg(checksh);
e1 = sdest(checksh);
e2 = sapex(checksh);
@@ -25509,9 +23630,9 @@ void tetgenmesh::decidefeaturepointsizes()
printf(" %d feature points.\n", featurecount);
}
- // Second only assign sizes for all Steiner points. A Steiner point p
- // inserted on a sharp segment s is assigned a size by interpolating
- // the sizes of the original endpoints of s.
+ // Second only assign sizes for all Steiner points which were inserted on
+ // sharp segments. The sizes are interpolated from the endpoints of
+ // the segments.
featurecount = 0;
points->traversalinit();
ploop = pointtraverse();
@@ -25526,8 +23647,6 @@ void tetgenmesh::decidefeaturepointsizes()
e1 = farsorg(checkseg); // The origin of this seg.
e2 = farsdest(checkseg); // The dest of this seg.
if (b->nobisect) { // '-Y' option.
- assert(e1[pointmtrindex] > 0); // SELF_CHECK
- assert(e2[pointmtrindex] > 0); // SELF_CHECK
featureflag = 1;
} else {
if ((e1[pointmtrindex] > 0) && (e2[pointmtrindex] > 0)) {
@@ -25541,67 +23660,7 @@ void tetgenmesh::decidefeaturepointsizes()
+ (lfs_0 / len) * (e2[pointmtrindex] - e1[pointmtrindex]);
featurecount++;
} // if (featureflag)
- } else if (pointtype(ploop) == FREEFACETVERTEX) {
- if (b->nobisect) { // -Y option.
- // Collect vertices in the Star(p) which are also in the facet
- // containing p.
- point2shorg(ploop, parentsh);
- checksh = parentsh;
- while (1) {
- assert(sorg(checksh) == ploop);
- adjpt = sdest(checksh);
- // Collect this vertex.
- verlist->newindex((void **) &parypt);
- *parypt = adjpt;
- // Go to the next subface at p. (counterclockwise)
- senext2self(checksh);
- spivotself(checksh);
- assert(checksh.sh != NULL);
- if (checksh.sh == parentsh.sh) break;
- if (sorg(checksh) != ploop) sesymself(checksh);
- }
- assert(verlist->objects > 0);
- // Using Shepard interpolation (p=1) to interpolate the size for 'p'.
- // Re-use len, lfs_0, lfs_1, lfs_2;
- lfs_1 = lfs_2 = 0;
- for (i = 0; i < verlist->objects; i++) {
- parypt = (point *) fastlookup(verlist, i);
- adjpt = *parypt;
- if (adjpt[pointmtrindex] > 0) {
- len = distance(adjpt, ploop);
- lfs_0 = 1.0 / len;
- lfs_1 += lfs_0 * adjpt[pointmtrindex];
- lfs_2 += lfs_0;
- }
- }
- assert(lfs_2 > 0);
- ploop[pointmtrindex] = lfs_1 / lfs_2;
- verlist->restart();
- featurecount++;
- } // if (b->nobisect)
- } else if (pointtype(ploop) == FREEVOLVERTEX) {
- if (b->nobisect) { // -Y option.
- getvertexstar(1, ploop, tetlist, verlist, NULL);
- // Using Shepard interpolation to interpolate the size for 'p'.
- // Re-use len, lfs_0, lfs_1, lfs_2;
- lfs_1 = lfs_2 = 0;
- for (i = 0; i < verlist->objects; i++) {
- parypt = (point *) fastlookup(verlist, i);
- adjpt = *parypt;
- if (adjpt[pointmtrindex] > 0) {
- len = distance(adjpt, ploop);
- lfs_0 = 1.0 / len;
- lfs_1 += lfs_0 * adjpt[pointmtrindex];
- lfs_2 += lfs_0;
- }
- }
- assert(lfs_2 > 0);
- ploop[pointmtrindex] = lfs_1 / lfs_2;
- tetlist->restart();
- verlist->restart();
- featurecount++;
- } // if (b->nobisect)
- }
+ }
} // if (ploop[pointmtrindex] == 0.0)
ploop = pointtraverse();
}
@@ -25611,7 +23670,8 @@ void tetgenmesh::decidefeaturepointsizes()
}
if (checkconstraints) {
- // A .var file exists. Adjust feature sizes.
+ // A .var file exists. Adjust feature sizes. And make sure that every
+ // corner of a constraining facet get a size.
if (in->facetconstraintlist) {
// Have facet area constrains.
subfaces->traversalinit();
@@ -25627,6 +23687,9 @@ void tetgenmesh::decidefeaturepointsizes()
if (ploop[pointmtrindex] > varlen) {
ploop[pointmtrindex] = varlen;
}
+ } else {
+ // This corner has no size yet. Set it.
+ ploop[pointmtrindex] = varlen;
}
} // j
}
@@ -25647,6 +23710,8 @@ void tetgenmesh::decidefeaturepointsizes()
if (ploop[pointmtrindex] > varlen) {
ploop[pointmtrindex] = varlen;
}
+ } else {
+ ploop[pointmtrindex] = varlen;
}
} // j
}
@@ -25664,22 +23729,24 @@ void tetgenmesh::decidefeaturepointsizes()
int tetgenmesh::checkseg4encroach(point pa, point pb, point checkpt)
{
- REAL ang;
- REAL prjpt[3], u, v, t;
-
// Check if the point lies inside the diametrical sphere of this seg.
- ang = interiorangle(checkpt, pa, pb, NULL);
- ang *= 2.0; // Compare it to PI/2 (90 degree).
+ REAL v1[3], v2[3];
- if (ang > PI) {
+ v1[0] = pa[0] - checkpt[0];
+ v1[1] = pa[1] - checkpt[1];
+ v1[2] = pa[2] - checkpt[2];
+ v2[0] = pb[0] - checkpt[0];
+ v2[1] = pb[1] - checkpt[1];
+ v2[2] = pb[2] - checkpt[2];
+
+ if (dot(v1, v2) < 0) {
// Inside.
if (b->metric || b->nobisect) { // -m or -Y option.
if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0)) {
- // In this case, we're sure that the projection of 'checkpt' lies
- // inside the segment [a,b]. Check if 'checkpt' lies inside the
- // protecting region of this seg.
+ // The projection of 'checkpt' lies inside the segment [a,b].
+ REAL prjpt[3], u, v, t;
projpt2edge(checkpt, pa, pb, prjpt);
- // Get the mesh size at the location 'prjpt'.
+ // Interoplate the mesh size at the location 'prjpt'.
u = distance(pa, pb);
v = distance(pa, prjpt);
t = v / u;
@@ -25707,6 +23774,7 @@ int tetgenmesh::checkseg4encroach(point pa, point pb, point checkpt)
// A segment needs to be split if it is in the following case: //
// (1) It is encroached by an existing vertex. //
// (2) It has bad quality (too long). //
+// (3) Its length is larger than the mesh sizes at its endpoints. //
// //
// Return 1 if it needs to be split, otherwise, return 0. 'pencpt' returns //
// an encroaching point if there exists. 'qflag' returns '1' if the segment //
@@ -25716,21 +23784,11 @@ int tetgenmesh::checkseg4encroach(point pa, point pb, point checkpt)
int tetgenmesh::checkseg4split(face *chkseg, point& encpt, int& qflag)
{
- triface searchtet, spintet;
- point forg, fdest, eapex;
- REAL ccent[3], len, r, d, diff;
+ REAL ccent[3], len, r;
int i;
- REAL ti, tj, t, midpt[3];
- REAL ang;
- int eid;
-
- forg = sorg(*chkseg);
- fdest = sdest(*chkseg);
-
- if (b->verbose > 2) {
- printf(" Check segment (%d, %d)\n", pointmark(forg), pointmark(fdest));
- }
+ point forg = sorg(*chkseg);
+ point fdest = sdest(*chkseg);
// Initialize the return values.
encpt = NULL;
@@ -25745,21 +23803,13 @@ int tetgenmesh::checkseg4split(face *chkseg, point& encpt, int& qflag)
// First check its quality.
if (checkconstraints && (areabound(*chkseg) > 0.0)) {
if (len > areabound(*chkseg)) {
- if (b->verbose > 2) {
- printf(" has too large size, len = %g (> %g)\n", len,
- areabound(*chkseg));
- }
qflag = 1;
return 1;
}
}
- if (b->fixedvolume) { // if (b->varvolume || b->fixedvolume) {
+ if (b->fixedvolume) {
if ((len * len * len) > b->maxvolume) {
- if (b->verbose > 2) {
- printf(" has too large size, len^3 = %g (> %g)\n", len*len*len,
- b->maxvolume);
- }
qflag = 1;
return 1;
}
@@ -25774,33 +23824,13 @@ int tetgenmesh::checkseg4split(face *chkseg, point& encpt, int& qflag)
}
}
- if (b->psc) {
- // Check if it satisfies the approximation requirement.
- eid = shellmark(*chkseg);
- if ((pointtype(forg) == ACUTEVERTEX)||(pointtype(forg) == RIDGEVERTEX)) {
- ti = in->getvertexparamonedge(in->geomhandle, pointmark(forg), eid);
- } else {
- ti = pointgeomuv(forg, 0);
- }
- if ((pointtype(fdest) == ACUTEVERTEX)||(pointtype(fdest) == RIDGEVERTEX)) {
- tj = in->getvertexparamonedge(in->geomhandle, pointmark(fdest), eid);
- } else {
- tj = pointgeomuv(fdest, 0);
- }
- t = 0.5 * (ti + tj);
- in->getsteineronedge(in->geomhandle, eid, t, midpt);
- ang = interiorangle(midpt, forg, fdest, NULL) / PI * 180.0;
- if (ang < b->facet_ang_tol) {
- // Refine this segment.
- if (b->verbose > 2) {
- printf(" has bad approx, ang = %g\n", ang);
- }
- qflag = 1;
- return 1;
- }
- } // if (b->psc)
// Second check if it is encroached.
+ triface searchtet, spintet;
+ point eapex;
+ REAL d, diff;
+ int t1ver;
+
sstpivot1(*chkseg, searchtet);
spintet = searchtet;
while (1) {
@@ -25820,9 +23850,6 @@ int tetgenmesh::checkseg4split(face *chkseg, point& encpt, int& qflag)
} // while (1)
if (encpt != NULL) {
- if (b->verbose > 2) {
- printf(" is encroached by %d\n", pointmark(encpt));
- }
return 1;
}
@@ -25844,21 +23871,9 @@ int tetgenmesh::checkseg4split(face *chkseg, point& encpt, int& qflag)
int tetgenmesh::splitsegment(face *splitseg, point encpt, int qflag,
int chkencflag)
{
- triface searchtet;
- face searchsh;
- point newpt, pa, pb;
- insertvertexflags ivf;
- REAL len; //, len1;
- int loc;
- //int i;
-
- pa = sorg(*splitseg);
- pb = sdest(*splitseg);
- len = distance(pa, pb);
-
- if (b->verbose > 2) {
- printf(" Split segment (%d, %d).\n", pointmark(pa), pointmark(pb));
- }
+ point pa = sorg(*splitseg);
+ point pb = sdest(*splitseg);
+ REAL len = distance(pa, pb);
if (qflag == 0) {
@@ -25867,77 +23882,58 @@ int tetgenmesh::splitsegment(face *splitseg, point encpt, int qflag,
// Avoid creating too many Steiner points.
return 0;
}
- }
-
- // Quickly check if we CAN split this segment.
- if ((encpt == NULL) && (qflag == 0)) {
- // Do not split this segment if the length is smaller than the mesh
- // size at one of its endpoints.
- if ((len < pa[pointmtrindex]) || (len < pb[pointmtrindex])) {
- return 0;
+ // Quickly check if we CAN split this segment.
+ if (encpt == NULL) {
+ // Do not split this segment if the length is smaller than the mesh
+ // size at one of its endpoints.
+ if ((len < pa[pointmtrindex]) || (len < pb[pointmtrindex])) {
+ return 0;
+ }
}
}
+ triface searchtet;
+ face searchsh;
+ point newpt;
+ insertvertexflags ivf;
+
makepoint(&newpt, FREESEGVERTEX);
getsteinerptonsegment(splitseg, encpt, newpt);
-
- // Split the segment by the "Bowyer-Watson" algorithm.
- // Parameters are chosen as follows:
- // - bowywat = 3, preserve subsegments and subfaces;
- // - flipflag = 3, check star & link facets for flipping;
- // - rejflag = 0, do insertion even if it encoraches upon
- // other subsegments or subfaces.
+ // Split the segment by the Bowyer-Watson algorithm.
sstpivot1(*splitseg, searchtet);
ivf.iloc = (int) ONEDGE;
- if (b->psc) {
- ivf.bowywat = 0; // Do not enlarge the initial cavity.
- ivf.validflag = 0; // Do not validate the initial cavity.
- } else {
- ivf.bowywat = 3; // Use the "Bowyer-Watson" algorithm to form cavity.
- ivf.validflag = 1; // Validate the B-W cavity.
- }
- ivf.lawson = 3;
- ivf.rejflag = 0;
+ ivf.bowywat = 3; // Use Bowyer-Watson algorithm;
+ ivf.validflag = 1; // Validate the B-W cavity.
+ ivf.lawson = b->conforming ? 2 : 0; // -D
+ ivf.rejflag = 0; // Do not check encroachment of new segments/facets.
if ((encpt == NULL) && (qflag == 0)) {
- // Do not insert the point if it lies inside some protecting balls.
- ivf.rejflag |= 4;
+ ivf.rejflag |= 4; // Do check encroachment of protecting balls.
}
ivf.chkencflag = chkencflag;
- ivf.sloc = ivf.iloc;
- ivf.sbowywat = ivf.bowywat; // Surface mesh options.
+ ivf.sloc = (int) INSTAR; // ivf.iloc;
+ ivf.sbowywat = 3; // ivf.bowywat; // Surface mesh options.
ivf.splitbdflag = 1;
ivf.respectbdflag = 1;
ivf.assignmeshsize = 1;
- loc = insertvertex(newpt, &searchtet, &searchsh, splitseg, &ivf);
-
- // The new vertex should not too close to an existing point.
- if (loc == (int) NEARVERTEX) {
- outnodes(0);
- outsubfaces(0);
- outsubsegments(0);
- assert(0);
- } else if (loc == ENCVERTEX) {
- // The point lies in some protecting balls. Rejected.
- pointdealloc(newpt);
- } else if (loc == (int) BADELEMENT) {
- // Failed to create a valid sub-cavity in surface mesh.
- pointdealloc(newpt);
- //prob_subseg_count++;
- } else if (loc == (int) ONEDGE) {
- // Flip not locally Delaunay link facets by the 'Lawson's algo'.
- lawsonflip3d(newpt, 4, 0, chkencflag, 0);
+
+
+ if (insertpoint(newpt, &searchtet, &searchsh, splitseg, &ivf)) {
st_segref_count++;
if (steinerleft > 0) steinerleft--;
+ if (flipstack != NULL) {
+ flipconstraints fc;
+ fc.chkencflag = chkencflag;
+ fc.enqflag = 2;
+ lawsonflip3d(&fc);
+ unflipqueue->restart();
+ }
return 1;
} else {
- // The vertex was not inserted. For unknown reasons.
- //pointdealloc(newpt);
- assert(0);
+ // Point is not inserted.
+ pointdealloc(newpt);
+ return 0;
}
-
- // Should not be here.
- return 0;
}
///////////////////////////////////////////////////////////////////////////////
@@ -25948,7 +23944,7 @@ int tetgenmesh::splitsegment(face *splitseg, point encpt, int qflag,
void tetgenmesh::repairencsegs(int chkencflag)
{
- badface *bface;
+ face *bface;
point encpt = NULL;
int qflag = 0;
@@ -25956,20 +23952,25 @@ void tetgenmesh::repairencsegs(int chkencflag)
// if an unlimited number of Steiner points is allowed.
while ((badsubsegs->items > 0) && (steinerleft != 0)) {
badsubsegs->traversalinit();
- bface = badfacetraverse(badsubsegs);
+ bface = (face *) badsubsegs->traverse();
while ((bface != NULL) && (steinerleft != 0)) {
- // A queued segment may have been deleted (split).
- if (bface->ss.sh[3] != NULL) {
- // A queued segment may have been processed.
- if (smarktest2ed(bface->ss)) {
- sunmarktest2(bface->ss);
- if (checkseg4split(&(bface->ss), encpt, qflag)) {
- splitsegment(&(bface->ss), encpt, qflag, chkencflag);
+ // Skip a deleleted element.
+ if (bface->shver >= 0) {
+ // A queued segment may have been deleted (split).
+ if ((bface->sh != NULL) && (bface->sh[3] != NULL)) {
+ // A queued segment may have been processed.
+ if (smarktest2ed(*bface)) {
+ sunmarktest2(*bface);
+ if (checkseg4split(bface, encpt, qflag)) {
+ splitsegment(bface, encpt, qflag, chkencflag);
+ }
}
}
+ // Remove this entry from list.
+ bface->shver = -1; // Signal it as a deleted element.
+ badsubsegs->dealloc((void *) bface);
}
- badfacedealloc(badsubsegs, bface); // Remove this entry from list.
- bface = badfacetraverse(badsubsegs);
+ bface = (face *) badsubsegs->traverse();
}
}
@@ -25982,19 +23983,37 @@ void tetgenmesh::repairencsegs(int chkencflag)
assert(0); // Unknown case.
}
badsubsegs->traversalinit();
- bface = badfacetraverse(badsubsegs);
+ bface = (face *) badsubsegs->traverse();
while (bface != NULL) {
- if (bface->ss.sh[3] != NULL) {
- if (smarktest2ed(bface->ss)) {
- sunmarktest2(bface->ss);
+ // Skip a deleleted element.
+ if (bface->shver >= 0) {
+ if ((bface->sh != NULL) && (bface->sh[3] != NULL)) {
+ if (smarktest2ed(*bface)) {
+ sunmarktest2(*bface);
+ }
}
}
- bface = badfacetraverse(badsubsegs);
+ bface = (face *) badsubsegs->traverse();
}
badsubsegs->restart();
}
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// enqueuesubface() Queue a subface or a subsegment for encroachment chk. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::enqueuesubface(memorypool *pool, face *chkface)
+{
+ if (!smarktest2ed(*chkface)) {
+ smarktest2(*chkface); // Only queue it once.
+ face *queface = (face *) pool->alloc();
+ *queface = *chkface;
+ }
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// checkfac4encroach() Check if a subface is encroached by a point. //
@@ -26005,8 +24024,6 @@ int tetgenmesh::checkfac4encroach(point pa, point pb, point pc, point checkpt,
REAL* cent, REAL* r)
{
REAL rd, len;
- REAL prjpt[3], n[3];
- REAL a, a1, a2, a3;
circumsphere(pa, pb, pc, NULL, cent, &rd);
assert(rd != 0);
@@ -26019,6 +24036,8 @@ int tetgenmesh::checkfac4encroach(point pa, point pb, point pc, point checkpt,
if ((pa[pointmtrindex] > 0) && (pb[pointmtrindex] > 0) &&
(pc[pointmtrindex] > 0)) {
// Get the projection of 'checkpt' in the plane of pa, pb, and pc.
+ REAL prjpt[3], n[3];
+ REAL a, a1, a2, a3;
projpt2face(checkpt, pa, pb, pc, prjpt);
// Get the face area of [a,b,c].
facenormal(pa, pb, pc, n, 1, NULL);
@@ -26040,10 +24059,6 @@ int tetgenmesh::checkfac4encroach(point pa, point pb, point pc, point checkpt,
if (len < rd) {
return 1; // Encroached.
}
- } else {
- // The projection lies outside the face.
- // In this case, 'p' must close to another face or a segment than
- // to this one. We ignore this boundary face.
}
} else {
return 1; // No protecting ball. Encroached.
@@ -26074,14 +24089,10 @@ int tetgenmesh::checkfac4encroach(point pa, point pb, point pc, point checkpt,
int tetgenmesh::checkfac4split(face *chkfac, point& encpt, int& qflag,
REAL *cent)
{
- triface searchtet;
- face checksh; // *parysh;
- face checkseg;
point pa, pb, pc;
- REAL area, rd, len, sintheta;
+ REAL area, rd, len;
REAL A[4][4], rhs[4], D;
int indx[4];
- REAL elen[3];
int i;
encpt = NULL;
@@ -26091,11 +24102,6 @@ int tetgenmesh::checkfac4split(face *chkfac, point& encpt, int& qflag,
pb = sdest(*chkfac);
pc = sapex(*chkfac);
- if (b->verbose > 2) {
- printf(" Check subface (%d, %d, %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc));
- }
-
// Compute the coefficient matrix A (3x3).
A[0][0] = pb[0] - pa[0];
A[0][1] = pb[1] - pa[1];
@@ -26108,100 +24114,56 @@ int tetgenmesh::checkfac4split(face *chkfac, point& encpt, int& qflag,
area = 0.5 * sqrt(dot(A[2], A[2])); // The area of [a,b,c].
// Compute the right hand side vector b (3x1).
- elen[0] = dot(A[0], A[0]); // edge [a,b]
- elen[1] = dot(A[1], A[1]); // edge [a,c]
- rhs[0] = 0.5 * elen[0];
- rhs[1] = 0.5 * elen[1];
+ rhs[0] = 0.5 * dot(A[0], A[0]); // edge [a,b]
+ rhs[1] = 0.5 * dot(A[1], A[1]); // edge [a,c]
rhs[2] = 0.0;
// Solve the 3 by 3 equations use LU decomposition with partial
- // pivoting and backward and forward substitute..
- if (lu_decmp(A, 3, indx, &D, 0)) {
- lu_solve(A, 3, indx, rhs, 0);
- cent[0] = pa[0] + rhs[0];
- cent[1] = pa[1] + rhs[1];
- cent[2] = pa[2] + rhs[2];
- rd = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]);
-
- if (b->verbose > 2) {
- printf(" circent: (%g, %g, %g)\n", cent[0], cent[1], cent[2]);
- printf(" cirradi: %g\n", rd);
- }
-
- // Check the quality (radius-edge ratio) of this subface.
- // Re-use variables 'A', 'rhs', and 'D'.
- A[2][0] = pb[0] - pc[0];
- A[2][1] = pb[1] - pc[1];
- A[2][2] = pb[2] - pc[2];
- elen[2] = dot(A[2], A[2]); // edge [b,c]
- // Get the shortest edge length in 'D'.
- D = elen[0]; // edge [a,b]
- for (i = 1; i < 3; i++) {
- if (D > elen[i]) D = elen[i];
- }
-
-
- D = sqrt(D);
- if (b->verbose > 2) {
- printf(" shortest edge length = %g\n", D);
- }
-
- rhs[3] = rd / D; // The radius-edge ratio.
-
- // Check if this subface is nearly degenerate.
- sintheta = 1.0 / (2.0 * rhs[3]);
- if (sintheta < sintheta_tol) {
- // Do not split this subface. Save it in list.
- if (b->verbose > 1) {
- printf(" !! A degenerated subface, theta = %g (deg)\n",
- asin(sintheta) / PI * 180.0);
- }
- return 0; // Do not split a degenerated subface.
- }
+ // pivoting and backward and forward substitute.
+ if (!lu_decmp(A, 3, indx, &D, 0)) {
+ // A degenerate triangle.
+ return 0;
+ }
- if (checkconstraints && (areabound(*chkfac) > 0.0)) {
- // Check if the subface has too big area.
- if (area > areabound(*chkfac)) {
- if (b->verbose > 2) {
- printf(" has too big area: %g (> %g)\n", area,
- areabound(*chkfac));
- }
- qflag = 1;
- return 1;
- }
+ lu_solve(A, 3, indx, rhs, 0);
+ cent[0] = pa[0] + rhs[0];
+ cent[1] = pa[1] + rhs[1];
+ cent[2] = pa[2] + rhs[2];
+ rd = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]);
+
+ if (checkconstraints && (areabound(*chkfac) > 0.0)) {
+ // Check if the subface has too big area.
+ if (area > areabound(*chkfac)) {
+ qflag = 1;
+ return 1;
}
+ }
- if (b->metric) { // -m option. Check mesh size.
- // Check if the ccent lies outside one of the prot.balls at vertices.
- if (((pa[pointmtrindex] > 0) && (rd > pa[pointmtrindex])) ||
- ((pb[pointmtrindex] > 0) && (rd > pb[pointmtrindex])) ||
- ((pc[pointmtrindex] > 0) && (rd > pc[pointmtrindex]))) {
- qflag = 1; // Enforce mesh size.
- return 1;
- }
+ if (b->metric) { // -m option. Check mesh size.
+ // Check if the ccent lies outside one of the prot.balls at vertices.
+ if (((pa[pointmtrindex] > 0) && (rd > pa[pointmtrindex])) ||
+ ((pb[pointmtrindex] > 0) && (rd > pb[pointmtrindex])) ||
+ ((pc[pointmtrindex] > 0) && (rd > pc[pointmtrindex]))) {
+ qflag = 1; // Enforce mesh size.
+ return 1;
}
+ }
+ triface searchtet;
- // Check if this subface is locally encroached.
- for (i = 0; i < 2; i++) {
- stpivot(*chkfac, searchtet);
- if (!ishulltet(searchtet)) {
- len = distance(oppo(searchtet), cent);
- if ((fabs(len - rd) / rd) < b->epsilon) len = rd;// Rounding.
- if (len < rd) {
- if (b->verbose > 2) {
- printf(" is encroached by point %d\n",
- pointmark(oppo(searchtet)));
- }
- encpt = oppo(searchtet);
- return 1;
- }
+ // Check if this subface is locally encroached.
+ for (i = 0; i < 2; i++) {
+ stpivot(*chkfac, searchtet);
+ if (!ishulltet(searchtet)) {
+ len = distance(oppo(searchtet), cent);
+ if ((fabs(len - rd) / rd) < b->epsilon) len = rd;// Rounding.
+ if (len < rd) {
+ encpt = oppo(searchtet);
+ return 1;
}
- sesymself(*chkfac);
}
- } else {
- assert(0);
- } // if (!lu_decomp)
+ sesymself(*chkfac);
+ }
return 0;
}
@@ -26224,26 +24186,9 @@ int tetgenmesh::checkfac4split(face *chkfac, point& encpt, int& qflag,
int tetgenmesh::splitsubface(face *splitfac, point encpt, int qflag,
REAL *ccent, int chkencflag)
{
- badface *bface;
- triface searchtet;
- face searchsh;
- face checkseg, *paryseg;
- point newpt, pa, pb, pc;
- insertvertexflags ivf;
- REAL rd;
- int splitflag;
- int loc;
- int i;
-
-
- pa = sorg(*splitfac);
- pb = sdest(*splitfac);
- pc = sapex(*splitfac);
-
- if (b->verbose > 2) {
- printf(" Split subface (%d, %d, %d).\n", pointmark(pa), pointmark(pb),
- pointmark(pc));
- }
+ point pa = sorg(*splitfac);
+ point pb = sdest(*splitfac);
+ point pc = sapex(*splitfac);
// Quickly check if we CAN split this subface.
@@ -26255,54 +24200,58 @@ int tetgenmesh::splitsubface(face *splitfac, point encpt, int qflag,
}
// Do not split this subface if the 'ccent' lies inside the protect balls
// of one of its vertices.
- rd = distance(ccent, pa);
+ REAL rd = distance(ccent, pa);
if ((rd <= pa[pointmtrindex]) || (rd <= pb[pointmtrindex]) ||
(rd <= pc[pointmtrindex])) {
- if (b->verbose > 2) {
- printf(" Encroaching a protecting ball. Rejected.\n");
- }
return 0;
}
}
+ face searchsh;
+ insertvertexflags ivf;
+ point newpt;
+ int i;
+
// Initialize the inserting point.
makepoint(&newpt, FREEFACETVERTEX);
+ // Split the subface at its circumcenter.
+ for (i = 0; i < 3; i++) newpt[i] = ccent[i];
- if (0) {
- } else {
- // Split the subface at its circumcenter.
- for (i = 0; i < 3; i++) newpt[i] = ccent[i];
- // Search a subface which contains 'newpt'.
- searchsh = *splitfac;
- // Calculate an above point. It lies above the plane containing
- // the subface [a,b,c], and save it in dummypoint. Moreover,
- // the vector cent->dummypoint is the normal of the plane.
- calculateabovepoint4(newpt, pa, pb, pc);
- // Parameters: 'aflag' = 1, - above point exists.
- // 'cflag' = 0, - non-convex, check co-planarity of the result.
- // 'rflag' = 0, - no need to round the locating result.
- ivf.iloc = (int) slocate(newpt, &searchsh, 1, 0, 0);
- if ((ivf.iloc == (int) ONFACE) || (ivf.iloc == (int) ONEDGE)) {
- // Insert this point.
- } else {
- pointdealloc(newpt);
- return 0;
- }
+ // Search a subface which contains 'newpt'.
+ searchsh = *splitfac;
+ // Calculate an above point. It lies above the plane containing
+ // the subface [a,b,c], and save it in dummypoint. Moreover,
+ // the vector cent->dummypoint is the normal of the plane.
+ calculateabovepoint4(newpt, pa, pb, pc);
+ // Parameters: 'aflag' = 1, - above point exists.
+ // 'cflag' = 0, - non-convex, check co-planarity of the result.
+ // 'rflag' = 0, - no need to round the locating result.
+ ivf.iloc = (int) slocate(newpt, &searchsh, 1, 0, 0);
+
+ if (!((ivf.iloc == (int) ONFACE) || (ivf.iloc == (int) ONEDGE))) {
+ pointdealloc(newpt);
+ return 0;
}
+
+ triface searchtet;
+ face *paryseg;
+ int splitflag;
+
// Insert the point.
stpivot(searchsh, searchtet);
//assert((ivf.iloc == (int) ONFACE) || (ivf.iloc == (int) ONEDGE));
- // Split the subface by the "Bowyer-Watson" algorithm.
- ivf.bowywat = 3; // Form B-W cavity.
- ivf.lawson = 3; // Queue faces of the cavity for flipping.
- ivf.rejflag = 1; // Reject it if it encroached upon any segment.
+ // Split the subface by the Bowyer-Watson algorithm.
+ ivf.bowywat = 3; //
+ //ivf.lawson = b->conforming ? 3 : 1;
+ ivf.lawson = b->conforming ? 2 : 0;
+ ivf.rejflag = 1; // Do check the encroachment of segments.
if (qflag == 0) {
ivf.rejflag |= 4; // Reject it if it encroached upon any vertex.
}
ivf.chkencflag = chkencflag;
- ivf.sloc = ivf.iloc;
- ivf.sbowywat = ivf.bowywat;
+ ivf.sloc = (int) INSTAR; // ivf.iloc;
+ ivf.sbowywat = 3; // ivf.bowywat;
ivf.splitbdflag = 1;
ivf.validflag = 1;
ivf.respectbdflag = 1;
@@ -26311,59 +24260,45 @@ int tetgenmesh::splitsubface(face *splitfac, point encpt, int qflag,
ivf.refineflag = 2;
ivf.refinesh = searchsh;
- loc = insertvertex(newpt, &searchtet, &searchsh, NULL, &ivf);
- if (loc == (int) ENCSEGMENT) {
- // The new point encroaches upon some segments.
- pointdealloc(newpt);
- assert(encseglist->objects > 0);
- // Select an encroached segment and split it.
- splitflag = 0;
- for (i = 0; i < encseglist->objects; i++) {
- paryseg = (face *) fastlookup(encseglist, i);
- if (splitsegment(paryseg, NULL, qflag, chkencflag | 1)) {
- splitflag = 1; // A point is inserted on a segment.
- break;
- }
+ if (insertpoint(newpt, &searchtet, &searchsh, NULL, &ivf)) {
+ st_facref_count++;
+ if (steinerleft > 0) steinerleft--;
+ if (flipstack != NULL) {
+ flipconstraints fc;
+ fc.chkencflag = chkencflag;
+ fc.enqflag = 2;
+ lawsonflip3d(&fc);
+ unflipqueue->restart();
}
- encseglist->restart();
- if (splitflag) {
- // Some segments may need to be repaired.
- repairencsegs(chkencflag | 1);
- // Queue this subface if it is still alive and not queued.
- if (splitfac->sh[3] != NULL) {
- if (!smarktest2ed(*splitfac)) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = *splitfac;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(*splitfac); // An alive badface.
+ return 1;
+ } else {
+ // Point was not inserted.
+ pointdealloc(newpt);
+ if (ivf.iloc == (int) ENCSEGMENT) {
+ // Select an encroached segment and split it.
+ splitflag = 0;
+ for (i = 0; i < encseglist->objects; i++) {
+ paryseg = (face *) fastlookup(encseglist, i);
+ if (splitsegment(paryseg, NULL, qflag, chkencflag | 1)) {
+ splitflag = 1; // A point is inserted on a segment.
+ break;
}
}
+ encseglist->restart();
+ if (splitflag) {
+ // Some segments may need to be repaired.
+ repairencsegs(chkencflag | 1);
+ // Queue this subface if it is still alive and not queued.
+ //if (splitfac->sh[3] != NULL) {
+ // enqueuesubface(badsubfacs, splitfac);
+ //}
+ }
+ return splitflag;
+ } else {
+ return 0;
}
- return splitflag;
- } else if (loc == (int) ENCVERTEX) {
- // The point lies inside some protecting balls. Rejected.
- pointdealloc(newpt);
- } else if (loc == (int) ONVERTEX) {
- pointdealloc(newpt);
- } else if (loc == (int) NEARVERTEX) {
- pointdealloc(newpt);
- } else if (loc == (int) BADELEMENT) {
- // Failed to create a valid sub-cavity in surface mesh.
- pointdealloc(newpt);
- } else if (loc == (int) ivf.iloc) {
- // Flip not locally Delaunay link facets.
- lawsonflip3d(newpt, 4, 0, chkencflag, 0);
- st_facref_count++;
- if (steinerleft > 0) steinerleft--;
- return 1; // A point is inserted on facet.
- } else {
- // Unknown error.
- assert(0);
}
-
- // Should not be here.
- return 0;
}
///////////////////////////////////////////////////////////////////////////////
@@ -26374,7 +24309,7 @@ int tetgenmesh::splitsubface(face *splitfac, point encpt, int qflag,
void tetgenmesh::repairencfacs(int chkencflag)
{
- badface *bface;
+ face *bface;
point encpt = NULL;
int qflag = 0;
REAL ccent[3];
@@ -26383,20 +24318,24 @@ void tetgenmesh::repairencfacs(int chkencflag)
// if an unlimited number of Steiner points is allowed.
while ((badsubfacs->items > 0) && (steinerleft != 0)) {
badsubfacs->traversalinit();
- bface = badfacetraverse(badsubfacs);
+ bface = (face *) badsubfacs->traverse();
while ((bface != NULL) && (steinerleft != 0)) {
- // A queued subface may have been deleted (split).
- if (bface->ss.sh[3] != NULL) {
- // A queued subface may have been processed.
- if (smarktest2ed(bface->ss)) {
- sunmarktest2(bface->ss);
- if (checkfac4split(&(bface->ss), encpt, qflag, ccent)) {
- splitsubface(&(bface->ss), encpt, qflag, ccent, chkencflag);
+ // Skip a deleted element.
+ if (bface->shver >= 0) {
+ // A queued subface may have been deleted (split).
+ if ((bface->sh != NULL) && (bface->sh[3] != NULL)) {
+ // A queued subface may have been processed.
+ if (smarktest2ed(*bface)) {
+ sunmarktest2(*bface);
+ if (checkfac4split(bface, encpt, qflag, ccent)) {
+ splitsubface(bface, encpt, qflag, ccent, chkencflag);
+ }
}
}
+ bface->shver = -1; // Signal it as a deleted element.
+ badsubfacs->dealloc((void *) bface); // Remove this entry from list.
}
- badfacedealloc(badsubfacs, bface); // Remove this entry from list.
- bface = badfacetraverse(badsubfacs);
+ bface = (face *) badsubfacs->traverse();
}
}
@@ -26409,19 +24348,37 @@ void tetgenmesh::repairencfacs(int chkencflag)
assert(0); // Unknown case.
}
badsubfacs->traversalinit();
- bface = badfacetraverse(badsubfacs);
+ bface = (face *) badsubfacs->traverse();
while (bface != NULL) {
- if (bface->ss.sh[3] != NULL) {
- if (smarktest2ed(bface->ss)) {
- sunmarktest2(bface->ss);
+ // Skip a deleted element.
+ if (bface->shver >= 0) {
+ if ((bface->sh != NULL) && (bface->sh[3] != NULL)) {
+ if (smarktest2ed(*bface)) {
+ sunmarktest2(*bface);
+ }
}
}
- bface = badfacetraverse(badsubfacs);
+ bface = (face *) badsubfacs->traverse();
}
badsubfacs->restart();
}
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// enqueuetetrahedron() Queue a tetrahedron for quality check. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::enqueuetetrahedron(triface *chktet)
+{
+ if (!marktest2ed(*chktet)) {
+ marktest2(*chktet); // Only queue it once.
