From 4d69aaee512c078e7a6a6a02cbcb48a69fd38762 Mon Sep 17 00:00:00 2001
From: Christophe Geuzaine <cgeuzaine@ulg.ac.be>
Date: Wed, 2 May 2007 07:59:29 +0000
Subject: [PATCH] - tetgen update - polished mesh option strings in gui -
merged modified extrusion patch from <mi.benham@free.fr>
---
Fltk/GUI.cpp | 10 +-
Geo/GModel.cpp | 4 +-
Geo/GModelIO_Mesh.cpp | 12 +-
Geo/GPoint.h | 9 +
Mesh/meshGEdge.cpp | 14 +-
Mesh/meshGRegionExtruded.cpp | 56 +-
contrib/Tetgen/README | 12 +-
contrib/Tetgen/predicates.cxx | 11 +
contrib/Tetgen/tetgen.cxx | 10428 +++++++++++++++++++++-----------
contrib/Tetgen/tetgen.h | 435 +-
10 files changed, 7215 insertions(+), 3776 deletions(-)
diff --git a/Fltk/GUI.cpp b/Fltk/GUI.cpp
index e8a95b2d06..aa90140b9d 100644
--- a/Fltk/GUI.cpp
+++ b/Fltk/GUI.cpp
@@ -1,4 +1,4 @@
-// $Id: GUI.cpp,v 1.605 2007-04-26 12:23:04 geuzaine Exp $
+// $Id: GUI.cpp,v 1.606 2007-05-02 07:59:27 geuzaine Exp $
//
// Copyright (C) 1997-2007 C. Geuzaine, J.-F. Remacle
//
@@ -2280,11 +2280,11 @@ void GUI::create_option_window()
Fl_Group *o = new Fl_Group(L + WB, WB + BH, width - 2 * WB, height - 2 * WB - BH, "Advanced");
o->hide();
- mesh_butt[1] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 1 * BH, BW, BH, "Compute characteritic lenghts automatically from curvatures" );
+ mesh_butt[1] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 1 * BH, BW, BH, "Compute characteritic lengths from curvatures" );
mesh_butt[1]->type(FL_TOGGLE_BUTTON);
mesh_butt[1]->callback(mesh_options_ok_cb);
- mesh_butt[5] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 2 * BH, BW, BH, "Constrain background mesh with characteristic length field");
+ mesh_butt[5] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 2 * BH, BW, BH, "Constrain background mesh with other length fields");
mesh_butt[5]->type(FL_TOGGLE_BUTTON);
mesh_butt[5]->callback(mesh_options_ok_cb);
@@ -2295,11 +2295,11 @@ void GUI::create_option_window()
#endif
mesh_butt[2]->callback(mesh_options_ok_cb);
- mesh_butt[3] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 4 * BH, BW, BH, "Optimize high order mesh (currently only for 2D-plane)");
+ mesh_butt[3] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 4 * BH, BW, BH, "Optimize high order mesh (only for 2D-plane)");
mesh_butt[3]->type(FL_TOGGLE_BUTTON);
mesh_butt[3]->callback(mesh_options_ok_cb);
- mesh_butt[21] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 5 * BH, BW, BH, "Impose C1 continuity (only for degrees 2 and 3 and 2D-plane)");
+ mesh_butt[21] = new Fl_Check_Button(L + 2 * WB, 2 * WB + 5 * BH, BW, BH, "Impose C1 continuity (only for 2D-plane, order 2 and 3)");
mesh_butt[21]->type(FL_TOGGLE_BUTTON);
mesh_butt[21]->callback(mesh_options_ok_cb);
diff --git a/Geo/GModel.cpp b/Geo/GModel.cpp
index 2dff9f5ff6..c47ebcb4fd 100644
--- a/Geo/GModel.cpp
+++ b/Geo/GModel.cpp
@@ -1,4 +1,4 @@
-// $Id: GModel.cpp,v 1.40 2007-04-21 19:40:00 geuzaine Exp $
+// $Id: GModel.cpp,v 1.41 2007-05-02 07:59:27 geuzaine Exp $
//
// Copyright (C) 1997-2007 C. Geuzaine, J.-F. Remacle
//
@@ -250,7 +250,7 @@ bool GModel::noPhysicalGroups()
static void addInGroup(GEntity* ge, std::map<int, std::vector<GEntity*> > &group)
{
for(unsigned int i = 0; i < ge->physicals.size(); i++){
- // phyicals can be stored with negative signs when the entity
+ // physicals can be stored with negative signs when the entity
// should be "reversed"
int p = std::abs(ge->physicals[i]);
if(std::find(group[p].begin(), group[p].end(), ge) == group[p].end())
diff --git a/Geo/GModelIO_Mesh.cpp b/Geo/GModelIO_Mesh.cpp
index f00eebe113..ba7fbf0fa4 100644
--- a/Geo/GModelIO_Mesh.cpp
+++ b/Geo/GModelIO_Mesh.cpp
@@ -1,4 +1,4 @@
-// $Id: GModelIO_Mesh.cpp,v 1.15 2007-04-21 19:40:00 geuzaine Exp $
+// $Id: GModelIO_Mesh.cpp,v 1.16 2007-05-02 07:59:27 geuzaine Exp $
//
// Copyright (C) 1997-2007 C. Geuzaine, J.-F. Remacle
//
@@ -571,9 +571,6 @@ int GModel::writeMSH(const std::string &name, double version, bool binary,
return 0;
}
- // binary format exists only in version 2
- if(binary) version = 2.0;
-
// if there are no physicals we save all the elements
if(noPhysicalGroups()) saveAll = true;
@@ -581,6 +578,9 @@ int GModel::writeMSH(const std::string &name, double version, bool binary,
// continuous sequence
int numVertices = renumberMeshVertices(saveAll);
+ // binary format exists only in version 2
+ if(binary) version = 2.0;
+
// get the number of elements (we assume that all the elements in a
// list have the same type, i.e., they are all of the same
// polynomial order)
@@ -725,10 +725,10 @@ int GModel::writePOS(const std::string &name, bool saveAll, double scalingFactor
return 0;
}
- int status = getMeshStatus();
-
if(noPhysicalGroups()) saveAll = true;
+ int status = getMeshStatus();
+
if(status >= 3){
fprintf(fp, "View \"Volumes\" {\n");
fprintf(fp, "T2(1.e5,30,%d){\"Elementary Entity\", \"Element Number\", "
diff --git a/Geo/GPoint.h b/Geo/GPoint.h
index 66b1690903..bd6a60b1df 100644
--- a/Geo/GPoint.h
+++ b/Geo/GPoint.h
@@ -20,6 +20,8 @@
//
// Please report all bugs and problems to <gmsh@geuz.org>.
+#include <math.h>
+
class GEntity;
class GPoint
@@ -48,6 +50,13 @@ class GPoint
par[0] = p[0];
par[1] = p[1];
}
+ double distance(GPoint &p)
+ {
+ double dx = X - p.x();
+ double dy = Y - p.y();
+ double dz = Z - p.z();
+ return sqrt(dx * dx + dy * dy + dz * dz);
+ }
};
#endif
diff --git a/Mesh/meshGEdge.cpp b/Mesh/meshGEdge.cpp
index eb4899aff0..61824ec7c4 100644
--- a/Mesh/meshGEdge.cpp
+++ b/Mesh/meshGEdge.cpp
@@ -1,4 +1,4 @@
-// $Id: meshGEdge.cpp,v 1.37 2007-04-26 09:47:38 remacle Exp $
+// $Id: meshGEdge.cpp,v 1.38 2007-05-02 07:59:27 geuzaine Exp $
//
// Copyright (C) 1997-2007 C. Geuzaine, J.-F. Remacle
//
@@ -189,14 +189,6 @@ void deMeshGEdge::operator() (GEdge *ge)
if(ge->meshRep) ge->meshRep->destroy();
}
-double GPointDist(GPoint &p1, GPoint &p2)
-{
- double dx = p1.x() - p2.x();
- double dy = p1.y() - p2.y();
- double dz = p1.z() - p2.z();
- return sqrt(dx * dx + dy * dy + dz * dz);
-}
-
void meshGEdge::operator() (GEdge *ge)
{
if(ge->geomType() == GEntity::DiscreteCurve) return;
@@ -276,8 +268,8 @@ void meshGEdge::operator() (GEdge *ge)
}
else{
double lc = BGM_MeshSize(ge, t, 0, V.x(), V.y(), V.z());
- if(GPointDist(V, last_p) > 0.7 * lc &&
- !(NUMP == N - 2 && GPointDist(V, end_p) < 0.7 * lc)){
+ if(V.distance(last_p) > 0.7 * lc &&
+ !(NUMP == N - 2 && V.distance(end_p) < 0.7 * lc)){
last_p = V;
ge->mesh_vertices[NUMP2 - 1] = new MEdgeVertex(V.x(), V.y(), V.z(), ge, t);
NUMP2++;
diff --git a/Mesh/meshGRegionExtruded.cpp b/Mesh/meshGRegionExtruded.cpp
index f69c5c6e30..f0e37e01cb 100644
--- a/Mesh/meshGRegionExtruded.cpp
+++ b/Mesh/meshGRegionExtruded.cpp
@@ -1,4 +1,4 @@
-// $Id: meshGRegionExtruded.cpp,v 1.13 2007-03-18 12:05:16 geuzaine Exp $
+// $Id: meshGRegionExtruded.cpp,v 1.14 2007-05-02 07:59:27 geuzaine Exp $
//
// Copyright (C) 1997-2007 C. Geuzaine, J.-F. Remacle
//
@@ -386,13 +386,53 @@ void phase1(GRegion *gr,
for(int j = 0; j < ep->mesh.NbLayer; j++) {
for(int k = 0; k < ep->mesh.NbElmLayer[j]; k++) {
std::vector<MVertex*> v;
- if(getExtrudedVertices(from->triangles[i], ep, j, k, pos, v) == 6){
- if(!edgeExists(v[0], v[4], edges))
- createEdge(v[1], v[3], edges);
- if(!edgeExists(v[4], v[2], edges))
- createEdge(v[1], v[5], edges);
- if(!edgeExists(v[3], v[2], edges))
- createEdge(v[0], v[5], edges);
+ if(getExtrudedVertices(from->triangles[i], ep, j, k, pos, v) == 6){
+#if 0 // this is the old version
+ if(!edgeExists(v[0], v[4], edges))
+ createEdge(v[1], v[3], edges);
+ if(!edgeExists(v[4], v[2], edges))
+ createEdge(v[1], v[5], edges);
+ if(!edgeExists(v[3], v[2], edges))
+ createEdge(v[0], v[5], edges);
+#else // new version from Michel Benhamou <mi.benham@free.fr>
+ int v0 = 0;
+ for(int l = 1; l < 6; l++){
+ if(v[l] < v[v0]) v0 = l;
+ }
+ v0 = (v0 + 2) % 3;
+ int vn[6];
+ for(int l = 0; l < 3; l++){
+ vn[l] = (v0 + l) % 3;
+ vn[l + 3] = vn[l] + 3;
+ }
+
+ if(v[vn[1]] < v[vn[0]]){
+ if(!edgeExists(v[vn[0]], v[vn[4]], edges))
+ createEdge(v[vn[1]], v[vn[3]], edges);
+ }
+ else{
+ if(!edgeExists(v[vn[1]], v[vn[3]], edges))
+ createEdge(v[vn[0]], v[vn[4]], edges);
+ }
+
+ if(v[vn[1]] < v[vn[4]]){
+ if(!edgeExists(v[vn[4]], v[vn[2]], edges))
+ createEdge(v[vn[1]], v[vn[5]], edges);
+ }
+ else{
+ if(!edgeExists(v[vn[1]], v[vn[5]], edges))
+ createEdge(v[vn[4]], v[vn[2]], edges);
+ }
+
+ if(v[vn[0]] < v[vn[3]]){
+ if(!edgeExists(v[vn[3]], v[vn[2]], edges))
+ createEdge(v[vn[0]], v[vn[5]], edges);
+ }
+ else{
+ if(!edgeExists(v[vn[0]], v[vn[5]], edges))
+ createEdge(v[vn[3]], v[vn[2]], edges);
+ }
+#endif
}
}
}
diff --git a/contrib/Tetgen/README b/contrib/Tetgen/README
index 429553ab84..125c22c4fa 100644
--- a/contrib/Tetgen/README
+++ b/contrib/Tetgen/README
@@ -1,14 +1,16 @@
-This is TetGen version 1.4.1 (released on July 28, 2006)
+This is TetGen version 1.4.2 (released on April 16, 2007)
-Please see the user's manul (available at the following link) for compiling
-and using TetGen.