+ triface *quetet = (triface *) badtetrahedrons->alloc();
+ *quetet = *chktet;
+ }
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// checktet4split() Check if the tet needs to be split. //
@@ -26450,11 +24407,6 @@ int tetgenmesh::checktet4split(triface *chktet, int &qflag, REAL *ccent)
pb = (point) chktet->tet[5];
pc = (point) chktet->tet[6];
- if (b->verbose > 2) {
- printf(" Check tet (%d, %d, %d, %d)\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd));
- }
-
// Get the edge vectors vda: d->a, vdb: d->b, vdc: d->c.
// Set the matrix A = [vda, vdb, vdc]^T.
for (i = 0; i < 3; i++) A[0][i] = vda[i] = pa[i] - pd[i];
@@ -26468,9 +24420,6 @@ int tetgenmesh::checktet4split(triface *chktet, int &qflag, REAL *ccent)
if (!lu_decmp(A, 3, indx, &D, 0)) {
// A degenerated tet (vol = 0).
- if (b->verbose > 2) {
- printf(" Min dihed = 0 (degree)\n");
- }
// Return its barycenter.
for (i = 0; i < 3; i++) {
ccent[i] = 0.25 * (pa[i] + pb[i] + pc[i] + pd[i]);
@@ -26481,9 +24430,6 @@ int tetgenmesh::checktet4split(triface *chktet, int &qflag, REAL *ccent)
// Check volume if '-a#' and '-a' options are used.
if (b->varvolume || b->fixedvolume) {
vol = fabs(A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0;
- if (b->verbose > 2) {
- printf(" volume = %g.\n", vol);
- }
if (b->fixedvolume) {
if (vol > b->maxvolume) {
qflag = 1;
@@ -26545,9 +24491,6 @@ int tetgenmesh::checktet4split(triface *chktet, int &qflag, REAL *ccent)
}
smlen = sqrt(smlen);
D = rd / smlen;
- if (b->verbose > 2) {
- printf(" Ratio-edge ratio = %g, smlen = %g\n", D, smlen);
- }
if (D > b->minratio) {
// A bad radius-edge ratio.
return 1;
@@ -26586,9 +24529,6 @@ int tetgenmesh::checktet4split(triface *chktet, int &qflag, REAL *ccent)
maxcosd = (cosd[i] > maxcosd ? cosd[i] : maxcosd);
//mincosd = (cosd[i] < mincosd ? cosd[i] : maxcosd);
}
- if (b->verbose > 2) {
- printf(" Min dihed = %g (degree)\n", acos(maxcosd) / PI * 180.0);
- }
if (maxcosd > cosmindihed) {
// Calculate the circumcenter of this tet.
// A bad dihedral angle.
@@ -26636,22 +24576,14 @@ int tetgenmesh::checktet4split(triface *chktet, int &qflag, REAL *ccent)
int tetgenmesh::splittetrahedron(triface* splittet, int qflag, REAL *ccent,
int chkencflag)
{
- badface *bface;
triface searchtet;
- face checkseg, *paryseg;
- point newpt, pa, *ppt = NULL;
+ face *paryseg;
+ point newpt, *ppt;
+ badface *bface;
insertvertexflags ivf;
- REAL rd;
int splitflag;
- int loc;
int i;
- if (b->verbose > 2) {
- ppt = (point *) &(splittet->tet[4]);
- printf(" Split tet (%d, %d, %d, %d).\n", pointmark(ppt[0]),
- pointmark(ppt[1]), pointmark(ppt[2]), pointmark(ppt[3]));
- }
-
if (qflag == 0) {
// It is a bad quality tet (not due to mesh size).
@@ -26659,12 +24591,9 @@ int tetgenmesh::splittetrahedron(triface* splittet, int qflag, REAL *ccent,
// Do a quick check if the 'ccent' lies inside the protect balls
// of one of the vertices of this tet.
ppt = (point *) &(splittet->tet[4]);
- rd = distance(ccent, ppt[0]);
+ REAL rd = distance(ccent, ppt[0]);
if ((rd <= ppt[0][pointmtrindex]) || (rd <= ppt[1][pointmtrindex]) ||
(rd <= ppt[2][pointmtrindex]) || (rd <= ppt[3][pointmtrindex])) {
- if (b->verbose > 2) {
- printf(" Encroaching a protecting ball. Rejected.\n");
- }
return 0;
}
}
@@ -26674,15 +24603,10 @@ int tetgenmesh::splittetrahedron(triface* splittet, int qflag, REAL *ccent,
searchtet = *splittet;
ivf.iloc = (int) OUTSIDE;
- // Parameters are chosen as follows:
- // - bowywat = 3, preserve subsegments and subfaces;
- // - flipflag = 3, check star & link facets for flipping;
- // - rejflag = 3, do not insert the point if it encroaches upon
- // any segment or subface.
- // - chkencflag = 4, (as input), only check tetrahedra.
- ivf.bowywat = 3;
- ivf.lawson = 3;
- ivf.rejflag = 3;
+ ivf.bowywat = 3; // Preserve subsegments and subfaces;
+ //ivf.lawson = b->conforming ? 3 : 1;
+ ivf.lawson = b->conforming ? 2 : 0;
+ ivf.rejflag = 3; // Do check for encroached segments and subfaces.
if (qflag == 0) {
ivf.rejflag |= 4; // Reject it if it lies in some protecting balls.
}
@@ -26696,101 +24620,73 @@ int tetgenmesh::splittetrahedron(triface* splittet, int qflag, REAL *ccent,
ivf.refineflag = 1;
ivf.refinetet = *splittet;
- loc = insertvertex(newpt, &searchtet, NULL, NULL, &ivf);
- if (loc == (int) ENCSEGMENT) {
- // There are encroached segments.
- pointdealloc(newpt);
- assert(encseglist->objects > 0);
- splitflag = 0;
- if (!b->nobisect) { // not -Y option
- // Select an encroached segment and split it.
- for (i = 0; i < encseglist->objects; i++) {
- paryseg = (face *) fastlookup(encseglist, i);
- if (splitsegment(paryseg, NULL, qflag, chkencflag | 3)) {
- splitflag = 1; // A point is inserted on a segment.
- break;
- }
- }
- } // if (!b->nobisect)
- encseglist->restart();
- if (splitflag) {
- // Some segments may need to be repaired.
- repairencsegs(chkencflag | 3);
- // Some subfaces may need to be repaired.
- repairencfacs(chkencflag | 2);
- // Queue the tet if it is still alive and not queued.
- if (splittet->tet[4] != NULL) {
- if (!marktest2ed(*splittet)) {
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = *splittet;
- marktest2(bface->tt); // Only queue it once.
- bface->forg = org(*splittet); // An alive badface.
- }
- }
+ if (insertpoint(newpt, &searchtet, NULL, NULL, &ivf)) {
+ // Vertex is inserted.
+ st_volref_count++;
+ if (steinerleft > 0) steinerleft--;
+ if (flipstack != NULL) {
+ flipconstraints fc;
+ fc.chkencflag = chkencflag;
+ fc.enqflag = 2;
+ lawsonflip3d(&fc);
+ unflipqueue->restart();
}
- return splitflag;
- } else if (loc == (int) ENCSUBFACE) {
- // There are encroached subfaces.
+ return 1;
+ } else {
+ // Point is not inserted.
pointdealloc(newpt);
- assert(encshlist->objects > 0);
- splitflag = 0;
- if (!b->nobisect) { // not -Y option
- // Select an encroached subface and split it.
- for (i = 0; i < encshlist->objects; i++) {
- bface = (badface *) fastlookup(encshlist, i);
- if (splitsubface(&(bface->ss),NULL,qflag,bface->cent,chkencflag | 2)) {
- splitflag = 1; // A point is inserted on a subface or a segment.
- break;
+ // Check if there are encroached segments/subfaces.
+ if (ivf.iloc == (int) ENCSEGMENT) {
+ splitflag = 0;
+ if (!b->nobisect) { // not -Y option
+ // Select an encroached segment and split it.
+ for (i = 0; i < encseglist->objects; i++) {
+ paryseg = (face *) fastlookup(encseglist, i);
+ if (splitsegment(paryseg, NULL, qflag, chkencflag | 3)) {
+ splitflag = 1; // A point is inserted on a segment.
+ break;
+ }
}
- }
- } // if (!b->nobisect)
- encshlist->restart();
- if (splitflag) {
- assert(badsubsegs->items == 0l); // repairencsegs(chkencflag | 3);
- // Some subfaces may need to be repaired.
- repairencfacs(chkencflag | 2);
- // Queue the tet if it is still alive.
- if (splittet->tet[4] != NULL) {
- if (!marktest2ed(*splittet)) {
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = *splittet;
- marktest2(bface->tt); // Only queue it once.
- bface->forg = org(*splittet); // An alive badface.
+ } // if (!b->nobisect)
+ encseglist->restart();
+ if (splitflag) {
+ // Some segments may need to be repaired.
+ repairencsegs(chkencflag | 3);
+ // Some subfaces may need to be repaired.
+ repairencfacs(chkencflag | 2);
+ // Queue the tet if it is still alive and not queued.
+ //if (splittet->tet[4] != NULL) {
+ // enqueuetetrahedron(splittet);
+ //}
+ }
+ return splitflag;
+ } else if (ivf.iloc == (int) ENCSUBFACE) {
+ splitflag = 0;
+ if (!b->nobisect) { // not -Y option
+ // Select an encroached subface and split it.
+ for (i = 0; i < encshlist->objects; i++) {
+ bface = (badface *) fastlookup(encshlist, i);
+ if (splitsubface(&(bface->ss),NULL,qflag,bface->cent,chkencflag|2)){
+ splitflag = 1; // A point is inserted on a subface or a segment.
+ break;
+ }
}
+ } // if (!b->nobisect)
+ encshlist->restart();
+ if (splitflag) {
+ assert(badsubsegs->items == 0l);
+ // Some subfaces may need to be repaired.
+ repairencfacs(chkencflag | 2);
+ // Queue the tet if it is still alive.
+ //if (splittet->tet[4] != NULL) {
+ // enqueuetetrahedron(splittet);
+ //}
}
+ return splitflag;
}
- return splitflag;
- } else if (loc == (int) OUTSIDE) {
- // There exists not boundary conforming segments/subfaces.
- pointdealloc(newpt);
- } else if (loc == (int) ONVERTEX) {
- // Found a coincident vertex. It should be a Steiner point.
- pa = org(searchtet);
- assert(pointtype(pa) == FREEVOLVERTEX);
- // Delete this new point.
- pointdealloc(newpt);
- } else if (loc == (int) NEARVERTEX) {
- // The point lies very close to an existing point.
- pa = point2ppt(newpt);
- assert(pointtype(pa) == FREEVOLVERTEX);
- // Delete this new point.
- pointdealloc(newpt);
- } else if (loc == (int) ENCVERTEX) {
- // The new point encoraches upon some protecting balls. Rejected.
- pointdealloc(newpt);
- } else if (loc == (int) BADELEMENT) {
- pointdealloc(newpt);
- } else {
- // Recover Delaunayness.
- lawsonflip3d(newpt, 4, 0, chkencflag, 0);
- // Vertex is inserted.
- st_volref_count++;
- if (steinerleft > 0) steinerleft--;
- return 1;
+ return 0;
}
-
- return 0;
}
///////////////////////////////////////////////////////////////////////////////
@@ -26801,7 +24697,7 @@ int tetgenmesh::splittetrahedron(triface* splittet, int qflag, REAL *ccent,
void tetgenmesh::repairbadtets(int chkencflag)
{
- badface *bface;
+ triface *bface;
REAL ccent[3];
int qflag = 0;
@@ -26809,20 +24705,24 @@ void tetgenmesh::repairbadtets(int chkencflag)
// if an unlimited number of Steiner points is allowed.
while ((badtetrahedrons->items > 0) && (steinerleft != 0)) {
badtetrahedrons->traversalinit();
- bface = badfacetraverse(badtetrahedrons);
+ bface = (triface *) badtetrahedrons->traverse();
while ((bface != NULL) && (steinerleft != 0)) {
- // A queued tet may have been deleted.
- if (!isdeadtet(bface->tt)) {
- // A queued tet may have been processed.
- if (marktest2ed(bface->tt)) {
- unmarktest2(bface->tt);
- if (checktet4split(&(bface->tt), qflag, ccent)) {
- splittetrahedron(&(bface->tt), qflag, ccent, chkencflag);
+ // Skip a deleted element.
+ if (bface->ver >= 0) {
+ // A queued tet may have been deleted.
+ if (!isdeadtet(*bface)) {
+ // A queued tet may have been processed.
+ if (marktest2ed(*bface)) {
+ unmarktest2(*bface);
+ if (checktet4split(bface, qflag, ccent)) {
+ splittetrahedron(bface, qflag, ccent, chkencflag);
+ }
}
}
+ bface->ver = -1; // Signal it as a deleted element.
+ badtetrahedrons->dealloc((void *) bface);
}
- badfacedealloc(badtetrahedrons, bface);
- bface = badfacetraverse(badtetrahedrons);
+ bface = (triface *) badtetrahedrons->traverse();
}
}
@@ -26836,14 +24736,17 @@ void tetgenmesh::repairbadtets(int chkencflag)
}
// Unmark all queued tet.
badtetrahedrons->traversalinit();
- bface = badfacetraverse(badtetrahedrons);
+ bface = (triface *) badtetrahedrons->traverse();
while (bface != NULL) {
- if (!isdeadtet(bface->tt)) {
- if (marktest2ed(bface->tt)) {
- unmarktest2(bface->tt);
+ // Skip a deleted element.
+ if (bface->ver >= 0) {
+ if (!isdeadtet(*bface)) {
+ if (marktest2ed(*bface)) {
+ unmarktest2(*bface);
+ }
}
}
- bface = badfacetraverse(badtetrahedrons);
+ bface = (triface *) badtetrahedrons->traverse();
}
// Clear the pool.
badtetrahedrons->restart();
@@ -26858,7 +24761,6 @@ void tetgenmesh::repairbadtets(int chkencflag)
void tetgenmesh::delaunayrefinement()
{
- badface *bface;
triface checktet;
face checksh;
face checkseg;
@@ -26866,13 +24768,16 @@ void tetgenmesh::delaunayrefinement()
int chkencflag;
long bak_segref_count, bak_facref_count, bak_volref_count;
+ long bak_flipcount = flip23count + flip32count + flip44count;
if (!b->quiet) {
printf("Refining mesh...\n");
}
if (b->verbose) {
- printf(" Edge length limit = %g.\n", b->minedgelength);
+ printf(" Min radiu-edge ratio = %g.\n", b->minratio);
+ printf(" Min dihedral angle = %g.\n", b->mindihedral);
+ //printf(" Min Edge length = %g.\n", b->minedgelength);
}
steinerleft = b->steinerleft; // Upperbound of # Steiner points (by -S#).
@@ -26884,7 +24789,7 @@ void tetgenmesh::delaunayrefinement()
} else {
if (!b->quiet) {
printf("\nWarning: ");
- printf("The desired number of Steiner points (%d) is reached.\n\n",
+ printf("The desired number of Steiner points (%d) has reached.\n\n",
b->steinerleft);
}
return; // No more Steiner points.
@@ -26902,6 +24807,7 @@ void tetgenmesh::delaunayrefinement()
encseglist = new arraypool(sizeof(face), 8);
encshlist = new arraypool(sizeof(badface), 8);
+
if (!b->nobisect) { // if no '-Y' option
if (b->verbose) {
printf(" Splitting encroached subsegments.\n");
@@ -26911,17 +24817,14 @@ void tetgenmesh::delaunayrefinement()
steinercount = points->items;
// Initialize the pool of encroached subsegments.
- badsubsegs = new memorypool(sizeof(badface), b->shellfaceperblock,
- memorypool::POINTER, 0);
+ badsubsegs = new memorypool(sizeof(face), b->shellfaceperblock,
+ sizeof(void *), 0);
// Add all segments into the pool.
subsegs->traversalinit();
checkseg.sh = shellfacetraverse(subsegs);
while (checkseg.sh != (shellface *) NULL) {
- bface = (badface *) badsubsegs->alloc();
- bface->ss = checkseg;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checkseg); // An alive badface.
+ enqueuesubface(badsubsegs, &checkseg);
checkseg.sh = shellfacetraverse(subsegs);
}
@@ -26944,17 +24847,14 @@ void tetgenmesh::delaunayrefinement()
bak_facref_count = st_facref_count;
// Initialize the pool of encroached subfaces.
- badsubfacs = new memorypool(sizeof(badface), b->shellfaceperblock,
- memorypool::POINTER, 0);
+ badsubfacs = new memorypool(sizeof(face), b->shellfaceperblock,
+ sizeof(void *), 0);
// Add all subfaces into the pool.
subfaces->traversalinit();
checksh.sh = shellfacetraverse(subfaces);
while (checksh.sh != (shellface *) NULL) {
- bface = (badface *) badsubfacs->alloc();
- bface->ss = checksh;
- smarktest2(bface->ss); // Only queue it once.
- bface->forg = sorg(checksh); // An alive badface.
+ enqueuesubface(badsubfacs, &checksh);
checksh.sh = shellfacetraverse(subfaces);
}
@@ -26985,17 +24885,13 @@ void tetgenmesh::delaunayrefinement()
cosmindihed = cos(b->mindihedral / 180.0 * PI);
// Initialize the pool of bad quality tetrahedra.
- badtetrahedrons = new memorypool(sizeof(badface), b->tetrahedraperblock,
- memorypool::POINTER, 0);
-
+ badtetrahedrons = new memorypool(sizeof(triface), b->tetrahedraperblock,
+ sizeof(void *), 0);
// Add all tetrahedra (no hull tets) into the pool.
tetrahedrons->traversalinit();
checktet.tet = tetrahedrontraverse();
while (checktet.tet != NULL) {
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = checktet;
- marktest2(bface->tt); // Only queue it once.
- bface->forg = org(checktet); // An alive badface.
+ enqueuetetrahedron(&checktet);
checktet.tet = tetrahedrontraverse();
}
@@ -27009,37 +24905,308 @@ void tetgenmesh::delaunayrefinement()
st_facref_count - bak_facref_count,
st_volref_count - bak_volref_count);
}
- } // if (b->reflevel > 2)
+ } // if (b->reflevel > 2)
+
+ if (b->verbose) {
+ if (flip23count + flip32count + flip44count > bak_flipcount) {
+ printf(" Performed %ld flips.\n", flip23count + flip32count +
+ flip44count - bak_flipcount);
+ }
+ }
+
+ if (steinerleft == 0) {
+ if (!b->quiet) {
+ printf("\nWarnning: ");
+ printf("The desired number of Steiner points (%d) is reached.\n\n",
+ b->steinerleft);
+ }
+ }
+
+
+ delete encseglist;
+ delete encshlist;
+
+ if (!b->nobisect) {
+ totalworkmemory += (badsubsegs->maxitems * badsubsegs->itembytes);
+ delete badsubsegs;
+ if (b->reflevel > 1) {
+ totalworkmemory += (badsubfacs->maxitems * badsubfacs->itembytes);
+ delete badsubfacs;
+ }
+ }
+ if (b->reflevel > 2) {
+ totalworkmemory += (badtetrahedrons->maxitems*badtetrahedrons->itembytes);
+ delete badtetrahedrons;
+ }
+}
+
+//// ////
+//// ////
+//// refine_cxx ///////////////////////////////////////////////////////////////
+
+//// optimize_cxx /////////////////////////////////////////////////////////////
+//// ////
+//// ////
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// lawsonflip3d() A three-dimensional Lawson's algorithm. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+long tetgenmesh::lawsonflip3d(flipconstraints *fc)
+{
+ triface fliptets[5], neightet, hulltet;
+ face checksh, casingout;
+ badface *popface, *bface;
+ point pd, pe, *pts;
+ REAL sign, ori;
+ long flipcount, totalcount = 0l;
+ long sliver_peels = 0l;
+ int t1ver;
+ int i;
+
+
+ while (1) {
+
+ if (b->verbose > 2) {
+ printf(" Lawson flip %ld faces.\n", flippool->items);
+ }
+ flipcount = 0l;
+
+ while (flipstack != (badface *) NULL) {
+ // Pop a face from the stack.
+ popface = flipstack;
+ fliptets[0] = popface->tt;
+ flipstack = flipstack->nextitem; // The next top item in stack.
+ flippool->dealloc((void *) popface);
+
+ // Skip it if it is a dead tet (destroyed by previous flips).
+ if (isdeadtet(fliptets[0])) continue;
+ // Skip it if it is not the same tet as we saved.
+ if (!facemarked(fliptets[0])) continue;
+
+ unmarkface(fliptets[0]);
+
+ if (ishulltet(fliptets[0])) continue;
+
+ fsym(fliptets[0], fliptets[1]);
+ if (ishulltet(fliptets[1])) {
+ if (nonconvex) {
+ // Check if 'fliptets[0]' it is a hull sliver.
+ tspivot(fliptets[0], checksh);
+ for (i = 0; i < 3; i++) {
+ if (!isshsubseg(checksh)) {
+ spivot(checksh, casingout);
+ //assert(casingout.sh != NULL);
+ if (sorg(checksh) != sdest(casingout)) sesymself(casingout);
+ stpivot(casingout, neightet);
+ if (neightet.tet == fliptets[0].tet) {
+ // Found a hull sliver 'neightet'. Let it be [e,d,a,b], where
+ // [e,d,a] and [d,e,b] are hull faces.
+ edestoppo(neightet, hulltet); // [a,b,e,d]
+ fsymself(hulltet); // [b,a,e,#]
+ if (oppo(hulltet) == dummypoint) {
+ pe = org(neightet);
+ if ((pointtype(pe) == FREEFACETVERTEX) ||
+ (pointtype(pe) == FREESEGVERTEX)) {
+ removevertexbyflips(pe);
+ }
+ } else {
+ eorgoppo(neightet, hulltet); // [b,a,d,e]
+ fsymself(hulltet); // [a,b,d,#]
+ if (oppo(hulltet) == dummypoint) {
+ pd = dest(neightet);
+ if ((pointtype(pd) == FREEFACETVERTEX) ||
+ (pointtype(pd) == FREESEGVERTEX)) {
+ removevertexbyflips(pd);
+ }
+ } else {
+ // Perform a 3-to-2 flip to remove the sliver.
+ fliptets[0] = neightet; // [e,d,a,b]
+ fnext(fliptets[0], fliptets[1]); // [e,d,b,c]
+ fnext(fliptets[1], fliptets[2]); // [e,d,c,a]
+ flip32(fliptets, 1, fc);
+ // Update counters.
+ flip32count--;
+ flip22count--;
+ sliver_peels++;
+ if (fc->remove_ndelaunay_edge) {
+ // Update the volume (must be decreased).
+ //assert(fc->tetprism_vol_sum <= 0);
+ tetprism_vol_sum += fc->tetprism_vol_sum;
+ fc->tetprism_vol_sum = 0.0; // Clear it.
+ }
+ }
+ }
+ break;
+ } // if (neightet.tet == fliptets[0].tet)
+ } // if (!isshsubseg(checksh))
+ senextself(checksh);
+ } // i
+ } // if (nonconvex)
+ continue;
+ }
+
+ // Test whether the face is locally Delaunay or not.
+ pts = (point *) fliptets[1].tet;
+ sign = insphere_s(pts[4], pts[5], pts[6], pts[7], oppo(fliptets[0]));
+
+ if (sign < 0) {
+ // A non-Delaunay face. Try to flip it.
+ pd = oppo(fliptets[0]);
+ pe = oppo(fliptets[1]);
+
+ // Check the convexity of its three edges. Stop checking either a
+ // locally non-convex edge (ori < 0) or a flat edge (ori = 0) is
+ // encountered, and 'fliptet' represents that edge.
+ for (i = 0; i < 3; i++) {
+ ori = orient3d(org(fliptets[0]), dest(fliptets[0]), pd, pe);
+ if (ori <= 0) break;
+ enextself(fliptets[0]);
+ }
+
+ if (ori > 0) {
+ // A 2-to-3 flip is found.
+ if (checksubfaceflag) {
+ // Do not flip if it is a subface.
+ if (issubface(fliptets[0])) continue;
+ }
+ // [0] [a,b,c,d],
+ // [1] [b,a,c,e]. no dummypoint.
+ flip23(fliptets, 0, fc);
+ flipcount++;
+ if (fc->remove_ndelaunay_edge) {
+ // Update the volume (must be decreased).
+ //assert(fc->tetprism_vol_sum <= 0);
+ tetprism_vol_sum += fc->tetprism_vol_sum;
+ fc->tetprism_vol_sum = 0.0; // Clear it.
+ }
+ continue;
+ } else { // ori <= 0
+ // The edge ('fliptets[0]' = [a',b',c',d]) is non-convex or flat,
+ // where the edge [a',b'] is one of [a,b], [b,c], and [c,a].
+ if (checksubsegflag) {
+ // Do not flip if it is a segment.
+ if (issubseg(fliptets[0])) continue;
+ }
+ // Check if there are three or four tets sharing at this edge.
+ esymself(fliptets[0]); // [b,a,d,c]
+ for (i = 0; i < 3; i++) {
+ fnext(fliptets[i], fliptets[i+1]);
+ }
+ if (fliptets[3].tet == fliptets[0].tet) {
+ // A 3-to-2 flip is found. (No hull tet.)
+ flip32(fliptets, 0, fc);
+ flipcount++;
+ if (fc->remove_ndelaunay_edge) {
+ // Update the volume (must be decreased).
+ //assert(fc->tetprism_vol_sum <= 0);
+ tetprism_vol_sum += fc->tetprism_vol_sum;
+ fc->tetprism_vol_sum = 0.0; // Clear it.
+ }
+ continue;
+ } else {
+ // There are more than 3 tets at this edge.
+ fnext(fliptets[3], fliptets[4]);
+ if (fliptets[4].tet == fliptets[0].tet) {
+ // There are exactly 4 tets at this edge.
+ if (nonconvex) {
+ if (apex(fliptets[3]) == dummypoint) {
+ // This edge is locally non-convex on the hull.
+ // It can be removed by a 4-to-4 flip.
+ ori = 0;
+ }
+ } // if (nonconvex)
+ if (ori == 0) {
+ // A 4-to-4 flip is found. (Two hull tets may be involved.)
+ // Current tets in 'fliptets':
+ // [0] [b,a,d,c] (d may be newpt)
+ // [1] [b,a,c,e]
+ // [2] [b,a,e,f] (f may be dummypoint)
+ // [3] [b,a,f,d]
+ esymself(fliptets[0]); // [a,b,c,d]
+ // A 2-to-3 flip replaces face [a,b,c] by edge [e,d].
+ // This creates a degenerate tet [e,d,a,b] (tmpfliptets[0]).
+ // It will be removed by the followed 3-to-2 flip.
+ flip23(fliptets, 0, fc); // No hull tet.
+ fnext(fliptets[3], fliptets[1]);
+ fnext(fliptets[1], fliptets[2]);
+ // Current tets in 'fliptets':
+ // [0] [...]
+ // [1] [b,a,d,e] (degenerated, d may be new point).
+ // [2] [b,a,e,f] (f may be dummypoint)
+ // [3] [b,a,f,d]
+ // A 3-to-2 flip replaces edge [b,a] by face [d,e,f].
+ // Hull tets may be involved (f may be dummypoint).
+ flip32(&(fliptets[1]), (apex(fliptets[3]) == dummypoint), fc);
+ flipcount++;
+ flip23count--;
+ flip32count--;
+ flip44count++;
+ if (fc->remove_ndelaunay_edge) {
+ // Update the volume (must be decreased).
+ //assert(fc->tetprism_vol_sum <= 0);
+ tetprism_vol_sum += fc->tetprism_vol_sum;
+ fc->tetprism_vol_sum = 0.0; // Clear it.
+ }
+ continue;
+ } // if (ori == 0)
+ }
+ }
+ } // if (ori <= 0)
+
+ // This non-Delaunay face is unflippable. Save it.
+ unflipqueue->newindex((void **) &bface);
+ bface->tt = fliptets[0];
+ bface->forg = org(fliptets[0]);
+ bface->fdest = dest(fliptets[0]);
+ bface->fapex = apex(fliptets[0]);
+ } // if (sign < 0)
+ } // while (flipstack)
+
+ if (b->verbose > 2) {
+ if (flipcount > 0) {
+ printf(" Performed %ld flips.\n", flipcount);
+ }
+ }
+ // Accumulate the counter of flips.
+ totalcount += flipcount;
- if (steinerleft == 0) {
- if (!b->quiet) {
- printf("\nWarnning: ");
- printf("The desired number of Steiner points (%d) is reached.\n\n",
- b->steinerleft);
+ assert(flippool->items == 0l);
+ // Return if no unflippable faces left.
+ if (unflipqueue->objects == 0l) break;
+ // Return if no flip has been performed.
+ if (flipcount == 0l) break;
+
+ // Try to flip the unflippable faces.
+ for (i = 0; i < unflipqueue->objects; i++) {
+ bface = (badface *) fastlookup(unflipqueue, i);
+ if (!isdeadtet(bface->tt) &&
+ (org(bface->tt) == bface->forg) &&
+ (dest(bface->tt) == bface->fdest) &&
+ (apex(bface->tt) == bface->fapex)) {
+ flippush(flipstack, &(bface->tt));
+ }
}
- }
+ unflipqueue->restart();
- delete encseglist;
- delete encshlist;
+ } // while (1)
- if (!b->nobisect) {
- delete badsubsegs;
- if (b->reflevel > 1) {
- delete badsubfacs;
+ if (b->verbose > 2) {
+ if (totalcount > 0) {
+ printf(" Performed %ld flips.\n", totalcount);
+ }
+ if (sliver_peels > 0) {
+ printf(" Removed %ld hull slivers.\n", sliver_peels);
+ }
+ if (unflipqueue->objects > 0l) {
+ printf(" %ld unflippable edges remained.\n", unflipqueue->objects);
}
}
- if (b->reflevel > 2) {
- delete badtetrahedrons;
- }
-}
-
-//// ////
-//// ////
-//// refine_cxx ///////////////////////////////////////////////////////////////
-//// optimize_cxx /////////////////////////////////////////////////////////////
-//// ////
-//// ////
+ return totalcount + sliver_peels;
+}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -27050,8 +25217,8 @@ void tetgenmesh::delaunayrefinement()
void tetgenmesh::recoverdelaunay()
{
arraypool *flipqueue, *nextflipqueue, *swapqueue;
- badface *bface, *parybface;
triface tetloop, neightet, *parytet;
+ badface *bface, *parybface;
point *ppt;
flipconstraints fc;
int i, j;
@@ -27060,28 +25227,16 @@ void tetgenmesh::recoverdelaunay()
printf("Recovering Delaunayness...\n");
}
- if (b->verbose) {
- printf(" max_flipstarsize = %d.\n", b->optmaxflipstarsize);
- printf(" max_fliplinklevel = %d.\n", b->delmaxfliplevel);
- }
-
- calc_tetprism_vol = 1;
tetprism_vol_sum = 0.0; // Initialize it.
- assert(flipstack == NULL);
- assert(unflipqueue->objects == 0l);
-
// Put all interior faces of the mesh into 'flipstack'.
tetrahedrons->traversalinit();
tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != NULL) {
for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
- // Avoid queue a face twice.
- fsym(tetloop, neightet);
- if (!ishulltet(neightet)) {
- if (!facemarked(neightet)) {
- flippush(flipstack, &tetloop);
- }
+ decode(tetloop.tet[tetloop.ver], neightet);
+ if (!facemarked(neightet)) {
+ flippush(flipstack, &tetloop);
}
}
ppt = (point *) &(tetloop.tet[4]);
@@ -27089,6 +25244,10 @@ void tetgenmesh::recoverdelaunay()
tetloop.tet = tetrahedrontraverse();
}
+ // Calulate a relatively lower bound for small improvement.
+ // Used to avoid rounding error in volume calculation.
+ fc.bak_tetprism_vol = tetprism_vol_sum * b->epsilon * 1e-3;
+
if (b->verbose) {
printf(" Initial obj = %.17g\n", tetprism_vol_sum);
}
@@ -27096,37 +25255,35 @@ void tetgenmesh::recoverdelaunay()
if (b->verbose > 1) {
printf(" Recover Delaunay [Lawson] : %ld\n", flippool->items);
}
- assert(unflipqueue->objects == 0l);
// First only use the basic Lawson's flip.
- lawsonflip3d(NULL, 4, 0, 0, 1);
+ fc.remove_ndelaunay_edge = 1;
+ fc.enqflag = 2;
+
+ lawsonflip3d(&fc);
if (b->verbose > 1) {
- printf(" New obj = %.17g\n", tetprism_vol_sum);
+ printf(" obj (after Lawson) = %.17g\n", tetprism_vol_sum);
}
if (unflipqueue->objects == 0l) {
- // The mesh is Delaunay.
- return;
+ return; // The mesh is Delaunay.
}
- // Set the common options.
- fc.remove_ndelaunay_edge = 1;
fc.unflip = 1; // Unflip if the edge is not flipped.
- fc.collectnewtets = 1;
+ fc.collectnewtets = 1; // new tets are returned in 'cavetetlist'.
+ fc.enqflag = 0;
- autofliplinklevel = 1; // Init value.
- b->fliplinklevel = -1;
+ autofliplinklevel = 1; // Init level.
+ b->fliplinklevel = -1; // No fixed level.
// For efficiency reason, we limit the maximium size of the edge star.
- // 'b->optmaxflipstarsize' is set by -OOOOO (5 Os), default is 10.
int bakmaxflipstarsize = b->flipstarsize;
- b->flipstarsize = b->optmaxflipstarsize;
+ b->flipstarsize = 10; // default
flipqueue = new arraypool(sizeof(badface), 10);
nextflipqueue = new arraypool(sizeof(badface), 10);
-
-
+
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
@@ -27134,60 +25291,61 @@ void tetgenmesh::recoverdelaunay()
while (flipqueue->objects > 0l) {
- while (flipqueue->objects > 0l) {
-
- if (b->verbose > 1) {
- printf(" Recover Delaunay [level = %2d] #: %ld.\n",
- autofliplinklevel, flipqueue->objects);
- }
-
- for (i = 0; i < flipqueue->objects; i++) {
- bface = (badface *) fastlookup(flipqueue, i);
- if (getedge(bface->forg, bface->fdest, &bface->tt)) {
- // Remember the the objective value (volume of all tetprisms).
- fc.bak_tetprism_vol = tetprism_vol_sum;
- if (removeedgebyflips(&(bface->tt), &fc) == 2) {
- if (b->verbose > 2) {
- printf(" Decreased quantity: %.17g.\n",
- fc.bak_tetprism_vol - tetprism_vol_sum);
+ if (b->verbose > 1) {
+ printf(" Recover Delaunay [level = %2d] #: %ld.\n",
+ autofliplinklevel, flipqueue->objects);
+ }
+
+ for (i = 0; i < flipqueue->objects; i++) {
+ bface = (badface *) fastlookup(flipqueue, i);
+ if (getedge(bface->forg, bface->fdest, &bface->tt)) {
+ if (removeedgebyflips(&(bface->tt), &fc) == 2) {
+ tetprism_vol_sum += fc.tetprism_vol_sum;
+ fc.tetprism_vol_sum = 0.0; // Clear it.
+ // Queue new faces for flips.
+ for (j = 0; j < cavetetlist->objects; j++) {
+ parytet = (triface *) fastlookup(cavetetlist, j);
+ // A queued new tet may be dead.
+ if (!isdeadtet(*parytet)) {
+ for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) {
+ // Avoid queue a face twice.
+ decode(parytet->tet[parytet->ver], neightet);
+ if (!facemarked(neightet)) {
+ flippush(flipstack, parytet);
+ }
+ } // parytet->ver
}
- // Queue new faces for flips.
- for (j = 0; j < cavetetlist->objects; j++) {
- parytet = (triface *) fastlookup(cavetetlist, j);
- // A queued new tet may be dead.
- if (!isdeadtet(*parytet)) {
- for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) {
- // Avoid queue a face twice.
- fsym(*parytet, neightet);
- if (!facemarked(neightet)) {
- flippush(flipstack, parytet);
- }
- } // parytet->ver
- }
- } // j
- cavetetlist->restart();
- // Remove locally non-Delaunay faces. New non-Delaunay edges
- // may be found. They are saved in 'unflipqueue'.
- lawsonflip3d(NULL, 4, 0, 0, 1);
- } else {
- // Unable to remove this edge. Save it.
- nextflipqueue->newindex((void **) &parybface);
+ } // j
+ cavetetlist->restart();
+ // Remove locally non-Delaunay faces. New non-Delaunay edges
+ // may be found. They are saved in 'unflipqueue'.
+ fc.enqflag = 2;
+ lawsonflip3d(&fc);
+ fc.enqflag = 0;
+ // There may be unflipable faces. Add them in flipqueue.
+ for (j = 0; j < unflipqueue->objects; j++) {
+ bface = (badface *) fastlookup(unflipqueue, j);
+ flipqueue->newindex((void **) &parybface);
*parybface = *bface;
}
+ unflipqueue->restart();
+ } else {
+ // Unable to remove this edge. Save it.
+ nextflipqueue->newindex((void **) &parybface);
+ *parybface = *bface;
+ // Normally, it should be zero.
+ //assert(fc.tetprism_vol_sum == 0.0);
+ // However, due to rounding errors, a tiny value may appear.
+ fc.tetprism_vol_sum = 0.0;
}
- } // i
-
- flipqueue->restart();
-
- // Swap the two flip queues.
- swapqueue = flipqueue;
- flipqueue = unflipqueue;
- unflipqueue = swapqueue;
- } // while (flipqueue->objects > 0l)
+ }
+ } // i
if (b->verbose > 1) {
- printf(" New obj = %.17g.\n", tetprism_vol_sum);
+ printf(" obj (after level %d) = %.17g.\n", autofliplinklevel,
+ tetprism_vol_sum);
}
+ flipqueue->restart();
// Swap the two flip queues.
swapqueue = flipqueue;
@@ -27195,14 +25353,13 @@ void tetgenmesh::recoverdelaunay()
nextflipqueue = swapqueue;
if (flipqueue->objects > 0l) {
- // 'b->delmaxfliplevel' is set by -OOOO, default is 1.
+ // default 'b->delmaxfliplevel' is 1.
if (autofliplinklevel >= b->delmaxfliplevel) {
// For efficiency reason, we do not search too far.
break;
}
autofliplinklevel+=b->fliplinklevelinc;
}
-
} // while (flipqueue->objects > 0l)
if (flipqueue->objects > 0l) {
@@ -27211,16 +25368,13 @@ void tetgenmesh::recoverdelaunay()
}
}
- b->flipstarsize = bakmaxflipstarsize;
-
- delete nextflipqueue;
- delete flipqueue;
-
- calc_tetprism_vol = 0;
-
if (b->verbose) {
- printf(" Final obj = %.17g\n", tetprism_vol_sum);
+ printf(" Final obj = %.17g\n", tetprism_vol_sum);
}
+
+ b->flipstarsize = bakmaxflipstarsize;
+ delete flipqueue;
+ delete nextflipqueue;
}
///////////////////////////////////////////////////////////////////////////////
@@ -27233,11 +25387,7 @@ int tetgenmesh::gettetrahedron(point pa, point pb, point pc, point pd,
triface *searchtet)
{
triface spintet;
-
- if (b->verbose > 2) {
- printf(" Get tet [%d,%d,%d,%d].\n", pointmark(pa), pointmark(pb),
- pointmark(pc), pointmark(pd));
- }
+ int t1ver;
if (getedge(pa, pb, searchtet)) {
spintet = *searchtet;
@@ -27286,18 +25436,20 @@ long tetgenmesh::improvequalitybyflips()
flipqueue = new arraypool(sizeof(badface), 10);
nextflipqueue = new arraypool(sizeof(badface), 10);
- // Flip edge options.
- b->fliplinklevel = -1;
- autofliplinklevel = 1; // Init value.
+ // Backup flip edge options.
+ int bakautofliplinklevel = autofliplinklevel;
+ int bakfliplinklevel = b->fliplinklevel;
+ int bakmaxflipstarsize = b->flipstarsize;
- // For efficiency reason, we limit the maximium size of the edge star.
- // 'b->optmaxflipstarsize' is set by -OOOOO (5 Os), default is 10.
- int bakmaxflipstarsize = b->flipstarsize;
- b->flipstarsize = b->optmaxflipstarsize;
+ // Set flip edge options.
+ autofliplinklevel = 1;
+ b->fliplinklevel = -1;
+ b->flipstarsize = 10; // b->optmaxflipstarsize;
fc.remove_large_angle = 1;
fc.unflip = 1;
fc.collectnewtets = 1;
+ fc.checkflipeligibility = 1;
totalremcount = 0l;
@@ -27320,40 +25472,37 @@ long tetgenmesh::improvequalitybyflips()
bface = (badface *) fastlookup(flipqueue, k);
if (gettetrahedron(bface->forg, bface->fdest, bface->fapex,
bface->foppo, &bface->tt)) {
+ //assert(!ishulltet(bface->tt));
// There are bad dihedral angles in this tet.
if (bface->tt.ver != 11) {
// The dihedral angles are permuted.
// Here we simply re-compute them. Slow!!.
ppt = (point *) & (bface->tt.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
- &maxdd, NULL);
+ &bface->key, NULL);
bface->forg = ppt[0];
bface->fdest = ppt[1];
bface->fapex = ppt[2];
bface->foppo = ppt[3];
bface->tt.ver = 11;
}
+ if (bface->key == 0) {
+ // Re-comput the quality values. Due to smoothing operations.
+ ppt = (point *) & (bface->tt.tet[4]);
+ tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
+ &bface->key, NULL);
+ }
cosdd = bface->cent;
remflag = 0;
for (i = 0; (i < 6) && !remflag; i++) {
if (cosdd[i] < cosmaxdihed) {
// Found a large dihedral angle.
bface->tt.ver = edge2ver[i]; // Go to the edge.
- if (b->verbose > 2) {
- printf(" Found a large angle [%d,%d,%d,%d] (%g).\n",
- pointmark(org(bface->tt)), pointmark(dest(bface->tt)),
- pointmark(apex(bface->tt)), pointmark(oppo(bface->tt)),
- acos(cosdd[i]) / PI * 180.0);
- }
fc.cosdihed_in = cosdd[i];
fc.cosdihed_out = 0.0; // 90 degree.
n = removeedgebyflips(&(bface->tt), &fc);
if (n == 2) {
// Edge is flipped.
- if (b->verbose > 2) {
- printf(" Reduced a large angle to %g degree.\n",
- acos(fc.cosdihed_out) / PI * 180.0);
- }
remflag = 1;
if (fc.cosdihed_out < cosmaxdihed) {
// Queue new bad tets for further improvements.
@@ -27361,8 +25510,6 @@ long tetgenmesh::improvequalitybyflips()
parytet = (triface *) fastlookup(cavetetlist, j);
if (!isdeadtet(*parytet)) {
ppt = (point *) & (parytet->tet[4]);
- //if (!marktest2ed(*parytet)) {
- assert(!marktest2ed(*parytet)); // SELF_CHECK
// Do not test a hull tet.
if (ppt[3] != dummypoint) {
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], ncosdd,
@@ -27381,8 +25528,7 @@ long tetgenmesh::improvequalitybyflips()
parybface->cent[n] = ncosdd[n];
}
}
- } // if (ppt[3] != dummypoint) {
- //}
+ } // if (ppt[3] != dummypoint)
}
} // j
} // if (fc.cosdihed_out < cosmaxdihed)
@@ -27413,12 +25559,12 @@ long tetgenmesh::improvequalitybyflips()
totalremcount += remcount;
if (unflipqueue->objects > 0l) {
- // 'b->optmaxfliplevel' is set by -OOO, default is 2.
- if (autofliplinklevel >= b->optmaxfliplevel) {
- // For efficiency reason, we do not search too far.
+ //if (autofliplinklevel >= b->optmaxfliplevel) {
+ if (autofliplinklevel >= b->optlevel) {
break;
}
autofliplinklevel+=b->fliplinklevelinc;
+ //b->flipstarsize = 10 + (1 << (b->optlevel - 1));
}
// Swap the two flip queues.
@@ -27427,6 +25573,9 @@ long tetgenmesh::improvequalitybyflips()
unflipqueue = swapqueue;
} // while (flipqueues->objects > 0)
+ // Restore original flip edge options.
+ autofliplinklevel = bakautofliplinklevel;
+ b->fliplinklevel = bakfliplinklevel;
b->flipstarsize = bakmaxflipstarsize;
delete flipqueue;
@@ -27451,8 +25600,8 @@ long tetgenmesh::improvequalitybyflips()
// has two orientations, ccw or cw, with respect to 'p'. 'ccw' indicates //
// the orientation is ccw (1) or not (0). //
// //
-// 'of' is a structure contains the parameters of the objective function. It //
-// is needed by the evaluation of the function value. //
+// 'opm' is a structure contains the parameters of the objective function. //
+// It is needed by the evaluation of the function value. //
// //
// The return value indicates weather the point is smoothed or not. //
// //
@@ -27473,16 +25622,6 @@ int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
int numdirs, iter;
int i, j, k;
- if (b->verbose > 2) {
- printf(" Smooth a point: %ld faces.\n", linkfacelist->objects);
- if (opm->min_max_dihedangle) {
- printf(" Init value = %g (degree).\n",
- acos(opm->initval - 1.0) / PI * 180.0);
- } else {
- printf(" Init value = %g.\n", opm->initval);
- }
- }
-
// Decide the number of moving directions.
numdirs = (int) linkfacelist->objects;
if (numdirs > opm->numofsearchdirs) {
@@ -27535,7 +25674,8 @@ int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
if (ori < 0.0) {
// Calcuate the objective function value.
if (opm->max_min_volume) {
- val = -ori;
+ //val = -ori;
+ val = - orient3dfast(pa, pb, pc, nextpt);
} else if (opm->max_min_aspectratio) {
val = tetaspectratio(pa, pb, pc, nextpt);
} else if (opm->min_max_dihedangle) {
@@ -27548,8 +25688,10 @@ int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
}
} else { // ori >= 0.0;
// An invalid new tet.
+ // This may happen if the mesh contains inverted elements.
if (opm->max_min_volume) {
- val = -ori;
+ //val = -ori;
+ val = - orient3dfast(pa, pb, pc, nextpt);
} else {
// Discard this point.
break; // j
@@ -27569,7 +25711,6 @@ int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
} // j
if (j == linkfacelist->objects) {
// The function value has been improved.
- assert(minval > opm->imprval);
opm->imprval = minval;
// Save the new location of the point.
for (j = 0; j < 3; j++) bestpt[j] = nextpt[j];
@@ -27616,54 +25757,9 @@ int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
if (iter > 0) {
// The point has been smooothed.
- opm->smthiter = iter; // Remember the number of iterations.
- if (b->verbose > 2) {
- printf(" Smoothed: %d iterations.\n", iter);
- if (opm->min_max_dihedangle) {
- printf(" Fina value = %g (degree).\n",
- acos(opm->imprval - 1.0) / PI * 180.0);
- } else {
- printf(" Fina value = %g.\n", opm->imprval);
- }
- }
+ opm->smthiter = iter; // Remember the number of iterations.
// The point has been smoothed. Update it to its new position.
for (i = 0; i < 3; i++) smtpt[i] = startpt[i];
-
- if (opm->flipflag) {
- // Push all affected faces into 'flipstack'.
- triface starttet, neightet;
- for (i = 0; i < linkfacelist->objects; i++) {
- parytet = (triface *) fastlookup(linkfacelist, i);
- starttet = *parytet;
- for (starttet.ver = 0; starttet.ver < 4; starttet.ver++) {
- fsym(starttet, neightet);
- if (!infected(neightet)) {
- flippush(flipstack, &starttet);
- }
- }
- infect(*parytet);
- }
- for (i = 0; i < linkfacelist->objects; i++) {
- parytet = (triface *) fastlookup(linkfacelist, i);
- uninfect(*parytet);
- }
- } else if (opm->checkencflag) {
- // Push all affected tets into pool.
- badface *bface;
- for (i = 0; i < linkfacelist->objects; i++) {
- parytet = (triface *) fastlookup(linkfacelist, i);
- if (!marktest2ed(*parytet)) {
- marktest2(*parytet); // Only queue it once.
- bface = (badface *) badtetrahedrons->alloc();
- bface->tt = *parytet;
- bface->forg = org(bface->tt);
- }
- }
- }
- } else {
- if (b->verbose > 2) {
- printf(" Not smoothed.\n");
- }
}
return iter;
@@ -27678,29 +25774,28 @@ int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
long tetgenmesh::improvequalitybysmoothing(optparameters *opm)
{
arraypool *flipqueue, *swapqueue;
+ triface *parytet;
badface *bface, *parybface;
point *ppt;
long totalsmtcount, smtcount;
int smtflag;
- int iter, i, k;
+ int iter, i, j, k;
//assert(unflipqueue->objects > 0l);
flipqueue = new arraypool(sizeof(badface), 10);
- totalsmtcount = 0l;
-
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
+ totalsmtcount = 0l;
iter = 0;
while (flipqueue->objects > 0l) {
smtcount = 0l;
- //while (flipqueue->objects > 0l) {
if (b->verbose > 1) {
printf(" Improving mesh qualiy by smoothing [%d]#: %ld.\n",
iter, flipqueue->objects);
@@ -27710,6 +25805,7 @@ long tetgenmesh::improvequalitybysmoothing(optparameters *opm)
bface = (badface *) fastlookup(flipqueue, k);
if (gettetrahedron(bface->forg, bface->fdest, bface->fapex,
bface->foppo, &bface->tt)) {
+ // Operate on it if it is not in 'unflipqueue'.
if (!marktested(bface->tt)) {
// Here we simply re-compute the quality. Since other smoothing
// operation may have moved the vertices of this tet.
@@ -27719,10 +25815,7 @@ long tetgenmesh::improvequalitybysmoothing(optparameters *opm)
if (bface->key < cossmtdihed) { // if (maxdd < cosslidihed) {
// It is a sliver. Try to smooth its vertices.
smtflag = 0;
- //if (opm->min_max_dihedangle) {
- opm->initval = bface->key + 1.0;
- //opm->checkencflag = 4; // Queue affected tets.
- //}
+ opm->initval = bface->key + 1.0;
for (i = 0; (i < 4) && !smtflag; i++) {
if (pointtype(ppt[i]) == FREEVOLVERTEX) {
getvertexstar(1, ppt[i], cavetetlist, NULL, NULL);
@@ -27735,78 +25828,61 @@ long tetgenmesh::improvequalitybysmoothing(optparameters *opm)
opm->smthiter = 0; // reset
smoothpoint(ppt[i], cavetetlist, 1, opm);
}
+ // This tet is modifed.
smtcount++;
- }
+ if ((opm->imprval - 1.0) < cossmtdihed) {
+ // There are slivers in new tets. Queue them.
+ for (j = 0; j < cavetetlist->objects; j++) {
+ parytet = (triface *) fastlookup(cavetetlist, j);
+ assert(!isdeadtet(*parytet));
+ // Operate it if it is not in 'unflipqueue'.
+ if (!marktested(*parytet)) {
+ // Evaluate its quality.
+ // Re-use ppt, bface->key, bface->cent.
+ ppt = (point *) & (parytet->tet[4]);
+ tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3],
+ bface->cent, &bface->key, NULL);
+ if (bface->key < cossmtdihed) {
+ // A new sliver. Queue it.
+ marktest(*parytet); // It is in unflipqueue.
+ unflipqueue->newindex((void **) &parybface);
+ parybface->tt = *parytet;
+ parybface->forg = ppt[0];
+ parybface->fdest = ppt[1];
+ parybface->fapex = ppt[2];
+ parybface->foppo = ppt[3];
+ parybface->tt.ver = 11;
+ parybface->key = 0.0;
+ }
+ }
+ } // j
+ } // if ((opm->imprval - 1.0) < cossmtdihed)
+ } // if (smtflag)
cavetetlist->restart();
- }
+ } // if (pointtype(ppt[i]) == FREEVOLVERTEX)
} // i
- if (smtflag) {
- // This tet is modifed.
- smtcount++;
- if ((opm->imprval - 1.0) < cossmtdihed) {
- // Queue new slivers.
- badtetrahedrons->traversalinit();
- bface = badfacetraverse(badtetrahedrons);
- while (bface != NULL) {
- assert(!isdeadtet(bface->tt));
- assert(marktest2ed(bface->tt));
- unmarktest2(bface->tt);
- if (!marktested(bface->tt)) {
- ppt = (point *) & (bface->tt.tet[4]);
- tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
- &(bface->key), NULL);
- if (bface->key < cossmtdihed) {
- // A new sliver. Queue it.
- marktest(bface->tt); // It is in unflipqueue.
- bface->forg = ppt[0];
- bface->fdest = ppt[1];
- bface->fapex = ppt[2];
- bface->foppo = ppt[3];
- bface->tt.ver = 11;
- unflipqueue->newindex((void **) &parybface);
- *parybface = *bface;
- }
- }
- bface = badfacetraverse(badtetrahedrons);
- }
- } else {
- // No new slivers. Only unmark the queued tets.
- badtetrahedrons->traversalinit();
- bface = badfacetraverse(badtetrahedrons);
- while (bface != NULL) {
- assert(!isdeadtet(bface->tt));
- assert(marktest2ed(bface->tt));
- unmarktest2(bface->tt);
- bface = badfacetraverse(badtetrahedrons);
- }
- }
- badtetrahedrons->restart();
- } else {
+ if (!smtflag) {
// Didn't smooth. Queue it again.
- // Adjust the vertices for flipping.
marktest(bface->tt); // It is in unflipqueue.
- bface->forg = ppt[0];
- bface->fdest = ppt[1];
- bface->fapex = ppt[2];
- bface->foppo = ppt[3];
- bface->tt.ver = 11;
unflipqueue->newindex((void **) &parybface);
- *parybface = *bface;
+ parybface->tt = bface->tt;
+ parybface->forg = ppt[0];
+ parybface->fdest = ppt[1];
+ parybface->fapex = ppt[2];
+ parybface->foppo = ppt[3];
+ parybface->tt.ver = 11;
+ parybface->key = 0.0;
}
- } // if (maxdd < cosslidihed)
+ } // if (maxdd < cosslidihed)
} // if (!marktested(...))
- } // gettetrahedron(...)
+ } // if (gettetrahedron(...))
} // k
flipqueue->restart();
- // } // while
-
// Unmark the tets in unflipqueue.
for (i = 0; i < unflipqueue->objects; i++) {
bface = (badface *) fastlookup(unflipqueue, i);
- assert(!isdeadtet(bface->tt));
- assert(marktested(bface->tt));
unmarktest(bface->tt);
}
@@ -27846,35 +25922,36 @@ int tetgenmesh::splitsliver(triface *slitet, REAL cosd, int chkencflag)
{
triface *abtets;
triface searchtet, spintet, *parytet;
- face checkseg;
point pa, pb, steinerpt;
optparameters opm;
insertvertexflags ivf;
REAL smtpt[3], midpt[3];
int success;
- int loc;
+ int t1ver;
int n, i;
- // 'slitet' is [c,d,a,b], where [c,d] has a big hihedral angle.
+ // 'slitet' is [c,d,a,b], where [c,d] has a big dihedral angle.
// Go to the opposite edge [a,b].
- eprev(*slitet, searchtet);
- esymself(searchtet);
- enextself(searchtet); // [a,b,c,d].
+ edestoppo(*slitet, searchtet); // [a,b,c,d].
// Do not split a segment.
- tsspivot1(searchtet, checkseg);
- if (checkseg.sh != NULL) {
+ if (issubseg(searchtet)) {
return 0;
}
// Count the number of tets shared at [a,b].
+ // Do not split it if it is a hull edge.
spintet = searchtet;
n = 0;
while (1) {
+ if (ishulltet(spintet)) break;
n++;
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
+ if (ishulltet(spintet)) {
+ return 0; // It is a hull edge.
+ }
assert(n >= 3);
// Get all tets at edge [a,b].
@@ -27928,19 +26005,11 @@ int tetgenmesh::splitsliver(triface *slitet, REAL cosd, int chkencflag)
cavetetlist->restart();
if (!success) {
- if (b->verbose > 2) {
- printf(" Unable to relocate the initial point.\n");
- }
delete [] abtets;
return 0;
}
- if (steinerleft == 0) {
- // The desired number of Steiner points is reached.
- return 0;
- }
-
// Insert the Steiner point.
makepoint(&steinerpt, FREEVOLVERTEX);
for (i = 0; i < 3; i++) steinerpt[i] = smtpt[i];
@@ -27951,24 +26020,22 @@ int tetgenmesh::splitsliver(triface *slitet, REAL cosd, int chkencflag)
caveoldtetlist->newindex((void **) &parytet);
*parytet = abtets[i];
}
+
searchtet = abtets[0]; // No need point location.
+ if (b->metric) {
+ locate(steinerpt, &searchtet, 0); // For size interpolation.
+ }
+
+ delete [] abtets;
+
ivf.iloc = (int) INSTAR;
- ivf.bowywat = 0; // Do not use Bowyer-Watson algorithm.
- ivf.lawson = 0; // Do not flip.
- ivf.rejflag = 0;
ivf.chkencflag = chkencflag;
- ivf.sloc = 0;
- ivf.sbowywat = 0;
- ivf.splitbdflag = 0;
- ivf.validflag = 0;
- ivf.respectbdflag = 0;
- ivf.assignmeshsize = 0;
+ ivf.assignmeshsize = b->metric;
- loc = insertvertex(steinerpt, &searchtet, NULL, NULL, &ivf);
- if (loc == (int) INSTAR) {
+ if (insertpoint(steinerpt, &searchtet, NULL, NULL, &ivf)) {
// The vertex has been inserted.
- st_volref_count++; //st_inpoly_count++;
+ st_volref_count++;
if (steinerleft > 0) steinerleft--;
return 1;
} else {
@@ -27976,8 +26043,6 @@ int tetgenmesh::splitsliver(triface *slitet, REAL cosd, int chkencflag)
pointdealloc(steinerpt);
return 0;
}
-
- delete [] abtets;
}
///////////////////////////////////////////////////////////////////////////////
@@ -27990,24 +26055,24 @@ long tetgenmesh::removeslivers(int chkencflag)
{
arraypool *flipqueue, *swapqueue;
badface *bface, *parybface;
+ triface slitet, *parytet;
point *ppt;
- REAL *cosdd;
+ REAL cosdd[6], maxcosd;
long totalsptcount, sptcount;
- int iter, j, k;
+ int iter, i, j, k;
//assert(unflipqueue->objects > 0l);
flipqueue = new arraypool(sizeof(badface), 10);
- totalsptcount = 0l;
-
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
+ totalsptcount = 0l;
iter = 0;
- while (flipqueue->objects > 0l) {
+ while ((flipqueue->objects > 0l) && (steinerleft != 0)) {
sptcount = 0l;
@@ -28016,74 +26081,63 @@ long tetgenmesh::removeslivers(int chkencflag)
iter, flipqueue->objects);
}
- for (k = 0; k < flipqueue->objects; k++) {
+ for (k = 0; (k < flipqueue->objects) && (steinerleft != 0); k++) {
bface = (badface *) fastlookup(flipqueue, k);
if (gettetrahedron(bface->forg, bface->fdest, bface->fapex,
bface->foppo, &bface->tt)) {
- //if (!marktested(bface->tt)) {
- // Here we simply re-compute the quality. Since other smoothing
+ if ((bface->key == 0) || (bface->tt.ver != 11)) {
+ // Here we need to re-compute the quality. Since other smoothing
// operation may have moved the vertices of this tet.
ppt = (point *) & (bface->tt.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
&bface->key, NULL);
- if (bface->key < cosslidihed) {
- // It is a sliver. Try to split it.
- cosdd = bface->cent;
- for (j = 0; j < 6; j++) {
- if (cosdd[j] < cosslidihed) {
- // Found a large dihedral angle.
- bface->tt.ver = edge2ver[j]; // Go to the edge.
- if (b->verbose > 2) {
- printf(" Found a bad tet [%d,%d,%d,%d] (%g).\n",
- pointmark(org(bface->tt)), pointmark(dest(bface->tt)),
- pointmark(apex(bface->tt)), pointmark(oppo(bface->tt)),
- acos(cosdd[j]) / PI * 180.0);
- }
- if (splitsliver(&(bface->tt), cosdd[j], chkencflag)) {
- sptcount++;
- break;
- }
+ }
+ if (bface->key < cosslidihed) {
+ // It is a sliver. Try to split it.
+ slitet.tet = bface->tt.tet;
+ //cosdd = bface->cent;
+ for (j = 0; j < 6; j++) {
+ if (bface->cent[j] < cosslidihed) {
+ // Found a large dihedral angle.
+ slitet.ver = edge2ver[j]; // Go to the edge.
+ if (splitsliver(&slitet, bface->cent[j], chkencflag)) {
+ sptcount++;
+ break;
}
- } // j
- if (j < 6) {
- // A sliver is split. Queue new slivers.
- badtetrahedrons->traversalinit();
- bface = badfacetraverse(badtetrahedrons);
- while (bface != NULL) {
- assert(!isdeadtet(bface->tt));
- assert(marktest2ed(bface->tt));
- unmarktest2(bface->tt);
- ppt = (point *) & (bface->tt.tet[4]);
- tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
- &(bface->key), NULL);
- if (bface->key < cosslidihed) {
- // A new sliver. Queue it.
- //marktest(bface->tt); // It is in unflipqueue.
- bface->forg = ppt[0];
- bface->fdest = ppt[1];
- bface->fapex = ppt[2];
- bface->foppo = ppt[3];
- bface->tt.ver = 11;
- unflipqueue->newindex((void **) &parybface);
- *parybface = *bface;
+ }
+ } // j
+ if (j < 6) {
+ // A sliver is split. Queue new slivers.
+ badtetrahedrons->traversalinit();
+ parytet = (triface *) badtetrahedrons->traverse();
+ while (parytet != NULL) {
+ unmarktest2(*parytet);
+ ppt = (point *) & (parytet->tet[4]);
+ tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], cosdd,
+ &maxcosd, NULL);
+ if (maxcosd < cosslidihed) {
+ // A new sliver. Queue it.
+ unflipqueue->newindex((void **) &parybface);
+ parybface->forg = ppt[0];
+ parybface->fdest = ppt[1];
+ parybface->fapex = ppt[2];
+ parybface->foppo = ppt[3];
+ parybface->tt.tet = parytet->tet;
+ parybface->tt.ver = 11;
+ parybface->key = maxcosd;
+ for (i = 0; i < 6; i++) {
+ parybface->cent[i] = cosdd[i];
}
- bface = badfacetraverse(badtetrahedrons);
}
- badtetrahedrons->restart();
- } else {
- // Didn't split. Queue it again.
- // Adjust the vertices for flipping.
- //marktest(bface->tt); // It is in unflipqueue.
- bface->forg = ppt[0];
- bface->fdest = ppt[1];
- bface->fapex = ppt[2];
- bface->foppo = ppt[3];
- bface->tt.ver = 11;
- unflipqueue->newindex((void **) &parybface);
- *parybface = *bface;
- } // if (j == 6)
- } // if (bface->key < cosslidihed)
- // } // if (!marktested(bface->tt))
+ parytet = (triface *) badtetrahedrons->traverse();
+ }
+ badtetrahedrons->restart();
+ } else {
+ // Didn't split. Queue it again.
+ unflipqueue->newindex((void **) &parybface);
+ *parybface = *bface;
+ } // if (j == 6)
+ } // if (bface->key < cosslidihed)
} // if (gettetrahedron(...))
} // k
@@ -28121,11 +26175,12 @@ long tetgenmesh::removeslivers(int chkencflag)
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::optimizemesh(int optflag)
+void tetgenmesh::optimizemesh()
{
badface *parybface;
triface checktet;
point *ppt;
+ int optpasses;
optparameters opm;
REAL ncosdd[6], maxdd;
long totalremcount, remcount;
@@ -28139,18 +26194,16 @@ void tetgenmesh::optimizemesh(int optflag)
printf("Optimizing mesh...\n");
}
- if (b->verbose > 1) {
- printf(" min_max_dihedral = %g.\n", b->optmaxdihedral);
- printf(" max_flipstarsize = %d.\n", b->optmaxflipstarsize);
- printf(" max_fliplinklevel = %d.\n", b->optmaxfliplevel);
- printf(" number of passes = %d.\n", b->optpasses);
- }
- totalsmtcount = totalsptcount = totalremcount = 0l;
+ optpasses = ((1 << b->optlevel) - 1);
- if (b->verbose > 1) {
- printf(" Removing large angles (> %g degree).\n", b->optmaxdihedral);
+ if (b->verbose) {
+ printf(" Optimization level = %d.\n", b->optlevel);
+ printf(" Optimization scheme = %d.\n", b->optscheme);
+ printf(" Min_Max dihed angle = %g.\n", b->optmaxdihedral);
}
+ totalsmtcount = totalsptcount = totalremcount = 0l;
+
cosmaxdihed = cos(b->optmaxdihedral / 180.0 * PI);
cossmtdihed = cos(b->optminsmtdihed / 180.0 * PI);
cosslidihed = cos(b->optminslidihed / 180.0 * PI);
@@ -28181,23 +26234,23 @@ void tetgenmesh::optimizemesh(int optflag)
totalremcount = improvequalitybyflips();
if ((unflipqueue->objects > 0l) &&
- ((b->optlevel & 2) || (b->optlevel & 4))) { // -O2 | -O4
-
- badtetrahedrons = new memorypool(sizeof(badface), b->tetrahedraperblock,
- memorypool::POINTER, 0);
+ ((b->optscheme & 2) || (b->optscheme & 4))) {
+ // The pool is only used by removeslivers().
+ badtetrahedrons = new memorypool(sizeof(triface), b->tetrahedraperblock,
+ sizeof(void *), 0);
// Smoothing options.
opm.min_max_dihedangle = 1;
opm.numofsearchdirs = 10;
// opm.searchstep = 0.001;
opm.maxiter = 30; // Limit the maximum iterations.
- opm.checkencflag = 4; // Queue affected tets after smoothing.
+ //opm.checkencflag = 4; // Queue affected tets after smoothing.
chkencflag = 4; // Queue affected tets after splitting a sliver.
iter = 0;
- while (iter < b->optpasses) {
+ while (iter < optpasses) {
smtcount = sptcount = remcount = 0l;
- if (b->optlevel & 2) {
+ if (b->optscheme & 2) {
smtcount += improvequalitybysmoothing(&opm);
totalsmtcount += smtcount;
if (smtcount > 0l) {
@@ -28206,7 +26259,7 @@ void tetgenmesh::optimizemesh(int optflag)
}
}
if (unflipqueue->objects > 0l) {
- if (b->optlevel & 4) {
+ if (b->optscheme & 4) {
sptcount += removeslivers(chkencflag);
totalsptcount += sptcount;
if (sptcount > 0l) {
@@ -28228,7 +26281,7 @@ void tetgenmesh::optimizemesh(int optflag)
delete badtetrahedrons;
- } // // -O2 | -O4
+ }
if (unflipqueue->objects > 0l) {
if (b->verbose > 1) {
@@ -28239,13 +26292,13 @@ void tetgenmesh::optimizemesh(int optflag)
if (b->verbose) {
if (totalremcount > 0l) {
- printf(" Removed %ld bad tets.\n", totalremcount);
+ printf(" Removed %ld edges.\n", totalremcount);
}
if (totalsmtcount > 0l) {
printf(" Smoothed %ld points.\n", totalsmtcount);
}
if (totalsptcount > 0l) {
- printf(" Split %ld bad tets.\n", totalsptcount);
+ printf(" Split %ld slivers.\n", totalsptcount);
}
}
}
@@ -28258,6 +26311,32 @@ void tetgenmesh::optimizemesh(int optflag)
//// ////
//// ////
+///////////////////////////////////////////////////////////////////////////////
+// //
+// printfcomma() Print a (large) number with the 'thousands separator'. //
+// //
+// The following code was simply copied from "stackoverflow". //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::printfcomma(unsigned long n)
+{
+ unsigned long n2 = 0;
+ int scale = 1;
+ while (n >= 1000) {
+ n2 = n2 + scale * (n % 1000);
+ n /= 1000;
+ scale *= 1000;
+ }
+ printf ("%ld", n);
+ while (scale != 1) {
+ scale /= 1000;
+ n = n2 / scale;
+ n2 = n2 % scale;
+ printf (",%03ld", n);
+ }
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// checkmesh() Test the mesh for topological consistency. //
@@ -28403,12 +26482,12 @@ int tetgenmesh::checkmesh(int topoflag)
// //
///////////////////////////////////////////////////////////////////////////////
-int tetgenmesh::checkshells(/*int sub2tet*/)
+int tetgenmesh::checkshells()
{
triface neightet, symtet;
face shloop, spinsh, nextsh;
face checkseg;
- point pa, pb; //, *ppt;
+ point pa, pb;
int bakcount;
int horrors, i;
@@ -28436,10 +26515,10 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
while ((nextsh.sh != NULL) && (nextsh.sh != shloop.sh)) {
if (nextsh.sh[3] == NULL) {
printf(" !! !! Wrong subface-subface connection (Dead subface).\n");
- printf(" First: x%lx (%d, %d, %d).\n", (unsigned long long) spinsh.sh,
+ printf(" First: x%lx (%d, %d, %d).\n", (uintptr_t) spinsh.sh,
pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
pointmark(sapex(spinsh)));
- printf(" Second: x%lx (DEAD)\n", (unsigned long long) nextsh.sh);
+ printf(" Second: x%lx (DEAD)\n", (uintptr_t) nextsh.sh);
horrors++;
break;
}
@@ -28447,10 +26526,10 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
if (!(((sorg(nextsh) == pa) && (sdest(nextsh) == pb)) ||
((sorg(nextsh) == pb) && (sdest(nextsh) == pa)))) {
printf(" !! !! Wrong subface-subface connection.\n");
- printf(" First: x%lx (%d, %d, %d).\n", (unsigned long long) spinsh.sh,
+ printf(" First: x%lx (%d, %d, %d).\n", (uintptr_t) spinsh.sh,
pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
pointmark(sapex(spinsh)));
- printf(" Scond: x%lx (%d, %d, %d).\n", (unsigned long long) nextsh.sh,
+ printf(" Scond: x%lx (%d, %d, %d).\n", (uintptr_t) nextsh.sh,
pointmark(sorg(nextsh)), pointmark(sdest(nextsh)),
pointmark(sapex(nextsh)));
horrors++;
@@ -28459,10 +26538,10 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
// Check they should not have the same apex.