+Please see the documentation of TetGen (available at the following link) for
+compiling and using TetGen.
http://tetgen.berlios.de/index.html
TetGen may be freely copied, modified, and redistributed under the
-following copyright notices stated in the file LICENSE.
+copyright notices stated in the file LICENSE.
Please send bugs/comments to Hang Si <si@wias-berlin.de>
+Thank you and enjoy!
+
Hang Si
-July 28, 2006
+April 16, 2007
diff --git a/contrib/Tetgen/predicates.cxx b/contrib/Tetgen/predicates.cxx
index 0d41e5badf..bc0bd39f9e 100644
--- a/contrib/Tetgen/predicates.cxx
+++ b/contrib/Tetgen/predicates.cxx
@@ -1869,6 +1869,17 @@ 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;
REAL adztail, bdztail, cdztail;
diff --git a/contrib/Tetgen/tetgen.cxx b/contrib/Tetgen/tetgen.cxx
index 348a256569..91035a6404 100644
--- a/contrib/Tetgen/tetgen.cxx
+++ b/contrib/Tetgen/tetgen.cxx
@@ -5,16 +5,18 @@
// A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator //
// //
// Version 1.4 //
-// January 14, 2006 //
+// April 16, 2007 //
// //
-// Copyright 2002, 2004, 2005, 2006 //
+// Copyright (C) 2002--2007 //
// Hang Si //
-// Rathausstr. 9, 10178 Berlin, Germany //
+// Research Group Numerical Mathematics and Scientific Computing //
+// Weierstrass Institute for Applied Analysis and Stochastics //
+// Mohrenstr. 39, 10117 Berlin, Germany //
// si@wias-berlin.de //
// //
-// You can obtain TetGen via internet: http://tetgen.berlios.de. It may be //
-// freely copied, modified, and redistributed under the copyright notices //
-// given in the file LICENSE. //
+// TetGen is freely available through the website: http://tetgen.berlios.de. //
+// It may be copied, modified, and redistributed for non-commercial use. //
+// Please consult the file LICENSE for the detailed copyright notices. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -22,7 +24,7 @@
// //
// tetgen.cxx //
// //
-// The C++ implementation file of the TetGen library. //
+// The TetGen library and program. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -64,15 +66,15 @@ void tetgenio::initialize()
{
firstnumber = 0; // Default item index is numbered from Zero.
mesh_dim = 3; // Default mesh dimension is 3.
+ useindex = true;
pointlist = (REAL *) NULL;
pointattributelist = (REAL *) NULL;
- addpointlist = (REAL *) NULL;
- addpointattributelist = (REAL *) NULL;
+ pointmtrlist = (REAL *) NULL;
pointmarkerlist = (int *) NULL;
numberofpoints = 0;
numberofpointattributes = 0;
- numberofaddpoints = 0;
+ numberofpointmtrs = 0;
tetrahedronlist = (int *) NULL;
tetrahedronattributelist = (REAL *) NULL;
@@ -105,11 +107,18 @@ void tetgenio::initialize()
numberoffacetconstraints = 0;
segmentconstraintlist = (REAL *) NULL;
numberofsegmentconstraints = 0;
- nodeconstraintlist = (REAL *) NULL;
- numberofnodeconstraints = 0;
pbcgrouplist = (pbcgroup *) NULL;
numberofpbcgroups = 0;
+
+ vpointlist = (REAL *) NULL;
+ vedgelist = (voroedge *) NULL;
+ vfacetlist = (vorofacet *) NULL;
+ vcelllist = (int **) NULL;
+ numberofvpoints = 0;
+ numberofvedges = 0;
+ numberofvfacets = 0;
+ numberofvcells = 0;
}
///////////////////////////////////////////////////////////////////////////////
@@ -140,11 +149,8 @@ void tetgenio::deinitialize()
if (pointattributelist != (REAL *) NULL) {
delete [] pointattributelist;
}
- if (addpointlist != (REAL *) NULL) {
- delete [] addpointlist;
- }
- if (addpointattributelist != (REAL *) NULL) {
- delete [] addpointattributelist;
+ if (pointmtrlist != (REAL *) NULL) {
+ delete [] pointmtrlist;
}
if (pointmarkerlist != (int *) NULL) {
delete [] pointmarkerlist;
@@ -210,9 +216,6 @@ void tetgenio::deinitialize()
if (segmentconstraintlist != (REAL *) NULL) {
delete [] segmentconstraintlist;
}
- if (nodeconstraintlist != (REAL *) NULL) {
- delete [] nodeconstraintlist;
- }
if (pbcgrouplist != (pbcgroup *) NULL) {
for (i = 0; i < numberofpbcgroups; i++) {
pg = &(pbcgrouplist[i]);
@@ -222,6 +225,24 @@ void tetgenio::deinitialize()
}
delete [] pbcgrouplist;
}
+ if (vpointlist != (REAL *) NULL) {
+ delete [] vpointlist;
+ }
+ if (vedgelist != (voroedge *) NULL) {
+ delete [] vedgelist;
+ }
+ if (vfacetlist != (vorofacet *) NULL) {
+ for (i = 0; i < numberofvfacets; i++) {
+ delete [] vfacetlist[i].elist;
+ }
+ delete [] vfacetlist;
+ }
+ if (vcelllist != (int **) NULL) {
+ for (i = 0; i < numberofvcells; i++) {
+ delete [] vcelllist[i];
+ }
+ delete [] vcelllist;
+ }
}
///////////////////////////////////////////////////////////////////////////////
@@ -274,13 +295,15 @@ bool tetgenio::load_node_call(FILE* infile, int markers, char* infilename)
attribindex = 0;
for (i = 0; i < numberofpoints; i++) {
stringptr = readnumberline(inputline, infile, infilename);
- if (i == 0) {
- firstnode = (int) strtol (stringptr, &stringptr, 0);
- if ((firstnode == 0) || (firstnode == 1)) {
- firstnumber = firstnode;
+ if (useindex) {
+ if (i == 0) {
+ firstnode = (int) strtol (stringptr, &stringptr, 0);
+ if ((firstnode == 0) || (firstnode == 1)) {
+ firstnumber = firstnode;
+ }
}
- }
- stringptr = findnextnumber(stringptr);
+ stringptr = findnextnumber(stringptr);
+ } // if (useindex)
if (*stringptr == '\0') {
printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
break;
@@ -372,34 +395,50 @@ bool tetgenio::load_node(char* filename)
return false;
}
printf("Opening %s.\n", innodefilename);
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
+ // Read the first line of the file.
stringptr = readnumberline(inputline, infile, innodefilename);
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- mesh_dim = 3;
+ // Is this list of points generated from rbox?
+ stringptr = strstr(inputline, "rbox");
+ if (stringptr == NULL) {
+ // Read number of points, number of dimensions, number of point
+ // attributes, and number of boundary markers.
+ stringptr = inputline;
+ numberofpoints = (int) strtol (stringptr, &stringptr, 0);
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ mesh_dim = 3;
+ } else {
+ mesh_dim = (int) strtol (stringptr, &stringptr, 0);
+ }
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ numberofpointattributes = 0;
+ } else {
+ numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
+ }
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ markers = 0;
+ } else {
+ markers = (int) strtol (stringptr, &stringptr, 0);
+ }
} else {
+ // It is a rbox (qhull) input file.
+ stringptr = inputline;
+ // Get the dimension.
mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberofpointattributes = 0;
- } else {
- numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- markers = 0;
- } else {
- markers = (int) strtol (stringptr, &stringptr, 0);
+ // Get the number of points.
+ stringptr = readnumberline(inputline, infile, innodefilename);
+ numberofpoints = (int) strtol (stringptr, &stringptr, 0);
+ // There is no index column.
+ useindex = 0;
}
- if ((mesh_dim != 3) && (mesh_dim != 2)) {
- printf("Input error: TetGen only works for 2D & 3D point sets.\n");
- fclose(infile);
- return false;
- }
+ // if ((mesh_dim != 3) && (mesh_dim != 2)) {
+ // printf("Input error: TetGen only works for 2D & 3D point sets.\n");
+ // fclose(infile);
+ // return false;
+ // }
if (numberofpoints < (mesh_dim + 1)) {
printf("Input error: TetGen needs at least %d points.\n", mesh_dim + 1);
fclose(infile);
@@ -415,91 +454,6 @@ bool tetgenio::load_node(char* filename)
return true;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// load_addnodes() Load a list of additional nodes into 'addpointlists'. //
-// //
-// 'filename' is the filename of the original inputfile without suffix. The //
-// additional nodes are found in file 'filename-a.node'. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenio::load_addnodes(char* filename)
-{
- FILE *infile;
- char addnodefilename[FILENAMESIZE];
- char inputline[INPUTLINESIZE];
- char *stringptr;
- REAL x, y, z;
- int index;
- int i;
-
- // Additional nodes are saved in file "filename-a.node".
- strcpy(addnodefilename, filename);
- strcat(addnodefilename, "-a.node");
- infile = fopen(addnodefilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", addnodefilename);
- } else {
- // Strange! However, it is not a fatal error.
- printf("Warning: Can't opening %s. Skipped.\n", addnodefilename);
- numberofaddpoints = 0;
- return false;
- }
-
- // Read the number of additional points.
- stringptr = readnumberline(inputline, infile, addnodefilename);
- numberofaddpoints = (int) strtol (stringptr, &stringptr, 0);
- if (numberofaddpoints == 0) {
- // It looks this file contains no point.
- fclose(infile);
- return false;
- }
- // Initialize 'addpointlist';
- addpointlist = new REAL[numberofaddpoints * mesh_dim];
- if (addpointlist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
-
- // Read the list of additional points.
- index = 0;
- for (i = 0; i < numberofaddpoints; i++) {
- stringptr = readnumberline(inputline, infile, addnodefilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
- break;
- }
- x = (REAL) strtod(stringptr, &stringptr);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no y coordinate.\n", firstnumber + i);
- break;
- }
- y = (REAL) strtod(stringptr, &stringptr);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Point %d has no z coordinate.\n", firstnumber + i);
- break;
- }
- z = (REAL) strtod(stringptr, &stringptr);
- addpointlist[index++] = x;
- addpointlist[index++] = y;
- addpointlist[index++] = z;
- }
- fclose(infile);
-
- if (i < numberofaddpoints) {
- // Failed to read to additional points due to some error.
- delete [] addpointlist;
- addpointlist = (REAL *) NULL;
- numberofaddpoints = 0;
- return false;
- }
- return true;
-}
-
///////////////////////////////////////////////////////////////////////////////
// //
// load_pbc() Load a list of pbc groups into 'pbcgrouplist'. //
@@ -716,43 +670,6 @@ bool tetgenio::load_var(char* filename)
}
}
- // Read the node constraint section. It is optional.
- stringptr = readnumberline(inputline, infile, NULL);
- if (stringptr != (char *) NULL && *stringptr != '\0') {
- numberofnodeconstraints = (int) strtol (stringptr, &stringptr, 0);
- } else {
- numberofnodeconstraints = 0;
- }
- if (numberofnodeconstraints > 0) {
- // Initialize 'nodeconstraintlist'.
- nodeconstraintlist = new REAL[numberofnodeconstraints * 2];
- index = 0;
- for (i = 0; i < numberofnodeconstraints; i++) {
- stringptr = readnumberline(inputline, infile, varfilename);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: node constraint %d has no node index.\n",
- firstnumber + i);
- break;
- } else {
- nodeconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: node constraint %d has no edge length bound.\n",
- firstnumber + i);
- break;
- } else {
- nodeconstraintlist[index++] = (REAL) strtod(stringptr, &stringptr);
- }
- }
- if (i < numberofnodeconstraints) {
- // This must be caused by an error.
- fclose(infile);
- return false;
- }
- }
-
fclose(infile);
return true;
}
@@ -772,8 +689,8 @@ bool tetgenio::load_mtr(char* filename)
char mtrfilename[FILENAMESIZE];
char inputline[INPUTLINESIZE];
char *stringptr;
- REAL attrib;
- int attribindex;
+ REAL mtr;
+ int mtrindex;
int i, j;
strcpy(mtrfilename, filename);
@@ -789,38 +706,33 @@ bool tetgenio::load_mtr(char* filename)
// Read number of points, number of columns (1, 3, or 6).
stringptr = readnumberline(inputline, infile, mtrfilename);
stringptr = findnextnumber(stringptr); // Skip number of points.