if (sapex(nextsh) == sapex(spinsh)) {
printf(" !! !! Existing two duplicated subfaces.\n");
- printf(" First: x%lx (%d, %d, %d).\n", (unsigned long long) spinsh.sh,
+ printf(" First: x%lx (%d, %d, %d).\n", (uintptr_t) spinsh.sh,
pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
pointmark(sapex(spinsh)));
- printf(" Scond: x%lx (%d, %d, %d).\n", (unsigned long long) nextsh.sh,
+ printf(" Scond: x%lx (%d, %d, %d).\n", (uintptr_t) nextsh.sh,
pointmark(sorg(nextsh)), pointmark(sdest(nextsh)),
pointmark(sapex(nextsh)));
horrors++;
@@ -28476,19 +26555,19 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
if (checkseg.sh != NULL) {
if (checkseg.sh[3] == NULL) {
printf(" !! !! Wrong subface-subseg connection (Dead subseg).\n");
- printf(" Sub: x%lx (%d, %d, %d).\n", (unsigned long long) shloop.sh,
+ printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t) shloop.sh,
pointmark(sorg(shloop)), pointmark(sdest(shloop)),
pointmark(sapex(shloop)));
- printf(" Sub: x%lx (Dead)\n", (unsigned long long) checkseg.sh);
+ printf(" Sub: x%lx (Dead)\n", (uintptr_t) checkseg.sh);
horrors++;
} else {
if (!(((sorg(checkseg) == pa) && (sdest(checkseg) == pb)) ||
((sorg(checkseg) == pb) && (sdest(checkseg) == pa)))) {
printf(" !! !! Wrong subface-subseg connection.\n");
- printf(" Sub: x%lx (%d, %d, %d).\n", (unsigned long long) shloop.sh,
+ printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t) shloop.sh,
pointmark(sorg(shloop)), pointmark(sdest(shloop)),
pointmark(sapex(shloop)));
- printf(" Seg: x%lx (%d, %d).\n", (unsigned long long) checkseg.sh,
+ printf(" Seg: x%lx (%d, %d).\n", (uintptr_t) checkseg.sh,
pointmark(sorg(checkseg)), pointmark(sdest(checkseg)));
horrors++;
}
@@ -28502,20 +26581,20 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
if (neightet.tet != NULL) {
if (neightet.tet[4] == NULL) {
printf(" !! !! Wrong sub-to-tet connection (Dead tet)\n");
- printf(" Sub: x%lx (%d, %d, %d).\n", (unsigned long long) shloop.sh,
+ printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t) shloop.sh,
pointmark(sorg(shloop)), pointmark(sdest(shloop)),
pointmark(sapex(shloop)));
- printf(" Tet: x%lx (DEAD)\n", (unsigned long long) neightet.tet);
+ printf(" Tet: x%lx (DEAD)\n", (uintptr_t) neightet.tet);
horrors++;
} else {
if (!((sorg(shloop) == org(neightet)) &&
(sdest(shloop) == dest(neightet)))) {
printf(" !! !! Wrong sub-to-tet connection\n");
- printf(" Sub: x%lx (%d, %d, %d).\n", (unsigned long long) shloop.sh,
+ printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t) shloop.sh,
pointmark(sorg(shloop)), pointmark(sdest(shloop)),
pointmark(sapex(shloop)));
printf(" Tet: x%lx (%d, %d, %d, %d).\n",
- (unsigned long long) neightet.tet, pointmark(org(neightet)),
+ (uintptr_t) neightet.tet, pointmark(org(neightet)),
pointmark(dest(neightet)), pointmark(apex(neightet)),
pointmark(oppo(neightet)));
horrors++;
@@ -28524,11 +26603,11 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
if (!((sorg(spinsh) == org(neightet)) &&
(sdest(spinsh) == dest(neightet)))) {
printf(" !! !! Wrong tet-sub connection.\n");
- printf(" Sub: x%lx (%d, %d, %d).\n", (unsigned long long) spinsh.sh,
+ printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t) spinsh.sh,
pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
pointmark(sapex(spinsh)));
printf(" Tet: x%lx (%d, %d, %d, %d).\n",
- (unsigned long long) neightet.tet, pointmark(org(neightet)),
+ (uintptr_t) neightet.tet, pointmark(org(neightet)),
pointmark(dest(neightet)), pointmark(apex(neightet)),
pointmark(oppo(neightet)));
horrors++;
@@ -28539,11 +26618,11 @@ int tetgenmesh::checkshells(/*int sub2tet*/)
if (!((sorg(spinsh) == org(symtet)) &&
(sdest(spinsh) == dest(symtet)))) {
printf(" !! !! Wrong tet-sub connection.\n");
- printf(" Sub: x%lx (%d, %d, %d).\n", (unsigned long long) spinsh.sh,
+ printf(" Sub: x%lx (%d, %d, %d).\n", (uintptr_t) spinsh.sh,
pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
pointmark(sapex(spinsh)));
printf(" Tet: x%lx (%d, %d, %d, %d).\n",
- (unsigned long long) symtet.tet, pointmark(org(symtet)),
+ (uintptr_t) symtet.tet, pointmark(org(symtet)),
pointmark(dest(symtet)), pointmark(apex(symtet)),
pointmark(oppo(symtet)));
horrors++;
@@ -28598,8 +26677,10 @@ int tetgenmesh::checksegments()
face sseg, checkseg;
point pa, pb;
int miscount;
+ int t1ver;
int horrors, i;
+
if (!b->quiet) {
printf(" Checking tet->seg connections...\n");
}
@@ -28623,9 +26704,9 @@ int tetgenmesh::checksegments()
((org(tetloop) == pb) && (dest(tetloop) == pa)))) {
printf(" !! Wrong tet-seg connection.\n");
printf(" Tet: x%lx (%d, %d, %d, %d) - Seg: x%lx (%d, %d).\n",
- (unsigned long long) tetloop.tet, pointmark(org(tetloop)),
+ (uintptr_t) tetloop.tet, pointmark(org(tetloop)),
pointmark(dest(tetloop)), pointmark(apex(tetloop)),
- pointmark(oppo(tetloop)), (unsigned long long) sseg.sh,
+ pointmark(oppo(tetloop)), (uintptr_t) sseg.sh,
pointmark(pa), pointmark(pb));
horrors++;
} else {
@@ -28636,11 +26717,11 @@ int tetgenmesh::checksegments()
if (checkseg.sh != sseg.sh) {
printf(" !! Wrong tet->seg connection.\n");
printf(" Tet: x%lx (%d, %d, %d, %d) - ",
- (unsigned long long) neightet.tet, pointmark(org(neightet)),
+ (uintptr_t) neightet.tet, pointmark(org(neightet)),
pointmark(dest(neightet)), pointmark(apex(neightet)),
pointmark(oppo(neightet)));
if (checkseg.sh != NULL) {
- printf("Seg x%lx (%d, %d).\n", (unsigned long long) checkseg.sh,
+ printf("Seg x%lx (%d, %d).\n", (uintptr_t) checkseg.sh,
pointmark(sorg(checkseg)),pointmark(sdest(checkseg)));
} else {
printf("Seg: NULL.\n");
@@ -28660,9 +26741,9 @@ int tetgenmesh::checksegments()
((org(neightet) == pb) && (dest(neightet) == pa)))) {
printf(" !! Wrong seg->tet connection (Wrong edge).\n");
printf(" Tet: x%lx (%d, %d, %d, %d) - Seg: x%lx (%d, %d).\n",
- (unsigned long long) neightet.tet, pointmark(org(neightet)),
+ (uintptr_t) neightet.tet, pointmark(org(neightet)),
pointmark(dest(neightet)), pointmark(apex(neightet)),
- pointmark(oppo(neightet)), (unsigned long long) sseg.sh,
+ pointmark(oppo(neightet)), (uintptr_t) sseg.sh,
pointmark(pa), pointmark(pb));
horrors++;
}
@@ -28679,7 +26760,7 @@ int tetgenmesh::checksegments()
printf(" !! A marked edge: (%d, %d, %d, %d) -- x%lx %d.\n",
pointmark(org(neightet)), pointmark(dest(neightet)),
pointmark(apex(neightet)), pointmark(oppo(neightet)),
- (unsigned long long) neightet.tet, neightet.ver);
+ (uintptr_t) neightet.tet, neightet.ver);
// Check if all tets at the edge are marked.
spintet = neightet;
while (1) {
@@ -28688,7 +26769,7 @@ int tetgenmesh::checksegments()
printf(" !! !! An unmarked edge (%d, %d, %d, %d) -- x%lx %d.\n",
pointmark(org(spintet)), pointmark(dest(spintet)),
pointmark(apex(spintet)), pointmark(oppo(spintet)),
- (unsigned long long) spintet.tet, spintet.ver);
+ (uintptr_t) spintet.tet, spintet.ver);
horrors++;
}
if (spintet.tet == neightet.tet) break;
@@ -28721,7 +26802,7 @@ int tetgenmesh::checksegments()
// sesymself(spinsh);
// printf(" !! Wrong ori at subface (%d, %d, %d) -- x%lx %d\n",
// pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
- // pointmark(sapex(spinsh)), (unsigned long long) spinsh.sh,
+ // pointmark(sapex(spinsh)), (uintptr_t) spinsh.sh,
// spinsh.shver);
// horrors++;
//}
@@ -28734,7 +26815,7 @@ int tetgenmesh::checksegments()
printf(" !! !! No seg at tet (%d, %d, %d, %d) -- x%lx %d\n",
pointmark(org(spintet)), pointmark(dest(spintet)),
pointmark(apex(spintet)), pointmark(oppo(spintet)),
- (unsigned long long) spintet.tet, spintet.ver);
+ (uintptr_t) spintet.tet, spintet.ver);
horrors++;
}
if (checkseg.sh != sseg.sh) {
@@ -28753,7 +26834,7 @@ int tetgenmesh::checksegments()
} else {
printf(" !! Wrong seg-subface (%d, %d, %d) -- x%lx %d connect\n",
pointmark(sorg(spinsh)), pointmark(sdest(spinsh)),
- pointmark(sapex(spinsh)), (unsigned long long) spinsh.sh,
+ pointmark(sapex(spinsh)), (uintptr_t) spinsh.sh,
spinsh.shver);
horrors++;
break;
@@ -29034,6 +27115,7 @@ int tetgenmesh::checkconforming(int flag)
REAL cent[3], radius, dist, diff, rd, len;
bool enq;
int encsubsegs, encsubfaces;
+ int t1ver;
int i;
REAL A[4][4], rhs[4], D;
@@ -29246,7 +27328,7 @@ void tetgenmesh::qualitystatistics()
for (i = 0; i < 4; i++) p[i] = (point) tetloop.tet[4 + i];
// Get the tet volume.
- tetvol = orient3d(p[1], p[0], p[2], p[3]) / 6.0;
+ tetvol = orient3dfast(p[1], p[0], p[2], p[3]) / 6.0;
total_tet_vol += tetvol;
total_tetprism_vol += tetprismvol(p[0], p[1], p[2], p[3]);
@@ -29550,6 +27632,97 @@ void tetgenmesh::qualitystatistics()
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// memorystatistics() Report the memory usage. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::memorystatistics()
+{
+ printf("Memory usage statistics:\n\n");
+
+ // Count the number of blocks of tetrahedra.
+ int tetblocks = 0;
+ tetrahedrons->pathblock = tetrahedrons->firstblock;
+ while (tetrahedrons->pathblock != NULL) {
+ tetblocks++;
+ tetrahedrons->pathblock = (void **) *(tetrahedrons->pathblock);
+ }
+
+ // Calculate the total memory (in bytes) used by storing meshes.
+ unsigned long totalmeshmemory = 0l, totalt2shmemory = 0l;
+ totalmeshmemory = points->maxitems * points->itembytes +
+ tetrahedrons->maxitems * tetrahedrons->itembytes;
+ if (b->plc || b->refine) {
+ totalmeshmemory += (subfaces->maxitems * subfaces->itembytes +
+ subsegs->maxitems * subsegs->itembytes);
+ totalt2shmemory = (tet2subpool->maxitems * tet2subpool->itembytes +
+ tet2segpool->maxitems * tet2segpool->itembytes);
+ }
+
+ unsigned long totalalgomemory = 0l;
+ totalalgomemory = cavetetlist->totalmemory + cavebdrylist->totalmemory +
+ caveoldtetlist->totalmemory +
+ flippool->maxitems * flippool->itembytes;
+ if (b->plc || b->refine) {
+ totalalgomemory += (subsegstack->totalmemory + subfacstack->totalmemory +
+ subvertstack->totalmemory +
+ suppsteinerptlist->totalmemory +
+ caveshlist->totalmemory + caveshbdlist->totalmemory +
+ cavesegshlist->totalmemory +
+ cavetetshlist->totalmemory +
+ cavetetseglist->totalmemory +
+ caveencshlist->totalmemory +
+ caveencseglist->totalmemory +
+ cavetetvertlist->totalmemory +
+ unflipqueue->totalmemory);
+ }
+
+ printf(" Maximum number of tetrahedra: %ld\n", tetrahedrons->maxitems);
+ printf(" Maximum number of tet blocks (blocksize = %d): %d\n",
+ b->tetrahedraperblock, tetblocks);
+ /*
+ if (b->plc || b->refine) {
+ printf(" Approximate memory for tetrahedral mesh (bytes): %ld\n",
+ totalmeshmemory);
+
+ printf(" Approximate memory for extra pointers (bytes): %ld\n",
+ totalt2shmemory);
+ } else {
+ printf(" Approximate memory for tetrahedralization (bytes): %ld\n",
+ totalmeshmemory);
+ }
+ printf(" Approximate memory for algorithms (bytes): %ld\n",
+ totalalgomemory);
+ printf(" Approximate memory for working arrays (bytes): %ld\n",
+ totalworkmemory);
+ printf(" Approximate total used memory (bytes): %ld\n",
+ totalmeshmemory + totalt2shmemory + totalalgomemory +
+ totalworkmemory);
+ */
+ if (b->plc || b->refine) {
+ printf(" Approximate memory for tetrahedral mesh (bytes): ");
+ printfcomma(totalmeshmemory); printf("\n");
+
+ printf(" Approximate memory for extra pointers (bytes): ");
+ printfcomma(totalt2shmemory); printf("\n");
+ } else {
+ printf(" Approximate memory for tetrahedralization (bytes): ");
+ printfcomma(totalmeshmemory); printf("\n");
+ }
+ printf(" Approximate memory for algorithms (bytes): ");
+ printfcomma(totalalgomemory); printf("\n");
+ printf(" Approximate memory for working arrays (bytes): ");
+ printfcomma(totalworkmemory); printf("\n");
+ printf(" Approximate total used memory (bytes): ");
+ printfcomma(totalmeshmemory + totalt2shmemory + totalalgomemory +
+ totalworkmemory);
+ printf("\n");
+
+ printf("\n");
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// statistics() Print all sorts of cool facts. //
@@ -29575,26 +27748,44 @@ void tetgenmesh::statistics()
tetnumber = tetrahedrons->items - hullsize;
facenumber = (tetnumber * 4l + hullsize) / 2l;
- printf("\n Mesh points: %ld\n", points->items);
+ if (b->weighted) { // -w option
+ printf("\n Mesh points: %ld\n", points->items - nonregularcount);
+ } else {
+ printf("\n Mesh points: %ld\n", points->items);
+ }
printf(" Mesh tetrahedra: %ld\n", tetnumber);
printf(" Mesh faces: %ld\n", facenumber);
- printf(" Mesh edges: %ld\n", meshedges);
+ if (meshedges > 0l) {
+ printf(" Mesh edges: %ld\n", meshedges);
+ } else {
+ if (!nonconvex) {
+ long vsize = points->items - dupverts - unuverts;
+ if (b->weighted) vsize -= nonregularcount;
+ meshedges = vsize + facenumber - tetnumber - 1;
+ printf(" Mesh edges: %ld\n", meshedges);
+ }
+ }
if (b->plc || b->refine) {
printf(" Mesh boundary faces: %ld\n", subfaces->items);
printf(" Mesh boundary edges: %ld\n", subsegs->items);
if (st_segref_count > 0l) {
- printf(" Steiner points in boundary edges: %ld\n", st_segref_count);
+ printf(" Steiner points on boundary edges: %ld\n", st_segref_count);
}
if (st_facref_count > 0l) {
- printf(" Steiner points in boundary faces: %ld\n", st_facref_count);
+ printf(" Steiner points on boundary faces: %ld\n", st_facref_count);
}
if (st_volref_count > 0l) {
- printf(" Steiner points in mesh domain: %ld\n", st_volref_count);
+ printf(" Steiner points inside mesh domain: %ld\n", st_volref_count);
}
} else {
printf(" Convex hull faces: %ld\n", hullsize);
- printf(" Convex hull edges: %ld\n", meshhulledges);
+ if (meshhulledges > 0l) {
+ printf(" Convex hull edges: %ld\n", meshhulledges);
+ }
+ }
+ if (b->weighted) { // -w option
+ printf(" Skipped non-regular points: %ld\n", nonregularcount);
}
printf("\n");
@@ -29605,6 +27796,9 @@ void tetgenmesh::statistics()
qualitystatistics();
}
}
+ if (tetrahedrons->items > 0l) {
+ memorystatistics();
+ }
}
}
@@ -29647,7 +27841,7 @@ void tetgenmesh::jettisonnodes()
jetflag = (pointtype(pointloop) == DUPLICATEDVERTEX) ||
(pointtype(pointloop) == UNUSEDVERTEX);
if (jetflag) {
- // It is a duplicated point, delete it.
+ // It is a duplicated or unused point, delete it.
pointdealloc(pointloop);
remcount++;
} else {
@@ -29662,27 +27856,116 @@ void tetgenmesh::jettisonnodes()
newidx++;
}
oldidx++;
- //if (oldidx == in->numberofpoints) {
- // // Update the numbe of input points (Because some were removed).
- // in->numberofpoints -= remcount;
- // // Remember this number for output original input nodes.
- // jettisoninverts = remcount;
- //}
pointloop = pointtraverse();
}
if (b->verbose) {
- printf(" %d duplicated vertices are removed.\n", dupverts);
- printf(" %d unused vertices are removed.\n", unuverts);
+ printf(" %ld duplicated vertices are removed.\n", dupverts);
+ printf(" %ld unused vertices are removed.\n", unuverts);
+ }
+ dupverts = 0l;
+ unuverts = 0l;
+
+ // The following line ensures that dead items in the pool of nodes cannot
+ // be allocated for the new created nodes. This ensures that the input
+ // nodes will occur earlier in the output files, and have lower indices.
+ points->deaditemstack = (void *) NULL;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// highorder() Create extra nodes for quadratic subparametric elements. //
+// //
+// 'highordertable' is an array (size = numberoftetrahedra * 6) for storing //
+// high-order nodes of each tetrahedron. This routine is used only when -o2 //
+// switch is used. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::highorder()
+{
+ triface tetloop, worktet, spintet;
+ point *extralist, *adjextralist;
+ point torg, tdest, newpoint;
+ int highorderindex;
+ int t1ver;
+ int i, j;
+
+ if (!b->quiet) {
+ printf("Adding vertices for second-order tetrahedra.\n");
+ }
+
+ // Initialize the 'highordertable'.
+ highordertable = new point[tetrahedrons->items * 6];
+ if (highordertable == (point *) NULL) {
+ terminatetetgen(1);
}
- dupverts = 0;
- unuverts = 0;
+
+ // This will overwrite the slot for element markers.
+ highorderindex = 11;
// The following line ensures that dead items in the pool of nodes cannot
- // be allocated for the new created nodes. This ensures that the input
- // nodes will occur earlier in the output files, and have lower indices.
+ // be allocated for the extra nodes associated with high order elements.
+ // This ensures that the primary nodes (at the corners of elements) will
+ // occur earlier in the output files, and have lower indices, than the
+ // extra nodes.
points->deaditemstack = (void *) NULL;
-}
+ // Assign an entry for each tetrahedron to find its extra nodes. At the
+ // mean while, initialize all extra nodes be NULL.
+ i = 0;
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ tetloop.tet[highorderindex] = (tetrahedron) &highordertable[i];
+ for (j = 0; j < 6; j++) {
+ highordertable[i + j] = (point) NULL;
+ }
+ i += 6;
+ tetloop.tet = tetrahedrontraverse();
+ }
+
+ // To create a unique node on each edge. Loop over all tetrahedra, and
+ // look at the six edges of each tetrahedron. If the extra node in
+ // the tetrahedron corresponding to this edge is NULL, create a node
+ // for this edge, at the same time, set the new node into the extra
+ // node lists of all other tetrahedra sharing this edge.
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ // Get the list of extra nodes.
+ extralist = (point *) tetloop.tet[highorderindex];
+ worktet.tet = tetloop.tet;
+ for (i = 0; i < 6; i++) {
+ if (extralist[i] == (point) NULL) {
+ // Go to the ith-edge.
+ worktet.ver = edge2ver[i];
+ // Create a new point in the middle of this edge.
+ torg = org(worktet);
+ tdest = dest(worktet);
+ makepoint(&newpoint, FREEVOLVERTEX);
+ for (j = 0; j < 3 + numpointattrib; j++) {
+ newpoint[j] = 0.5 * (torg[j] + tdest[j]);
+ }
+ // Interpolate its metrics.
+ for (j = 0; j < in->numberofpointmtrs; j++) {
+ newpoint[pointmtrindex + j] =
+ 0.5 * (torg[pointmtrindex + j] + tdest[pointmtrindex + j]);
+ }
+ // Set this point into all extra node lists at this edge.
+ spintet = worktet;
+ while (1) {
+ if (!ishulltet(spintet)) {
+ adjextralist = (point *) spintet.tet[highorderindex];
+ adjextralist[ver2edge[spintet.ver]] = newpoint;
+ }
+ fnextself(spintet);
+ if (spintet.tet == worktet.tet) break;
+ }
+ } // if (!extralist[i])
+ } // i
+ tetloop.tet = tetrahedrontraverse();
+ }
+}
///////////////////////////////////////////////////////////////////////////////
// //
@@ -29691,28 +27974,18 @@ void tetgenmesh::jettisonnodes()
// This routine is called when '-p' or '-r', and '-E' options are used. The //
// total number of edges depends on the genus of the input surface mesh. //
// //
+// NOTE: This routine must be called after outelements(). So all elements //
+// have been indexed. //
+// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::numberedges()
{
triface worktet, spintet;
- int firstindex, eindex;
int ishulledge;
+ int t1ver;
int i;
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
-
- // First indexing all tetrahedra.
- tetrahedrons->traversalinit();
- eindex = firstindex;
- worktet.tet = tetrahedrontraverse();
- while (worktet.tet != NULL) {
- setelemindex(worktet.tet, eindex);
- eindex++;
- worktet.tet = tetrahedrontraverse();
- }
-
meshedges = meshhulledges = 0l;
tetrahedrons->traversalinit();
@@ -29758,7 +28031,7 @@ void tetgenmesh::outnodes(tetgenio* out)
char outnodefilename[FILENAMESIZE];
face parentsh;
point pointloop;
- int nextras, bmark, marker = 0;
+ int nextras, bmark, marker = 0, weightDT = 0;
int coordindex, attribindex;
int pointnumber, firstindex;
int index, i;
@@ -29776,7 +28049,11 @@ void tetgenmesh::outnodes(tetgenio* out)
}
}
- nextras = in->numberofpointattributes;
+ nextras = numpointattrib;
+ if (b->weighted) { // -w
+ if (b->weighted_param == 0) weightDT = 1; // Weighted DT.
+ }
+
bmark = !b->nobound && in->pointmarkerlist;
if (out == (tetgenio *) NULL) {
@@ -29860,7 +28137,13 @@ void tetgenmesh::outnodes(tetgenio* out)
pointloop[0], pointloop[1], pointloop[2]);
for (i = 0; i < nextras; i++) {
// Write an attribute.
- fprintf(outfile, " %.17g", pointloop[4 + i]);
+ if ((i == 0) && weightDT) {
+ fprintf(outfile, " %.17g", pointloop[0] * pointloop[0] +
+ pointloop[1] * pointloop[1] + pointloop[2] * pointloop[2]
+ - pointloop[3 + i]);
+ } else {
+ fprintf(outfile, " %.17g", pointloop[3 + i]);
+ }
}
if (bmark) {
// Write the boundary marker.
@@ -29892,7 +28175,13 @@ void tetgenmesh::outnodes(tetgenio* out)
// Point attributes.
for (i = 0; i < nextras; i++) {
// Output an attribute.
- out->pointattributelist[attribindex++] = pointloop[4 + i];
+ if ((i == 0) && weightDT) {
+ out->pointattributelist[attribindex++] =
+ pointloop[0] * pointloop[0] + pointloop[1] * pointloop[1] +
+ pointloop[2] * pointloop[2] - pointloop[3 + i];
+ } else {
+ out->pointattributelist[attribindex++] = pointloop[3 + i];
+ }
}
if (bmark) {
// Output the boundary marker.
@@ -30012,7 +28301,6 @@ void tetgenmesh::outelements(tetgenio* out)
FILE *outfile = NULL;
char outelefilename[FILENAMESIZE];
tetrahedron* tptr;
- triface worktet, spintet;
point p1, p2, p3, p4;
point *extralist;
REAL *talist = NULL;
@@ -30020,10 +28308,9 @@ void tetgenmesh::outelements(tetgenio* out)
long ntets;
int firstindex, shift;
int pointindex, attribindex;
- int highorderindex = 10; // The reserved pointer.
+ int highorderindex = 11;
int elementnumber;
int eextras;
- int ishulledge;
int i;
if (out == (tetgenio *) NULL) {
@@ -30042,7 +28329,7 @@ void tetgenmesh::outelements(tetgenio* out)
// The number of tets excluding hull tets.
ntets = tetrahedrons->items - hullsize;
- eextras = in->numberoftetrahedronattributes;
+ eextras = numelemattrib;
if (out == (tetgenio *) NULL) {
outfile = fopen(outelefilename, "w");
if (outfile == (FILE *) NULL) {
@@ -30086,8 +28373,13 @@ void tetgenmesh::outelements(tetgenio* out)
tptr = tetrahedrontraverse();
elementnumber = firstindex; // in->firstnumber;
while (tptr != (tetrahedron *) NULL) {
- p1 = (point) tptr[4];
- p2 = (point) tptr[5];
+ if (!b->reversetetori) {
+ p1 = (point) tptr[4];
+ p2 = (point) tptr[5];
+ } else {
+ p1 = (point) tptr[5];
+ p2 = (point) tptr[4];
+ }
p3 = (point) tptr[6];
p4 = (point) tptr[7];
if (out == (tetgenio *) NULL) {
@@ -30095,9 +28387,9 @@ void tetgenmesh::outelements(tetgenio* out)
fprintf(outfile, "%5d %5d %5d %5d %5d", elementnumber,
pointmark(p1) - shift, pointmark(p2) - shift,
pointmark(p3) - shift, pointmark(p4) - shift);
- if (0) { // if (b->order == 2) {
+ if (b->order == 2) {
extralist = (point *) tptr[highorderindex];
- // Tetrahedron number, indices for four points plus six extra points.
+ // indices for six extra points.
fprintf(outfile, " %5d %5d %5d %5d %5d %5d",
pointmark(extralist[0]) - shift, pointmark(extralist[1]) - shift,
pointmark(extralist[2]) - shift, pointmark(extralist[3]) - shift,
@@ -30112,7 +28404,7 @@ void tetgenmesh::outelements(tetgenio* out)
tlist[pointindex++] = pointmark(p2) - shift;
tlist[pointindex++] = pointmark(p3) - shift;
tlist[pointindex++] = pointmark(p4) - shift;
- if (0) { // if (b->order == 2) {
+ if (b->order == 2) {
extralist = (point *) tptr[highorderindex];
tlist[pointindex++] = pointmark(extralist[0]) - shift;
tlist[pointindex++] = pointmark(extralist[1]) - shift;
@@ -30125,44 +28417,12 @@ void tetgenmesh::outelements(tetgenio* out)
talist[attribindex++] = elemattribute(tptr, i);
}
}
- //if (b->neighout) {
- // Remember the index of this element.
- setelemindex(tptr, elementnumber);
- //}
+ // Remember the index of this element (for counting edges).
+ setelemindex(tptr, elementnumber);
tptr = tetrahedrontraverse();
elementnumber++;
}
- // Count the number of edges (# Voronoi faces).
- meshedges = meshhulledges = 0l;
-
- tetrahedrons->traversalinit();
- tptr = tetrahedrontraverse();
- while (tptr != (tetrahedron *) NULL) {
- // Count the number of Voronoi faces. Look at the six edges of this
- // tet. Count an edge only if this tet's pointer is smaller than
- // those of other non-hull tets which share this edge.
- worktet.tet = tptr;
- for (i = 0; i < 6; i++) {
- worktet.ver = edge2ver[i];
- ishulledge = 0;
- fnext(worktet, spintet);
- do {
- if (!ishulltet(spintet)) {
- if (elemindex(spintet.tet) < elemindex(worktet.tet)) break;
- } else {
- ishulledge = 1;
- }
- fnextself(spintet);
- } while (spintet.tet != worktet.tet);
- // Count this edge if no adjacent tets are smaller than this tet.
- if (spintet.tet == worktet.tet) {
- meshedges++;
- if (ishulledge) meshhulledges++;
- }
- }
- tptr = tetrahedrontraverse();
- }
if (out == (tetgenio *) NULL) {
fprintf(outfile, "# Generated by %s\n", b->commandline);
@@ -30174,11 +28434,6 @@ void tetgenmesh::outelements(tetgenio* out)
// //
// outfaces() Output all faces to a .face file or a tetgenio object. //
// //
-// The total number of faces f can be calculated as following: Let t be the //
-// total number of tets. Since each tet has 4 faces, the number t * 4 counts //
-// each interior face twice and each hull face once. So f = (t * 4 + h) / 2, //
-// where h is the total number of hull faces (which is known). //
-// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::outfaces(tetgenio* out)
@@ -30194,7 +28449,13 @@ void tetgenmesh::outfaces(tetgenio* out)
int faceid, marker = 0;
int firstindex, shift;
int facenumber;
- int index;
+ int index = 0;
+
+ // For -o2 option.
+ triface workface;
+ point *extralist, pp[3] = {0,0,0};
+ int highorderindex = 11;
+ int o2index = 0, i;
if (out == (tetgenio *) NULL) {
strcpy(facefilename, b->outfilename);
@@ -30211,7 +28472,6 @@ void tetgenmesh::outfaces(tetgenio* out)
ntets = tetrahedrons->items - hullsize;
faces = (ntets * 4l + hullsize) / 2l;
- //bmark = !b->nobound && in->facetmarkerlist;
if (out == (tetgenio *) NULL) {
outfile = fopen(facefilename, "w");
@@ -30227,6 +28487,9 @@ void tetgenmesh::outfaces(tetgenio* out)
printf("Error: Out of memory.\n");
terminatetetgen(1);
}
+ if (b->order == 2) {
+ out->o2facelist = new int[faces * 3];
+ }
// Allocate memory for 'trifacemarkerlist' if necessary.
if (!b->nobound) {
out->trifacemarkerlist = new int[faces];
@@ -30246,7 +28509,6 @@ void tetgenmesh::outfaces(tetgenio* out)
out->numberoftrifaces = faces;
elist = out->trifacelist;
emlist = out->trifacemarkerlist;
- index = 0;
}
// Determine the first index (0 or 1).
@@ -30271,6 +28533,16 @@ void tetgenmesh::outfaces(tetgenio* out)
torg = org(tface);
tdest = dest(tface);
tapex = apex(tface);
+ if (b->order == 2) { // -o2
+ // Get the three extra vertices on edges.
+ extralist = (point *) (tface.tet[highorderindex]);
+ // The extra vertices are on edges opposite the corners.
+ enext(tface, workface);
+ for (i = 0; i < 3; i++) {
+ pp[i] = extralist[ver2edge[workface.ver]];
+ enextself(workface);
+ }
+ }
if (!b->nobound) {
// Get the boundary marker of this face.
if (b->plc || b->refine) {
@@ -30306,6 +28578,10 @@ void tetgenmesh::outfaces(tetgenio* out)
fprintf(outfile, "%5d %4d %4d %4d", facenumber,
pointmark(torg) - shift, pointmark(tdest) - shift,
pointmark(tapex) - shift);
+ if (b->order == 2) { // -o2
+ fprintf(outfile, " %4d %4d %4d", pointmark(pp[0]) - shift,
+ pointmark(pp[1]) - shift, pointmark(pp[2]) - shift);
+ }
if (!b->nobound) {
// Output a boundary marker.
fprintf(outfile, " %d", marker);
@@ -30319,6 +28595,11 @@ void tetgenmesh::outfaces(tetgenio* out)
elist[index++] = pointmark(torg) - shift;
elist[index++] = pointmark(tdest) - shift;
elist[index++] = pointmark(tapex) - shift;
+ if (b->order == 2) { // -o2
+ out->o2facelist[o2index++] = pointmark(pp[0]) - shift;
+ out->o2facelist[o2index++] = pointmark(pp[1]) - shift;
+ out->o2facelist[o2index++] = pointmark(pp[2]) - shift;
+ }
if (!b->nobound) {
emlist[facenumber - in->firstnumber] = marker;
}
@@ -30454,6 +28735,14 @@ void tetgenmesh::outsubfaces(tetgenio* out)
int neigh1 = 0, neigh2 = 0;
int facenumber;
+ // For -o2 option.
+ triface workface;
+ point *extralist, pp[3] = {0,0,0};
+ int highorderindex = 11;
+ int o2index = 0, i;
+
+ int t1ver; // used by fsymself()
+
if (out == (tetgenio *) NULL) {
strcpy(facefilename, b->outfilename);
strcat(facefilename, ".face");
@@ -30467,8 +28756,6 @@ void tetgenmesh::outsubfaces(tetgenio* out)
}
}
- //bmark = !b->nobound && in->facetmarkerlist;
-
if (out == (tetgenio *) NULL) {
outfile = fopen(facefilename, "w");
if (outfile == (FILE *) NULL) {
@@ -30483,6 +28770,9 @@ void tetgenmesh::outsubfaces(tetgenio* out)
if (out->trifacelist == (int *) NULL) {
terminatetetgen(1);
}
+ if (b->order == 2) {
+ out->o2facelist = new int[subfaces->items * 3];
+ }
if (!b->nobound) {
// Allocate memory for 'trifacemarkerlist'.
out->trifacemarkerlist = new int[subfaces->items];
@@ -30514,18 +28804,39 @@ void tetgenmesh::outsubfaces(tetgenio* out)
facenumber = firstindex; // in->firstnumber;
while (faceloop.sh != (shellface *) NULL) {
stpivot(faceloop, abuttingtet);
+ // If there is a tetrahedron containing this subface, orient it so
+ // that the normal of this face points to inside of the volume by
+ // right-hand rule.
+ if (abuttingtet.tet != NULL) {
+ if (ishulltet(abuttingtet)) {
+ fsymself(abuttingtet);
+ assert(!ishulltet(abuttingtet));
+ }
+ }
if (abuttingtet.tet != NULL) {
- // If there is a tetrahedron containing this subface, orient it so
- // that the normal of this face points to inside of the volume by
- // right-hand rule.
torg = org(abuttingtet);
tdest = dest(abuttingtet);
tapex = apex(abuttingtet);
+ if (b->order == 2) { // -o2
+ // Get the three extra vertices on edges.
+ extralist = (point *) (abuttingtet.tet[highorderindex]);
+ workface = abuttingtet;
+ for (i = 0; i < 3; i++) {
+ pp[i] = extralist[ver2edge[workface.ver]];
+ enextself(workface);
+ }
+ }
} else {
// This may happen when only a surface mesh be generated.
torg = sorg(faceloop);
tdest = sdest(faceloop);
tapex = sapex(faceloop);
+ if (b->order == 2) { // -o2
+ // There is no extra node list available.
+ pp[0] = torg;
+ pp[1] = tdest;
+ pp[2] = tapex;
+ }
}
if (!b->nobound) {
if (in->facetmarkerlist) {
@@ -30552,6 +28863,10 @@ void tetgenmesh::outsubfaces(tetgenio* out)
fprintf(outfile, "%5d %4d %4d %4d", facenumber,
pointmark(torg) - shift, pointmark(tdest) - shift,
pointmark(tapex) - shift);
+ if (b->order == 2) { // -o2
+ fprintf(outfile, " %4d %4d %4d", pointmark(pp[0]) - shift,
+ pointmark(pp[1]) - shift, pointmark(pp[2]) - shift);
+ }
if (!b->nobound) {
fprintf(outfile, " %d", marker);
}
@@ -30564,6 +28879,11 @@ void tetgenmesh::outsubfaces(tetgenio* out)
elist[index++] = pointmark(torg) - shift;
elist[index++] = pointmark(tdest) - shift;
elist[index++] = pointmark(tapex) - shift;
+ if (b->order == 2) { // -o2
+ out->o2facelist[o2index++] = pointmark(pp[0]) - shift;
+ out->o2facelist[o2index++] = pointmark(pp[1]) - shift;
+ out->o2facelist[o2index++] = pointmark(pp[2]) - shift;
+ }
if (!b->nobound) {
emlist[index1++] = marker;
}
@@ -30602,9 +28922,15 @@ void tetgenmesh::outedges(tetgenio* out)
int ishulledge;
int firstindex, shift;
int edgenumber, marker;
- int index, index1;
+ int index = 0, index1 = 0, index2 = 0;
+ int t1ver;
int i;
+ // For -o2 option.
+ point *extralist, pp = NULL;
+ int highorderindex = 11;
+ int o2index = 0;
+
if (out == (tetgenio *) NULL) {
strcpy(edgefilename, b->outfilename);
strcat(edgefilename, ".edge");
@@ -30618,6 +28944,20 @@ void tetgenmesh::outedges(tetgenio* out)
}
}
+ if (meshedges == 0l) {
+ if (nonconvex) {
+ numberedges(); // Count the edges.
+ } else {
+ // Use Euler's characteristic to get the numbe of edges.
+ // It states V - E + F - C = 1, hence E = V + F - C - 1.
+ long tsize = tetrahedrons->items - hullsize;
+ long fsize = (tsize * 4l + hullsize) / 2l;
+ long vsize = points->items - dupverts - unuverts;
+ if (b->weighted) vsize -= nonregularcount;
+ meshedges = vsize + fsize - tsize - 1;
+ }
+ }
+
if (out == (tetgenio *) NULL) {
outfile = fopen(edgefilename, "w");
if (outfile == (FILE *) NULL) {
@@ -30633,14 +28973,18 @@ void tetgenmesh::outedges(tetgenio* out)
printf("Error: Out of memory.\n");
terminatetetgen(1);
}
+ if (b->order == 2) { // -o2 switch
+ out->o2edgelist = new int[meshedges];
+ }
if (!b->nobound) {
out->edgemarkerlist = new int[meshedges];
}
+ if (b->neighout > 1) { // '-nn' switch.
+ out->edgeadjtetlist = new int[meshedges];
+ }
out->numberofedges = meshedges;
elist = out->edgelist;
emlist = out->edgemarkerlist;
- index = 0;
- index1 = 0; // if (!b->nobound)
}
// Determine the first index (0 or 1).
@@ -30654,9 +28998,7 @@ void tetgenmesh::outedges(tetgenio* out)
tetloop.tet = tetrahedrontraverse();
edgenumber = firstindex; // in->firstnumber;
while (tetloop.tet != (tetrahedron *) NULL) {
- // Count the number of Voronoi faces. Look at the six edges of this
- // tet. Count an edge only if this tet's pointer is smaller than
- // those of other non-hull tets which share this edge.
+ // Count the number of Voronoi faces.
worktet.tet = tetloop.tet;
for (i = 0; i < 6; i++) {
worktet.ver = edge2ver[i];
@@ -30674,13 +29016,24 @@ void tetgenmesh::outedges(tetgenio* out)
if (spintet.tet == worktet.tet) {
torg = org(worktet);
tdest = dest(worktet);
+ if (b->order == 2) { // -o2
+ // Get the extra vertex on this edge.