- i = (int) strtol (stringptr, &stringptr, 0);
- if ((i != 1) && (i != 3) && (i != 6)) {
- // Column number doesn't match. Do nothing with this file.
- fclose(infile);
- return false;
+ if (*stringptr != '\0') {
+ numberofpointmtrs = (int) strtol (stringptr, &stringptr, 0);
}
-
- // Metric tensors are saved in pointattributelist.
- if (pointattributelist != (REAL *) NULL) {
- delete [] pointattributelist;
- pointattributelist = (REAL *) NULL;
+ if (numberofpointmtrs == 0) {
+ // Column number doesn't match. Set a default number (1).
+ numberofpointmtrs = 1;
}
- numberofpointattributes = i;
- // Allocate space for pointattributelist.
- pointattributelist = new REAL[numberofpoints * numberofpointattributes];
- if (pointattributelist == (REAL *) NULL) {
+
+ // Allocate space for pointmtrlist.
+ pointmtrlist = new REAL[numberofpoints * numberofpointmtrs];
+ if (pointmtrlist == (REAL *) NULL) {
printf("Error: Out of memory.\n");
terminatetetgen(1);
}
- attribindex = 0;
+ mtrindex = 0;
for (i = 0; i < numberofpoints; i++) {
// Read metrics.
stringptr = readnumberline(inputline, infile, mtrfilename);
- for (j = 0; j < numberofpointattributes; j++) {
- // stringptr = findnextnumber(stringptr);
+ for (j = 0; j < numberofpointmtrs; j++) {
if (*stringptr == '\0') {
printf("Error: Metric %d is missing value #%d in %s.\n",
i + firstnumber, j + 1, mtrfilename);
terminatetetgen(1);
}
- attrib = (REAL) strtod(stringptr, &stringptr);
- pointattributelist[attribindex++] = attrib;
+ mtr = (REAL) strtod(stringptr, &stringptr);
+ pointmtrlist[mtrindex++] = mtr;
+ stringptr = findnextnumber(stringptr);
}
}
@@ -1817,20 +1729,21 @@ bool tetgenio::load_stl(char* filename)
// the .mesh will be added in this case). .mesh is the file format of Medit, //
// a user-friendly interactive mesh viewing program. //
// //
-// This routine ONLY reads the sections containing vertices and triangles, //
-// other sections (such as tetrahedra, edges, ...) are ignored. //
+// This routine ONLY reads the sections containing vertices, triangles, and //
+// quadrilaters. Other sections (such as tetrahedra, edges, ...) are ignored.//
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenio::load_medit(char* filename)
{
FILE *fp;
- tetgenio::facet *f;
+ tetgenio::facet *tmpflist, *f;
tetgenio::polygon *p;
char infilename[FILENAMESIZE];
char buffer[INPUTLINESIZE];
char *bufferp, *str;
double *coord;
+ int *tmpfmlist;
int dimension = 0;
int nverts = 0;
int nfaces = 0;
@@ -1931,6 +1844,7 @@ bool tetgenio::load_medit(char* filename)
}
if (nfaces == 0) {
// Find if it is the keyword "Triangles" or "Quadrilaterals".
+ corners = 0;
str = strstr(bufferp, "Triangles");
if (!str) str = strstr(bufferp, "triangles");
if (!str) str = strstr(bufferp, "TRIANGLES");
@@ -1953,13 +1867,32 @@ bool tetgenio::load_medit(char* filename)
}
nfaces = strtol(bufferp, &bufferp, 0);
// Allocate memory for 'tetgenio'
- if (nfaces > 0) {
- numberoffacets = nfaces;
- facetlist = new tetgenio::facet[nfaces];
- facetmarkerlist = new int[nfaces];
+ if (nfaces > 0) {
+ if (numberoffacets > 0) {
+ // facetlist has already been allocated. Enlarge arrays.
+ tmpflist = new tetgenio::facet[numberoffacets + nfaces];
+ tmpfmlist = new int[numberoffacets + nfaces];
+ // Copy the data of old arrays into new arrays.
+ for (i = 0; i < numberoffacets; i++) {
+ f = &(tmpflist[i]);
+ tetgenio::init(f);
+ *f = facetlist[i];
+ tmpfmlist[i] = facetmarkerlist[i];
+ }
+ // Release old arrays.
+ delete [] facetlist;
+ delete [] facetmarkerlist;
+ // Remember the new arrays.
+ facetlist = tmpflist;
+ facetmarkerlist = tmpfmlist;
+ } else {
+ // This is the first time to allocate facetlist.
+ facetlist = new tetgenio::facet[nfaces];
+ facetmarkerlist = new int[nfaces];
+ }
}
// Read the following list of faces.
- for (i = 0; i < nfaces; i++) {
+ for (i = numberoffacets; i < numberoffacets + nfaces; i++) {
bufferp = readline(buffer, fp, &line_count);
if (bufferp == NULL) {
printf("Unexpected end of file on line %d in file %s\n",
@@ -2001,10 +1934,12 @@ bool tetgenio::load_medit(char* filename)
facetmarkerlist[i] = (int) strtol(bufferp, &bufferp, 0);
}
}
- continue;
+ // Have read in a list of triangles/quads.
+ numberoffacets += nfaces;
+ nfaces = 0;
}
}
- if (nverts > 0 && nfaces > 0) break; // Ignore other data.
+ // if (nverts > 0 && nfaces > 0) break; // Ignore other data.
}
// Close file
@@ -2092,38 +2027,43 @@ bool tetgenio::load_tetmesh(char* filename)
printf("File I/O Error: Cannot access file %s.\n", infilename);
return false;
}
- // Read number of points, number of dimensions, number of point
- // attributes, and number of boundary markers.
- stringptr = readnumberline(inputline, infile, infilename);
- numberofpoints = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- mesh_dim = 3;
+ // Read the first line of the file.
+ stringptr = readnumberline(inputline, infile, infilename);
+ // Is this list of points generated from rbox?
+ stringptr = strstr(inputline, "rbox");
+ if (stringptr == NULL) {
+ // Read number of points, number of dimensions, number of point
+ // attributes, and number of boundary markers.
+ stringptr = inputline;
+ numberofpoints = (int) strtol (stringptr, &stringptr, 0);
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ mesh_dim = 3;
+ } else {
+ mesh_dim = (int) strtol (stringptr, &stringptr, 0);
+ }
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ numberofpointattributes = 0;
+ } else {
+ numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
+ }
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ markers = 0; // Default value.
+ } else {
+ markers = (int) strtol (stringptr, &stringptr, 0);
+ }
} else {
+ // It is a rbox (qhull) input file.
+ stringptr = inputline;
+ // Get the dimension.
mesh_dim = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberofpointattributes = 0;
- } else {
- numberofpointattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- markers = 0; // Default value.
- } else {
- markers = (int) strtol (stringptr, &stringptr, 0);
- }
-
- if (mesh_dim != 3) {
- printf("Error: load_tetmesh() only works for 3D points.\n");
- fclose(infile);
- return false;
- }
- if (numberofpoints < 4) {
- printf("File I/O error: Input should has at least 4 points.\n");
- fclose(infile);
- return false;
+ // Get the number of points.
+ stringptr = readnumberline(inputline, infile, infilename);
+ numberofpoints = (int) strtol (stringptr, &stringptr, 0);
+ // There is no index column.
+ useindex = 0;
}
// Load the list of nodes.
@@ -2134,86 +2074,92 @@ bool tetgenio::load_tetmesh(char* filename)
fclose(infile);
// Read the elements from an .ele file.
- infilename = inelefilename;
- infile = fopen(infilename, "r");
- if (infile != (FILE *) NULL) {
- printf("Opening %s.\n", infilename);
- // Read number of elements, number of corners (4 or 10), number of
- // element attributes.
- stringptr = readnumberline(inputline, infile, infilename);
- numberoftetrahedra = (int) strtol (stringptr, &stringptr, 0);
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberofcorners = 4; // Default read 4 nodes per element.
- } else {
- numberofcorners = (int) strtol (stringptr, &stringptr, 0);
- }
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- numberoftetrahedronattributes = 0; // Default no attribute.
- } else {
- numberoftetrahedronattributes = (int) strtol (stringptr, &stringptr, 0);
- }
- if (numberofcorners != 4 && numberofcorners != 10) {
- printf("Error: Wrong number of corners %d (should be 4 or 10).\n",
- numberofcorners);
- fclose(infile);
- return false;
- }
- // Allocate memory for tetrahedra.
- if (numberoftetrahedra > 0) {
- tetrahedronlist = new int[numberoftetrahedra * numberofcorners];
- if (tetrahedronlist == (int *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
+ if (mesh_dim == 3) {
+ infilename = inelefilename;
+ infile = fopen(infilename, "r");
+ if (infile != (FILE *) NULL) {
+ printf("Opening %s.\n", infilename);
+ // Read number of elements, number of corners (4 or 10), number of
+ // element attributes.
+ stringptr = readnumberline(inputline, infile, infilename);
+ numberoftetrahedra = (int) strtol (stringptr, &stringptr, 0);
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ numberofcorners = 4; // Default read 4 nodes per element.
+ } else {
+ numberofcorners = (int) strtol(stringptr, &stringptr, 0);
}
- // Allocate memory for output tetrahedron attributes if necessary.
- if (numberoftetrahedronattributes > 0) {
- tetrahedronattributelist = new REAL[numberoftetrahedra *
- numberoftetrahedronattributes];
- if (tetrahedronattributelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ numberoftetrahedronattributes = 0; // Default no attribute.
+ } else {
+ numberoftetrahedronattributes = (int) strtol(stringptr, &stringptr, 0);
}
- }
- // Read the list of tetrahedra.
- index = 0;
- attribindex = 0;
- for (i = 0; i < numberoftetrahedra; i++) {
- // Read tetrahedron index and the tetrahedron's corners.
- stringptr = readnumberline(inputline, infile, infilename);
- for (j = 0; j < numberofcorners; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- printf("Error: Tetrahedron %d is missing vertex %d in %s.\n",
- i + firstnumber, j + 1, infilename);
+ if (numberofcorners != 4 && numberofcorners != 10) {
+ printf("Error: Wrong number of corners %d (should be 4 or 10).\n",
+ numberofcorners);
+ fclose(infile);
+ return false;
+ }
+ // Allocate memory for tetrahedra.
+ if (numberoftetrahedra > 0) {
+ tetrahedronlist = new int[numberoftetrahedra * numberofcorners];
+ if (tetrahedronlist == (int *) NULL) {
+ printf("Error: Out of memory.\n");
terminatetetgen(1);
}
- corner = (int) strtol(stringptr, &stringptr, 0);
- if (corner < firstnumber || corner >= numberofpoints + firstnumber) {
- printf("Error: Tetrahedron %d has an invalid vertex index.\n",
- i + firstnumber);
- terminatetetgen(1);
+ // Allocate memory for output tetrahedron attributes if necessary.
+ if (numberoftetrahedronattributes > 0) {
+ tetrahedronattributelist = new REAL[numberoftetrahedra *
+ numberoftetrahedronattributes];
+ if (tetrahedronattributelist == (REAL *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
}
- tetrahedronlist[index++] = corner;
}
- // Read the tetrahedron's attributes.
- for (j = 0; j < numberoftetrahedronattributes; j++) {
- stringptr = findnextnumber(stringptr);
- if (*stringptr == '\0') {
- attrib = 0.0;
- } else {
- attrib = (REAL) strtod(stringptr, &stringptr);
+ // Read the list of tetrahedra.
+ index = 0;
+ attribindex = 0;
+ for (i = 0; i < numberoftetrahedra; i++) {
+ // Read tetrahedron index and the tetrahedron's corners.
+ stringptr = readnumberline(inputline, infile, infilename);
+ for (j = 0; j < numberofcorners; j++) {
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Tetrahedron %d is missing vertex %d in %s.\n",
+ i + firstnumber, j + 1, infilename);
+ terminatetetgen(1);
+ }
+ corner = (int) strtol(stringptr, &stringptr, 0);
+ if (corner < firstnumber || corner >= numberofpoints + firstnumber) {
+ printf("Error: Tetrahedron %d has an invalid vertex index.\n",
+ i + firstnumber);
+ terminatetetgen(1);
+ }
+ tetrahedronlist[index++] = corner;
+ }
+ // Read the tetrahedron's attributes.
+ for (j = 0; j < numberoftetrahedronattributes; j++) {
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ attrib = 0.0;
+ } else {
+ attrib = (REAL) strtod(stringptr, &stringptr);
+ }
+ tetrahedronattributelist[attribindex++] = attrib;
}
- tetrahedronattributelist[attribindex++] = attrib;
}
+ fclose(infile);
}
- fclose(infile);
- }
+ } // if (meshdim == 3)
// Read the hullfaces or subfaces from a .face file if it exists.
- infilename = infacefilename;
+ if (mesh_dim == 3) {
+ infilename = infacefilename;
+ } else {
+ infilename = inelefilename;
+ }
infile = fopen(infilename, "r");
if (infile != (FILE *) NULL) {
printf("Opening %s.\n", infilename);
@@ -2221,6 +2167,10 @@ bool tetgenio::load_tetmesh(char* filename)
stringptr = readnumberline(inputline, infile, infilename);
numberoftrifaces = (int) strtol (stringptr, &stringptr, 0);
stringptr = findnextnumber(stringptr);
+ if (mesh_dim == 2) {
+ // Skip a number.
+ stringptr = findnextnumber(stringptr);
+ }
if (*stringptr == '\0') {
markers = 0; // Default there is no marker per face.
} else {
@@ -2357,7 +2307,167 @@ bool tetgenio::load_tetmesh(char* filename)
///////////////////////////////////////////////////////////////////////////////
// //
-// save_nodes() Save points to a .node file. //
+// load_voronoi() Load a Voronoi diagram from files. //
+// //
+// 'filename' is the inputfile without suffix. The Voronoi diagram is read //
+// from files: filename.v.node, filename.v.edge, and filename.v.face. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenio::load_voronoi(char* filename)
+{
+ FILE *infile;
+ char innodefilename[FILENAMESIZE];
+ char inedgefilename[FILENAMESIZE];
+ char inputline[INPUTLINESIZE];
+ char *stringptr, *infilename;
+ voroedge *vedge;
+ REAL x, y, z;
+ int firstnode, corner;
+ int index;
+ int i, j;
+
+ // Assembling the actual file names we want to open.
+ strcpy(innodefilename, filename);
+ strcpy(inedgefilename, filename);
+ strcat(innodefilename, ".v.node");
+ strcat(inedgefilename, ".v.edge");
+
+ // Read the points from a .v.node file.
+ infilename = innodefilename;
+ printf("Opening %s.\n", infilename);
+ infile = fopen(infilename, "r");
+ if (infile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot access file %s.\n", infilename);
+ return false;
+ }
+ // Read the first line of the file.
+ stringptr = readnumberline(inputline, infile, infilename);
+ // Is this list of points generated from rbox?
+ stringptr = strstr(inputline, "rbox");
+ if (stringptr == NULL) {
+ // Read number of points, number of dimensions, number of point
+ // attributes, and number of boundary markers.
+ stringptr = inputline;
+ numberofvpoints = (int) strtol (stringptr, &stringptr, 0);
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ mesh_dim = 3; // Default.
+ } else {
+ mesh_dim = (int) strtol (stringptr, &stringptr, 0);
+ }
+ useindex = 1; // There is an index column.
+ } else {
+ // It is a rbox (qhull) input file.
+ stringptr = inputline;
+ // Get the dimension.
+ mesh_dim = (int) strtol (stringptr, &stringptr, 0);
+ // Get the number of points.
+ stringptr = readnumberline(inputline, infile, infilename);
+ numberofvpoints = (int) strtol (stringptr, &stringptr, 0);
+ useindex = 0; // No index column.
+ }
+ // Initialize 'vpointlist'.
+ vpointlist = new REAL[numberofvpoints * 3];
+ if (vpointlist == (REAL *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
+ // Read the point section.
+ index = 0;
+ for (i = 0; i < numberofvpoints; i++) {
+ stringptr = readnumberline(inputline, infile, infilename);
+ if (useindex) {
+ if (i == 0) {
+ firstnode = (int) strtol (stringptr, &stringptr, 0);
+ if ((firstnode == 0) || (firstnode == 1)) {
+ firstnumber = firstnode;
+ }
+ }
+ stringptr = findnextnumber(stringptr);
+ } // if (useindex)
+ if (*stringptr == '\0') {
+ printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
+ terminatetetgen(1);
+ }
+ x = (REAL) strtod(stringptr, &stringptr);
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Point %d has no y coordinate.\n", firstnumber + i);
+ terminatetetgen(1);
+ }
+ y = (REAL) strtod(stringptr, &stringptr);
+ if (mesh_dim == 3) {
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Point %d has no z coordinate.\n", firstnumber + i);
+ terminatetetgen(1);
+ }
+ z = (REAL) strtod(stringptr, &stringptr);
+ } else {
+ z = 0.0; // mesh_dim == 2;
+ }
+ vpointlist[index++] = x;
+ vpointlist[index++] = y;
+ vpointlist[index++] = z;
+ }
+ fclose(infile);
+
+ // Read the Voronoi edges from a .v.edge file if it exists.
+ infilename = inedgefilename;
+ infile = fopen(infilename, "r");
+ if (infile != (FILE *) NULL) {
+ printf("Opening %s.\n", infilename);
+ // Read number of boundary edges.
+ stringptr = readnumberline(inputline, infile, infilename);
+ numberofvedges = (int) strtol (stringptr, &stringptr, 0);
+ if (numberofvedges > 0) {
+ vedgelist = new voroedge[numberofvedges];
+ }
+ // Read the list of faces.
+ index = 0;
+ for (i = 0; i < numberofvedges; i++) {
+ // Read edge index and the edge's two endpoints.
+ stringptr = readnumberline(inputline, infile, infilename);
+ vedge = &(vedgelist[i]);
+ for (j = 0; j < 2; j++) {
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Edge %d is missing vertex %d in %s.\n",
+ i + firstnumber, j + 1, infilename);
+ terminatetetgen(1);
+ }
+ corner = (int) strtol(stringptr, &stringptr, 0);
+ j == 0 ? vedge->v1 = corner : vedge->v2 = corner;
+ }
+ if (vedge->v2 < 0) {
+ for (j = 0; j < mesh_dim; j++) {
+ stringptr = findnextnumber(stringptr);
+ if (*stringptr == '\0') {
+ printf("Error: Edge %d is missing normal in %s.\n",
+ i + firstnumber, infilename);
+ terminatetetgen(1);
+ }
+ vedge->vnormal[j] = (REAL) strtod(stringptr, &stringptr);
+ }
+ if (mesh_dim == 2) {
+ vedge->vnormal[2] = 0.0;
+ }
+ } else {
+ vedge->vnormal[0] = 0.0;
+ vedge->vnormal[1] = 0.0;
+ vedge->vnormal[2] = 0.0;
+ }
+ }
+ fclose(infile);
+ }
+
+ return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// save_nodes() Save points to a .node file. //
// //
// 'filename' is a string containing the file name without suffix. //
// //
@@ -2367,6 +2477,7 @@ void tetgenio::save_nodes(char* filename)
{
FILE *fout;
char outnodefilename[FILENAMESIZE];
+ char outmtrfilename[FILENAMESIZE];
int i, j;
sprintf(outnodefilename, "%s.node", filename);
@@ -2391,8 +2502,22 @@ void tetgenio::save_nodes(char* filename)
}
fprintf(fout, "\n");
}
-
fclose(fout);
+
+ // If the point metrics exist, output them to a .mtr file.
+ if ((numberofpointmtrs > 0) && (pointmtrlist != (REAL *) NULL)) {
+ sprintf(outmtrfilename, "%s.mtr", filename);
+ printf("Saving metrics to %s\n", outmtrfilename);
+ fout = fopen(outmtrfilename, "w");
+ fprintf(fout, "%d %d\n", numberofpoints, numberofpointmtrs);
+ for (i = 0; i < numberofpoints; i++) {
+ for (j = 0; j < numberofpointmtrs; j++) {
+ fprintf(fout, "%.16g ", pointmtrlist[i * numberofpointmtrs + j]);
+ }
+ fprintf(fout, "\n");
+ }
+ fclose(fout);
+ }
}
///////////////////////////////////////////////////////////////////////////////
@@ -2772,16 +2897,16 @@ tetgenbehavior::tetgenbehavior()
{
// Initialize command line switches.
plc = 0;
- refine = 0;
quality = 0;
- smooth = 1;
+ refine = 0;
+ coarse = 0;
metric = 0;
- bgmesh = 0;
minratio = 2.0;
goodratio = 0.0;
minangle = 20.0;
goodangle = 0.0;
- maxdihedral = 170.0;
+ maxdihedral = 165.0;
+ mindihedral = 5.0;
varvolume = 0;
fixedvolume = 0;
maxvolume = -1.0;
@@ -2791,15 +2916,18 @@ tetgenbehavior::tetgenbehavior()
offcenter = 0;
conformdel = 0;
alpha1 = sqrt(2.0);
- alpha2 = 0.5;
+ alpha2 = 1.0;
alpha3 = 0.6;
zeroindex = 0;
facesout = 0;
edgesout = 0;
neighout = 0;
+ voroout = 0;
meditview = 0;
gidview = 0;
geomview = 0;
+ optlevel = 3;
+ optpasses = 3;
order = 1;
nojettison = 0;
nobound = 0;
@@ -2815,7 +2943,6 @@ tetgenbehavior::tetgenbehavior()
docheck = 0;
quiet = 0;
verbose = 0;
- tol = 0;
useshelles = 0;
epsilon = 1.0e-8;
epsilon2 = 1.0e-5;
@@ -2824,6 +2951,7 @@ tetgenbehavior::tetgenbehavior()
commandline[0] = '\0';
infilename[0] = '\0';
outfilename[0] = '\0';
+ addinfilename[0] = '\0';
bgmeshfilename[0] = '\0';
}
@@ -2835,7 +2963,12 @@ tetgenbehavior::tetgenbehavior()
void tetgenbehavior::versioninfo()
{
- printf("Version 1.4.1 (July 06, 2006).\n");
+ printf("Version 1.4.2 (April 16, 2007).\n");
+ printf("\n");
+ printf("Copyright (C) 2002 - 2007\n");
+ printf("Hang Si\n");
+ printf("Mohrenstr. 39, 10117 Berlin, Germany\n");
+ printf("si@wias-berlin.de\n");
}
///////////////////////////////////////////////////////////////////////////////
@@ -2846,27 +2979,28 @@ void tetgenbehavior::versioninfo()
void tetgenbehavior::syntax()
{
- printf(" tetgen [-pq__a__AriMYS__T__dzjo_fengGOJBNEFICQVvh] input_file\n");
- printf(" -p Tetrahedralizes a piecewise linear complex.\n");
- printf(" -q Quality mesh generation. A minimum radius-edge ratio may\n");
- printf(" be specified (default 2.0).\n");
+ printf(" tetgen [-prq_Ra_AiMYS_T_dzo_fenvgGOJBNEFICQVh] input_file\n");
+ printf(" -p Tetrahedralizes a piecewise linear complex (PLC).\n");
+ printf(" -r Reconstructs a previously generated mesh.\n");
+ printf(" -q Quality mesh generation (adding new mesh points to ");
+ printf("improve mesh quality).\n");
+ printf(" -R Mesh coarsening (deleting redundant mesh points).\n");
printf(" -a Applies a maximum tetrahedron volume constraint.\n");
printf(" -A Assigns attributes to identify tetrahedra in different ");
printf("regions.\n");
- printf(" -r Reconstructs and Refines a previously generated mesh.\n");
printf(" -i Inserts a list of additional points into mesh.\n");
printf(" -M Does not merge coplanar facets.\n");
printf(" -Y Suppresses boundary facets/segments splitting.\n");
- printf(" -S Specifies maximum number of added Steiner points.\n");
- printf(" -T Set a tolerance for coplanar test (default 1e-8).\n");
- printf(" -d Diagnoses the validation of the input PLC.\n");
+ printf(" -S Specifies maximum number of added points.\n");
+ printf(" -T Sets a tolerance for coplanar test (default 1e-8).\n");
+ printf(" -d Detects self-intersections of facets of the PLC.\n");
printf(" -z Numbers all output items starting from zero.\n");
printf(" -o2 Generates second-order subparametric elements.\n");
- printf(" -P Outputs triangulated PLC facets to .smesh file.\n");
- printf(" -f Outputs all faces (instead of boundary faces) to .face ");
+ printf(" -f Outputs all faces to .face file.");
printf("file.\n");
- printf(" -e Outputs subsegments to .edge file.\n");
+ printf(" -e Outputs all edges to .edge file.\n");
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(" -G Outputs mesh to .msh file for viewing by Gid.\n");
printf(" -O Outputs mesh to .off file for viewing by Geomview.\n");
@@ -2879,7 +3013,6 @@ void tetgenbehavior::syntax()
printf(" -C Checks the consistency of the final mesh.\n");
printf(" -Q Quiet: No terminal output except errors.\n");
printf(" -V Verbose: Detailed information, more terminal output.\n");
- printf(" -v Prints the version information.\n");
printf(" -h Help: A brief instruction for using TetGen.\n");
}
@@ -2896,11 +3029,6 @@ void tetgenbehavior::usage()
printf("Triangulator\n");
versioninfo();
printf("\n");
- printf("Copyright 2002, 2004, 2005, 2006\n");
- printf("Hang Si\n");
- printf("Rathausstr. 9, 10178 Berlin, Germany\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");
@@ -2974,7 +3102,7 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
int startindex;
int increment;
int meshnumber;
- int Rcount;
+ int scount;
int i, j, k;
char workstring[1024];
@@ -2990,7 +3118,7 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
}
// Rcount used to count the number of '-R' be used.