+ extralist = (point *) worktet.tet[highorderindex];
+ pp = extralist[ver2edge[worktet.ver]];
+ }
if (out == (tetgenio *) NULL) {
fprintf(outfile, "%5d %4d %4d", edgenumber,
pointmark(torg) - shift, pointmark(tdest) - shift);
+ if (b->order == 2) { // -o2
+ fprintf(outfile, " %4d", pointmark(pp) - shift);
+ }
} else {
// Output three vertices of this face;
elist[index++] = pointmark(torg) - shift;
elist[index++] = pointmark(tdest) - shift;
+ if (b->order == 2) { // -o2
+ out->o2edgelist[o2index++] = pointmark(pp) - shift;
+ }
}
if (!b->nobound) {
if (b->plc || b->refine) {
@@ -30704,6 +29057,13 @@ void tetgenmesh::outedges(tetgenio* out)
emlist[index1++] = marker;
}
}
+ if (b->neighout > 1) { // '-nn' switch.
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " %d", elemindex(tetloop.tet));
+ } else {
+ out->edgeadjtetlist[index2++] = elemindex(tetloop.tet);
+ }
+ }
if (out == (tetgenio *) NULL) {
fprintf(outfile, "\n");
}
@@ -30737,6 +29097,18 @@ void tetgenmesh::outsubsegments(tetgenio* out)
int marker;
int edgenumber;
+ // For -o2 option.
+ triface workface, spintet;
+ point *extralist, pp = NULL;
+ int highorderindex = 11;
+ int o2index = 0;
+
+ // For -nn option.
+ int neigh = -1;
+ int index2 = 0;
+
+ int t1ver; // used by fsymself()
+
if (out == (tetgenio *) NULL) {
strcpy(edgefilename, b->outfilename);
strcat(edgefilename, ".edge");
@@ -30761,13 +29133,20 @@ void tetgenmesh::outsubsegments(tetgenio* out)
} else {
// Allocate memory for 'edgelist'.
out->edgelist = new int[subsegs->items * 2];
+ out->edgelist = new int[subsegs->items * (b->order == 1 ? 2 : 3)];
if (out->edgelist == (int *) NULL) {
terminatetetgen(1);
}
+ if (b->order == 2) {
+ out->o2edgelist = new int[subsegs->items];
+ }
out->edgemarkerlist = new int[subsegs->items];
if (out->edgemarkerlist == (int *) NULL) {
terminatetetgen(1);
}
+ if (b->neighout > 1) {
+ out->edgeadjtetlist = new int[subsegs->items];
+ }
out->numberofedges = subsegs->items;
elist = out->edgelist;
}
@@ -30787,18 +29166,64 @@ void tetgenmesh::outsubsegments(tetgenio* out)
while (edgeloop.sh != (shellface *) NULL) {
torg = sorg(edgeloop);
tdest = sdest(edgeloop);
+ if ((b->order == 2) || (b->neighout > 1)) {
+ sstpivot1(edgeloop, workface);
+ if (workface.tet != NULL) {
+ // We must find a non-hull tet.
+ if (ishulltet(workface)) {
+ spintet = workface;
+ while (1) {
+ fnextself(spintet);
+ if (!ishulltet(spintet)) break;
+ if (spintet.tet == workface.tet) break;
+ }
+ assert(!ishulltet(spintet));
+ workface = spintet;
+ }
+ }
+ }
+ if (b->order == 2) { // -o2
+ // Get the extra vertex on this edge.
+ if (workface.tet != NULL) {
+ extralist = (point *) workface.tet[highorderindex];
+ pp = extralist[ver2edge[workface.ver]];
+ } else {
+ pp = torg; // There is no extra node available.
+ }
+ }
+ if (b->neighout > 1) { // -nn
+ if (workface.tet != NULL) {
+ neigh = elemindex(workface.tet);
+ } else {
+ neigh = -1;
+ }
+ }
marker = shellmark(edgeloop);
if (marker == 0) {
marker = 1; // Default marker of a boundary edge is 1.
}
if (out == (tetgenio *) NULL) {
- fprintf(outfile, "%5d %4d %4d %d\n", edgenumber,
- pointmark(torg) - shift, pointmark(tdest) - shift, marker);
+ fprintf(outfile, "%5d %4d %4d", edgenumber,
+ pointmark(torg) - shift, pointmark(tdest) - shift);
+ if (b->order == 2) { // -o2
+ fprintf(outfile, " %4d", pointmark(pp) - shift);
+ }
+ fprintf(outfile, " %d", marker);
+ if (b->neighout > 1) { // -nn
+ fprintf(outfile, " %4d", neigh);
+ }
+ fprintf(outfile, "\n");
} else {
// Output three vertices of this face;
elist[index++] = pointmark(torg) - shift;
elist[index++] = pointmark(tdest) - shift;
+ if (b->order == 2) { // -o2
+ out->o2edgelist[o2index++] = pointmark(pp) - shift;
+ }
out->edgemarkerlist[i++] = marker;
+ if (b->neighout > 1) { // -nn
+ out->edgeadjtetlist[index2++] = neigh;
+ }
}
edgenumber++;
edgeloop.sh = shellfacetraverse(subsegs);
@@ -30912,6 +29337,12 @@ void tetgenmesh::outneighbors(tetgenio* out)
// internal Delaunay vertex. It is an unbounded polyhedron for a Delaunay //
// vertex belonging to the convex hull. //
// //
+// aunay tetrahedralization - the power diagram - of the weighted point set. //
+// Note that the vertices of the power disgram are the centers of the ortho- //
+// spheres of the tetrahedra. //
+// //
+// NOTE: This routine is only used when the input is only a set of point. //
+// //
// Comment: Special thanks to Victor Liu for finding and fixing few bugs. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -30934,6 +29365,8 @@ void tetgenmesh::outvoronoi(tetgenio* out)
int index, shift, end1, end2;
int i, j;
+ int t1ver; // used by fsymself()
+
// Output Voronoi vertices to .v.node file.
if (out == (tetgenio *) NULL) {
strcpy(outfilename, b->outfilename);
@@ -30974,8 +29407,9 @@ void tetgenmesh::outvoronoi(tetgenio* out)
// The number of Delaunay faces (Voronoi edges).
faces = (4l * ntets + hullsize) / 2l;
// The number of Delaunay edges (Voronoi faces).
- // edges = points->items + faces - ntets - 1;
- edges = meshedges; // Counted in outelements() or numberedges();
+ long vsize = points->items - dupverts - unuverts;
+ if (b->weighted) vsize -= nonregularcount;
+ edges = vsize + faces - ntets - 1;
if (out == (tetgenio *) NULL) {
outfile = fopen(outfilename, "w");
@@ -31004,7 +29438,12 @@ void tetgenmesh::outvoronoi(tetgenio* out)
pt[i] = (point) tetloop.tet[4 + i];
setpoint2tet(pt[i], encode(tetloop));
}
- circumsphere(pt[0], pt[1], pt[2], pt[3], ccent, NULL);
+ if (b->weighted) {
+ orthosphere(pt[0], pt[1], pt[2], pt[3], pt[0][3], pt[1][3], pt[2][3],
+ pt[3][3], ccent, NULL);
+ } else {
+ circumsphere(pt[0], pt[1], pt[2], pt[3], ccent, NULL);
+ }
if (out == (tetgenio *) NULL) {
fprintf(outfile, "%4d %16.8e %16.8e %16.8e\n", vpointcount + shift,
ccent[0], ccent[1], ccent[2]);
@@ -31277,7 +29716,8 @@ void tetgenmesh::outvoronoi(tetgenio* out)
vpointcount = 0;
while (ploop != (point) NULL) {
if ((pointtype(ploop) != UNUSEDVERTEX) &&
- (pointtype(ploop) != DUPLICATEDVERTEX)) {
+ (pointtype(ploop) != DUPLICATEDVERTEX) &&
+ (pointtype(ploop) != NREGULARVERTEX)) {
getvertexstar(1, ploop, tetlist, ptlist, NULL);
// Mark all vertices. Check if it is a hull vertex.
ishullvert = 0;
@@ -31337,14 +29777,6 @@ void tetgenmesh::outvoronoi(tetgenio* out)
if (out == (tetgenio *) NULL) {
fprintf(outfile, "\n");
}
- // DEBUG BEGIN
- for (i = 0; i < ptlist->objects; i++) {
- neipt = * (point *) fastlookup(ptlist, i);
- if (neipt != dummypoint) {
- assert(!pinfected(neipt));
- }
- }
- // DEBUG END
tetlist->restart();
ptlist->restart();
vpointcount++;
@@ -31583,13 +30015,18 @@ void tetgenmesh::outmesh2medit(char* mfilename)
tetrahedrons->traversalinit();
tetptr = tetrahedrontraverse();
while (tetptr != (tetrahedron *) NULL) {
- p1 = (point) tetptr[4];
- p2 = (point) tetptr[5];
+ if (!b->reversetetori) {
+ p1 = (point) tetptr[4];
+ p2 = (point) tetptr[5];
+ } else {
+ p1 = (point) tetptr[5];
+ p2 = (point) tetptr[4];
+ }
p3 = (point) tetptr[6];
p4 = (point) tetptr[7];
fprintf(outfile, "%5d %5d %5d %5d",
pointmark(p1), pointmark(p2), pointmark(p3), pointmark(p4));
- if (in->numberoftetrahedronattributes > 0) {
+ if (numelemattrib > 0) {
fprintf(outfile, " %.17g", elemattribute(tetptr, 0));
} else {
fprintf(outfile, " 0");
@@ -31639,7 +30076,7 @@ void tetgenmesh::outmesh2vtk(char* ofilename)
{
FILE *outfile;
char vtkfilename[FILENAMESIZE];
- point pointloop;
+ point pointloop, p1, p2, p3, p4;
tetrahedron* tptr;
double x, y, z;
int n1, n2, n3, n4;
@@ -31698,10 +30135,15 @@ void tetgenmesh::outmesh2vtk(char* ofilename)
return;
}
while (tptr != (tetrahedron *) NULL) {
- point p1 = (point) tptr[4];
- point p2 = (point) tptr[5];
- point p3 = (point) tptr[6];
- point p4 = (point) tptr[7];
+ if (!b->reversetetori) {
+ p1 = (point) tptr[4];
+ p2 = (point) tptr[5];
+ } else {
+ p1 = (point) tptr[5];
+ p2 = (point) tptr[4];
+ }
+ p3 = (point) tptr[6];
+ p4 = (point) tptr[7];
n1 = pointmark(p1) - in->firstnumber;
n2 = pointmark(p2) - in->firstnumber;
n3 = pointmark(p3) - in->firstnumber;
@@ -31756,186 +30198,149 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
tetgenio *addin, tetgenio *bgmin)
{
tetgenmesh m;
- clock_t tv[17]; // Timing informations (defined in time.h)
+ clock_t tv[10], ts[5]; // Timing informations (defined in time.h)
+ REAL cps = (REAL) CLOCKS_PER_SEC;
tv[0] = clock();
m.b = b;
m.in = in;
+ m.addin = addin;
- if ((bgmin != NULL) &&
- ((bgmin->numberofpoints > 0) && (bgmin->pointmtrlist != NULL))) {
+ if ((b->metric) && (bgmin->numberofpoints > 0)) {
m.bgm = new tetgenmesh(); // Create an empty background mesh.
m.bgm->b = b;
m.bgm->in = bgmin;
}
-#ifdef INEXACT_GEOM_PRED
- if (!b->quiet) {
- printf("Using inexact geometric predicates.\n");
- }
-#else
- exactinit();
-#endif
-
m.initializepools();
m.transfernodes();
+ exactinit(b->verbose, b->noexact, b->nostaticfilter,
+ m.xmax - m.xmin, m.ymax - m.ymin, m.zmax - m.zmin);
+
tv[1] = clock();
if (b->refine) {
m.reconstructmesh();
} else { // b->plc
- if (!b->diagnose) {
- m.incrementaldelaunay(tv[16]);
- }
+ m.incrementaldelaunay(ts[0]);
}
tv[2] = clock();
if (!b->quiet) {
if (b->refine) {
- printf("Mesh reconstruction seconds: %g\n",
- (tv[2] - tv[1]) / (REAL) CLOCKS_PER_SEC);
+ printf("Mesh reconstruction seconds: %g\n", ((REAL)(tv[2]-tv[1])) / cps);
} else {
- if (!b->diagnose) {
- printf("Delaunay seconds: %g\n",
- (tv[2] - tv[1]) / (REAL) CLOCKS_PER_SEC);
- if (b->verbose) {
- printf(" Point sorting seconds: %g\n",
- (tv[16] - tv[1]) / (REAL) CLOCKS_PER_SEC);
-#ifdef WITH_RUNTIME_COUNTERS
- printf(" Point location seconds: %g\n",
- m.t_ptloc / (REAL) CLOCKS_PER_SEC);
- printf(" Point insertion seconds: %g\n",
- m.t_ptinsert / (REAL) CLOCKS_PER_SEC);
-#endif
- }
+ printf("Delaunay seconds: %g\n", ((REAL)(tv[2]-tv[1])) / cps);
+ if (b->verbose) {
+ printf(" Point sorting seconds: %g\n", ((REAL)(ts[0]-tv[1])) / cps);
}
}
}
- if (b->plc) {
+ if (b->plc) { // -p
m.meshsurface();
- }
- tv[3] = clock();
+ ts[0] = clock();
- if (!b->quiet) {
- if (b->plc) {
- printf("Surface mesh seconds: %g\n",
- (tv[3] - tv[2]) / (REAL) CLOCKS_PER_SEC);
+ if (!b->quiet) {
+ printf("Surface mesh seconds: %g\n", ((REAL)(ts[0]-tv[2])) / cps);
+ }
+
+ if (b->diagnose) { // -d
+ m.detectinterfaces();
+
+ ts[1] = clock();
+
+ if (!b->quiet) {
+ printf("Self-intersection seconds: %g\n", ((REAL)(ts[1]-ts[0])) / cps);
+ }
+
+ // Only output when self-intersecting faces exist.
+ if (m.subfaces->items > 0l) {
+ m.outnodes(out);
+ m.outsubfaces(out);
+ }
+
+ return;
}
}
- if (b->plc && b->diagnose) { // -d
- m.detectinterfaces();
+ tv[3] = clock();
+
+ if ((b->metric) && (m.bgm != NULL)) { // -m
+ m.bgm->initializepools();
+ m.bgm->transfernodes();
+ m.bgm->reconstructmesh();
- tv[4] = clock();
+ ts[0] = clock();
if (!b->quiet) {
- printf("Self-intersection seconds: %g\n",
- (tv[4] - tv[3]) / (REAL) CLOCKS_PER_SEC);
+ printf("Background mesh reconstruct seconds: %g\n",
+ ((REAL)(ts[0] - tv[3])) / cps);
}
- // Only output when self-intersecting faces exist.
- if (m.subfaces->items > 0l) {
- m.outnodes(out);
- m.outsubfaces(out);
- }
+ if (b->metric) { // -m
+ m.interpolatemeshsize();
- return;
- }
+ ts[1] = clock();
- if (b->plc) {
- if (b->nobisect) { // with -Y option
- m.recoverboundary(tv[15]);
- } else {
- m.constraineddelaunay(tv[15]);
+ if (!b->quiet) {
+ printf("Size interpolating seconds: %g\n",((REAL)(ts[1]-ts[0])) / cps);
+ }
}
}
tv[4] = clock();
- if (!b->quiet) {
- if (b->plc) {
- printf("Boundary recovery seconds: %g\n",
- (tv[4] - tv[3]) / (REAL) CLOCKS_PER_SEC);
+ if (b->plc) { // -p
+ if (b->nobisect) { // -Y
+ m.recoverboundary(ts[0]);
+ } else {
+ m.constraineddelaunay(ts[0]);
+ }
+
+ ts[1] = clock();
+
+ if (!b->quiet) {
+ printf("Boundary recovery seconds: %g\n", ((REAL)(ts[1]-tv[4])) / cps);
if (b->verbose) {
- printf(" Segment recovery seconds: %g\n",
- (tv[15] - tv[3]) / (REAL) CLOCKS_PER_SEC);
- printf(" Facet recovery seconds: %g\n",
- (tv[4] - tv[15]) / (REAL) CLOCKS_PER_SEC);
+ printf(" Segment recovery seconds: %g\n",((REAL)(ts[0]-tv[4]))/ cps);
+ printf(" Facet recovery seconds: %g\n", ((REAL)(ts[1]-ts[0])) / cps);
}
}
- }
- if (b->plc && !b->convex) {
m.carveholes();
- }
- tv[5] = clock();
+ ts[2] = clock();
- if (!b->quiet) {
- if (b->plc && !b->convex) {
+ if (!b->quiet) {
printf("Exterior tets removal seconds: %g\n",
- (tv[5] - tv[4]) / (REAL) CLOCKS_PER_SEC);
- }
- }
-
- if (b->plc && b->nobisect) {
- m.suppresssteinerpoints();
- }
-
- tv[6] = clock();
-
- if (!b->quiet) {
- if (b->plc && b->nobisect) {
- printf("Steiner suppression seconds: %g\n",
- (tv[6] - tv[5]) / (REAL) CLOCKS_PER_SEC);
+ ((REAL)(ts[2]-ts[1])) / cps);
}
- }
- if (b->plc && b->nobisect) {
- m.recoverdelaunay();
- }
+ if (b->nobisect) { // -Y
+ m.suppresssteinerpoints();
- tv[7] = clock();
+ ts[3] = clock();
- if (!b->quiet) {
- if (b->plc && b->nobisect) {
- printf("Delaunay recovery seconds: %g\n",
- (tv[7] - tv[6]) / (REAL) CLOCKS_PER_SEC);
- }
- }
+ if (!b->quiet) {
+ printf("Steiner suppression seconds: %g\n",((REAL)(ts[3]-ts[2]))/cps);
+ }
- if ((b->plc || b->refine) && (b->metric && (m.bgm != NULL))) {
- m.bgm->initializepools();
- m.bgm->transfernodes();
- m.bgm->reconstructmesh();
- }
+ m.recoverdelaunay();
- tv[8] = clock();
+ ts[4] = clock();
- if (!b->quiet) {
- if ((b->plc || b->refine) && (b->metric && (m.bgm != NULL))) {
- printf("Background mesh reconstruct seconds: %g\n",
- (tv[8] - tv[7]) / (REAL) CLOCKS_PER_SEC);
+ if (!b->quiet) {
+ printf("Delaunay recovery seconds: %g\n", ((REAL)(ts[4]-ts[3])) / cps);
+ }
}
}
- if ((b->plc || b->refine) && (b->metric && (m.bgm != NULL))) {
- m.interpolatemeshsize();
- }
-
- tv[9] = clock();
-
- if (!b->quiet) {
- if ((b->plc || b->refine) && (b->metric && (m.bgm != NULL))) {
- printf("Size interpolating seconds: %g\n",
- (tv[9] - tv[8]) / (REAL) CLOCKS_PER_SEC);
- }
- }
+ tv[5] = clock();
if ((b->plc || b->refine) && b->insertaddpoints) { // -i
if ((addin != NULL) && (addin->numberofpoints > 0)) {
@@ -31943,44 +30348,38 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
}
}
- tv[10] = clock();
+ tv[6] = clock();
if (!b->quiet) {
if ((b->plc || b->refine) && b->insertaddpoints) {
if ((addin != NULL) && (addin->numberofpoints > 0)) {
- printf("Constrained points seconds: %g\n",
- (tv[10] - tv[9]) / (REAL) CLOCKS_PER_SEC);
+ printf("Constrained points seconds: %g\n", ((REAL)(tv[6]-tv[5]))/cps);
}
}
}
- tv[11] = clock();
-
-
- if ((b->plc || b->refine) && b->quality) {
+ if (b->quality) {
m.delaunayrefinement();
}
- tv[12] = clock();
+ tv[7] = clock();
if (!b->quiet) {
- if ((b->plc || b->refine) && b->quality) {
- printf("Refinement seconds: %g\n",
- (tv[12] - tv[11]) / (REAL) CLOCKS_PER_SEC);
+ if (b->quality) {
+ printf("Refinement seconds: %g\n", ((REAL)(tv[7] - tv[6])) / cps);
}
}
- if ((b->plc || b->refine) && (b->optlevel > 0)) {
- m.optimizemesh(1);
+ if ((b->plc || b->refine) && (b->optlevel > 0) && !b->conforming) {
+ m.optimizemesh();
}
- tv[13] = clock();
+ tv[8] = clock();
if (!b->quiet) {
- if ((b->plc || b->refine) && (b->optlevel > 0)) {
- printf("Optimization seconds: %g\n",
- (tv[13] - tv[12]) / (REAL) CLOCKS_PER_SEC);
+ if ((b->plc || b->refine) && (b->optlevel > 0) && !b->conforming) {
+ printf("Optimization seconds: %g\n", ((REAL)(tv[8] - tv[7])) / cps);
}
}
@@ -31989,6 +30388,9 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.jettisonnodes();
}
+ if (b->order == 2) {
+ m.highorder();
+ }
if (!b->quiet) {
printf("\n");
@@ -32007,11 +30409,10 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.outnodes(out);
}
- if (b->noelewritten == 1) {
+ if (b->noelewritten) {
if (!b->quiet) {
printf("NOT writing an .ele file.\n");
}
- m.numberedges();
} else {
if (m.tetrahedrons->items > 0l) {
m.outelements(out);
@@ -32041,11 +30442,17 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
}
- if (b->edgesout) {
- if (b->edgesout > 1) {
- m.outedges(out); // -ee, output all mesh edges.
+ if (b->nofacewritten) {
+ if (!b->quiet) {
+ printf("NOT writing an .edge file.\n");
+ }
+ } else {
+ if (b->edgesout) { // -e
+ m.outedges(out); // output all mesh edges.
} else {
- m.outsubsegments(out); // -e, only output subsegments.
+ if (b->plc || b->refine) {
+ m.outsubsegments(out); // output subsegments.
+ }
}
}
@@ -32078,13 +30485,11 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
}
- tv[14] = clock();
+ tv[9] = clock();
if (!b->quiet) {
- printf("\nOutput seconds: %g\n",
- (tv[14] - tv[13]) / (REAL) CLOCKS_PER_SEC);
- printf("Total running seconds: %g\n",
- (tv[14] - tv[0]) / (REAL) CLOCKS_PER_SEC);
+ printf("\nOutput seconds: %g\n", ((REAL)(tv[9] - tv[8])) / cps);
+ printf("Total running seconds: %g\n", ((REAL)(tv[9] - tv[0])) / cps);
}
if (b->docheck) {
diff --git a/contrib/Tetgen1.5/tetgen.h b/contrib/Tetgen1.5/tetgen.h
index 41634d03f4..664ddc3f77 100644
--- a/contrib/Tetgen1.5/tetgen.h
+++ b/contrib/Tetgen1.5/tetgen.h
@@ -2,21 +2,17 @@
// //
// TetGen //
// //
-// A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator //
+// A Quality Tetrahedral Mesh Generator and A 3D Delaunay Triangulator //
// //
// Version 1.5 //
-// February 21, 2012 //
+// (March 27, 2013) //
// //
-// PRE-RELEASE TEST CODE. //
-// PLEASE DO NOT DISTRIBUTE !! //
-// PLEASE HELP ME TO IMPROVE IT !! //
-// //
-// Copyright (C) 2002--2012 //
+// Copyright (C) 2002--2013 //
// Hang Si //
// Research Group: Numerical Mathematics and Scientific Computing //
// Weierstrass Institute for Applied Analysis and Stochastics (WIAS) //
// Mohrenstr. 39, 10117 Berlin, Germany //
-// Hang.Si@wias-berlin.de //
+// si@wias-berlin.de //
// //
// TetGen is freely available through the website: http://www.tetgen.org. //
// It may be copied, modified, and redistributed for non-commercial use. //
@@ -28,46 +24,51 @@
#ifndef tetgenH
#define tetgenH
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <math.h>
-#include <time.h>
-#include <assert.h>
-
// To compile TetGen as a library instead of an executable program, define
// the TETLIBRARY symbol.
// #define TETLIBRARY
-// Uncomment the following line to disable assert macros. These macros are
-// inserted in places where I hope to catch bugs.
+// Uncomment the following line to disable assert macros. These macros were
+// inserted in the code where I hoped to catch bugs. They may slow down the
+// speed of TetGen.
// #define NDEBUG
-// To insert lots of self-checks for internal errors, define the SELF_CHECK
-// symbol. This will slow down the program a bit.
+// TetGen default uses the double precision (64 bit) for a real number.
+// Alternatively, one can use the single precision (32 bit) 'float' if the
+// memory is limited.
-// #define SELF_CHECK
+#define REAL double // #define REAL float
-// Default, TetGen uses the double precision for a real number.
+// Maximum number of characters in a file name (including the null).
-#define REAL double
+#define FILENAMESIZE 1024
-// The types 'intptr_t' and 'uintptr_t' are signed and unsigned integer types,
-// respectively. They are guaranteed to be the same width as a pointer.
-// They are defined in <stdint.h> by the C99 Standard.
-// However, Microsoft Visual C++ doesn't ship with this header file yet. We
-// need to define them.
-// Thanks to Steven G. Johnson (MIT) for the following code.
+// Maximum number of chars in a line read from a file (including the null).
-// Define the _MSC_VER symbol if you are using Microsoft Visual C++.
+#define INPUTLINESIZE 2048
-// #define _MSC_VER
+// TetGen only uses the C standard library.
-// Define the _WIN64 symbol if you are running TetGen on Win64.
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <time.h>
+#include <assert.h>
-// #define _WIN64
+// The types 'intptr_t' and 'uintptr_t' are signed and unsigned integer types,
+// respectively. They are guaranteed to be the same width as a pointer.
+// They are defined in <stdint.h> by the C99 Standard. However, Microsoft
+// Visual C++ 2003 -- 2008 (Visual C++ 7.1 - 9) doesn't ship with this header
+// file. In such case, we can define them by ourself.
+// Update (learned from Stack Overflow): Visual Studio 2010 and Visual C++ 2010
+// Express both have stdint.h
+
+// The following piece of code was provided by Steven Johnson (MIT). Define the
+// symbol _MSC_VER if you are using Microsoft Visual C++. Moreover, define
+// the _WIN64 symbol if you are running TetGen on Win64 systems.
#ifdef _MSC_VER // Microsoft Visual C++
# ifdef _WIN64
@@ -81,23 +82,31 @@
# include <stdint.h>
#endif
-// Maximum number of characters in a file name (including the null).
-
-#define FILENAMESIZE 1024
-
-// Maximum number of chars in a line read from a file (including the null).
-
-#define INPUTLINESIZE 2048
-
///////////////////////////////////////////////////////////////////////////////
// //
// tetgenio //
// //
-// A structure for transfering data into and out of TetGen. //
+// A structure for transfering data into and out of TetGen's mesh structure, //
+// 'tetgenmesh' (declared below). //
+// //
+// The input of TetGen is either a 3D point set, or a 3D piecewise linear //
+// complex (PLC), or a tetrahedral mesh. Depending on the input object and //
+// the specified options, the output of TetGen is either a Delaunay (or wei- //
+// ghted Delaunay) tetrahedralization, or a constrained (Delaunay) tetrahed- //
+// ralization, or a quality tetrahedral mesh. //
+// //
+// A piecewise linear complex (PLC) represents a 3D polyhedral domain with //
+// possibly internal boundaries(subdomains). It is introduced in [Miller et //
+// al, 1996]. Basically it is a set of "cells", i.e., vertices, edges, poly- //
+// gons, and polyhedra, and the inetrsection of any two of its cells is the //
+// union of other cells of it. //
// //
-// It holds a collection of arrays of data, i.e., points, facets, tetrahedra,//
-// and so forth. It contains functions to read and write (input and output) //
-// files of TetGen as well as other supported mesh files. //
+// TetGen uses a set of files to describe the inputs and outputs. Each file //
+// is identified from its file extension (.node, .ele, .face, .edge, etc). //
+// //
+// The 'tetgenio' structure is a collection of arrays of data, i.e., points, //
+// facets, tetrahedra, and so forth. It contains functions to read and write //
+// (input and output) files of TetGen as well as other supported mesh files. //
// //
// Once an object of tetgenio is declared, no array is created. One has to //
// allocate enough memory for them. On deletion of this object, the memory //
@@ -114,18 +123,18 @@ class tetgenio {
public:
// A "polygon" describes a simple polygon (no holes). It is not necessarily
- // convex. Each polygon contains number of corners (points) and the same
- // number of sides (edges).
- // Note that the points of the polygon must be given in either counter-
- // clockwise or clockwise order and they form a ring, so every two
- // consective points forms an edge of the polygon.
+ // convex. Each polygon contains a number of corners (points) and the same
+ // number of sides (edges). The points of the polygon must be given in
+ // either counterclockwise or clockwise order and they form a ring, so
+ // every two consective points forms an edge of the polygon.
typedef struct {
int *vertexlist;
int numberofvertices;
} polygon;
- // A "facet" describes a facet. Each facet is a polygonal region possibly
- // with holes, edges, and points in it.
+ // A "facet" describes a polygonal region possibly with holes, edges, and
+ // points floating in it. Each facet consists of a list of polygons and
+ // a list of hole points (which lie strictly inside holes).
typedef struct {
polygon *polygonlist;
int numberofpolygons;
@@ -157,19 +166,6 @@ public:
int *elist;
} vorofacet;
- // The periodic boundary condition group data structure. A "pbcgroup"
- // contains the definition of a pbc and the list of pbc point pairs.
- // 'fmark1' and 'fmark2' are the facetmarkers of the two pbc facets f1
- // and f2, respectively. 'transmat' is the transformation matrix which
- // maps a point in f1 into f2. An array of pbc point pairs are saved
- // in 'pointpairlist'. The first point pair is at indices [0] and [1],
- // followed by remaining pairs. Two integers per pair.
- typedef struct {
- int fmark1, fmark2;
- REAL transmat[4][4];
- int numberofpointpairs;
- int *pointpairlist;
- } pbcgroup;
// Additional parameters associated with an input (or mesh) vertex.
// These informations are provided by CAD libraries.
@@ -179,9 +175,6 @@ public:
int type; // 0, 1, or 2.
} pointparam;
- // A callback function for mesh refinement.
- typedef bool (* TetSizeFunc)(REAL*, REAL*, REAL*, REAL*, REAL*, REAL);
-
// Callback functions for meshing PSCs.
typedef REAL (* GetVertexParamOnEdge)(void*, int, int);
typedef void (* GetSteinerOnEdge)(void*, int, REAL, REAL*);
@@ -189,6 +182,9 @@ public:
typedef void (* GetEdgeSteinerParamOnFace)(void*, int, REAL, int, REAL*);
typedef void (* GetSteinerOnFace)(void*, int, REAL*, REAL*);
+ // A callback function for mesh refinement.
+ typedef bool (* TetSizeFunc)(REAL*, REAL*, REAL*, REAL*, REAL*, REAL);
+
// Items are numbered starting from 'firstnumber' (0 or 1), default is 0.
int firstnumber;
@@ -206,95 +202,108 @@ public:
// attributes occupy 'numberofpointattributes' REALs.
// 'pointmtrlist': An array of metric tensors at points. Each point's
// tensor occupies 'numberofpointmtr' REALs.
- // `pointmarkerlist': An array of point markers; one integer per point.
+ // 'pointmarkerlist': An array of point markers; one integer per point.
REAL *pointlist;
REAL *pointattributelist;
REAL *pointmtrlist;
- int *pointmarkerlist;
+ int *pointmarkerlist;
pointparam *pointparamlist;
int numberofpoints;
int numberofpointattributes;
int numberofpointmtrs;
- // `elementlist': An array of element (triangle or tetrahedron) corners.
- // The first element's first corner is at index [0], followed by its
- // other corners in counterclockwise order, followed by any other
- // nodes if the element represents a nonlinear element. Each element
- // occupies `numberofcorners' ints.
- // `elementattributelist': An array of element attributes. Each
- // element's attributes occupy `numberofelementattributes' REALs.
- // `elementconstraintlist': An array of constraints, i.e. triangle's
- // area or tetrahedron's volume; one REAL per element. Input only.
- // `neighborlist': An array of element neighbors; 3 or 4 ints per
- // element. Output only.
- int *tetrahedronlist;
+ // 'tetrahedronlist': An array of tetrahedron corners. The first
+ // tetrahedron's first corner is at index [0], followed by its other
+ // corners, followed by six nodes on the edges of the tetrahedron if the
+ // second order option (-o2) is applied. Each tetrahedron occupies
+ // 'numberofcorners' ints. The second order nodes are ouput only.
+ // 'tetrahedronattributelist': An array of tetrahedron attributes. Each
+ // tetrahedron's attributes occupy 'numberoftetrahedronattributes' REALs.
+ // 'tetrahedronvolumelist': An array of constraints, i.e. tetrahedron's
+ // volume; one REAL per element. Input only.
+ // 'neighborlist': An array of tetrahedron neighbors; 4 ints per element.
+ // Output only.
+ int *tetrahedronlist;
REAL *tetrahedronattributelist;
REAL *tetrahedronvolumelist;
- int *neighborlist;
+ int *neighborlist;
int numberoftetrahedra;
int numberofcorners;
int numberoftetrahedronattributes;
- // `facetlist': An array of facets. Each entry is a structure of facet.
- // `facetmarkerlist': An array of facet markers; one int per facet.
+ // 'facetlist': An array of facets. Each entry is a structure of facet.
+ // 'facetmarkerlist': An array of facet markers; one int per facet.
facet *facetlist;
int *facetmarkerlist;
int numberoffacets;
- // `holelist': An array of holes. The first hole's x, y and z
- // coordinates are at indices [0], [1] and [2], followed by the
- // remaining holes. Three REALs per hole.
+ // 'holelist': An array of holes (in volume). Each hole is given by a
+ // seed (point) which lies strictly inside it. The first seed's x, y and z
+ // coordinates are at indices [0], [1] and [2], followed by the
+ // remaining seeds. Three REALs per hole.
REAL *holelist;
int numberofholes;
- // `regionlist': An array of regional attributes and volume constraints.
- // The first constraint's x, y and z coordinates are at indices [0],
- // [1] and [2], followed by the regional attribute at index [3], foll-
- // owed by the maximum volume at index [4]. Five REALs per constraint.
- // Note that each regional attribute is used only if you select the `A'
+ // 'regionlist': An array of regions (subdomains). Each region is given by
+ // a seed (point) which lies strictly inside it. The first seed's x, y and
+ // z coordinates are at indices [0], [1] and [2], followed by the regional
+ // attribute at index [3], followed by the maximum volume at index [4].
+ // Five REALs per region.
+ // Note that each regional attribute is used only if you select the 'A'
// switch, and each volume constraint is used only if you select the
- // `a' switch (with no number following).
+ // 'a' switch (with no number following).
REAL *regionlist;
int numberofregions;
- // `facetconstraintlist': An array of facet maximal area constraints.
- // Two REALs per constraint. The first (at index [0]) is the facet
- // marker (cast it to int), the second (at index [1]) is its maximum
- // area bound.
+ // 'facetconstraintlist': An array of facet constraints. Each constraint
+ // specifies a maximum area bound on the subfaces of that facet. The
+ // first facet constraint is given by a facet marker at index [0] and its
+ // maximum area bound at index [1], followed by the remaining facet con-
+ // straints. Two REALs per facet constraint. Note: the facet marker is
+ // actually an integer.
REAL *facetconstraintlist;
int numberoffacetconstraints;
- // `segmentconstraintlist': An array of segment max. length constraints.
- // Three REALs per constraint. The first two (at indcies [0] and [1])
- // are the indices of the endpoints of the segment, the third (at index
- // [2]) is its maximum length bound.
+ // 'segmentconstraintlist': An array of segment constraints. Each constraint
+ // specifies a maximum length bound on the subsegments of that segment.
+ // The first constraint is given by the two endpoints of the segment at
+ // index [0] and [1], and the maximum length bound at index [2], followed
+ // by the remaining segment constraints. Three REALs per constraint.
+ // Note the segment endpoints are actually integers.
REAL *segmentconstraintlist;
int numberofsegmentconstraints;
- // 'pbcgrouplist': An array of periodic boundary condition groups.
- pbcgroup *pbcgrouplist;
- int numberofpbcgroups;
-
- // `trifacelist': An array of triangular face endpoints. The first
- // face's endpoints are at indices [0], [1] and [2], followed by the
- // remaining faces. Three ints per face.
- // `adjtetlist': An array of adjacent tetrahedra to the faces of
- // trifacelist. Each face has at most two adjacent tets, the first
- // face's adjacent tets are at [0], [1]. Two ints per face. A '-1'
- // indicates outside (no adj. tet). This list is output when '-nn'
- // switch is used.
- // `trifacemarkerlist': An array of face markers; one int per face.
+
+ // 'trifacelist': An array of face (triangle) corners. The first face's
+ // three corners are at indices [0], [1] and [2], followed by the remaining
+ // faces. Three ints per face.
+ // 'trifacemarkerlist': An array of face markers; one int per face.
+ // 'o2facelist': An array of second order nodes (on the edges) of the face.
+ // It is output only if the second order option (-o2) is applied. The
+ // first face's three second order nodes are at [0], [1], and [2],
+ // followed by the remaining faces. Three ints per face.
+ // 'adjtetlist': An array of adjacent tetrahedra to the faces. The first
+ // face's two adjacent tetrahedra are at indices [0] and [1], followed by
+ // the remaining faces. A '-1' indicates outside (no adj. tet). This list
+ // is output when '-nn' switch is used. Output only.
int *trifacelist;
- int *adjtetlist;
int *trifacemarkerlist;
+ int *o2facelist;
+ int *adjtetlist;
int numberoftrifaces;
- // `edgelist': An array of edge endpoints. The first edge's endpoints
- // are at indices [0] and [1], followed by the remaining edges. Two
- // ints per edge.
- // `edgemarkerlist': An array of edge markers; one int per edge.
+ // 'edgelist': An array of edge endpoints. The first edge's endpoints
+ // are at indices [0] and [1], followed by the remaining edges.
+ // Two ints per edge.
+ // 'edgemarkerlist': An array of edge markers; one int per edge.
+ // 'o2edgelist': An array of midpoints of edges. It is output only if the
+ // second order option (-o2) is applied. One int per edge.
+ // 'edgeadjtetlist': An array of adjacent tetrahedra to the edges. One
+ // tetrahedron (an integer) per edge.
int *edgelist;
int *edgemarkerlist;
+ int *o2edgelist;
+ int *edgeadjtetlist;
int numberofedges;
// 'vpointlist': An array of Voronoi vertex coordinates (like pointlist).
@@ -312,9 +321,6 @@ public:
int numberofvfacets;
int numberofvcells;
- // A callback function.
- TetSizeFunc tetunsuitable;
-
// Variable (and callback functions) for meshing PSCs.
void *geomhandle;
GetVertexParamOnEdge getvertexparamonedge;
@@ -323,6 +329,9 @@ public:
GetEdgeSteinerParamOnFace getedgesteinerparamonface;
GetSteinerOnFace getsteineronface;
+ // A callback function.
+ TetSizeFunc tetunsuitable;
+
// Input & output routines.
bool load_node_call(FILE* infile, int markers, int uvflag, char*);
bool load_node(char*);
@@ -370,8 +379,8 @@ public:
// Initialize routine.
void initialize()
{
- firstnumber = 0; // Default item index is numbered from Zero.
- mesh_dim = 3; // Default mesh dimension is 3.
+ firstnumber = 0;
+ mesh_dim = 3;
useindex = 1;
pointlist = (REAL *) NULL;
@@ -388,22 +397,25 @@ public:
tetrahedronvolumelist = (REAL *) NULL;
neighborlist = (int *) NULL;
numberoftetrahedra = 0;
- numberofcorners = 4; // Default is 4 nodes per element.
+ numberofcorners = 4;
numberoftetrahedronattributes = 0;
trifacelist = (int *) NULL;
- adjtetlist = (int *) NULL;
trifacemarkerlist = (int *) NULL;
+ o2facelist = (int *) NULL;
+ adjtetlist = (int *) NULL;
numberoftrifaces = 0;
- facetlist = (facet *) NULL;
- facetmarkerlist = (int *) NULL;
- numberoffacets = 0;
-
edgelist = (int *) NULL;
edgemarkerlist = (int *) NULL;
+ o2edgelist = (int *) NULL;
+ edgeadjtetlist = (int *) NULL;
numberofedges = 0;
+ facetlist = (facet *) NULL;
+ facetmarkerlist = (int *) NULL;
+ numberoffacets = 0;
+
holelist = (REAL *) NULL;
numberofholes = 0;
@@ -415,8 +427,6 @@ public:
segmentconstraintlist = (REAL *) NULL;
numberofsegmentconstraints = 0;
- pbcgrouplist = (pbcgroup *) NULL;
- numberofpbcgroups = 0;
vpointlist = (REAL *) NULL;
vedgelist = (voroedge *) NULL;
@@ -437,17 +447,12 @@ public:
getsteineronface = NULL;
}
- // Free the memory allocated in 'tetgenio'.
+ // Free the memory allocated in 'tetgenio'. Note that it assumes that the
+ // memory was alocated by the "new" operator (C++).
void deinitialize()
{
- facet *f;
- polygon *p;
- pbcgroup *pg;
int i, j;
- // Notince that this routine assumes that the memory was allocated by
- // C++ memory allocation operator 'new'.
-
if (pointlist != (REAL *) NULL) {
delete [] pointlist;
}
@@ -480,12 +485,15 @@ public:
if (trifacelist != (int *) NULL) {
delete [] trifacelist;
}
- if (adjtetlist != (int *) NULL) {
- delete [] adjtetlist;
- }
if (trifacemarkerlist != (int *) NULL) {
delete [] trifacemarkerlist;
}
+ if (o2facelist != (int *) NULL) {
+ delete [] o2facelist;
+ }
+ if (adjtetlist != (int *) NULL) {
+ delete [] adjtetlist;
+ }
if (edgelist != (int *) NULL) {
delete [] edgelist;
@@ -493,8 +501,16 @@ public:
if (edgemarkerlist != (int *) NULL) {
delete [] edgemarkerlist;
}
+ if (o2edgelist != (int *) NULL) {
+ delete [] o2edgelist;
+ }
+ if (edgeadjtetlist != (int *) NULL) {
+ delete [] edgeadjtetlist;
+ }
if (facetlist != (facet *) NULL) {
+ facet *f;
+ polygon *p;
for (i = 0; i < numberoffacets; i++) {
f = &facetlist[i];
for (j = 0; j < f->numberofpolygons; j++) {
@@ -524,15 +540,6 @@ public:
if (segmentconstraintlist != (REAL *) NULL) {
delete [] segmentconstraintlist;
}
- if (pbcgrouplist != (pbcgroup *) NULL) {
- for (i = 0; i < numberofpbcgroups; i++) {
- pg = &(pbcgrouplist[i]);
- if (pg->pointpairlist != (int *) NULL) {
- delete [] pg->pointpairlist;
- }
- }
- delete [] pbcgrouplist;
- }
if (vpointlist != (REAL *) NULL) {
delete [] vpointlist;
}
@@ -563,12 +570,16 @@ public:
// //
// tetgenbehavior //
// //
-// A structure to maintain the switches and parameters of TetGen. //
+// A structure for maintaining the switches and parameters used by TetGen's //
+// mesh data structure and algorithms. //
// //
-// parse_commandline() provides an simple interface to set the vaules of the //
-// variables. It accepts the standard parameters (e.g., 'argc' and 'argv') //
-// that pass to C/C++ main() function. Alternatively a string which contains //
-// the command line options can be used as its parameter. //
+// All switches and parameters are initialized with default values. They can //
+// be set by the command line arguments (a list of strings) of TetGen. //
+// //
+// NOTE: Some of the switches are incompatible. While some may depend on //
+// other switches. The routine parse_commandline() sets the switches from //
+// the command line (a list of strings) and checks the consistency of the //
+// applied switches. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -576,93 +587,94 @@ class tetgenbehavior {
public:
- // Switches of TetGen. They are briefly described in the function syntax().
- // Plerase consult the user's manual for complete explanations. The last
- // column indicates their initial values.
- int plc; // '-p' switch, 0.
- int psc; // '-s' switch, 0.
- int quality; // '-q' switch, 0.
- int refine; // '-r' switch, 0.
- int metric; // '-m' switch, 0.
- int nobisect; // '-Y' switch, 0.
- int weighted; // '-w' switch, 0.
- int varvolume; // '-a' switch without number, 0.
- int fixedvolume; // '-a' switch with number, 0.
- int incrflip; // '-l' switch, 0.
- int flipinsert; // '-L' switch, 0.
- int btree; // '-u' switch, 0.
- int hilbertcurve; // '-U' switch, 0.
- int insertaddpoints; // '-i' switch, 0.
- int regionattrib; // '-A' switch, 0.
- int conforming; // '-D' switch, 0.
- int diagnose; // '-d' switch, 0.
- int convex; // '-c' switch, 0.
- int zeroindex; // '-z' switch, 0.
- int facesout; // '-f' switch, 0.
- int edgesout; // '-e' switch, 0.
- int neighout; // '-n' switch, 0.
- int voroout; // '-v',switch, 0.
- int meditview; // '-g' switch, 0.
- int vtkview; // '-K' switch, 0.
- int nobound; // '-B' switch, 0.
- int nonodewritten; // '-N' switch, 0.
- int noelewritten; // '-E' switch, 0.
- int nofacewritten; // '-F' switch, 0.
- int noiterationnum; // '-I' switch, 0.
- int nomerge; // '-M' switch, 0.
- int nojettison; // '-J' switch, 0.
- int docheck; // '-C' switch, 0.
- int quiet; // '-Q' switch, 0.
- int verbose; // '-V' switch, 0.
-
- // Parameters of TetGen. They are numbers specified after switches. The
- // last colume indicates their initial values.
- int vertexperblock; // after '-b', 4092.
- int tetrahedraperblock; // after '-b', 8188.
- int shellfaceperblock; // after '-b', 4092.
- int nobisect_param; // after '-Y', 1.
- int weighted_param; // after '-w', 0.
- int flipinsert_random; // after '-L', 0.
- int flipinsert_ori4dexact; // after '-L', 0.
- int fliplinklevel; // after '-L', -1.
- int flipstarsize; // after '-LL', -1.
- int fliplinklevelinc; // after '-LLLL', 1.
- int max_btreenode_size; // after '-u', 100.
- int reflevel; // after '-D', 3.
- int optlevel; // after '-O', 7.
- int optpasses; // after '-OO', 3.
- int optmaxfliplevel; // after '-OOO', 2.
- int delmaxfliplevel; // after '-OOOO', 1.
- int optmaxflipstarsize; // after '-OOOOO', 10.
- int order; // after '-o', 1.
- int steinerleft; // after '-S', 0.
- REAL facet_ang_tol; // after '-p', 179.9.
- REAL maxvolume; // after '-a', -1.0.
- REAL minratio; // after '-q', 0.0.
- REAL mindihedral; // after '-qq', 5.0.
- REAL optmaxdihedral; // after '-o', 165.0.
- REAL optminsmtdihed; // after '-oo', 175.0.
- REAL optminslidihed; // after '-ooo', 179.0.
- REAL epsilon; // after '-T', 1.0e-8.
- REAL minedgelength; // The shortest length of an edge, after '-l', 0.0.
-
- // Variables used to save command line switches and in/out file names.
+ // Switches of TetGen.
+ int plc; // '-p', 0.
+ int psc; // '-s', 0.
+ int refine; // '-r', 0.
+ int quality; // '-q', 0.
+ int nobisect; // '-Y', 0.
+ int weighted; // '-w', 0.
+ int brio_hilbert; // '-b', 1.
+ int incrflip; // '-l', 0.
+ int flipinsert; // '-L', 0.
+ int metric; // '-m', 0.
+ int varvolume; // '-a', 0.
+ int fixedvolume; // '-a', 0.
+ int regionattrib; // '-A', 0.
+ int conforming; // '-D', 0.
+ int insertaddpoints; // '-i', 0.
+ int diagnose; // '-d', 0.
+ int convex; // '-c', 0.
+ int nomergefacet; // '-M', 0.
+ int nomergevertex; // '-M', 0.
+ int noexact; // '-X', 0.
+ int nostaticfilter; // '-X', 0.
+ int zeroindex; // '-z', 0.
+ int facesout; // '-f', 0.
+ int edgesout; // '-e', 0.
+ int neighout; // '-n', 0.
+ int voroout; // '-v', 0.
+ int meditview; // '-g', 0.
+ int vtkview; // '-k', 0.
+ int nobound; // '-B', 0.
+ int nonodewritten; // '-N', 0.
+ int noelewritten; // '-E', 0.
+ int nofacewritten; // '-F', 0.
+ int noiterationnum; // '-I', 0.
+ int nojettison; // '-J', 0.
+ int reversetetori; // '-R', 0.
+ int docheck; // '-C', 0.
+ int quiet; // '-Q', 0.
+ int verbose; // '-V', 0.
+
+ // Parameters of TetGen.
+ int vertexperblock; // '-x', 4092.
+ int tetrahedraperblock; // '-x', 8188.
+ int shellfaceperblock; // '-x', 2044.
+ int nobisect_param; // '-Y', 1.
+ int weighted_param; // '-w', 0.
+ int fliplinklevel; // -1.
+ int flipstarsize; // -1.
+ int fliplinklevelinc; // 1.
+ int reflevel; // '-D', 3.
+ int optlevel; // '-O', 2.
+ int optscheme; // '-O', 7.
+ int delmaxfliplevel; // 1.
+ int order; // '-o', 1.
+ int steinerleft; // '-S', 0.
+ int no_sort; // 0.
+ int hilbert_order; // '-b///', 52.
+ int hilbert_limit; // '-b//' 8.
+ int brio_threshold; // '-b' 64.
+ REAL brio_ratio; // '-b/' 0.125.
+ REAL facet_ang_tol; // '-p', 179.9.
+ REAL maxvolume; // '-a', -1.0.
+ REAL minratio; // '-q', 0.0.
+ REAL mindihedral; // '-q', 5.0.
+ REAL optmaxdihedral; // 165.0.
+ REAL optminsmtdihed; // 179.0.
+ REAL optminslidihed; // 179.0.
+ REAL epsilon; // '-T', 1.0e-8.
+ REAL minedgelength; // 0.0.
+
+ // Strings of command line arguments and input/output file names.
char commandline[1024];
char infilename[1024];
char outfilename[1024];
char addinfilename[1024];
char bgmeshfilename[1024];
- // The input object type of TetGen. They are recognized by the input file
- // extensions. Currently the following objects are supported:
+ // The input object of TetGen. They are recognized by either the input
+ // file extensions or by the specified options.
+ // Currently the following objects are supported:
// - NODES, a list of nodes (.node);
// - POLY, a piecewise linear complex (.poly or .smesh);
// - OFF, a polyhedron (.off, Geomview's file format);
- // - PLY, a polyhedron (.ply, file format from gatech);
+ // - PLY, a polyhedron (.ply, file format from gatech, only ASCII);
// - STL, a surface mesh (.stl, stereolithography format);
// - MEDIT, a surface mesh (.mesh, Medit's file format);
// - MESH, a tetrahedral mesh (.ele).
- // If no extension is available, the imposed commandline switch
+ // If no extension is available, the imposed commandline switch
// (-p or -r) implies the object.
enum objecttype {NODES, POLY, OFF, PLY, STL, MEDIT, VTK, MESH} object;
@@ -681,17 +693,18 @@ public:
{
plc = 0;
psc = 0;
- quality = 0;
refine = 0;
- metric = 0;
+ quality = 0;
nobisect = 0;
+ metric = 0;
weighted = 0;
- varvolume = 0;
- fixedvolume = 0;
+ brio_hilbert = 1;
incrflip = 0;
flipinsert = 0;
- btree = 0;
- hilbertcurve = 0;
+ varvolume = 0;
+ fixedvolume = 0;
+ noexact = 0;
+ nostaticfilter = 0;
insertaddpoints = 0;
regionattrib = 0;
conforming = 0;
@@ -709,8 +722,10 @@ public:
noelewritten = 0;
nofacewritten = 0;
noiterationnum = 0;
- nomerge = 0;
+ nomergefacet = 0;
+ nomergevertex = 0;
nojettison = 0;
+ reversetetori = 0;
docheck = 0;
quiet = 0;
verbose = 0;
@@ -720,24 +735,24 @@ public:
shellfaceperblock = 4092;
nobisect_param = 1;
weighted_param = 0;
- flipinsert_random = 0;
- flipinsert_ori4dexact = 0;
fliplinklevel = -1; // No limit on linklevel.
flipstarsize = -1; // No limit on flip star size.
fliplinklevelinc = 1;
- max_btreenode_size = 100; // Default use b-tree sorting.
reflevel = 3;
- optlevel = 7; // 1 & 2 & 4, // min_max_dihedral.
- optpasses = 3;
- optmaxfliplevel = 2;
+ optscheme = 7; // 1 & 2 & 4, // min_max_dihedral.
+ optlevel = 2;
delmaxfliplevel = 1;
- optmaxflipstarsize = 10;
order = 1;
steinerleft = -1;
+ no_sort = 0;
+ hilbert_order = 52; //-1;
+ hilbert_limit = 8;
+ brio_threshold = 64;
+ brio_ratio = 0.125;
facet_ang_tol = 179.9;
maxvolume = -1.0;
minratio = 2.0;
- mindihedral = 0.0; // 5.0;
+ mindihedral = 5.0;
optmaxdihedral = 165.00; // without -q, default is 179.0
optminsmtdihed = 179.00; // without -q, default is 179.999
optminslidihed = 179.00; // without -q, default is 179.999
@@ -757,45 +772,42 @@ public:
///////////////////////////////////////////////////////////////////////////////
// //
-// Geometric predicates //
-// //
-// Return one of the values +1, 0, and -1 on basic geometric questions such //
-// as the orientation of point sets, in-circle, and in-sphere tests. They //
-// are basic units for implmenting geometric algorithms. TetGen uses two 3D //
-// geometric predicates: the orientation and in-sphere tests. //
-// //
-// Orientation test: let a, b, c be a sequence of 3 non-collinear points in //
-// R^3. They defines a unique hypeplane H. Let H+ and H- be the two spaces //
-// separated by H, which are defined as follows (using the left-hand rule): //
-// make a fist using your left hand in such a way that your fingers follow //
-// the order of a, b and c, then your thumb is pointing to H+. Given any //
-// point d in R^3, the orientation test returns +1 if d lies in H+, -1 if d //
-// lies in H-, or 0 if d lies on H. //
-// //
-// In-sphere test: let a, b, c, d be 4 non-coplanar points in R^3. They //
-// defines a unique circumsphere S. Given any point e in R^3, the in-sphere //
-// test returns +1 if e lies inside S, or -1 if e lies outside S, or 0 if e //
-// lies on S. //
-// //
-// The following routines use arbitrary precision floating-point arithmetic. //
-// They are provided by J. R. Schewchuk in public domain (http://www.cs.cmu. //
-// edu/~quake/robust.html). The source code are in "predicates.cxx". //
+// Robust Geometric predicates //
+// //
+// Geometric predicates are simple tests of spatial relations of a set of d- //
+// dimensional points, such as the orientation test and the point-in-sphere //
+// test. Each of these tests is performed by evaluating the sign of a deter- //
+// minant of a matrix whose entries are the coordinates of these points. If //
+// the computation is performed by using the floating-point numbers, e.g., //
+// the single or double precision numbers in C/C++, roundoff error may cause //
+// an incorrect result. This may either lead to a wrong result or eventually //
+// lead to a failure of the program. Computing the predicates exactly will //
+// avoid the error and make the program robust. //
+// //
+// The following routines are the robust geometric predicates for 3D orient- //
+// ation test and point-in-sphere test. They were implemented by Shewchuk. //
+// The source code are generously provided by him in the public domain, //
+// http://www.cs.cmu.edu/~quake/robust.html. predicates.cxx is a C++ version //
+// of the original C code. //
+// //
+// The original predicates of Shewchuk only use "dynamic filters", i.e., it //
+// computes the error at run time step by step. TetGen first adds a "static //
+// filter" in each predicate. It estimates the maximal possible error in all //
+// cases. So it can safely and quickly answer many easy cases. //
// //
///////////////////////////////////////////////////////////////////////////////
-REAL exactinit();
+void exactinit(int, int, int, REAL, REAL, REAL);
REAL orient3d(REAL *pa, REAL *pb, REAL *pc, REAL *pd);
REAL insphere(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe);
REAL orient4d(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe,
REAL ah, REAL bh, REAL ch, REAL dh, REAL eh);
-REAL orient4dexact(REAL *pa, REAL *pb, REAL *pc, REAL *pd, REAL *pe,
- REAL ah, REAL bh, REAL ch, REAL dh, REAL eh);
///////////////////////////////////////////////////////////////////////////////
// //
// tetgenmesh //
// //
-// The object to generate tetrahedral meshes. //
+// A structure for creating and updating tetrahedral meshes. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -803,64 +815,45 @@ class tetgenmesh {
public:
- // Labels that signify the type of a vertex.
- enum verttype {UNUSEDVERTEX, DUPLICATEDVERTEX, RIDGEVERTEX, ACUTEVERTEX,
- FACETVERTEX, VOLVERTEX, FREESEGVERTEX, FREEFACETVERTEX,
- FREEVOLVERTEX, HIDDENVERTEX, DEADVERTEX};
-
- // Labels that signify the type of a subsegment.
- enum shestype {NSHARP, SHARP, FAKESH};
-
- // Labels that signify the result of triangle-triangle intersection test.
- enum interresult {DISJOINT, INTERSECT, SHAREVERT, SHAREEDGE, SHAREFACE,
- TOUCHEDGE, TOUCHFACE, ACROSSVERT, ACROSSEDGE, ACROSSFACE,
- COLLISIONFACE, ACROSSSEG, ACROSSSUB};
-
- // Labels that signify the result of point location.
- enum locateresult {OUTSIDE, INTETRAHEDRON, ONFACE, ONEDGE, ONVERTEX, INSTAR,
- ENCVERTEX, ENCSEGMENT, ENCSUBFACE, NEARVERTEX,BADELEMENT};
-
///////////////////////////////////////////////////////////////////////////////
// //
// Mesh data structure //
// //
-// A tetrahedral mesh of a 3D domain is a 3D simplicial complex T whose und- //
-// erlying space is homeomorphic to the domain. T contains a 2D subcomplex S //
-// which is a triangular mesh of the boundary of the domain. S contains a 1D //
-// subcomplex L which is a linear mesh of the boundary of the surface. Faces //
-// and edges in S and L are respectivly called subfaces and segments to dis- //
-// tinguish them from others in T. //
-// //
-// The data structure to represent a tetrahedral mesh stores the tetrahedra //
-// and vertices of T. Each tetrahedron is a structure including informations //
-// of its vertices and adjacencies. Each vertex carries its geometric coord- //
-// inates. The faces and edges of T are implicitly represented by tetrahedra.//
-// This representation has a clear separation between combinatoric and geom- //
-// etric data of a tetrahedral mesh. //
-// //
-// A hull face of T is the face on the exterior domain boundary, i.e., it is //
-// contained by only one tetrahedron in T. TetGen adds fictitious tetrahedra //
-// (one-to-one) at the hull faces of T, and connects them to an "infinite //
-// vertex" which has no geometric coordinates. One can imagine such a vertex //
-// lies in 4D space and is visible by all tetrahedra containing hull faces. //
-// The extended set of tetrahedra with the infinite vertex is a tetrahedral- //
-// ization of a compact 3-manifold without bounday. It has the property that //
-// every face is shared by exactly two tetrahedra. //
-// //
-// The data structure stores explicitly the subfaces and segments (which are //
-// in surface mesh S and the linear mesh L, respectively. Additional inform- //
-// ations are stored in tetrahedra and subfaces to remember their relations. //
+// A tetrahedral mesh T of a 3D piecewise linear complex (PLC) X is a 3D //
+// simplicial complex whose underlying space is equal to the space of X. T //
+// contains a 2D subcomplex S which is a triangular mesh of the boundary of //
+// X. S contains a 1D subcomplex L which is a linear mesh of the boundary of //
+// S. Faces and edges in S and L are respectively called subfaces and segme- //
+// nts to distinguish them from others in T. //
+// //
+// TetGen stores the tetrahedra and vertices of T. The baisc structure of a //
+// tetrahedron contains pointers to its vertices and adjacent tetrahedra. A //
+// vertex stores its x-, y-, and z-coordinates, and a pointer to a tetrahed- //
+// ron containing it. Both tetrahedra and vertices may contain user data. //
+// //
+// Each face of T belongs to either two tetrahedra or one tetrahedron. In //
+// the latter case, the face is an exterior boundary face of T. TetGen adds //
+// fictitious tetrahedra (one-to-one) at such faces, and connects them to an //
+// "infinite vertex" (which has no geometric coordinates). One can imagine //
+// such a vertex lies in 4D space and is visible by all exterior boundary //
+// faces. The extended set of tetrahedra (including the infinite vertex) is //
+// a tetrahedralization of a 3-pseudomanifold without bounday. It has the //
+// property that every face is shared by exactly two tetrahedra. //
+// //
+// The current version of TetGen stores explicitly the subfaces and segments //
+// (which are in surface mesh S and the linear mesh L), respectively. Extra //
+// pointers are allocated in tetrahedra and subfaces to point each others. //
// //
///////////////////////////////////////////////////////////////////////////////
// The tetrahedron data structure. It includes the following fields:
// - a list of four adjoining tetrahedra;
// - a list of four vertices;
- // - a list of four subfaces (optional, for -p switch);
- // - a list of six segments (optional, for -p switch);
+ // - a pointer to a list of four subfaces (optional, for -p switch);
+ // - a pointer to a list of six segments (optional, for -p switch);
// - a list of user-defined floating-point attributes (optional);
// - a volume constraint (optional, for -a switch);
- // - an integer of element marker;
+ // - an integer of element marker (and flags);
// The structure of a tetrahedron is an array of pointers. Its actual size
// (the length of the array) is determined at runtime.
@@ -873,8 +866,7 @@ public:
// - two adjoining tetrahedra;
// - an area constraint (optional, for -q switch);
// - an integer for boundary marker;
- // - an integer for type: SHARPSEGMENT, NONSHARPSEGMENT, ...;
- // - an integer for pbc group (optional, if in->pbcgrouplist exists);
+ // - an integer for type, flags, etc.
typedef REAL **shellface;
@@ -884,11 +876,11 @@ public:
// - u, v coordinates (optional, for -s switch);
// - a metric tensor (optional, for -q or -m switch);
// - a pointer to an adjacent tetrahedron;
- // - a pointer to a parent (or a duplicate) point, or a bsp_tree node;
+ // - a pointer to a parent (or a duplicate) point;
// - a pointer to an adjacent subface or segment (optional, -p switch);
// - a pointer to a tet in background mesh (optional, for -m switch);
// - an integer for boundary marker (point index);
- // - an integer for point type.
+ // - an integer for point type (and flags).
// - an integer for geometry tag (optional, for -s switch).
// The structure of a point is an array of REALs. Its acutal size is
// determined at the runtime.
@@ -897,23 +889,21 @@ public:
///////////////////////////////////////////////////////////////////////////////
// //
-// Ordered tetrahedra //
+// Handles //
// //
-// The four vertices of a tetrahedron can be permuted in 24 different seque- //
-// nces. We call each sequence resulted by an even permutation an "ordered //
-// tetrahedron". There are total 12 ordered tetrahedra. They form a group //
-// which is isomorphic to the alternating group of 4 elements. Geometrically,//
-// if we direct the three edges within a face of a tetrahedron by the count- //
-// erclockwise order viewed from the opposite vertex of this face (using ei- //
-// ther right-hand or left-hand rule). There are total twelve directed edges //
-// in the tetrahedron. Each of them corresponds to an ordered tetrahedron. //
+// Navigation and manipulation in a tetrahedralization are accomplished by //
+// opertating on structures referred as ``handles". A handle is a pair (t,v),//
+// where t is a pointer to a tetrahedron, and v is a 4-bit integer, in the //
+// range from 0 to 11. v is called the ``version'' of a tetrahedron, it rep- //
+// resents a directed edge of a specific face of the tetrahedron. //
// //
-// We represent an order tetrahedron by a pair (t, v), where t is a pointer //
-// to the tetrahedron and v is a four-bit integer, in the range from 0 to 11,//
-// identifying the ordered version of the tetrahedron. Assume the faces of //
-// the tetrahedron is numbered from 0 to 3, and the edges in a face is numb- //
-// ered from 0 to 2. The first two bits of v is used to identify the face of //
-// the tetrahedron. The other two bits of v identify the edge in the face. //
+// There are 12 even permutations of the four vertices, each of them corres- //
+// ponds to a directed edge (a version) of the tetrahedron. The 12 versions //
+// can be groupped into 4 distinct ``edge rings'' in 4 ``oriented faces'' of //
+// this tetrahedron. One can encode each version (a directed edge) into a //
+// 4-bit integer such that the two upper bits encode the index (from 0 to 2) //
+// of this edge in the edge ring, and the two lower bits encode the index ( //
+// from 0 to 3) of the oriented face which contains this edge. //
// //
// The four vertices of a tetrahedron are indexed from 0 to 3 (accodring to //
// their storage in the data structure). Give each face the same index as //
@@ -927,19 +917,10 @@ public:
// face 2 | 2 (2/3) 6 (2/1) 10 (2/0) //
// face 3 | 3 (3/0) 7 (3/1) 11 (3/2) //
// //
-// Ordered triangles //
-// //
-// The three vertices of a triangle can be permuted in 6 different sequences //
-// which form a group isomorphic to the symmetric group of 3 elements. Each //
-// permutation of the vertices is called an ordered triangle. The first two //
-// vertices of an ordered triangle defines an directed edge. There are total //
-// six directed edge in the triangle. They can be divided into two groups, //
-// which correspond the two orientations of the triangle, respectively. //
-// //
-// We represent an ordered triangle by a pair (s, v), where s is a pointer //
-// to the triangle and v is a three-bit integer, in the range from 0 to 5, //
-// identifying the directed edge of the triangle. Using the first bit of v //
-// to identify the orientation, the other two bits of v identify the edge. //
+// Similarily, navigation and manipulation in a (boundary) triangulation are //
+// done by using handles of triangles. Each handle is a pair (s, v), where s //
+// is a pointer to a triangle, and v is a version in the range from 0 to 5. //
+// Each version corresponds to a directed edge of this triangle. //
// //
// Number the three vertices of a triangle from 0 to 2 (according to their //
// storage in the data structure). Give each edge the same index as the node //
@@ -950,6 +931,9 @@ public:
// ccw orieation | 0 2 4 //
// cw orieation | 1 3 5 //
// //
+// In the following, a 'triface' is a handle of tetrahedron, and a 'face' is //
+// a handle of a triangle. //
+// //
///////////////////////////////////////////////////////////////////////////////
class triface {
@@ -974,12 +958,110 @@ public:
}
};
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Arraypool //
+// //
+// A dynamic linear array. (It is written by J. Shewchuk) //
+// //
+// Each arraypool contains an array of pointers to a number of blocks. Each //
+// block contains the same fixed number of objects. Each index of the array //
+// addesses a particular object in the pool. The most significant bits add- //
+// ress the index of the block containing the object. The less significant //
+// bits address this object within the block. //
+// //
+// 'objectbytes' is the size of one object in blocks; 'log2objectsperblock' //
+// is the base-2 logarithm of 'objectsperblock'; 'objects' counts the number //
+// of allocated objects; 'totalmemory' is the totoal memorypool in bytes. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class arraypool {
+
+ public:
+
+ int objectbytes;
+ int objectsperblock;
+ int log2objectsperblock;
+ int objectsperblockmark;
+ int toparraylen;
+ char **toparray;
+ long objects;
+ unsigned long totalmemory;
+
+ void restart();
+ void poolinit(int sizeofobject, int log2objperblk);
+ char* getblock(int objectindex);
+ void* lookup(int objectindex);
+ int newindex(void **newptr);
+
+ arraypool(int sizeofobject, int log2objperblk);
+ ~arraypool();
+ };
+
+// fastlookup() -- A fast, unsafe operation. Return the pointer to the object
+// with a given index. Note: The object's block must have been allocated,
+// i.e., by the function newindex().
+
+#define fastlookup(pool, index) \
+ (void *) ((pool)->toparray[(index) >> (pool)->log2objectsperblock] + \
+ ((index) & (pool)->objectsperblockmark) * (pool)->objectbytes)
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Memorypool //
+// //
+// A structure for memory allocation. (It is written by J. Shewchuk) //
+// //
+// firstblock is the first block of items. nowblock is the block from which //
+// items are currently being allocated. nextitem points to the next slab //
+// of free memory for an item. deaditemstack is the head of a linked list //
+// (stack) of deallocated items that can be recycled. unallocateditems is //
+// the number of items that remain to be allocated from nowblock. //
+// //
+// Traversal is the process of walking through the entire list of items, and //
+// is separate from allocation. Note that a traversal will visit items on //
+// the "deaditemstack" stack as well as live items. pathblock points to //
+// the block currently being traversed. pathitem points to the next item //
+// to be traversed. pathitemsleft is the number of items that remain to //
+// be traversed in pathblock. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class memorypool {
+
+ public:
+
+ void **firstblock, **nowblock;
+ void *nextitem;
+ void *deaditemstack;
+ void **pathblock;
+ void *pathitem;
+ int alignbytes;
+ int itembytes, itemwords;
+ int itemsperblock;
+ long items, maxitems;
+ int unallocateditems;
+ int pathitemsleft;
+
+ memorypool();
+ memorypool(int, int, int, int);
+ ~memorypool();
+
+ void poolinit(int, int, int, int);
+ void restart();
+ void *alloc();
+ void dealloc(void*);
+ void traversalinit();
+ void *traverse();
+ };
+
///////////////////////////////////////////////////////////////////////////////
// //
// badface //
// //
-// A multiple usages structure. Despite of its name, a 'badface' can be used //
-// to represent the following objects: //
+// Despite of its name, a 'badface' can be used to represent one of the //
+// following objects: //
// - a face of a tetrahedron which is (possibly) non-Delaunay; //
// - an encroached subsegment or subface; //
// - a bad-quality tetrahedron, i.e, has too large radius-edge ratio; //
@@ -991,12 +1073,12 @@ public:
class badface {
public:
triface tt;
- face ss;
+ face ss;
REAL key, cent[6]; // circumcenter or cos(dihedral angles) at 6 edges.
point forg, fdest, fapex, foppo, noppo;
- badface *previtem, *nextitem;
+ badface *nextitem;
badface() : key(0), forg(0), fdest(0), fapex(0), foppo(0), noppo(0),
- previtem(0), nextitem(0) {}
+ nextitem(0) {}
};
///////////////////////////////////////////////////////////////////////////////
@@ -1011,11 +1093,12 @@ public:
public:
- int iloc, bowywat, lawson;
- int rejflag, chkencflag;
- int sloc, sbowywat;
+ int iloc; // input/output.
+ int bowywat, lawson;
int splitbdflag, validflag, respectbdflag;
+ int rejflag, chkencflag, cdtflag;
int assignmeshsize;
+ int sloc, sbowywat;
// Used by Delaunay refinement.
int refineflag; // 0, 1, 2, 3
@@ -1023,12 +1106,11 @@ public:
face refinesh;
insertvertexflags() {
- // All flags are initialized as 0.
iloc = bowywat = lawson = 0;
- rejflag = chkencflag = 0;
- sloc = sbowywat = 0;
splitbdflag = validflag = respectbdflag = 0;
+ rejflag = chkencflag = cdtflag = 0;
assignmeshsize = 0;
+ sloc = sbowywat = 0;
refineflag = 0;
refinetet.tet = NULL;
@@ -1049,11 +1131,9 @@ public:
public:
- point seg[2]; // A constraining edge to be recovered.
- point fac[3]; // A constraining face to be recovered.
-
- point remvert; // A vertex to be removed.
- //point remedge[2]; // A non-Delaunay edge to be removed.
+ // Elementary flip flags.
+ int enqflag; // (= flipflag)
+ int chkencflag;
// Control flags
int unflip; // Undo the performed flips.
@@ -1062,37 +1142,22 @@ public:
// Optimization flags.
int remove_ndelaunay_edge; // Remove a non-Delaunay edge.
- // remedge[0] and remedge[1] store the endpoints of a
- // non-Delaunay edge to be removed.
REAL bak_tetprism_vol; // The value to be minimized.
-
+ REAL tetprism_vol_sum;
int remove_large_angle; // Remove a large dihedral angle at edge.
REAL cosdihed_in; // The input cosine of the dihedral angle (> 0).
- // Only perform a flip if new angles are less than it.
REAL cosdihed_out; // The improved cosine of the dihedral angle.
- // Counters.
- int maxflippedlinklevelcount; // Maximal flipped link levels.
- int misfliplinklevelcount; // Number of missed flip possibilities.
- int chrismastreecount; // Number of Chrismas trees (unflippable case).
- int convexhulledgecount; // Number of convex hull edges (unflippable case).
- int encsegcount; // Number of hitted segments.
- int rejf23count, rejf32count; // Number of rejections by checkflipeligi..
-
- void clearcounters() {
- maxflippedlinklevelcount = 0;
- misfliplinklevelcount = 0;
- chrismastreecount = 0;
- convexhulledgecount = 0;
- encsegcount = 0;
- rejf23count = rejf32count = 0;
- }
+ // Boundary recovery flags.
+ int checkflipeligibility;
+ point seg[2]; // A constraining edge to be recovered.
+ point fac[3]; // A constraining face to be recovered.