- Rcount = 0;
+ scount = 0;
for (i = startindex; i < argc; i++) {
// Remember the command line switches.
@@ -3011,12 +3139,10 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
plc = 1;
} else if (argv[i][j] == 'r') {
refine = 1;
- } else if (argv[i][j] == 'm') {
- metric = 1;
- } else if (argv[i][j] == 'b') {
- bgmesh = 1;
+ } else if (argv[i][j] == 'R') {
+ coarse = 1;
} else if (argv[i][j] == 'q') {
- quality = 1;
+ quality++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3027,10 +3153,37 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- minratio = (REAL) strtod(workstring, (char **) NULL);
- }
+ if (quality == 1) {
+ minratio = (REAL) strtod(workstring, (char **) NULL);
+ } else if (quality == 2) {
+ mindihedral = (REAL) strtod(workstring, (char **) NULL);
+ } else if (quality == 3) {
+ maxdihedral = (REAL) strtod(workstring, (char **) NULL);
+ } else if (quality == 4) {
+ alpha2 = (REAL) strtod(workstring, (char **) NULL);
+ } else if (quality == 5) {
+ alpha1 = (REAL) strtod(workstring, (char **) NULL);
+ }
+ }
+ } else if (argv[i][j] == 'm') {
+ metric++;
+ 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 (metric == 1) {
+ alpha1 = (REAL) strtod(workstring, (char **) NULL);
+ } else if (metric == 2) {
+ alpha2 = (REAL) strtod(workstring, (char **) NULL);
+ }
+ }
} else if (argv[i][j] == 'a') {
- quality = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
fixedvolume = 1;
@@ -3058,9 +3211,11 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
} else if (argv[i][j] == 'f') {
facesout = 1;
} else if (argv[i][j] == 'e') {
- edgesout = 1;
+ edgesout++;
} else if (argv[i][j] == 'n') {
neighout++;
+ } else if (argv[i][j] == 'v') {
+ voroout = 1;
} else if (argv[i][j] == 'g') {
meditview = 1;
} else if (argv[i][j] == 'G') {
@@ -3103,6 +3258,7 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
steiner = (int) strtol(workstring, (char **) NULL, 0);
}
} else if (argv[i][j] == 's') {
+ scount++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3114,34 +3270,15 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- maxdihedral = (REAL) strtod(workstring, (char **) NULL);
- if (maxdihedral >= 180.0) smooth = 0;
- }
- } else if (argv[i][j] == 'R') {
- Rcount++;
- 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++;
+ if (scount == 1) {
+ optlevel = (int) strtol(workstring, (char **) NULL, 0);
+ } else if (scount == 2) {
+ optpasses = (int) strtol(workstring, (char **) NULL, 0);
}
- workstring[k] = '\0';
- if (Rcount == 1) {
- alpha1 = (REAL) strtod(workstring, (char **) NULL);
- } else if (Rcount == 2) {
- alpha2 = (REAL) strtod(workstring, (char **) NULL);
- } else if (Rcount == 3) {
- alpha3 = (REAL) strtod(workstring, (char **) NULL);
- }
}
} else if (argv[i][j] == 'D') {
conformdel++;
} else if (argv[i][j] == 'T') {
- tol++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
@@ -3153,11 +3290,7 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
k++;
}
workstring[k] = '\0';
- if (tol == 1) {
- epsilon = (REAL) strtod(workstring, (char **) NULL);
- } else if (tol == 2) {
- epsilon2 = (REAL) strtod(workstring, (char **) NULL);
- }
+ epsilon = (REAL) strtod(workstring, (char **) NULL);
}
} else if (argv[i][j] == 'C') {
docheck++;
@@ -3167,9 +3300,9 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
quiet = 1;
} else if (argv[i][j] == 'V') {
verbose++;
- } else if (argv[i][j] == 'v') {
- versioninfo();
- terminatetetgen(0);
+ // } else if (argv[i][j] == 'v') {
+ // versioninfo();
+ // terminatetetgen(0);
} else if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
(argv[i][j] == '?')) {
usage();
@@ -3224,7 +3357,7 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
}
}
plc = plc || diagnose;
- useshelles = plc || refine || quality;
+ useshelles = plc || refine || coarse || quality;
goodratio = minratio;
goodratio *= goodratio;
@@ -3235,7 +3368,7 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
}
if (refine && (plc || noiterationnum)) {
printf("Error: Switches %s cannot use together with -r.\n",
- "-p, -d, -c, and -I");
+ "-p, -d, and -I");
return false;
}
if (diagnose && (quality || insertaddpoints || (order == 2) || neighout
@@ -3255,6 +3388,12 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
if (refine || !plc) {
regionattrib = 0;
}
+ // If '-a' or '-aa' is in use, enable '-q' option too.
+ if (fixedvolume || varvolume) {
+ if (quality == 0) {
+ quality = 1;
+ }
+ }
// Calculate the goodangle for testing bad subfaces.
goodangle = cos(minangle * PI / 180.0);
goodangle *= goodangle;
@@ -3291,6 +3430,9 @@ bool tetgenbehavior::parse_commandline(int argc, char **argv)
workstring[increment + 2] = '\0';
sprintf(outfilename, workstring, meshnumber + 1);
}
+ // Additional input file name has the end ".a".
+ strcpy(addinfilename, infilename);
+ strcat(addinfilename, ".a");
// Background filename has the form "*.b.ele", "*.b.node", ...
strcpy(bgmeshfilename, infilename);
strcat(bgmeshfilename, ".b");
@@ -4046,18 +4188,15 @@ void* tetgenmesh::link::insert(int pos, void* insitem)
///////////////////////////////////////////////////////////////////////////////
// //
-// del() Delete a node containing the given pointer. //
+// del() Delete a node. //
// //
// Returns a pointer of the deleted data. If you try to delete a non-existed //
// node (e.g. link is empty or a wrong index is given) return NULL. //
// //
///////////////////////////////////////////////////////////////////////////////
-void* tetgenmesh::link::del(void* delitem)
+void* tetgenmesh::link::deletenode(void** deadnode)
{
- void **deadnode = (void **) ((void **) delitem - 2);
-
- // now delete the nownode
void **nextnode = (void **) *deadnode;
void **prevnode = (void **) *(deadnode + 1);
*prevnode = (void *) nextnode;
@@ -4085,7 +4224,7 @@ void* tetgenmesh::link::del(int pos)
if (!locate(pos) || (linkitems == 0)) {
return (void *) NULL;
}
- return del((void *) ((void **) nextlinkitem + 2));
+ return deletenode((void **) nextlinkitem);
}
///////////////////////////////////////////////////////////////////////////////
@@ -4220,6 +4359,26 @@ int tetgenmesh::locver2nextf[4][6][2] = {
{ {2, 3}, {-1, -1}, {1, 1}, {-1, -1}, {0, 5}, {-1, -1} }
};
+// The edge number (from 0 to 5) of a tet is defined as follows:
+// 0 - (v0, v1), 1 - (v1, v2), 2 - (v2, v0)
+// 3 - (v3, v0), 4 - (v3, v1), 5 - (v3, v2).
+
+int tetgenmesh::locver2edge[4][6] = {
+ {0, 0, 1, 1, 2, 2},
+ {3, 3, 4, 4, 0, 0},
+ {4, 4, 5, 5, 1, 1},
+ {5, 5, 3, 3, 2, 2}
+};
+
+int tetgenmesh::edge2locver[6][2] = {
+ {0, 0}, // 0 v0 -> v1
+ {0, 2}, // 1 v1 -> v2
+ {0, 4}, // 2 v2 -> v1
+ {1, 0}, // 3 v0 -> v3
+ {1, 2}, // 4 v1 -> v3
+ {2, 2} // 5 v2 -> v3
+};
+
//
// End of tables initialization.
//
@@ -4369,12 +4528,67 @@ inline void tetgenmesh::enext2self(triface& t) {
// If f1 exists, return true. Otherwise, return false, i.e., f0 is a
// boundary or hull face.
-inline bool tetgenmesh::fnext(triface& t1, triface& t2) {
- return getnextface(&t1, &t2);
-}
-
-inline bool tetgenmesh::fnextself(triface& t) {
- return getnextface(&t, NULL);
+inline bool tetgenmesh::fnext(triface& t1, triface& t2)
+{
+ // Get the next face.
+ t2.loc = locver2nextf[t1.loc][t1.ver][0];
+ // Is the next face in the same tet?
+ if (t2.loc != -1) {
+ // It's in the same tet. Get the edge version.
+ t2.ver = locver2nextf[t1.loc][t1.ver][1];
+ t2.tet = t1.tet;
+ } else {
+ // The next face is in the neigbhour of 't1'.
+ sym(t1, t2);
+ if (t2.tet != dummytet) {
+ // Find the corresponding edge in t2.
+ point torg;
+ int tloc, tver, i;
+ t2.ver = 0;
+ torg = org(t1);
+ for (i = 0; (i < 3) && (org(t2) != torg); i++) {
+ enextself(t2);
+ }
+ // Go to the next face in t2.
+ tloc = t2.loc;
+ tver = t2.ver;
+ t2.loc = locver2nextf[tloc][tver][0];
+ t2.ver = locver2nextf[tloc][tver][1];
+ }
+ }
+ return t2.tet != dummytet;
+}
+
+inline bool tetgenmesh::fnextself(triface& t1)
+{
+ triface t2;
+
+ // Get the next face.
+ t2.loc = locver2nextf[t1.loc][t1.ver][0];
+ // Is the next face in the same tet?
+ if (t2.loc != -1) {
+ // It's in the same tet. Get the edge version.
+ t2.ver = locver2nextf[t1.loc][t1.ver][1];
+ t1.loc = t2.loc;
+ t1.ver = t2.ver;
+ } else {
+ // The next face is in the neigbhour of 't1'.
+ sym(t1, t2);
+ if (t2.tet != dummytet) {
+ // Find the corresponding edge in t2.
+ point torg;
+ int i;
+ t2.ver = 0;
+ torg = org(t1);
+ for (i = 0; (i < 3) && (org(t2) != torg); i++) {
+ enextself(t2);
+ }
+ t1.loc = locver2nextf[t2.loc][t2.ver][0];
+ t1.ver = locver2nextf[t2.loc][t2.ver][1];
+ t1.tet = t2.tet;
+ }
+ }
+ return t2.tet != dummytet;
}
// enextfnext() and enext2fnext() are combination primitives of enext(),
@@ -4708,6 +4922,32 @@ inline void tetgenmesh::ssdissolve(face& s) {
// End of primitives for interacting between subfaces and subsegs
//
+//
+// Begin of primitives for interacting between tet and subsegs.
+//
+
+inline void tetgenmesh::tsspivot1(triface& t, face& seg)
+{
+ shellface sptr = (shellface) t.tet[8 + locver2edge[t.loc][t.ver]];
+ sdecode(sptr, seg);
+}
+
+// Only bond/dissolve at tet's side, but not vice versa.
+
+inline void tetgenmesh::tssbond1(triface& t, face& seg)
+{
+ t.tet[8 + locver2edge[t.loc][t.ver]] = (tetrahedron) sencode(seg);
+}
+
+inline void tetgenmesh::tssdissolve1(triface& t)
+{
+ t.tet[8 + locver2edge[t.loc][t.ver]] = (tetrahedron) dummysh;
+}
+
+//
+// End of primitives for interacting between tet and subsegs.
+//
+
//
// Begin of primitives for points
//
@@ -4840,64 +5080,6 @@ inline bool tetgenmesh::issymexist(triface* t) {
return ptr != dummytet;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// getnextface() Get the successor of 'tface1' in the face ring. //
-// //
-// If 'tface1' is not a boundary (or hull) face, then its successor in the //
-// face ring exists. The successor is returned in 'tface2' if it is not a //
-// NULL, or the 'tface1' itself is used to return this face. On finish, the //
-// function returns TRUE. //
-// //
-// If 'tface1' is a boundary (or hull) face, its successor does not exist. //
-// This case, return FALSE and 'tface1' remains unchanged. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::getnextface(triface* tface1, triface* tface2)
-{
- point torg, tdest;
- int tloc, tver;
-
- // Where the next face locates, in 'tface1' or in its neigbhour? It can be
- // quickly determined by checking the edge ring of 'tface1'.
- // if (EdgeRing(tface1->ver) == CW) {
- if ((tface1->ver & 01) == CW) {
- // The next face is in the neigbhour of 'tface1'.
- if (!issymexist(tface1)) {
- // Hit outer space - The next face does not exist.
- return false;
- }
- torg = org(*tface1);
- tdest = dest(*tface1);
- if (tface2) {
- sym(*tface1, *tface2);
- findedge(tface2, torg, tdest);
- } else {
- symself(*tface1);
- findedge(tface1, torg, tdest);
- }
- } else {
- // The next face is in 'tface1'.
- if (tface2) {
- *tface2 = *tface1;
- }
- }
-
- if (tface2) {
- tloc = tface2->loc;
- tver = tface2->ver;
- tface2->loc = locver2nextf[tloc][tver][0];
- tface2->ver = locver2nextf[tloc][tver][1];
- } else {
- tloc = tface1->loc;
- tver = tface1->ver;
- tface1->loc = locver2nextf[tloc][tver][0];
- tface1->ver = locver2nextf[tloc][tver][1];
- }
- return true;
-}
-
///////////////////////////////////////////////////////////////////////////////
// //
// getnextsface() Finds the next subface in the face ring. //
@@ -4967,13 +5149,13 @@ void tetgenmesh::tsspivot(triface* checkedge, face* checkseg)
do {
tspivot(spintet, parentsh);
// Does spintet have a (non-fake) subface attached?
- if (parentsh.sh != dummysh && !isdead(&parentsh)) {
- // Find a subface!
+ if ((parentsh.sh != dummysh) && (sapex(parentsh) != NULL)) {
+ // Find a subface! Find the edge in it.
findedge(&parentsh, org(*checkedge), dest(*checkedge));
sspivot(parentsh, *checkseg);
if (checkseg->sh != dummysh) {
// Find a subsegment! Correct its edge direction before return.
- if (sorg(*checkseg) != sorg(parentsh)) {
+ if (sorg(*checkseg) != org(*checkedge)) {
sesymself(*checkseg);
}
}
@@ -5477,7 +5659,7 @@ void tetgenmesh::printtet(triface* tface)
if (b->useshelles) {
tmpface = *tface;
facecount = 0;
- while(facecount < 4) {
+ while(facecount < 6) {
tmpface.loc = facecount;
tspivot(tmpface, tmpsh);
if(tmpsh.sh != dummysh) {
@@ -5523,8 +5705,6 @@ void tetgenmesh::printsh(face* sface)
if (sapex(*sface) != NULL) {
if (shelltype(*sface) == SHARP) {
printf(" (sharp)");
- } else if (shelltype(*sface) == SKINNY) {
- printf(" (skinny)");
}
} else {
if (shelltype(*sface) == SHARP) {
@@ -7365,6 +7545,72 @@ void tetgenmesh::tetallnormal(point pa, point pb, point pc, point pd,
for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// tetaspectratio() Calculate the aspect ratio of the tetrahedron. //
+// //
+// The aspect ratio of a tet is R/h, where R is the circumradius and h is //
+// the shortest height of the tet. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+REAL tetgenmesh::tetaspectratio(point pa, point pb, point pc, point pd)
+{
+ REAL vda[3], vdb[3], vdc[3];
+ REAL N[4][3], A[4][4], rhs[4], D;
+ REAL H[4], volume, radius2, minheightinv;
+ int indx[4];
+ int i, j;
+
+ // Set the matrix A = [vda, vdb, vdc]^T.
+ for (i = 0; i < 3; i++) A[0][i] = vda[i] = pa[i] - pd[i];
+ for (i = 0; i < 3; i++) A[1][i] = vdb[i] = pb[i] - pd[i];
+ for (i = 0; i < 3; i++) A[2][i] = vdc[i] = pc[i] - pd[i];
+ // Lu-decompose the matrix A.
+ lu_decmp(A, 3, indx, &D, 0);
+ // Get the volume of abcd.
+ volume = (A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0;
+ // Check if it is zero.
+ if (volume == 0.0) return 1.0e+200; // A degenerate tet.
+ // if (volume < 0.0) volume = -volume;
+ // Check the radiu-edge ratio of the tet.
+ rhs[0] = 0.5 * dot(vda, vda);
+ rhs[1] = 0.5 * dot(vdb, vdb);
+ rhs[2] = 0.5 * dot(vdc, vdc);
+ lu_solve(A, 3, indx, rhs, 0);
+ // Get the circumcenter.
+ // for (i = 0; i < 3; i++) circumcent[i] = pd[i] + rhs[i];
+ // Get the square of the circumradius.
+ radius2 = dot(rhs, rhs);
+
+ // Compute the 4 face normals (N[0], ..., N[3]).
+ for (j = 0; j < 3; j++) {
+ for (i = 0; i < 3; i++) rhs[i] = 0.0;
+ rhs[j] = 1.0; // Positive means the inside direction
+ lu_solve(A, 3, indx, rhs, 0);
+ for (i = 0; i < 3; i++) N[j][i] = rhs[i];
+ }
+ // Get the fourth normal by summing up the first three.
+ for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
+ // Normalized the normals.
+ for (i = 0; i < 4; i++) {
+ // H[i] is the inverse of the height of its corresponding face.
+ H[i] = sqrt(dot(N[i], N[i]));
+ // if (H[i] > 0.0) {
+ // for (j = 0; j < 3; j++) N[i][j] /= H[i];
+ // }
+ }
+ // Get the radius of the inscribed sphere.
+ // insradius = 1.0 / (H[0] + H[1] + H[2] + H[3]);
+ // Get the biggest H[i] (corresponding to the smallest height).
+ minheightinv = H[0];
+ for (i = 1; i < 3; i++) {
+ if (H[i] > minheightinv) minheightinv = H[i];
+ }
+
+ return sqrt(radius2) * minheightinv;
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// circumsphere() Calculate the smallest circumsphere (center and radius) //
@@ -7891,29 +8137,41 @@ void tetgenmesh::initializepools()
varconstraint = 1;
}
- // The index within each point at which its local feature size is found.
- // It is saved directly after the list of point attributes.
- if (b->bgmesh && (bgm != (tetgenmesh *) NULL)) {
- // A background mesh is in use. That point attributes should be the
- // same as that of the background mesh.
- pointlfsindex = 3 + bgm->in->numberofpointattributes;
+ // The index within each point at which its metric tensor is found. It is
+ // saved directly after the list of point attributes.
+ pointmtrindex = 3 + in->numberofpointattributes;
+ // Decide the size (1, 3, or 6) of the metric tensor.
+ if (b->metric) {
+ // For '-m' option. A tensor field is provided (*.mtr or *.b.mtr file).
+ if (bgm != (tetgenmesh *) NULL) {
+ // A background mesh is allocated. It may not exist though.
+ sizeoftensor = (bgm->in != (tetgenio *) NULL) ?
+ bgm->in->numberofpointmtrs : in->numberofpointmtrs;
+ } else {
+ // No given background mesh - Itself is a background mesh.
+ sizeoftensor = in->numberofpointmtrs;
+ }
+ // Make sure sizeoftensor is at least 1.
+ sizeoftensor = (sizeoftensor > 0) ? sizeoftensor : 1;
} else {
- pointlfsindex = 3 + in->numberofpointattributes;
+ // For '-q' option. Make sure to have space for saving a scalar value.
+ sizeoftensor = b->quality ? 1 : 0;
}
- // The index within each point at which a element pointer is found, where
+ // The index within each point at which an element pointer is found, where
// the index is measured in pointers. Ensure the index is aligned to a
// sizeof(tetrahedron)-byte address.
- point2simindex = ((pointlfsindex + b->quality) * sizeof(REAL)
+ point2simindex = ((pointmtrindex + sizeoftensor) * sizeof(REAL)
+ sizeof(tetrahedron) - 1) / sizeof(tetrahedron);
if (b->plc || b->refine) {
// Increase the point size by three pointers, which are:
// - a pointer to a tet, read by point2tet();
// - a pointer to a subface/subsegment , read by point2sh();
// - a pointer to a parent point, read by point2ppt()).
- pointsize = (point2simindex + 3) * sizeof(tetrahedron);
- if (bgm != (tetgenmesh *) NULL) {
- // Increase the size by one pointer to a tet of the background mesh.
+ if (b->metric) {
+ // Increase one pointer to a tet of the background mesh.
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)
@@ -7941,7 +8199,11 @@ void tetgenmesh::initializepools()
// The number of bytes occupied by a tetrahedron. There are four pointers
// to other tetrahedra, four pointers to corners, and possibly four
// pointers to subfaces.
- elesize = (8 + b->useshelles * 4) * sizeof(tetrahedron);
+ elesize = (8 + b->useshelles * 6) * sizeof(tetrahedron);
+ // If Voronoi diagram is wanted, make sure we have additional space.
+ if (b->voroout && (b->useshelles == 0)) {
+ elesize = (8 + 4) * sizeof(tetrahedron);
+ }
// 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);
@@ -7958,15 +8220,15 @@ void tetgenmesh::initializepools()
elesize = volumeboundindex * sizeof(REAL);
}
// If element neighbor graph is requested (-n switch), an additional
- // integer is allocated for each element.
- if (b->neighout) {
- elemmarkerindex = (elesize + sizeof(int) - 1) / sizeof(int);
+ // integer is allocated for each element.
+ elemmarkerindex = (elesize + sizeof(int) - 1) / sizeof(int);
+ if (b->neighout || b->voroout) {
elesize = (elemmarkerindex + 1) * sizeof(int);
}
// If -o2 switch is used, an additional pointer pointed to the list of
// higher order nodes is allocated for each element.
+ highorderindex = (elesize + sizeof(tetrahedron) - 1) / sizeof(tetrahedron);
if (b->order == 2) {
- highorderindex = (elesize + sizeof(tetrahedron) - 1) / sizeof(tetrahedron);
elesize = (highorderindex + 1) * sizeof(tetrahedron);
}
// Having determined the memory size of an element, initialize the pool.
@@ -8172,6 +8434,8 @@ void tetgenmesh::maketetrahedron(triface *newtet)
newtet->tet[9 ] = (tetrahedron) dummysh;
newtet->tet[10] = (tetrahedron) dummysh;
newtet->tet[11] = (tetrahedron) dummysh;
+ newtet->tet[12] = (tetrahedron) dummysh;
+ newtet->tet[13] = (tetrahedron) dummysh;
}
for (int i = 0; i < in->numberoftetrahedronattributes; i++) {
setelemattribute(newtet->tet, i, 0.0);
@@ -8219,7 +8483,7 @@ void tetgenmesh::makeshellface(memorypool *pool, face *newface)
// Set the boundary marker to zero.
setshellmark(*newface, 0);
// Set the type.
- setshelltype(*newface, NSHARPNSKINNY);
+ setshelltype(*newface, NSHARP);
if (checkpbcs) {
// Set the pbcgroup be ivalid.
setshellpbcgroup(*newface, -1);
@@ -8244,21 +8508,19 @@ void tetgenmesh::makepoint(point* pnewpoint)
(*pnewpoint)[1] = 0.0;
(*pnewpoint)[2] = 0.0;
// Initialize the list of user-defined attributes.
- if (bgm != (tetgenmesh *) NULL) {
- for (i = 0; i < bgm->in->numberofpointattributes; i++) {
- (*pnewpoint)[3 + i] = 0.0;
- }
- } else {
- for (i = 0; i < in->numberofpointattributes; i++) {
- (*pnewpoint)[3 + i] = 0.0;
- }
+ for (i = 0; i < in->numberofpointattributes; i++) {
+ (*pnewpoint)[3 + i] = 0.0;
+ }
+ // Initialize the metric tensor.