+ point remvert; // A vertex to be removed.
+
flipconstraints() {
- seg[0] = NULL;
- fac[0] = NULL;
- remvert = NULL;
- //remedge[0] = NULL;
+ enqflag = 0;
+ chkencflag = 0;
unflip = 0;
collectnewtets = 0;
@@ -1100,12 +1165,15 @@ public:
remove_ndelaunay_edge = 0;
bak_tetprism_vol = 0.0;
-
+ tetprism_vol_sum = 0.0;
remove_large_angle = 0;
cosdihed_in = 0.0;
cosdihed_out = 0.0;
- clearcounters();
+ checkflipeligibility = 0;
+ seg[0] = NULL;
+ fac[0] = NULL;
+ remvert = NULL;
}
};
@@ -1134,11 +1202,6 @@ public:
int maxiter; // Maximum smoothing iterations (disabled by -1).
int smthiter; // Performed iterations.
- int expstarflag;
- int expstarcount;
-
- int flipflag;
- int checkencflag;
optparameters() {
max_min_volume = 0;
@@ -1148,142 +1211,47 @@ public:
initval = imprval = 0.0;
numofsearchdirs = 10;
- searchstep = 0.01;
- maxiter = -1; // Unlimited smoothing iterations.
- smthiter = 0;
-
- expstarflag = 0;
- expstarcount = 0;
-
- flipflag = 0;
- checkencflag = 0;
- }
- };
-
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Arraypool //
-// //
-// A dynamic linear array. //
-// (It is simply copied from Shewchuk's Starbase.c, which is provided as //
-// part of Stellar, a program for improving tetrahedral meshes.) //
-// //
-// Each arraypool contains an array of pointers to a number of blocks. Each //
-// block contains the same fixed number of objects. Each index of the array //
-// addesses a particular object in the pool. The most significant bits add- //
-// ress the index of the block containing the object. The less significant //
-// bits address this object within the block. //
-// //
-// 'objectbytes' is the size of one object in blocks; 'log2objectsperblock' //
-// is the base-2 logarithm of 'objectsperblock'; 'objects' counts the number //
-// of allocated objects; 'totalmemory' is the totoal memorypool in bytes. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class arraypool {
-
- public:
-
- int objectbytes;
- int objectsperblock;
- int log2objectsperblock;
- int toparraylen;
- char **toparray;
- long objects;
- unsigned long totalmemory;
-
- void restart();
- void poolinit(int sizeofobject, int log2objperblk);
- char* getblock(int objectindex);
- void* lookup(int objectindex);
- int newindex(void **newptr);
-
- arraypool(int sizeofobject, int log2objperblk);
- ~arraypool();
- };
-
-// fastlookup() -- A fast, unsafe operation. Return the pointer to the object
-// with a given index. Note: The object's block must have been allocated,
-// i.e., by the function newindex().
-
-#define fastlookup(pool, index) \
- (void *) ((pool)->toparray[(index) >> (pool)->log2objectsperblock] + \
- ((index) & ((pool)->objectsperblock - 1)) * (pool)->objectbytes)
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// Memorypool //
-// //
-// A type used to allocate memory. //
-// (It is simply copied from Shewchuk's triangle.c.) //
-// //
-// firstblock is the first block of items. nowblock is the block from which //
-// items are currently being allocated. nextitem points to the next slab //
-// of free memory for an item. deaditemstack is the head of a linked list //
-// (stack) of deallocated items that can be recycled. unallocateditems is //
-// the number of items that remain to be allocated from nowblock. //
-// //
-// Traversal is the process of walking through the entire list of items, and //
-// is separate from allocation. Note that a traversal will visit items on //
-// the "deaditemstack" stack as well as live items. pathblock points to //
-// the block currently being traversed. pathitem points to the next item //
-// to be traversed. pathitemsleft is the number of items that remain to //
-// be traversed in pathblock. //
+ searchstep = 0.01;
+ maxiter = -1; // Unlimited smoothing iterations.
+ smthiter = 0;
+
+ }
+ };
+
+
+
+///////////////////////////////////////////////////////////////////////////////
// //
-// itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest //
-// what sort of word the record is primarily made up of. alignbytes //
-// determines how new records should be aligned in memory. itembytes and //
-// itemwords are the length of a record in bytes (after rounding up) and //
-// words. itemsperblock is the number of items allocated at once in a //
-// single block. items is the number of currently allocated items. //
-// maxitems is the maximum number of items that have been allocated at //
-// once; it is the current number of items plus the number of records kept //
-// on deaditemstack. //
+// Labels (enumeration declarations) used by TetGen. //
// //
///////////////////////////////////////////////////////////////////////////////
- class memorypool {
-
- public:
-
- // Labels that signify whether a record consists primarily of pointers
- // or of floating-point words. Used for data alignment.
- enum wordtype {POINTER, FLOATINGPOINT};
+ // Labels that signify the type of a vertex.
+ enum verttype {UNUSEDVERTEX, DUPLICATEDVERTEX, RIDGEVERTEX, ACUTEVERTEX,
+ FACETVERTEX, VOLVERTEX, FREESEGVERTEX, FREEFACETVERTEX,
+ FREEVOLVERTEX, NREGULARVERTEX, DEADVERTEX};
+
+ // Labels that signify the type of a subsegment.
+ enum shestype {NSHARP, SHARP};
- void **firstblock, **nowblock;
- void *nextitem;
- void *deaditemstack;
- void **pathblock;
- void *pathitem;
- wordtype itemwordtype;
- int alignbytes;
- int itembytes, itemwords;
- int itemsperblock;
- long items, maxitems;
- int unallocateditems;
- int pathitemsleft;
+ // Labels that signify the result of triangle-triangle intersection test.
+ enum interresult {DISJOINT, INTERSECT, SHAREVERT, SHAREEDGE, SHAREFACE,
+ TOUCHEDGE, TOUCHFACE, ACROSSVERT, ACROSSEDGE, ACROSSFACE,
+ COLLISIONFACE, ACROSSSEG, ACROSSSUB};
- memorypool();
- memorypool(int, int, enum wordtype, int);
- ~memorypool();
-
- void poolinit(int, int, enum wordtype, int);
- void restart();
- void *alloc();
- void dealloc(void*);
- void traversalinit();
- void *traverse();
- };
+ // Labels that signify the result of point location.
+ enum locateresult {UNKNOWN, OUTSIDE, INTETRAHEDRON, ONFACE, ONEDGE, ONVERTEX,
+ ENCVERTEX, ENCSEGMENT, ENCSUBFACE, NEARVERTEX, NONREGULAR,
+ INSTAR, BADELEMENT};
///////////////////////////////////////////////////////////////////////////////
// //
-// Class variables //
+// Variables of TetGen //
// //
///////////////////////////////////////////////////////////////////////////////
// Pointer to the input data (a set of nodes, a PLC, or a mesh).
- tetgenio *in;
+ tetgenio *in, *addin;
// Pointer to the switches and parameters.
tetgenbehavior *b;
@@ -1291,9 +1259,8 @@ public:
// Pointer to a background mesh (contains size specification map).
tetgenmesh *bgm;
- // Memorypools to store mesh elements: tetrahedra, subfaces, segments,
- // and vertices. And memorypools for storing pointers which connect
- // tetrahedra and subfaces and segments.
+ // Memorypools to store mesh elements (points, tetrahedra, subfaces, and
+ // segments) and extra pointers between tetrahedra, subfaces, and segments.
memorypool *tetrahedrons, *subfaces, *subsegs, *points;
memorypool *tet2subpool, *tet2segpool;
@@ -1302,17 +1269,8 @@ public:
// A memorypool to store faces to be flipped.
memorypool *flippool;
- // A stack of faces to be flipped.
- badface *flipstack;
- // Two queues for handling unflippable edges.
- arraypool *unflipqueue; //, *flipqueue;
-
- // Entry to find the binary tree nodes (-u option).
- arraypool *btreenode_list;
- // The maximum size of a btree node (number after -u option) is
- int max_btreenode_size; // <= b->max_btreenode_size.
- // The maximum btree depth (for bookkeeping).
- int max_btree_depth;
+ arraypool *unflipqueue;
+ badface *flipstack;
// Arrays used for point insertion (the Bowyer-Watson algorithm).
arraypool *cavetetlist, *cavebdrylist, *caveoldtetlist;
@@ -1324,46 +1282,31 @@ public:
arraypool *subsegstack, *subfacstack, *subvertstack;
arraypool *suppsteinerptlist;
- // The infinite vertex.
- point dummypoint;
-
- // Two handles used for facet recovery in CDT.
- triface firsttopface, firstbotface;
-
- // Three points define a plane (used in formcavity()).
- point plane_pa, plane_pb, plane_pc;
-
- // Two arraies of encroached segments and subfaces (in mesh refinement).
+ // Arrays of encroached segments and subfaces (for mesh refinement).
arraypool *encseglist, *encshlist;
- // Pointer to a recently visited tetrahedron, subface.
+ // The infinite vertex.
+ point dummypoint;
+ // The recently visited tetrahedron, subface.
triface recenttet;
face recentsh;
// PI is the ratio of a circle's circumference to its diameter.
static REAL PI;
- // The increasement of link levels, default is 1.
- int autofliplinklevel;
+ // Array (size = numberoftetrahedra * 6) for storing high-order nodes of
+ // tetrahedra (only used when -o2 switch is selected).
+ point *highordertable;
- // The volume of tetrahedral-prisms (in 4D).
- REAL tetprism_vol_sum;
- int calc_tetprism_vol;
- // Other variables.
- REAL xmax, xmin, ymax, ymin, zmax, zmin; // Bounding box of points.
- REAL longest; // The longest possible edge length.
- long hullsize; // Number of faces of convex hull.
- long insegments; // Number of input segments.
- long meshedges; // Number of output mesh edges.
- long meshhulledges; // Number of hull mesh edges.
- int steinerleft; // Number of Steiner points not yet used.
+ // Various variables.
+ int numpointattrib; // Number of point attributes.
+ int numelemattrib; // Number of tetrahedron attributes.
int sizeoftensor; // Number of REALs per metric tensor.
int pointmtrindex; // Index to find the metric tensor of a point.
int pointparamindex; // Index to find the u,v coordinates of a point.
int point2simindex; // Index to find a simplex adjacent to a point.
int pointmarkindex; // Index to find boundary marker of a point.
- int point2pbcptindex; // Index to find a pbc point to a point.
int elemattribindex; // Index to find attributes of a tetrahedron.
int volumeboundindex; // Index to find volume bound of a tetrahedron.
int elemmarkerindex; // Index to find marker of a tetrahedron.
@@ -1372,82 +1315,64 @@ public:
int checksubsegflag; // Are there segments in the tetrahedralization yet?
int checksubfaceflag; // Are there subfaces in the tetrahedralization yet?
int checkinverttetflag; // Are there inverted (degenerated) tets yet?
- int checkpbcs; // Are there periodic boundary conditions?
int checkconstraints; // Are there variant (node, seg, facet) constraints?
int nonconvex; // Is current mesh non-convex?
- int dupverts; // Are there duplicated vertices?
- int unuverts; // Are there unused vertices?
+ int autofliplinklevel; // The increasement of link levels, default is 1.
long samples; // Number of random samples for point location.
unsigned long randomseed; // Current random number seed.
REAL cosmaxdihed, cosmindihed; // The cosine values of max/min dihedral.
- REAL cossmtdihed;
- REAL cosslidihed; // The cosine value of max dihedral of a sliver.
+ REAL cossmtdihed; // The cosine value of a bad dihedral to be smoothed.
+ REAL cosslidihed; // The cosine value of the max dihedral of a sliver.
REAL minfaceang, minfacetdihed; // The minimum input (dihedral) angles.
- REAL sintheta_tol; // The tolerance for sin(small angle).
+ REAL tetprism_vol_sum; // The total volume of tetrahedral-prisms (in 4D).
+ REAL longest; // The longest possible edge length.
+ REAL xmax, xmin, ymax, ymin, zmax, zmin; // Bounding box of points.
- // Algorithm statistical counters.
- long ptloc_count, ptloc_max_count;
- long orient3dcount, inspherecount, insphere_sos_count;
+ // Counters.
+ long insegments; // Number of input segments.
+ long hullsize; // Number of exterior boundary faces.
+ long meshedges; // Number of mesh edges.
+ long meshhulledges; // Number of boundary mesh edges.
+ long steinerleft; // Number of Steiner points not yet used.
+ long dupverts; // Are there duplicated vertices?
+ long unuverts; // Are there unused vertices?
+ long nonregularcount; // Are there non-regular vertices?
+ long st_segref_count, st_facref_count, st_volref_count; // Steiner points.
+ long fillregioncount, cavitycount, cavityexpcount;
long flip14count, flip26count, flipn2ncount;
- long flip23count, flip32count, flip44count, flip22count;
- long maxbowatcavsize, totalbowatcavsize, totaldeadtets;
- long triedgcount, triedgcopcount;
- long across_face_count, across_edge_count, across_max_count;
- long fillregioncount, missingsubfacecount, crossingtetcount;
- long cavitycount, cavityexpcount, maxcavsize, maxregionsize;
- long maxcrossfacecount, maxflipsequence;
- long dbg_ignore_facecount, dbg_unflip_facecount;
- long ccent_relocate_count;
- long opt_sliver_peels;
- long r1count, r2count, r3count;
- long maxfliplinklevel, maxflipstarsize;
- long flipstarcount, sucflipstarcount, skpflipstarcount;
- long st_segref_count, st_facref_count, st_volref_count;
-
- long rejrefinetetcount, rejrefineshcount;
-
-#ifdef WITH_RUNTIME_COUNTERS
- clock_t t_ptloc, t_ptinsert; // Time counters for DT operations.
-#endif
+ long flip23count, flip32count, flip44count, flip41count;
+ long flip31count, flip22count;
+ unsigned long totalworkmemory; // Total memory used by working arrays.
+
+
///////////////////////////////////////////////////////////////////////////////
// //
// Mesh manipulation primitives //
// //
-// A serial of mesh operations such as topological maintenance, navigation, //
-// local modification, etc., is accomplished through a set of mesh manipul- //
-// ation primitives. These primitives are indeed very simple functions which //
-// take one or two handles ('triface's and 'face's) as parameters, perform //
-// basic operations such as "glue two tetrahedra at a face", "return the //
-// origin of a tetrahedron", "return the subface adjoining at the face of a //
-// tetrahedron", and so on. //
-// //
///////////////////////////////////////////////////////////////////////////////
// Fast lookup tables for mesh manipulation primitives.
- static int mod12[36];
- static int mod6[18];
- static int edgepivot[12];
- static int orgpivot [12];
- static int destpivot[12];
- static int apexpivot[12];
- static int oppopivot[12];
- static int ver2edge[12];
- static int edge2ver[6];
+ static int bondtbl[12][12], fsymtbl[12][12];
+ static int esymtbl[12], enexttbl[12], eprevtbl[12];
+ static int enextesymtbl[12], eprevesymtbl[12];
+ static int eorgoppotbl[12], edestoppotbl[12];
+ static int facepivot1[12], facepivot2[12][12];
+ static int orgpivot[12], destpivot[12], apexpivot[12], oppopivot[12];
+ static int tsbondtbl[12][6], stbondtbl[12][6];
+ static int tspivottbl[12][6], stpivottbl[12][6];
+ static int ver2edge[12], edge2ver[6], epivot[12];
+ static int sorgpivot [6], sdestpivot[6], sapexpivot[6];
static int snextpivot[6];
- static int sorgpivot [6];
- static int sdestpivot[6];
- static int sapexpivot[6];
- static int epivot[4];
+
+ void inittables();
// Primitives for tetrahedra.
- inline void decode(tetrahedron ptr, triface& t);
inline tetrahedron encode(triface& t);
inline tetrahedron encode2(tetrahedron* ptr, int ver);
+ inline void decode(tetrahedron ptr, triface& t);
inline void bond(triface& t1, triface& t2);
inline void dissolve(triface& t);
- inline void fsym(triface& t1, triface& t2);
- inline void fsymself(triface& t);
inline void esym(triface& t1, triface& t2);
inline void esymself(triface& t);
inline void enext(triface& t1, triface& t2);
@@ -1458,10 +1383,14 @@ public:
inline void enextesymself(triface& t);
inline void eprevesym(triface& t1, triface& t2);
inline void eprevesymself(triface& t);
+ inline void eorgoppo(triface& t1, triface& t2);
+ inline void eorgoppoself(triface& t);
+ inline void edestoppo(triface& t1, triface& t2);
+ inline void edestoppoself(triface& t);
+ inline void fsym(triface& t1, triface& t2);
+ inline void fsymself(triface& t);
inline void fnext(triface& t1, triface& t2);
inline void fnextself(triface& t);
- inline void fprev(triface& t1, triface& t2);
- inline void fprevself(triface& t);
inline point org (triface& t);
inline point dest(triface& t);
inline point apex(triface& t);
@@ -1529,8 +1458,6 @@ public:
inline void setshellmark(face& s, int value);
inline enum shestype shelltype(face& s);
inline void setshelltype(face& s, enum shestype value);
- inline int shellpbcgroup(face& s);
- inline void setshellpbcgroup(face& s, int value);
inline void sinfect(face& s);
inline void suninfect(face& s);
inline bool sinfected(face& s);
@@ -1594,8 +1521,6 @@ public:
inline void setpoint2ppt(point pt, point value);
inline tetrahedron point2bgmtet(point pt);
inline void setpoint2bgmtet(point pt, tetrahedron value);
- inline point point2pbcpt(point pt);
- inline void setpoint2pbcpt(point pt, point value);
// Advanced primitives.
inline void point2tetorg(point pt, triface& t);
@@ -1614,32 +1539,53 @@ public:
tetrahedron *alltetrahedrontraverse();
void shellfacedealloc(memorypool*, shellface*);
shellface *shellfacetraverse(memorypool*);
- void badfacedealloc(memorypool*, badface*);
- badface *badfacetraverse(memorypool*);
void pointdealloc(point);
point pointtraverse();
- void maketetrahedron(triface*);
- void makeshellface(memorypool*, face*);
- void makepoint(point*, enum verttype);
void makeindex2pointmap(point*&);
void makepoint2submap(memorypool*, int*&, face*&);
+ void maketetrahedron(triface*);
+ void makeshellface(memorypool*, face*);
+ void makepoint(point*, enum verttype);
void initializepools();
///////////////////////////////////////////////////////////////////////////////
// //
-// Geometric predicates and calculations //
+// Advanced geometric predicates and calculations //
+// //
+// TetGen uses a simplified symbolic perturbation scheme from Edelsbrunner, //
+// et al [*]. Hence the point-in-sphere test never returns a zero. The idea //
+// is to perturb the weights of vertices in the fourth dimension. TetGen //
+// uses the indices of the vertices decide the amount of perturbation. It is //
+// implemented in the routine insphere_s().
+// //
+// The routine tri_edge_test() determines whether or not a triangle and an //
+// edge intersect in 3D. If they intersect, their intersection type is also //
+// reported. This test is a combination of n 3D orientation tests (n is bet- //
+// ween 3 and 9). It uses the robust orient3d() test to make the branch dec- //
+// isions. The routine tri_tri_test() determines whether or not two triang- //
+// les intersect in 3D. It also uses the robust orient3d() test. //
+// //
+// There are a number of routines to calculate geometrical quantities, e.g., //
+// circumcenters, angles, dihedral angles, face normals, face areas, etc. //
+// They are so far done by the default floating-point arithmetics which are //
+// non-robust. They should be improved in the future. //
// //
///////////////////////////////////////////////////////////////////////////////
- // Triangle-edge intersection test
+ // Symbolic perturbations (robust)
+ REAL insphere_s(REAL*, REAL*, REAL*, REAL*, REAL*);
+ REAL orient4d_s(REAL*, REAL*, REAL*, REAL*, REAL*,
+ REAL, REAL, REAL, REAL, REAL);
+
+ // Triangle-edge intersection test (robust)
int tri_edge_2d(point, point, point, point, point, point, int, int*, int*);
- int tri_edge_tail(point, point, point, point, point, point, REAL, REAL, int,
+ int tri_edge_tail(point, point, point, point, point, point, REAL, REAL, int,
int*, int*);
int tri_edge_test(point, point, point, point, point, point, int, int*, int*);
- // Triangle-triangle intersection test
+ // Triangle-triangle intersection test (robust)
int tri_edge_inter_tail(point, point, point, point, point, REAL, REAL);
int tri_tri_inter(point, point, point, point, point, point);
@@ -1649,13 +1595,12 @@ public:
bool lu_decmp(REAL lu[4][4], int n, int* ps, REAL* d, int N);
void lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N);
- // Geometric predicates
+ // An embedded 2-dimensional geometric predicate (non-robust)
REAL incircle3d(point pa, point pb, point pc, point pd);
- REAL insphere_s(REAL*, REAL*, REAL*, REAL*, REAL*);
- REAL orient4d_s(REAL*, REAL*, REAL*, REAL*, REAL*,
- REAL, REAL, REAL, REAL, REAL);
- // Geometric calculations
+ // Geometric calculations (non-robust)
+ REAL orient3dfast(REAL *pa, REAL *pb, REAL *pc, REAL *pd);
+ inline REAL norm2(REAL x, REAL y, REAL z);
inline REAL distance(REAL* p1, REAL* p2);
void facenormal(point pa, point pb, point pc, REAL *n, int pivot, REAL *lav);
REAL shortdistance(REAL* p, REAL* e1, REAL* e2);
@@ -1668,51 +1613,133 @@ public:
void tetallnormal(point, point, point, point, REAL N[4][3], REAL* volume);
REAL tetaspectratio(point, point, point, point);
bool circumsphere(REAL*, REAL*, REAL*, REAL*, REAL* cent, REAL* radius);
+ bool orthosphere(REAL*,REAL*,REAL*,REAL*,REAL,REAL,REAL,REAL,REAL*,REAL*);
void planelineint(REAL*, REAL*, REAL*, REAL*, REAL*, REAL*, REAL*);
REAL tetprismvol(REAL* pa, REAL* pb, REAL* pc, REAL* pd);
+ bool calculateabovepoint(arraypool*, point*, point*, point*);
+ void calculateabovepoint4(point, point, point, point);
///////////////////////////////////////////////////////////////////////////////
// //
// Local mesh transformations //
// //
+// A local transformation replaces a small set of tetrahedra with another //
+// set of tetrahedra which fills the same space and the same boundaries. //
+// In 3D, the most simplest local transformations are the elementary flips //
+// peformed within the convex hull of five vertices: 2-to-3, 3-to-2, 1-to-4, //
+// and 4-to-1 flips, where the numbers indicate the number of tetrahedra //
+// before and after each flip. The 1-to-4 and 4-to-1 flip involve inserting //
+// or deleting a vertex, respectively. //
+// There are complex local transformations which can be decomposed as a //
+// combination of elementary flips. For example,a 4-to-4 flip which replaces //
+// two coplanar edges can be regarded by a 2-to-3 flip and a 3-to-2 flip. //
+// Note that the first 2-to-3 flip will temporarily create a degenerate tet- //
+// rahedron which is removed immediately by the followed 3-to-2 flip. More //
+// generally, a n-to-m flip, where n > 3, m = (n - 2) * 2, which removes an //
+// edge can be done by first performing a sequence of (n - 3) 2-to-3 flips //
+// followed by a 3-to-2 flip. //
+// //
+// The routines flip23(), flip32(), and flip41() perform the three element- //
+// ray flips. The flip14() is available inside the routine insertpoint(). //
+// //
+// The routines flipnm() and flipnm_post() implement a generalized edge flip //
+// algorithm which uses a combination of elementary flips. //
+// //
+// The routine insertpoint() implements a variant of Bowyer-Watson's cavity //
+// algorithm to insert a vertex. It works for arbitray tetrahedralization, //
+// either Delaunay, or constrained Delaunay, or non-Delaunay. //
+// //
///////////////////////////////////////////////////////////////////////////////
- void flippush(badface*&, triface*);
-
// The elementary flips.
- void flip23(triface*, int, int, int);
- void flip32(triface*, int, int, int);
- void flip41(triface*, int, int, int);
+ void flip23(triface*, int, flipconstraints* fc);
+ void flip32(triface*, int, flipconstraints* fc);
+ void flip41(triface*, int, flipconstraints* fc);
// A generalized edge flip.
int flipnm(triface*, int n, int level, int, flipconstraints* fc);
int flipnm_post(triface*, int n, int nn, int, flipconstraints* fc);
- // Incremental flips.
- long lawsonflip3d(point, int flipflag, int, int, int flipedgeflag);
-
// Point insertion.
- int insertvertex(point newpt, triface *searchtet, face *splitsh, face*,
- insertvertexflags *ivf);
+ int insertpoint(point, triface*, face*, face*, insertvertexflags*);
+ void insertpoint_abort(face*, insertvertexflags*);
///////////////////////////////////////////////////////////////////////////////
// //
// Delaunay tetrahedralization //
// //
+// The routine incrementaldelaunay() implemented two incremental algorithms //
+// for constructing Delaunay tetrahedralizations (DTs): the Bowyer-Watson //
+// (B-W) algorithm and the incremental flip algorithm of Edelsbrunner and //
+// Shah, "Incremental topological flipping works for regular triangulation," //
+// Algorithmica, 15:233-241, 1996. //
+// //
+// The routine incrementalflip() implements the flip algorithm of [Edelsbru- //
+// nner and Shah, 1996]. It flips a queue of locally non-Delaunay faces (in //
+// an arbitrary order). The success is guaranteed when the Delaunay tetrah- //
+// edralization is constructed incrementally by adding one vertex at a time. //
+// //
+// The routine locate() finds a tetrahedron contains a new point in current //
+// DT. It uses a simple stochastic walk algorithm: starting from an arbitr- //
+// ary tetrahedron in DT, it finds the destination by visit one tetrahedron //
+// at a time, randomly chooses a tetrahedron if there are more than one //
+// choices. This algorithm terminates due to Edelsbrunner's acyclic theorem. //
+// Choose a good starting tetrahedron is crucial to the speed of the walk. //
+// TetGen originally uses the "jump-and-walk" algorithm of Muecke, E.P., //
+// Saias, I., and Zhu, B. "Fast Randomized Point Location Without Preproces- //
+// sing." In Proceedings of the 12th ACM Symposium on Computational Geometry,//
+// 274-283, 1996. It first randomly samples several tetrahedra in the DT //
+// and then choosing the closet one to start walking. //
+// The above algorithm slows download dramatically as the number of points //
+// grows -- reported in Amenta, N., Choi, S. and Rote, G., "Incremental //
+// construction con {BRIO}," In Proceedings of 19th ACM Symposium on //
+// Computational Geometry, 211-219, 2003. On the other hand, Liu and //
+// Snoeyink showed that the point location can be made in constant time if //
+// the points are pre-sorted so that the nearby points in space have nearby //
+// indices, then adding the points in this order. They sorted the points //
+// along the 3D Hilbert curve. //
+// //
+// The routine hilbert_sort3() sorts a set of 3D points along the 3D Hilbert //
+// curve. It recursively splits a point set according to the Hilbert indices //
+// mapped to the subboxes of the bounding box of the point set. //
+// The Hilbert indices is calculated by Butz's algorithm in 1971. A nice //
+// exposition of this algorithm can be found in the paper of Hamilton, C., //
+// "Compact Hilbert Indices", Technical Report CS-2006-07, Computer Science, //
+// Dalhousie University, 2006 (the Section 2). My implementation also refer- //
+// enced Steven Witham's implementation of "Hilbert walk" (hopefully, it is //
+// still available at: http://www.tiac.net/~sw/2008/10/Hilbert/). //
+// //
+// TetGen sorts the points using the method in the paper of Boissonnat,J.-D.,//
+// Devillers, O. and Hornus, S. "Incremental Construction of the Delaunay //
+// Triangulation and the Delaunay Graph in Medium Dimension," In Proceedings //
+// of the 25th ACM Symposium on Computational Geometry, 2009. //
+// It first randomly sorts the points into subgroups using the Biased Rand-//
+// omized Insertion Ordering (BRIO) of Amenta et al 2003, then sorts the //
+// points in each subgroup along the 3D Hilbert curve. Inserting points in //
+// this order ensures a randomized "sprinkling" of the points over the //
+// domain, while sorting of each subset ensures locality. //
+// //
///////////////////////////////////////////////////////////////////////////////
void transfernodes();
// Point sorting.
- void btree_sort(point*, int, int, REAL, REAL, REAL, REAL, REAL, REAL, int);
- void btree_insert(point insertpt);
- void btree_search(point searchpt, triface* searchtet);
- void ordervertices(point* vertexarray, int arraysize);
+ int transgc[8][3][8], tsb1mod3[8];
+ void hilbert_init(int n);
+ int hilbert_split(point* vertexarray, int arraysize, int gc0, int gc1,
+ REAL, REAL, REAL, REAL, REAL, REAL);
+ void hilbert_sort3(point* vertexarray, int arraysize, int e, int d,
+ REAL, REAL, REAL, REAL, REAL, REAL, int depth);
+ void brio_multiscale_sort(point*,int,int threshold,REAL ratio,int* depth);
// Point location.
unsigned long randomnation(unsigned int choices);
void randomsample(point searchpt, triface *searchtet);
- enum locateresult locate(point searchpt, triface*, int, int);
+ enum locateresult locate(point searchpt, triface *searchtet, int);
+
+ // Incremental flips.
+ void flippush(badface*&, triface*);
+ int incrementalflip(point newpt, flipconstraints *fc);
// Incremental Delaunay construction.
void initialdelaunay(point pa, point pb, point pc, point pd);
@@ -1724,9 +1751,6 @@ public:
// //
///////////////////////////////////////////////////////////////////////////////
- bool calculateabovepoint(arraypool*, point*, point*, point*);
- void calculateabovepoint4(point, point, point, point);
-
void flipshpush(face*);
void flip22(face*, int, int);
void flip31(face*, int);
@@ -1746,53 +1770,116 @@ public:
void meshsurface();
void interecursive(shellface** subfacearray, int arraysize, int axis,
- REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
- REAL bzmin, REAL bzmax, int* internum);
+ REAL, REAL, REAL, REAL, REAL, REAL, int* internum);
void detectinterfaces();
///////////////////////////////////////////////////////////////////////////////
// //
// Constrained Delaunay tetrahedralization //
// //
+// A constrained Delaunay tetrahedralization (CDT) is a variation of a Dela- //
+// unay tetrahedralization (DT) that is constrained to respect the boundary //
+// of a 3D PLC (domain). In a CDT of a 3D PLC, every vertex or edge of the //
+// PLC is also a vertex or an edge of the CDT, every polygon of the PLC is a //
+// union of triangles of the CDT. A crucial difference between a CDT and a //
+// DT is that triangles in the PLC's polygons are not required to be locally //
+// Delaunay, which frees the CDT to better respect the PLC's polygons. CDTs //
+// have optimal properties similar to those of DTs. //
+// //
+// Steiner Points and Steiner CDTs. It is known that even a simple 3D polyh- //
+// edron may not have a tetrahedralization which only uses its own vertices. //
+// Some extra points, so-called "Steiner points" are needed in order to form //
+// a tetrahedralization of such polyhedron. It is true for tetrahedralizing //
+// a 3D PLC as well. A Steiner CDT of a 3D PLC is a CDT containing Steiner //
+// points. The CDT algorithms of TetGen in general create Steiner CDTs. //
+// Almost all of the Steiner points are added in the edges of the PLC. They //
+// guarantee the existence of a CDT of the modified PLC. //
+// //
+// The routine constraineddelaunay() starts from a DT of the vertices of a //
+// PLC and creates a (Steiner) CDT of the PLC (including Steiner points). It //
+// is constructed by two steps, (1) segment recovery and (2) facet (polygon) //
+// recovery. Each step is accomplished by its own algorithm. //
+// //
+// The routine delaunizesegments() implements the segment recovery algorithm //
+// of Si, H. and Gaertner, K. "Meshing Piecewise Linear Complexes by Constr- //
+// ained Delaunay Tetrahedralizations," In Proceedings of the 14th Internat- //
+// ional Meshing Roundtable, 147--163, 2005. It adds Steiner points into //
+// non-Delaunay segments until all subsegments appear together in a DT. The //
+// running time of this algorithm is proportional to the number of added //
+// Steiner points. //
+// //
+// There are two incremental facet recovery algorithms: the cavity re-trian- //
+// gulation algorithm of Si, H. and Gaertner, K. "3D Boundary Recovery by //
+// Constrained Delaunay Tetrahedralization," Interational Journal for Numer- //
+// ical Methods in Engineering, 85:1341-1364, 2011, and the flip algorithm //
+// of Shewchuk, J. "Updating and Constructing Constrained Delaunay and //
+// Constrained Regular Triangulations by Flips." In Proceedings of the 19th //
+// ACM Symposium on Computational Geometry, 86-95, 2003. //
+// //
+// It is guaranteed in theory, no Steiner point is needed in both algorithms //
+// However, a facet with non-coplanar vertices might cause the additions of //
+// Steiner points. It is discussed in the paper of Si, H., and Shewchuk, J.,//
+// "Incrementally Constructing and Updating Constrained Delaunay //
+// Tetrahedralizations with Finite Precision Coordinates." In Proceedings of //
+// the 21th International Meshing Roundtable, 2012. //
+// //
+// Our implementation of the facet recovery algorithms recover a "missing //
+// region" at a time. Each missing region is a subset of connected interiors //
+// of a polygon. The routine formcavity() creates the cavity of crossing //
+// tetrahedra of the missing region. //
+// //
+// The cavity re-triangulation algorithm is implemented by three subroutines,//
+// delaunizecavity(), fillcavity(), and carvecavity(). Since it may fail due //
+// to non-coplanar vertices, the subroutine restorecavity() is used to rest- //
+// ore the original cavity. //
+// //
+// The routine flipinsertfacet() implements the flip algorithm. The subrout- //
+// ine flipcertify() is used to maintain the priority queue of flips. //
+// //
+// The routine refineregion() is called when the facet recovery algorithm //
+// fail to recover a missing region. It inserts Steiner points to refine the //
+// missing region. In order to avoid inserting Steiner points very close to //
+// existing segments. The classical encroachment rules of the Delaunay //
+// refinement algorithm are used to choose the Steiner points. //
+// //
+// The routine constrainedfacets() does the facet recovery by using either //
+// the cavity re-triangulation algorithm (default) or the flip algorithm. It //
+// results a CDT of the (modified) PLC (including Steiner points). //
+// //
///////////////////////////////////////////////////////////////////////////////
void markacutevertices();
- void reportselfintersect(face *seg, face *shface);
-
- enum interresult finddirection(triface* searchtet, point endpt, int);
+ enum interresult finddirection(triface* searchtet, point endpt);
enum interresult scoutsegment(point, point, triface*, point*, arraypool*);
void getsteinerptonsegment(face* seg, point refpt, point steinpt);
void delaunizesegments();
enum interresult scoutsubface(face* searchsh, triface* searchtet);
- void formmissingregion(face* missh, arraypool* missingshs,
- arraypool* missingshbds, arraypool* missingshverts,
- arraypool *adjtets);
- int scoutcrossedge(triface& crosstet, arraypool*, arraypool* missingshs);
- bool formcavity(triface* searchtet, arraypool* missingshs,
- arraypool* crosstets, arraypool* topfaces,
- arraypool* botfaces, arraypool* toppoints,
- arraypool* botpoints);
-
- // Facet recovery by local re-tetrahedralization [Si and Gaertner'05,'11].
- void delaunizecavity(arraypool *cavpoints, arraypool *cavfaces,
- arraypool *cavshells, arraypool *newtets,
- arraypool *crosstets, arraypool *misfaces);
- bool fillcavity(arraypool* topshells, arraypool* botshells,
- arraypool* midfaces, arraypool* missingshs);
- void carvecavity(arraypool *crosstets, arraypool *topnewtets,
- arraypool *botnewtets);
- void restorecavity(arraypool *crosstets, arraypool *topnewtets,
- arraypool *botnewtets);
-
- // Facet recovery by flips [Shewchuk'03].
- void flipcertify(triface *chkface, badface **pqueue);
- void flipinsertfacet(arraypool *crosstets, arraypool *toppoints,
- arraypool *botpoints, arraypool *midpoints);
+ void formregion(face*, arraypool*, arraypool*, arraypool*);
+ int scoutcrossedge(triface& crosstet, arraypool*, arraypool*);
+ bool formcavity(triface*, arraypool*, arraypool*, arraypool*, arraypool*,
+ arraypool*, arraypool*);
+
+ // Facet recovery by cavity re-triangulation [Si and Gaertner 2011].
+ void delaunizecavity(arraypool*, arraypool*, arraypool*, arraypool*,
+ arraypool*, arraypool*);
+ bool fillcavity(arraypool*, arraypool*, arraypool*, arraypool*,
+ arraypool*, arraypool*, triface* crossedge);
+ void carvecavity(arraypool*, arraypool*, arraypool*);
+ void restorecavity(arraypool*, arraypool*, arraypool*, arraypool*);
+
+ // Facet recovery by flips [Shewchuk 2003].