+ for (i = 0; i < sizeoftensor; i++) {
+ (*pnewpoint)[pointmtrindex + i] = 0.0;
}
if (b->plc || b->refine) {
// Initialize the point-to-simplex filed.
setpoint2tet(*pnewpoint, NULL);
setpoint2sh(*pnewpoint, NULL);
setpoint2ppt(*pnewpoint, NULL);
- if (bgm != (tetgenmesh *) NULL) {
+ if (b->metric) {
setpoint2bgmtet(*pnewpoint, NULL);
}
if (checkpbcs) {
@@ -8269,7 +8531,7 @@ void tetgenmesh::makepoint(point* pnewpoint)
// Initialize the point marker (starting from in->firstnumber).
ptmark = (int) points->items - (in->firstnumber == 1 ? 0 : 1);
setpointmark(*pnewpoint, ptmark);
- // Initialize the point type be UNUSEDVERTEX.
+ // Initialize the point type.
setpointtype(*pnewpoint, UNUSEDVERTEX);
}
@@ -8289,8 +8551,24 @@ void tetgenmesh::makepoint(point* pnewpoint)
unsigned long tetgenmesh::randomnation(unsigned int choices)
{
- randomseed = (randomseed * 1366l + 150889l) % 714025l;
- return randomseed / (714025l / choices + 1);
+ unsigned long newrandom;
+
+ if (choices >= 714025l) {
+ newrandom = (randomseed * 1366l + 150889l) % 714025l;
+ randomseed = (newrandom * 1366l + 150889l) % 714025l;
+ newrandom = newrandom * (choices / 714025l) + randomseed;
+ if (newrandom >= choices) {
+ return newrandom - choices;
+ } else {
+ return newrandom;
+ }
+ } else {
+ randomseed = (randomseed * 1366l + 150889l) % 714025l;
+ return randomseed % choices;
+ }
+ // Old function.
+ // randomseed = (randomseed * 1366l + 150889l) % 714025l;
+ // return randomseed / (714025l / choices + 1);
}
///////////////////////////////////////////////////////////////////////////////
@@ -8363,8 +8641,12 @@ enum tetgenmesh::locateresult tetgenmesh::preciselocate(point searchpt,
}
// 'searchtet' should be a valid tetrahedron now.
#ifdef SELF_CHECK
- assert(!isdead(searchtet) && (searchtet->tet != dummytet));
+ // assert(!isdead(searchtet) && (searchtet->tet != dummytet));
#endif
+ if (isdead(searchtet)) {
+ printf("Warning: Point location failed.\n");
+ return OUTSIDE;
+ }
searchtet->ver = 0; // Keep in CCW edge ring.
// Find a face of 'searchtet' such that the 'searchpt' lies strictly
@@ -8499,8 +8781,8 @@ enum tetgenmesh::locateresult tetgenmesh::preciselocate(point searchpt,
// //
///////////////////////////////////////////////////////////////////////////////
-enum tetgenmesh::locateresult tetgenmesh::
-locate(point searchpt, triface *searchtet)
+enum tetgenmesh::locateresult tetgenmesh::locate(point searchpt,
+ triface *searchtet)
{
tetrahedron *firsttet, *tetptr;
void **sampleblock;
@@ -8519,8 +8801,12 @@ locate(point searchpt, triface *searchtet)
symself(*searchtet);
}
#ifdef SELF_CHECK
- assert(!isdead(searchtet));
+ // assert(!isdead(searchtet));
#endif
+ if (isdead(searchtet)) {
+ printf("Warning: Point location failed.\n");
+ return OUTSIDE;
+ }
// Get the distance from the suggested starting tet to the point we seek.
searchdist = distance2(searchtet->tet, searchpt);
@@ -8602,9 +8888,8 @@ locate(point searchpt, triface *searchtet)
// //
///////////////////////////////////////////////////////////////////////////////
-enum tetgenmesh::locateresult tetgenmesh::
-adjustlocate(point searchpt, triface* searchtet, enum locateresult precise,
- REAL epspp)
+enum tetgenmesh::locateresult tetgenmesh::adjustlocate(point searchpt,
+ triface* searchtet, enum locateresult precise, REAL epspp)
{
point torg, tdest, tapex, toppo;
REAL s1, s2, s3, s4;
@@ -8753,6 +9038,77 @@ adjustlocate(point searchpt, triface* searchtet, enum locateresult precise,
return INTETRAHEDRON;
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// hullwalk() Find a tetrahedron on the hull to continue search. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+enum tetgenmesh::locateresult tetgenmesh::hullwalk(point searchpt,
+ triface *hulltet)
+{
+ list* travtetlist;
+ triface travtet, neightet;
+ point pa, pb, pc;
+ enum locateresult loc;
+ REAL ori;
+ int i;
+
+ travtetlist = new list(sizeof(triface), NULL, 256);
+ travtet = *hulltet;
+ infect(travtet);
+ travtetlist->append(&travtet);
+
+ loc = OUTSIDE;
+ for (i = 0; i < travtetlist->len(); i++) {
+ travtet = * (triface *)(* travtetlist)[i];
+ // Choose the CCW-edgering in face.
+ travtet.ver = 0;
+ // Look for a side where pt lies below it.
+ for (travtet.loc = 0; travtet.loc < 4; travtet.loc++) {
+ pa = org(travtet);
+ pb = dest(travtet);
+ pc = apex(travtet);
+ ori = orient3d(pa, pb, pc, searchpt);
+ if (ori > 0.0) break;
+ }
+ // Is pt above all (or coplanar with some of) the four sides?
+ if (travtet.loc == 4) {
+ hulltet->tet = travtet.tet;
+ loc = adjustlocate(searchpt, hulltet, INTETRAHEDRON, b->epsilon);
+ assert(loc != OUTSIDE);
+ } else { // ori > 0.0
+ // pt is below (behind) this side. We want to walk through it.
+ sym(travtet, neightet);
+ if (neightet.tet == dummytet) {
+ // This is a hull side. Is p approximately on this side.
+ loc = adjustlocate(searchpt, &travtet, OUTSIDE, b->epsilon);
+ }
+ if (loc == OUTSIDE) {
+ // Let's collect all the neighbors for next searching.
+ for (travtet.loc = 0; travtet.loc < 4; travtet.loc++) {
+ sym(travtet, neightet);
+ if ((neightet.tet != dummytet) && !infected(neightet)) {
+ // Neighbor exists and not visited.
+ infect(neightet);
+ travtetlist->append(&neightet);
+ }
+ } // for (travtet.loc = 0;
+ } // if (loc == OUTSIDE)
+ } // if (travtet.loc == 4)
+ if (loc != OUTSIDE) break;
+ } // for (i = 0; i < travtetlist->len(); i++)
+
+ // Uninfect traversed tets.
+ for (i = 0; i < travtetlist->len(); i++) {
+ travtet = * (triface *)(* travtetlist)[i];
+ uninfect(travtet);
+ }
+
+ delete travtetlist;
+ return loc;
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// locatesub() Find a point in the surface mesh of a facet. //
@@ -9179,26 +9535,21 @@ adjustlocateseg(point searchpt, face* searchseg, enum locateresult precise,
// //
// categorizeface() Determine the flip type of a given face. //
// //
-// On input, 'horiz' represents the face we want to flip (you can imagine it //
-// is parallel to the horizon). Let the tetrahedron above it be abcd, where //
-// abc is 'horiz'. //
+// On input, 'horiz' represents the face abc we want to flip (imagine it is //
+// parallel to the horizon). Let the tet above it be abcd. //
// //
// This routine determines the suitable type of flip operation for 'horiz'. //
// - Returns T23 if a 2-to-3 flip is applicable. 'horiz' is same as input. //
-// - Returns T32 if a 3-to-2 flip is applicable. 'horiz' is adjusted so //
-// that the primary edge of 'horiz' is the flipable edge. //
-// - Returns T22 if a 2-to-2 or 4-to-4 flip is applicable. 'horiz' is //
-// adjusted so that the primary edge of 'horiz' is the flipable edge. //
-// - Returns FORBIDDENFACE indicates although a 2-to-3 flip is applicable, //
-// but it is a subface and should not be flipped away. //
-// - Returns FORBIDDENEDGE indicates although a 3-to-2, or 2-to-2, or //
-// 4-to-4 flip is applicable, but the flipable edge is a subsegment and //
-// should not be flipped away. 'horiz' is adjusted so that the primary //
-// edge of 'horiz' is the flipable edge. //
-// - Returns UNFLIPABLE indicates it is unflipable due to the absence of //
-// a tetrahedron. 'horiz' is adjusted so that the primary edge of 'horiz'//
-// is the unflipable edge. Possibly, It is a subsegment. //
-// - Returns NONCONVEX indicates it is unflipable and is locally Delaunay. //
+// - Returns T32 if a 3-to-2 flip is applicable. 'horiz' returns the edge //
+// of abc which is the flipable. //
+// - Returns T22 if a 2-to-2 or 4-to-4 flip is applicable. 'horiz' returns //
+// the edge of abc which is flipable. //
+// - Returns N32 indicates it is unflipable due to the absence of a tet. //
+// 'horize' returns the unflipable edge. //
+// - Returns N40 indicates it is unflipable and is locally Delaunay. //
+// - Returns FORBIDDENFACE indicates abc is a subface. //
+// - Returns FORBIDDENEDGE indicates the flipable edge of abc is a segment.//
+// 'horize' returns the flipable edge. //
// //
// Given a face abc, with two adjoining tetrahedra abcd and bace. If abc is //
// flipable, i.e., T23, T32, T22 or T44, its flip type can be determined by //
@@ -9224,7 +9575,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
sym(horiz, symhoriz);
if (symhoriz.tet == dummytet) {
// A hull face is unflipable and locally Delaunay.
- return NONCONVEX;
+ return N40;
}
adjustedgering(horiz, CCW);
@@ -9309,7 +9660,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
return FORBIDDENEDGE;
}
}
- return UNFLIPABLE;
+ return N32;
}
ori2 = orient3d(pb, pc, pd, pe);
if (checksubfaces && ori2 != 0.0) {
@@ -9356,7 +9707,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
return FORBIDDENEDGE;
}
}
- return UNFLIPABLE;
+ return N32;
}
ori3 = orient3d(pc, pa, pd, pe);
if (checksubfaces && ori3 != 0.0) {
@@ -9406,7 +9757,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
return FORBIDDENEDGE;
}
}
- return UNFLIPABLE;
+ return N32;
}
if (ori1 == 0.0) {
// e is coplanar with abd.
@@ -9415,7 +9766,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
// assert(!(ori2 == 0.0 && ori3 == 0.0));
// Three points (d, e, and a or b) are collinear, abc is unflipable
// and locally Delaunay.
- return NONCONVEX;
+ return N40;
}
} else if (ori2 == 0.0) {
// e is coplanar with bcd.
@@ -9424,7 +9775,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
// assert(!(ori1 == 0.0 && ori3 == 0.0));
// Three points (d, e, and b or c) are collinear, abc is unflipable
// and locally Delaunay.
- return NONCONVEX;
+ return N40;
}
// Adjust 'horiz' and 'symhoriz' be the edge bc.
enextself(horiz);
@@ -9436,7 +9787,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
// assert(!(ori1 == 0.0 && ori2 == 0.0));
// Three points (d, e, and c or a) are collinear, abc is unflipable
// and locally Delaunay.
- return NONCONVEX;
+ return N40;
}
// Adjust 'horiz' and 'symhoriz' be the edge ca.
enext2self(horiz);
@@ -9489,14 +9840,14 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
pc = apex(horiz);
// Be careful not to create an inverted tetrahedron. Check the case.
ori1 = orient3d(pc, pd, pe, pa);
- if (ori1 <= 0) return NONCONVEX;
+ if (ori1 <= 0) return N40;
ori1 = orient3d(pd, pc, pe, pb);
- if (ori1 <= 0) return NONCONVEX;
+ if (ori1 <= 0) return N40;
if (pf != (point) NULL) {
ori1 = orient3d(pd, pf, pe, pa);
- if (ori1 <= 0) return NONCONVEX;
+ if (ori1 <= 0) return N40;
ori1 = orient3d(pf, pd, pe, pb);
- if (ori1 <= 0) return NONCONVEX;
+ if (ori1 <= 0) return N40;
}
}
if (pf == (point) NULL) {
@@ -9511,7 +9862,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
}
} else {
// ab has more than four faces around it, unflipable.
- return UNFLIPABLE;
+ return N32;
}
} else if (adjtet == 1) {
// One of its three edges is locally non-convex. Type T32 is possible.
@@ -9566,7 +9917,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
}
if (ori1 <= 0.0) {
// a lies above or is coplanar cde, abc is locally Delaunay.