+ void flipcertify(triface *chkface, badface **pqueue, point, point, point);
+ void flipinsertfacet(arraypool*, arraypool*, arraypool*, arraypool*);
bool fillregion(arraypool* missingshs, arraypool*, arraypool* newshs);
- void refineregion();
+
+ int insertpoint_cdt(point, triface*, face*, face*, insertvertexflags*,
+ arraypool*, arraypool*, arraypool*, arraypool*,
+ arraypool*, arraypool*);
+ void refineregion(face&, arraypool*, arraypool*, arraypool*, arraypool*,
+ arraypool*, arraypool*);
void constrainedfacets();
@@ -1804,7 +1891,6 @@ public:
// //
///////////////////////////////////////////////////////////////////////////////
- // A call back function.
int checkflipeligibility(int fliptype, point, point, point, point, point,
int level, int edgepivot, flipconstraints* fc);
@@ -1840,15 +1926,46 @@ public:
void reconstructmesh();
int scoutpoint(point, triface*, int randflag);
- REAL getpointmeshsize(point, triface*, int iloc, int posflag);
+ REAL getpointmeshsize(point, triface*, int iloc);
void interpolatemeshsize();
+ void insertconstrainedpoints(point *insertarray, int arylen);
void insertconstrainedpoints(tetgenio *addio);
///////////////////////////////////////////////////////////////////////////////
// //
// Mesh refinement //
// //
+// The purpose of mesh refinement is to obtain a tetrahedral mesh with well- //
+// -shaped tetrahedra and appropriate mesh size. It is necessary to insert //
+// new Steiner points to achieve this property. The questions are (1) how to //
+// choose the Steiner points? and (2) how to insert them? //
+// //
+// Delaunay refinement is a technique first developped by Chew [1989] and //
+// Ruppert [1993, 1995] to generate quality triangular meshes in the plane. //
+// It provides guarantee on the smallest angle of the triangles. Rupper's //
+// algorithm guarantees that the mesh is size-optimal (to within a constant //
+// factor) among all meshes with the same quality. //
+// Shewchuk generalized Ruppert's algorithm into 3D in his PhD thesis //
+// [Shewchuk 1997]. A short version of his algorithm appears in "Tetrahedral //
+// Mesh Generation by Delaunay Refinement," In Proceedings of the 14th ACM //
+// Symposium on Computational Geometry, 86-95, 1998. It guarantees that all //
+// tetrahedra of the output mesh have a "radius-edge ratio" (equivalent to //
+// the minimal face angle) bounded. However, it does not remove slivers, a //
+// type of very flat tetrahedra which can have no small face angles but have //
+// very small (and large) dihedral angles. Moreover, it may not terminate if //
+// the input PLC contains "sharp features", e.g., two edges (or two facets) //
+// meet at an acute angle (or dihedral angle). //
+// //
+// TetGen uses the basic Delaunay refinement scheme to insert Steiner points.//
+// While it always maintains a constrained Delaunay mesh. The algorithm is //
+// described in Si, H., "Adaptive Constrained Delaunay Mesh Generation," //
+// International Journal for Numerical Methods in Engineering, 75:856-880. //
+// This algorithm always terminates and sharp features are easily preserved. //
+// The mesh has good quality (same as Shewchuk's Delaunay refinement algoro- //
+// thm) in the bulk of the mesh domain. Moreover, it supports the generation //
+// of adaptive mesh accoording to a (isotropic) mesh sizing function. //
+// //
///////////////////////////////////////////////////////////////////////////////
void marksharpsegments();
@@ -1859,14 +1976,15 @@ public:
int splitsegment(face *splitseg, point encpt, int qflag, int chkencflag);
void repairencsegs(int chkencflag);
+ void enqueuesubface(memorypool*, face*);
int checkfac4encroach(point, point, point, point checkpt, REAL*, REAL*);
int checkfac4split(face *chkfac, point& encpt, int& qflag, REAL *ccent);
- int splitsubface(face *splitfac, point encpt, int qflag, REAL *ccent,
- int chkencflag);
+ int splitsubface(face *splitfac, point encpt, int qflag, REAL *ccent, int);
void repairencfacs(int chkencflag);
+ void enqueuetetrahedron(triface*);
int checktet4split(triface *chktet, int& qflag, REAL *ccent);
- int splittetrahedron(triface* splittet,int qflag,REAL *ccent,int chkencflag);
+ int splittetrahedron(triface* splittet,int qflag,REAL *ccent, int);
void repairbadtets(int chkencflag);
void delaunayrefinement();
@@ -1877,6 +1995,7 @@ public:
// //
///////////////////////////////////////////////////////////////////////////////
+ long lawsonflip3d(flipconstraints *fc);
void recoverdelaunay();
int gettetrahedron(point, point, point, point, triface *);
@@ -1888,7 +2007,7 @@ public:
int splitsliver(triface *, REAL, int);
long removeslivers(int);
- void optimizemesh(int optflag);
+ void optimizemesh();
///////////////////////////////////////////////////////////////////////////////
// //
@@ -1905,7 +2024,9 @@ public:
int checkconforming(int);
// Mesh statistics.
+ void printfcomma(unsigned long n);
void qualitystatistics();
+ void memorystatistics();
void statistics();
///////////////////////////////////////////////////////////////////////////////
@@ -1932,6 +2053,7 @@ public:
void outmesh2vtk(char*);
+
///////////////////////////////////////////////////////////////////////////////
// //
// Constructor & destructor //
@@ -1940,8 +2062,8 @@ public:
tetgenmesh()
{
+ in = addin = NULL;
b = NULL;
- in = NULL;
bgm = NULL;
tetrahedrons = subfaces = subsegs = points = NULL;
@@ -1952,7 +2074,6 @@ public:
dummypoint = NULL;
flipstack = NULL;
unflipqueue = NULL;
- btreenode_list = NULL;
cavetetlist = cavebdrylist = caveoldtetlist = NULL;
cavetetshlist = cavetetseglist = cavetetvertlist = NULL;
@@ -1963,19 +2084,15 @@ public:
suppsteinerptlist = NULL;
encseglist = encshlist = NULL;
- plane_pa = plane_pb = plane_pc = (point) NULL;
+ highordertable = NULL;
- xmax = xmin = ymax = ymin = zmax = zmin = 0.0;
- longest = 0.0;
- hullsize = 0l;
- insegments = 0l;
- meshedges = meshhulledges = 0l;
- steinerleft = -1;
+
+ numpointattrib = numelemattrib = 0;
+ sizeoftensor = 0;
pointmtrindex = 0;
pointparamindex = 0;
pointmarkindex = 0;
point2simindex = 0;
- point2pbcptindex = 0;
elemattribindex = 0;
volumeboundindex = 0;
shmarkindex = 0;
@@ -1983,47 +2100,31 @@ public:
checksubsegflag = 0;
checksubfaceflag = 0;
checkinverttetflag = 0;
- checkpbcs = 0;
checkconstraints = 0;
nonconvex = 0;
- dupverts = 0;
- unuverts = 0;
+ autofliplinklevel = 1;
samples = 0l;
randomseed = 1l;
minfaceang = minfacetdihed = PI;
- sintheta_tol = sin(0.001 * PI / 180.0);
-
- autofliplinklevel = 1;
-
tetprism_vol_sum = 0.0;
- calc_tetprism_vol = 0;
+ longest = 0.0;
+ xmax = xmin = ymax = ymin = zmax = zmin = 0.0;
- ptloc_count = ptloc_max_count = 0l;
- orient3dcount = 0l;
- inspherecount = insphere_sos_count = 0l;
- flip14count = flip26count = flipn2ncount = 0l;
- flip23count = flip32count = flip44count = flip22count = 0l;
- maxbowatcavsize = totalbowatcavsize = totaldeadtets = 0l;
- triedgcount = triedgcopcount = 0l;
- across_face_count = across_edge_count = across_max_count = 0l;
- fillregioncount = missingsubfacecount = crossingtetcount = 0l;
- cavitycount = cavityexpcount = 0l;
- maxcavsize = maxregionsize = 0l;
- maxcrossfacecount = maxflipsequence = 0l;
- dbg_ignore_facecount = dbg_unflip_facecount = 0l;
- ccent_relocate_count = 0l;
- opt_sliver_peels = 0l;
- r1count = r2count = r3count = 0l;
+ insegments = 0l;
+ hullsize = 0l;
+ meshedges = meshhulledges = 0l;
+ steinerleft = -1;
+ dupverts = 0l;
+ unuverts = 0l;
+ nonregularcount = 0l;
st_segref_count = st_facref_count = st_volref_count = 0l;
+ fillregioncount = cavitycount = cavityexpcount = 0l;
+ flip14count = flip26count = flipn2ncount = 0l;
+ flip23count = flip32count = flip44count = flip41count = 0l;
+ flip22count = flip31count = 0l;
+ totalworkmemory = 0l;
- maxfliplinklevel = maxflipstarsize = 0l;
- flipstarcount = sucflipstarcount = skpflipstarcount = 0l;
-
- rejrefinetetcount = rejrefineshcount = 0l;
-#ifdef WITH_RUNTIME_COUNTERS
- t_ptloc = t_ptinsert = (clock_t) 0;
-#endif
} // tetgenmesh()
~tetgenmesh()
@@ -2032,31 +2133,29 @@ public:
delete bgm;
}
+ if (points != (memorypool *) NULL) {
+ delete points;
+ delete [] dummypoint;
+ }
+
if (tetrahedrons != (memorypool *) NULL) {
delete tetrahedrons;
}
+
if (subfaces != (memorypool *) NULL) {
delete subfaces;
- }
- if (subsegs != (memorypool *) NULL) {
delete subsegs;
}
- if (points != (memorypool *) NULL) {
- delete points;
- }
+
if (tet2segpool != NULL) {
delete tet2segpool;
- }
- if (tet2subpool != NULL) {
delete tet2subpool;
}
+
if (flippool != NULL) {
delete flippool;
delete unflipqueue;
}
- if (dummypoint != (point) NULL) {
- delete [] dummypoint;
- }
if (cavetetlist != NULL) {
delete cavetetlist;
@@ -2079,10 +2178,11 @@ public:
delete subsegstack;
delete subfacstack;
delete subvertstack;
+ delete suppsteinerptlist;
}
- if (suppsteinerptlist != NULL) {
- delete suppsteinerptlist;
+ if (highordertable != NULL) {
+ delete [] highordertable;
}
} // ~tetgenmesh()
@@ -2136,7 +2236,7 @@ inline void terminatetetgen(int x)
printf("Hint: use -d option to detect all self-intersections.\n");
break;
case 4:
- printf("A very small input feature was size detected. Program stopped.\n");
+ printf("A very small input feature size was detected. Program stopped.\n");
printf("Hint: use -T option to set a smaller tolerance.\n");
break;
case 5:
@@ -2144,7 +2244,7 @@ inline void terminatetetgen(int x)
printf("Hint: use -Y option to avoid adding Steiner points in boundary.\n");
break;
case 10:
- printf("An input error was detected Program stopped.\n");
+ printf("An input error was detected. Program stopped.\n");
break;
} // switch (x)
exit(x);
@@ -2153,24 +2253,12 @@ inline void terminatetetgen(int x)
///////////////////////////////////////////////////////////////////////////////
// //
-// Inline functions of mesh data structures //
+// Primitives for tetrahedra //
// //
///////////////////////////////////////////////////////////////////////////////
-//
-// Begin of primitives for tetrahedra
-//
-
-// decode() converts a pointer to an ordered tetrahedron. The version is
-// extracted from the four least significant bits of the pointer.
-
-inline void tetgenmesh::decode(tetrahedron ptr, triface& t) {
- (t).ver = (int) ((uintptr_t) (ptr) & (uintptr_t) 15);
- (t).tet = (tetrahedron *) ((uintptr_t) (ptr) ^ (uintptr_t) (t).ver);
-}
-
-// encode() compress an ordered tetrahedron into a single pointer. It
-// relies on the assumption that all tetrahedra are aligned to sixteen-
+// encode() compress a handle into a single pointer. It relies on the
+// assumption that all addresses of tetrahedra are aligned to sixteen-
// byte boundaries, so that the last four significant bits are zero.
inline tetgenmesh::tetrahedron tetgenmesh::encode(triface& t) {
@@ -2181,135 +2269,139 @@ inline tetgenmesh::tetrahedron tetgenmesh::encode2(tetrahedron* ptr, int ver) {
return (tetrahedron) ((uintptr_t) (ptr) | (uintptr_t) (ver));
}
-// bond() connects two adjacent tetrahedra together. t1 and t2 must refer
-// to the same face and the same edge. Note that the edge directions of
-// t1 and t2 are reversed.
-// Since an edge of t1 can be bonded to any of the three edges of t2. We
-// choose to bond the edge of t2 which is symmetric to the 0-th edge of
-// t1, and vice versa. Now assume t1 is at i-th edge and t2 is at j-th
-// edge, where i, j in {0, 1, 2}. The edge in t2 symmetric to 0-th edge
-// of t1 is mod3[i + j].
-// Since the edge number is coded in the two higher bits of the version,
-// both i, j are in {0, 4, 8}. The edge in t2 symmetric to 0-th edge
-// of t1 is mod12[i + j].
+// decode() converts a pointer to a handle. The version is extracted from
+// the four least significant bits of the pointer.
-inline void tetgenmesh::bond(triface& t1, triface& t2) {
- (t1).tet[(t1).ver & 3] = encode2((t2).tet,
- ((t2).ver & 3) + mod12[((t1).ver & 12) + ((t2).ver & 12)]);
- (t2).tet[(t2).ver & 3] = encode2((t1).tet,
- ((t1).ver & 3) + mod12[((t1).ver & 12) + ((t2).ver & 12)]);
+inline void tetgenmesh::decode(tetrahedron ptr, triface& t) {
+ (t).ver = (int) ((uintptr_t) (ptr) & (uintptr_t) 15);
+ (t).tet = (tetrahedron *) ((uintptr_t) (ptr) ^ (uintptr_t) (t).ver);
}
-// dissolve() a bond (from one side).
+// bond() connects two tetrahedra together. (t1,v1) and (t2,v2) must
+// refer to the same face and the same edge.
-inline void tetgenmesh::dissolve(triface& t) {
- t.tet[t.ver & 3] = NULL;
+inline void tetgenmesh::bond(triface& t1, triface& t2) {
+ t1.tet[t1.ver & 3] = encode2(t2.tet, bondtbl[t1.ver][t2.ver]);
+ t2.tet[t2.ver & 3] = encode2(t1.tet, bondtbl[t2.ver][t1.ver]);
}
-// fsym() finds the adjacent tetrahedron at the same face and the same edge.
-inline void tetgenmesh::fsym(triface& t1, triface& t2) {
- tetrahedron ptr = (t1).tet[(t1).ver & 3];
- int offset = 12 - ((t1).ver & 12);
- decode(ptr, t2);
- (t2).ver = mod12[(t2).ver + offset];
-}
+// dissolve() a bond (from one side).
-inline void tetgenmesh::fsymself(triface& t) {
- tetrahedron ptr = (t).tet[(t).ver & 3];
- int offset = 12 - ((t).ver & 12);
- decode(ptr, t);
- (t).ver = mod12[(t).ver + offset];
+inline void tetgenmesh::dissolve(triface& t) {
+ t.tet[t.ver & 3] = NULL;
}
-// enext() finds the next edge (counterclockwise) on the same face.
+// enext() finds the next edge (counterclockwise) in the same face.
inline void tetgenmesh::enext(triface& t1, triface& t2) {
- (t2).tet = (t1).tet;
- (t2).ver = mod12[(t1).ver + 4];
+ t2.tet = t1.tet;
+ t2.ver = enexttbl[t1.ver];
}
inline void tetgenmesh::enextself(triface& t) {
- (t).ver = mod12[(t).ver + 4];
+ t.ver = enexttbl[t.ver];
}
-// eprev() finds the next edge (clockwise) on the same face.
+// eprev() finds the next edge (clockwise) in the same face.
inline void tetgenmesh::eprev(triface& t1, triface& t2) {
- (t2).tet = (t1).tet;
- (t2).ver = mod12[(t1).ver + 8];
+ t2.tet = t1.tet;
+ t2.ver = eprevtbl[t1.ver];
}
inline void tetgenmesh::eprevself(triface& t) {
- (t).ver = mod12[(t).ver + 8];
+ t.ver = eprevtbl[t.ver];
}
-// esym() finds the reversed edge. It is on the other face of the
+// esym() finds the reversed edge. It is in the other face of the
// same tetrahedron.
inline void tetgenmesh::esym(triface& t1, triface& t2) {
(t2).tet = (t1).tet;
- (t2).ver = edgepivot[(t1).ver];
+ (t2).ver = esymtbl[(t1).ver];
}
inline void tetgenmesh::esymself(triface& t) {
- (t).ver = edgepivot[(t).ver];
+ (t).ver = esymtbl[(t).ver];
}
-// enextesym() finds the reversed edge of the next edge. It is on the other
-// face of the same tetrahedron.
+// enextesym() finds the reversed edge of the next edge. It is in the other
+// face of the same tetrahedron. It is the combination esym() * enext().
inline void tetgenmesh::enextesym(triface& t1, triface& t2) {
- enext(t1, t2);
- esymself(t2);
+ t2.tet = t1.tet;
+ t2.ver = enextesymtbl[t1.ver];
}
inline void tetgenmesh::enextesymself(triface& t) {
- enextself(t);
- esymself(t);
+ t.ver = enextesymtbl[t.ver];
}
-// eprevesym() finds the reversed edge of the previous edge. It is on the
-// other face of the same tetrahedron.
+// eprevesym() finds the reversed edge of the previous edge.
inline void tetgenmesh::eprevesym(triface& t1, triface& t2) {
- eprev(t1, t2);
- esymself(t2);
+ t2.tet = t1.tet;
+ t2.ver = eprevesymtbl[t1.ver];
}
inline void tetgenmesh::eprevesymself(triface& t) {
- eprevself(t);
- esymself(t);
+ t.ver = eprevesymtbl[t.ver];
}
-// fnext() finds the next face while rotating about an edge according to
-// a right-hand rule. The face is in the adjacent tetrahedron. It is
-// equivalent to the combination: fsym() * esym().
+// eorgoppo() Finds the opposite face of the origin of the current edge.
+// Return the opposite edge of the current edge.
-inline void tetgenmesh::fnext(triface& t1, triface& t2) {
- esym(t1, t2);
- fsymself(t2);
+inline void tetgenmesh::eorgoppo(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = eorgoppotbl[t1.ver];
+}
+
+inline void tetgenmesh::eorgoppoself(triface& t) {
+ t.ver = eorgoppotbl[t.ver];
+}
+
+// edestoppo() Finds the opposite face of the destination of the current
+// edge. Return the opposite edge of the current edge.
+
+inline void tetgenmesh::edestoppo(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = edestoppotbl[t1.ver];
}
-inline void tetgenmesh::fnextself(triface& t) {
- esymself(t);
- fsymself(t);
+inline void tetgenmesh::edestoppoself(triface& t) {
+ t.ver = edestoppotbl[t.ver];
}
-// fprev() finds the next face while rotating about an edge according to
-// a left-hand rule. The face is in the adjacent tetrahedron. It is
-// equivalent to the combination: esym() * fsym().
+// fsym() finds the adjacent tetrahedron at the same face and the same edge.
-inline void tetgenmesh::fprev(triface& t1, triface& t2) {
- fsym(t1, t2);
- esymself(t2);
+inline void tetgenmesh::fsym(triface& t1, triface& t2) {
+ decode((t1).tet[(t1).ver & 3], t2);
+ t2.ver = fsymtbl[t1.ver][t2.ver];
}
-inline void tetgenmesh::fprevself(triface& t) {
- fsymself(t);
- esymself(t);
+
+#define fsymself(t) \
+ t1ver = (t).ver; \
+ decode((t).tet[(t).ver & 3], (t));\
+ (t).ver = fsymtbl[t1ver][(t).ver]
+
+// fnext() finds the next face while rotating about an edge according to
+// a right-hand rule. The face is in the adjacent tetrahedron. It is
+// the combination: fsym() * esym().
+
+inline void tetgenmesh::fnext(triface& t1, triface& t2) {
+ decode(t1.tet[facepivot1[t1.ver]], t2);
+ t2.ver = facepivot2[t1.ver][t2.ver];
}
+
+#define fnextself(t) \
+ t1ver = (t).ver; \
+ decode((t).tet[facepivot1[(t).ver]], (t)); \
+ (t).ver = facepivot2[t1ver][(t).ver]
+
+
// The following primtives get or set the origin, destination, face apex,
// or face opposite of an ordered tetrahedron.
@@ -2408,17 +2500,12 @@ inline void tetgenmesh::uninfect(triface& t) {
((int *) (t.tet))[elemmarkerindex] &= ~1;
}
-// Test a tetrahedron for viral infection.
-
inline bool tetgenmesh::infected(triface& t) {
return (((int *) (t.tet))[elemmarkerindex] & 1) != 0;
}
// marktest(), marktested(), unmarktest() -- primitives to flag or unflag a
-// tetrahedron. The last second bit of the element marker is marked (1)
-// or unmarked (0).
-// One needs them in forming Bowyer-Watson cavity, to mark a tetrahedron if
-// it has been checked (for Delaunay case) so later check can be avoided.
+// tetrahedron. Use the second lowerest bit of the element marker.
inline void tetgenmesh::marktest(triface& t) {
((int *) (t.tet))[elemmarkerindex] |= 2;
@@ -2435,8 +2522,6 @@ inline bool tetgenmesh::marktested(triface& t) {
// markface(), unmarkface(), facemarked() -- primitives to flag or unflag a
// face of a tetrahedron. From the last 3rd to 6th bits are used for
// face markers, e.g., the last third bit corresponds to loc = 0.
-// One use of the face marker is in flip algorithm. Each queued face (check
-// for locally Delaunay) is marked.
inline void tetgenmesh::markface(triface& t) {
((int *) (t.tet))[elemmarkerindex] |= (4 << (t.ver & 3));
@@ -2453,7 +2538,7 @@ inline bool tetgenmesh::facemarked(triface& t) {
// markedge(), unmarkedge(), edgemarked() -- primitives to flag or unflag an
// edge of a tetrahedron. From the last 7th to 12th bits are used for
// edge markers, e.g., the last 7th bit corresponds to the 0th edge, etc.
-// Remark: The last 7th bit is marked by 2^6 = 64.
+// Remark: The last 7th bit is marked by 2^6 = 64.
inline void tetgenmesh::markedge(triface& t) {
((int *) (t.tet))[elemmarkerindex] |= (int) (64 << ver2edge[(t).ver]);
@@ -2506,7 +2591,6 @@ inline void tetgenmesh::increaseelemcounter(triface& t) {
inline void tetgenmesh::decreaseelemcounter(triface& t) {
int c = elemcounter(t);
- assert(c > 0); // Never get a negative counter.
setelemcounter(t, c - 1);
}
@@ -2522,13 +2606,11 @@ inline bool tetgenmesh::isdeadtet(triface& t) {
return ((t.tet == NULL) || (t.tet[4] == NULL));
}
-//
-// End of primitives for tetrahedra
-//
-
-//
-// Begin of primitives for subfaces/subsegments
-//
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for subfaces and subsegments //
+// //
+///////////////////////////////////////////////////////////////////////////////
// Each subface contains three pointers to its neighboring subfaces, with
// edge versions. To save memory, both information are kept in a single
@@ -2540,7 +2622,7 @@ inline bool tetgenmesh::isdeadtet(triface& t) {
inline void tetgenmesh::sdecode(shellface sptr, face& s) {
s.shver = (int) ((uintptr_t) (sptr) & (uintptr_t) 7);
- s.sh = (shellface *) ((uintptr_t) (sptr) & ~ (uintptr_t) 7);
+ s.sh = (shellface *) ((uintptr_t) (sptr) ^ (uintptr_t) (s.shver));
}
inline tetgenmesh::shellface tetgenmesh::sencode(face& s) {
@@ -2775,17 +2857,6 @@ inline void tetgenmesh::setshelltype(face& s, enum shestype value)
((((int *) ((s).sh))[shmarkindex + 1]) & 255);
}
-// These two primitives set or read the pbc group of the subface.
-
-inline int tetgenmesh::shellpbcgroup(face& s)
-{
- return ((int *) (s.sh))[shmarkindex + 2];
-}
-
-inline void tetgenmesh::setshellpbcgroup(face& s, int value)
-{
- ((int *) (s.sh))[shmarkindex + 2] = value;
-}
// sinfect(), sinfected(), suninfect() -- primitives to flag or unflag a
// subface. The last bit of ((int *) ((s).sh))[shmarkindex+1] is flaged.
@@ -2810,8 +2881,7 @@ inline bool tetgenmesh::sinfected(face& s)
}
// smarktest(), smarktested(), sunmarktest() -- primitives to flag or unflag
-// a subface.
-// The last 2nd bit of ((int *) ((s).sh))[shmarkindex+1] is flaged.
+// a subface.The last 2nd bit of the integer is flaged.
inline void tetgenmesh::smarktest(face& s)
{
@@ -2831,8 +2901,7 @@ inline bool tetgenmesh::smarktested(face& s)
}
// smarktest2(), smarktest2ed(), sunmarktest2() -- primitives to flag or
-// unflag a subface.
-// The last 3rd bit of ((int *) ((s).sh))[shmarkindex+1] is flaged.
+// unflag a subface. The last 3rd bit of the integer is flaged.
inline void tetgenmesh::smarktest2(face& s)
{
@@ -2870,50 +2939,34 @@ inline bool tetgenmesh::smarktest3ed(face& s)
return ((((int *) ((s).sh))[shmarkindex+1] & (int) 8) != 0);
}
-//
-// End of primitives for subfaces/subsegments
-//
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for interacting between tetrahedra and subfaces //
+// //
+///////////////////////////////////////////////////////////////////////////////
-//
-// Begin of primitives for interacting between tetrahedra and subfaces
-//
// tsbond() bond a tetrahedron (t) and a subface (s) together.
// Note that t and s must be the same face and the same edge. Moreover,
// t and s have the same orientation.
// Since the edge number in t and in s can be any number in {0,1,2}. We bond
// the edge in s which corresponds to t's 0th edge, and vice versa.
-inline void tetgenmesh::tsbond(triface& t, face& s)
+inline void tetgenmesh::tsbond(triface& t, face& s)
{
- int soffset, toffset, ver;
-
if ((t).tet[9] == NULL) {
// Allocate space for this tet.
(t).tet[9] = (tetrahedron) tet2subpool->alloc();
- // NULL all fields in this space.
+ // Initialize.
for (int i = 0; i < 4; i++) {
((shellface *) (t).tet[9])[i] = NULL;
}
}
-
- assert(org(t) == sorg(s)); // FOR DEBUG
-
- if (((s).shver & 1) == 0) {
- // t and s have the same orientation.
- soffset = mod6[6 - (((t).ver & 12) >> 1)]; // {0,2,4}
- toffset = mod12[12 - (((s).shver & 6) << 1)]; // {0,4,8}
- } else {
- // t and s have revsered orientations.
- soffset = (((t).ver & 12) >> 1); // {0,2,4}
- toffset = (((s).shver & 6) << 1); // {0,4,8}
- }
-
// Bond t <== s.
- ver = ((s).shver & 1) + mod6[((s).shver & 6) + soffset];
- ((shellface *) (t).tet[9])[(t).ver & 3] = sencode2((s).sh, ver);
+ ((shellface *) (t).tet[9])[(t).ver & 3] =
+ sencode2((s).sh, tsbondtbl[t.ver][s.shver]);
// Bond s <== t.
- ver = ((t).ver & 3) + mod12[((t).ver & 12) + toffset];
- s.sh[9 + ((s).shver & 1)] = (shellface) encode2((t).tet, ver);
+ s.sh[9 + ((s).shver & 1)] =
+ (shellface) encode2((t).tet, stbondtbl[t.ver][s.shver]);
}
// tspivot() finds a subface (s) abutting on the given tetrahdera (t).
@@ -2923,47 +2976,37 @@ inline void tetgenmesh::tsbond(triface& t, face& s)
inline void tetgenmesh::tspivot(triface& t, face& s)
{
- int soffset;
-
if ((t).tet[9] == NULL) {
(s).sh = NULL;
return;
}
-
// Get the attached subface s.
sdecode(((shellface *) (t).tet[9])[(t).ver & 3], (s));
-
- // Set the right edge in s.
- if (((s).shver & 1) == 0) {
- soffset = (((t).ver & 12) >> 1); // {0,2,4}
- } else {
- soffset = mod6[6 - (((t).ver & 12) >> 1)]; // {0,2,4}
- }
- (s).shver = ((s).shver & 1) + mod6[((s).shver & 6) + soffset];
+ (s).shver = tspivottbl[t.ver][s.shver];
}
+// Quickly check if the handle (t, v) is a subface.
+#define issubface(t) \
+ ((t).tet[9] && ((t).tet[9])[(t).ver & 3])
+
// stpivot() finds a tetrahedron (t) abutting a given subface (s).
// Return the t (if it exists) with the same edge and the same
// orientation of s.
inline void tetgenmesh::stpivot(face& s, triface& t)
{
- int toffset;
-
decode((tetrahedron) s.sh[9 + (s.shver & 1)], t);
-
if ((t).tet == NULL) {
return;
}
-
- if (((s).shver & 1) == 0) {
- toffset = (((s).shver & 6) << 1); // {0,4,8}
- } else {
- toffset = mod12[12 - (((s).shver & 6) << 1)]; // {0,4,8}
- }
- (t).ver = ((t).ver & 3) + mod12[((t).ver & 12) + toffset];
+ (t).ver = stpivottbl[t.ver][s.shver];
}
+// Quickly check if this subface is attached to a tetrahedron.
+
+#define isshtet(s) \
+ ((s).sh[9 + ((s).shver & 1)])
+
// tsdissolve() dissolve a bond (from the tetrahedron side).
inline void tetgenmesh::tsdissolve(triface& t)
@@ -2981,13 +3024,11 @@ inline void tetgenmesh::stdissolve(face& s)
(s).sh[10] = NULL;
}
-//
-// End of primitives for interacting between tetrahedra and subfaces
-//
-
-//
-// Begin of primitives for interacting between subfaces and subsegs
-//
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for interacting between subfaces and segments //
+// //
+///////////////////////////////////////////////////////////////////////////////
// ssbond() bond a subface to a subsegment.
@@ -3014,24 +3055,26 @@ inline void tetgenmesh::ssdissolve(face& s)
inline void tetgenmesh::sspivot(face& s, face& edge)
{
- shellface sptr = (shellface) s.sh[6 + (s.shver >> 1)];
- sdecode(sptr, edge);
+ sdecode((shellface) s.sh[6 + (s.shver >> 1)], edge);
}
-//
-// End of primitives for interacting between subfaces and subsegs
-//
+// Quickly check if the edge is a subsegment.
+
+#define isshsubseg(s) \
+ ((s).sh[6 + ((s).shver >> 1)])
-//
-// Begin of primitives for interacting between tet and subsegs.
-//
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for interacting between tetrahedra and segments //
+// //
+///////////////////////////////////////////////////////////////////////////////
inline void tetgenmesh::tssbond1(triface& t, face& s)
{
if ((t).tet[8] == NULL) {
// Allocate space for this tet.
(t).tet[8] = (tetrahedron) tet2segpool->alloc();
- // NULL all fields in this space.
+ // Initialization.
for (int i = 0; i < 6; i++) {
((shellface *) (t).tet[8])[i] = NULL;
}
@@ -3065,18 +3108,21 @@ inline void tetgenmesh::tsspivot1(triface& t, face& s)
}
}
+// Quickly check whether 't' is a segment or not.
+
+#define issubseg(t) \
+ ((t).tet[8] && ((t).tet[8])[ver2edge[(t).ver]])
+
inline void tetgenmesh::sstpivot1(face& s, triface& t)
{
decode((tetrahedron) s.sh[9], t);
}
-//
-// End of primitives for interacting between tet and subsegs.
-//
-
-//
-// Begin of primitives for points
-//
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for points //
+// //
+///////////////////////////////////////////////////////////////////////////////
inline int tetgenmesh::pointmark(point pt) {
return ((int *) (pt))[pointmarkindex];
@@ -3133,8 +3179,8 @@ inline bool tetgenmesh::pinfected(point pt) {
return (((int *) (pt))[pointmarkindex + 1] & (int) 1) != 0;
}
-// pmarktest(), punmarktest(), pmarktested() -- primitives to mark or unmark
-// a point.
+// pmarktest(), punmarktest(), pmarktested() -- more primitives to
+// flag or unflag a point.
inline void tetgenmesh::pmarktest(point pt) {
((int *) (pt))[pointmarkindex + 1] |= (int) 2;
@@ -3148,8 +3194,6 @@ inline bool tetgenmesh::pmarktested(point pt) {
return (((int *) (pt))[pointmarkindex + 1] & (int) 2) != 0;
}
-// pmarktest2(), ...
-
inline void tetgenmesh::pmarktest2(point pt) {
((int *) (pt))[pointmarkindex + 1] |= (int) 4;
}
@@ -3162,8 +3206,6 @@ inline bool tetgenmesh::pmarktest2ed(point pt) {
return (((int *) (pt))[pointmarkindex + 1] & (int) 4) != 0;
}
-// pmarktest3(), ...
-
inline void tetgenmesh::pmarktest3(point pt) {
((int *) (pt))[pointmarkindex + 1] |= (int) 8;
}
@@ -3176,7 +3218,6 @@ inline bool tetgenmesh::pmarktest3ed(point pt) {
return (((int *) (pt))[pointmarkindex + 1] & (int) 8) != 0;
}
-
// These following primitives set and read a pointer to a tetrahedron
// a subface/subsegment, a point, or a tet of background mesh.
@@ -3213,15 +3254,6 @@ inline void tetgenmesh::setpoint2bgmtet(point pt, tetrahedron value) {
((tetrahedron *) (pt))[point2simindex + 3] = value;
}
-// These primitives set and read a pointer to its pbc point.
-
-inline tetgenmesh::point tetgenmesh::point2pbcpt(point pt) {
- return (point) ((tetrahedron *) (pt))[point2pbcptindex];
-}
-
-inline void tetgenmesh::setpoint2pbcpt(point pt, point value) {
- ((tetrahedron *) (pt))[point2pbcptindex] = (tetrahedron) value;
-}
// point2tetorg() Get the tetrahedron whose origin is the point.
@@ -3290,19 +3322,19 @@ inline tetgenmesh::point tetgenmesh::farsdest(face& s)
return sdest(travesh);
}
-//
-// End of primitives for points
-//
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Linear algebra operators. //
+// //
+///////////////////////////////////////////////////////////////////////////////
// dot() returns the dot product: v1 dot v2.
-
inline REAL tetgenmesh::dot(REAL* v1, REAL* v2)
{
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}
// cross() computes the cross product: n = v1 cross v2.
-
inline void tetgenmesh::cross(REAL* v1, REAL* v2, REAL* n)
{
n[0] = v1[1] * v2[2] - v2[1] * v1[2];
@@ -3311,7 +3343,6 @@ inline void tetgenmesh::cross(REAL* v1, REAL* v2, REAL* n)
}
// distance() computs the Euclidean distance between two points.
-
inline REAL tetgenmesh::distance(REAL* p1, REAL* p2)
{
return sqrt((p2[0] - p1[0]) * (p2[0] - p1[0]) +
@@ -3319,24 +3350,11 @@ inline REAL tetgenmesh::distance(REAL* p1, REAL* p2)
(p2[2] - p1[2]) * (p2[2] - p1[2]));
}
-// Linear algebra operators.
-
-#define NORM2(x, y, z) ((x) * (x) + (y) * (y) + (z) * (z))
-
-#define DIST(p1, p2) \
- sqrt(NORM2((p2)[0] - (p1)[0], (p2)[1] - (p1)[1], (p2)[2] - (p1)[2]))
-
-#define DOT(v1, v2) \
- ((v1)[0] * (v2)[0] + (v1)[1] * (v2)[1] + (v1)[2] * (v2)[2])
-
-#define CROSS(v1, v2, n) \
- (n)[0] = (v1)[1] * (v2)[2] - (v2)[1] * (v1)[2];\
- (n)[1] = -((v1)[0] * (v2)[2] - (v2)[0] * (v1)[2]);\
- (n)[2] = (v1)[0] * (v2)[1] - (v2)[0] * (v1)[1]
-
-#define SETVECTOR3(V, a0, a1, a2) (V)[0] = (a0); (V)[1] = (a1); (V)[2] = (a2)
+inline REAL tetgenmesh::norm2(REAL x, REAL y, REAL z)
+{
+ return (x) * (x) + (y) * (y) + (z) * (z);
+}
-#define SWAP2(a0, a1, tmp) (tmp) = (a0); (a0) = (a1); (a1) = (tmp)
#endif // #ifndef tetgenH
--
GitLab