- return NONCONVEX;
+ return N40;
}
ori2 = orient3d(pd, pc, pe, pb);
if (checksubfaces && ori2 != 0.0) {
@@ -9597,7 +9948,7 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
}
if (ori2 <= 0.0) {
// b lies above dce, unflipable, and abc is locally Delaunay.
- return NONCONVEX;
+ return N40;
}
// Edge ab crosses face cde properly.
if (checksubfaces) {
@@ -9622,14 +9973,14 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
printf("Warning: A tetrahedron spans two subfaces of a facet.\n");
}
// Temporarily, let it be there.
- return UNFLIPABLE;
+ return N32;
}
}
return T32;
} else {
// The convex hull of {a, b, c, d, e} has only four vertices, abc is
// unflipable, furthermore, it is locally Delaunay.
- return NONCONVEX;
+ return N40;
}
}
@@ -9647,12 +9998,14 @@ enum tetgenmesh::fliptype tetgenmesh::categorizeface(triface& horiz)
void tetgenmesh::enqueueflipface(triface& checkface, queue* flipqueue)
{
badface *queface;
+ triface symface;
- queface = (badface *) flipqueue->push((void *) NULL);
- queface->tt = checkface;
- queface->forg = org(checkface);
- queface->fdest = dest(checkface);
- queface->fapex = apex(checkface);
+ sym(checkface, symface);
+ if (symface.tet != dummytet) {
+ queface = (badface *) flipqueue->push((void *) NULL);
+ queface->tt = checkface;
+ queface->foppo = oppo(symface);
+ }
}
void tetgenmesh::enqueueflipedge(face& checkedge, queue* flipqueue)
@@ -9686,10 +10039,14 @@ void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
triface abcd, bace; // Old configuration.
triface oldabd, oldbcd, oldcad;
triface abdcasing, bcdcasing, cadcasing;
- face abdsh, bcdsh, cadsh;
triface oldbae, oldcbe, oldace;
triface baecasing, cbecasing, acecasing;
+ triface worktet;
+ face abdsh, bcdsh, cadsh; // The six subfaces on the CH.
face baesh, cbesh, acesh;
+ face abseg, bcseg, caseg; // The nine segs on the CH.
+ face adseg, bdseg, cdseg;
+ face aeseg, beseg, ceseg;
triface edab, edbc, edca; // New configuration.
point pa, pb, pc, pd, pe;
REAL attrib, volume;
@@ -9697,27 +10054,25 @@ void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
abcd = *flipface;
adjustedgering(abcd, CCW); // abcd represents edge ab.
- sym(abcd, bace);
- findedge(&bace, dest(abcd), org(abcd)); // bace represents edge ba.
pa = org(abcd);
pb = dest(abcd);
pc = apex(abcd);
pd = oppo(abcd);
+ // sym(abcd, bace);
+ // findedge(&bace, dest(abcd), org(abcd)); // bace represents edge ba.
+ sym(abcd, bace);
+ bace.ver = 0; // CCW.
+ for (i = 0; (i < 3) && (org(bace) != pb); i++) {
+ enextself(bace);
+ }
pe = oppo(bace);
if (b->verbose > 2) {
- printf(" Do T23 on face (%d, %d, %d, %d).\n", pointmark(pa),
- pointmark(pb), pointmark(pc), pointmark(pd));
+ printf(" Do T23 on face (%d, %d, %d) %d, %d.\n", pointmark(pa),
+ pointmark(pb), pointmark(pc), pointmark(pd), pointmark(pe));
}
flip23s++;
-#ifdef SELF_CHECK
- // Edge de must cross face abc properly.
- assert(orient3d(pa, pb, pd, pe) >= 0.0);
- assert(orient3d(pb, pc, pd, pe) >= 0.0);
- assert(orient3d(pc, pa, pd, pe) >= 0.0);
-#endif
-
// Storing the old configuration outside the convex hull.
fnext(abcd, oldabd);
enextfnext(abcd, oldbcd);
@@ -9738,6 +10093,24 @@ void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
tspivot(oldbae, baesh);
tspivot(oldcbe, cbesh);
tspivot(oldace, acesh);
+ } else if (checksubsegs) {
+ tsspivot1(abcd, abseg);
+ enext(abcd, worktet);
+ tsspivot1(worktet, bcseg);
+ enext2(abcd, worktet);
+ tsspivot1(worktet, caseg);
+ enext2(oldabd, worktet);
+ tsspivot1(worktet, adseg);
+ enext2(oldbcd, worktet);
+ tsspivot1(worktet, bdseg);
+ enext2(oldcad, worktet);
+ tsspivot1(worktet, cdseg);
+ enext(oldbae, worktet);
+ tsspivot1(worktet, aeseg);
+ enext(oldcbe, worktet);
+ tsspivot1(worktet, beseg);
+ enext(oldace, worktet);
+ tsspivot1(worktet, ceseg);
}
// Creating the new configuration inside the convex hull.
@@ -9771,10 +10144,10 @@ void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
// Clear old bonds in edab(was abcd) and edbc(was bace).
for (i = 0; i < 4; i ++) {
- edab.loc = i;
- dissolve(edab);
- edbc.loc = i;
- dissolve(edbc);
+ edab.tet[i] = (tetrahedron) dummytet;
+ }
+ for (i = 0; i < 4; i ++) {
+ edbc.tet[i] = (tetrahedron) dummytet;
}
// Bond the faces inside the convex hull.
edab.loc = 0;
@@ -9798,7 +10171,7 @@ void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
edca.loc = 2;
bond(edca, cadcasing);
edca.loc = 3;
- bond(edca, acecasing);
+ bond(edca, acecasing);
// There may exist subfaces that need to be bonded to new configuarton.
if (checksubfaces) {
// Clear old flags in edab(was abcd) and edbc(was bace).
@@ -9832,6 +10205,55 @@ void tetgenmesh::flip23(triface* flipface, queue* flipqueue)
edca.loc = 3;
tsbond(edca, acesh);
}
+ } else if (checksubsegs) {
+ for (i = 0; i < 6; i++) {
+ edab.tet[8 + i] = (tetrahedron) dummysh;
+ }
+ for (i = 0; i < 6; i++) {
+ edbc.tet[8 + i] = (tetrahedron) dummysh;
+ }
+ edab.loc = edab.ver = 0;
+ edbc.loc = edab.ver = 0;
+ edca.loc = edab.ver = 0;
+ // Operate in tet edab (5 edges).
+ enext(edab, worktet);
+ tssbond1(worktet, adseg);
+ enext2(edab, worktet);
+ tssbond1(worktet, aeseg);
+ fnext(edab, worktet);
+ enextself(worktet);
+ tssbond1(worktet, bdseg);
+ enextself(worktet);
+ tssbond1(worktet, beseg);
+ enextfnext(edab, worktet);
+ enextself(worktet);
+ tssbond1(worktet, abseg);
+ // Operate in tet edbc (5 edges)
+ enext(edbc, worktet);
+ tssbond1(worktet, bdseg);
+ enext2(edbc, worktet);
+ tssbond1(worktet, beseg);
+ fnext(edbc, worktet);
+ enextself(worktet);
+ tssbond1(worktet, cdseg);
+ enextself(worktet);
+ tssbond1(worktet, ceseg);
+ enextfnext(edbc, worktet);
+ enextself(worktet);
+ tssbond1(worktet, bcseg);
+ // Operate in tet edca (5 edges)
+ enext(edca, worktet);
+ tssbond1(worktet, cdseg);
+ enext2(edca, worktet);
+ tssbond1(worktet, ceseg);
+ fnext(edca, worktet);
+ enextself(worktet);
+ tssbond1(worktet, adseg);
+ enextself(worktet);
+ tssbond1(worktet, aeseg);
+ enextfnext(edca, worktet);
+ enextself(worktet);
+ tssbond1(worktet, caseg);
}
edab.loc = 0;
@@ -9889,40 +10311,44 @@ void tetgenmesh::flip32(triface* flipface, queue* flipqueue)
triface edab, edbc, edca; // Old configuration.
triface oldabd, oldbcd, oldcad;
triface abdcasing, bcdcasing, cadcasing;
- face abdsh, bcdsh, cadsh;
triface oldbae, oldcbe, oldace;
triface baecasing, cbecasing, acecasing;
+ triface worktet;
+ face abdsh, bcdsh, cadsh;
face baesh, cbesh, acesh;
+ face abseg, bcseg, caseg; // The nine segs on the CH.
+ face adseg, bdseg, cdseg;
+ face aeseg, beseg, ceseg;
triface abcd, bace; // New configuration.
point pa, pb, pc, pd, pe;
int i;
edab = *flipface;
adjustedgering(edab, CCW);
- fnext(edab, edbc);
- symself(edbc);
- findedge(&edbc, org(edab), dest(edab));
- fnext(edbc, edca);
- symself(edca);
- findedge(&edca, org(edab), dest(edab));
pa = apex(edab);
pb = oppo(edab);
- pc = oppo(edbc);
pd = dest(edab);
pe = org(edab);
+ fnext(edab, edbc);
+ symself(edbc);
+ edbc.ver = 0;
+ for (i = 0; (i < 3) && (org(edbc) != pe); i++) {
+ enextself(edbc);
+ }
+ pc = oppo(edbc);
+ fnext(edbc, edca);
+ symself(edca);
+ edca.ver = 0;
+ for (i = 0; (i < 3) && (org(edca) != pe); i++) {
+ enextself(edca);
+ }
if (b->verbose > 2) {
- printf(" Do T32 on face (%d, %d, %d, %d).\n",
- pointmark(pe), pointmark(pd), pointmark(pa), pointmark(pb));
+ printf(" Do T32 on edge (%d, %d) %d, %d, %d.\n", pointmark(pe),
+ pointmark(pd), pointmark(pa), pointmark(pb), pointmark(pc));
}
flip32s++;
-#ifdef SELF_CHECK
- // Edge de must cross face abc properly.
- // assert(orient3d(pa, pb, pc, pd) <= 0.0);
- // assert(orient3d(pb, pa, pc, pe) <= 0.0);
-#endif
-
// Storing the old configuration outside the convex hull.
enextfnext(edab, oldabd);
enext2fnext(edab, oldbae);
@@ -9943,6 +10369,28 @@ void tetgenmesh::flip32(triface* flipface, queue* flipqueue)
tspivot(oldbae, baesh);
tspivot(oldcbe, cbesh);
tspivot(oldace, acesh);
+ } else if (checksubsegs) {
+ enext(edab, worktet);
+ tsspivot1(worktet, adseg);
+ enext2(edab, worktet);
+ tsspivot1(worktet, aeseg);
+ enext(edbc, worktet);
+ tsspivot1(worktet, bdseg);
+ enext2(edbc, worktet);
+ tsspivot1(worktet, beseg);
+ enext(edca, worktet);
+ tsspivot1(worktet, cdseg);
+ enext2(edca, worktet);
+ tsspivot1(worktet, ceseg);
+ enextfnext(edab, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, abseg);
+ enextfnext(edbc, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, bcseg);
+ enextfnext(edca, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, caseg);
}
// Creating the new configuration inside the convex hull.
@@ -9961,10 +10409,10 @@ void tetgenmesh::flip32(triface* flipface, queue* flipqueue)
// Clear the old bonds in abcd (was edab) and bace (was edbc).
for (i = 0; i < 4; i ++) {
- abcd.loc = i;
- dissolve(abcd);
- bace.loc = i;
- dissolve(bace);
+ abcd.tet[i] = (tetrahedron) dummytet;
+ }
+ for (i = 0; i < 4; i ++) {
+ bace.tet[i] = (tetrahedron) dummytet;
}
// Bond the inside face of the convex hull.
abcd.loc = 0;
@@ -9986,35 +10434,72 @@ void tetgenmesh::flip32(triface* flipface, queue* flipqueue)
if (checksubfaces) {
// Clear old bonds in abcd(was edab) and bace(was edbc).
for (i = 0; i < 4; i ++) {
- abcd.loc = i;
- tsdissolve(abcd);
- bace.loc = i;
- tsdissolve(bace);
+ abcd.tet[8 + i] = (tetrahedron) dummysh;
+ }
+ for (i = 0; i < 4; i ++) {
+ bace.tet[8 + i] = (tetrahedron) dummysh;
}
if (abdsh.sh != dummysh) {
abcd.loc = 1;
tsbond(abcd, abdsh);
}
- if (baesh.sh != dummysh) {
- bace.loc = 1;
- tsbond(bace, baesh);
- }
if (bcdsh.sh != dummysh) {
abcd.loc = 2;
tsbond(abcd, bcdsh);
}
- if (cbesh.sh != dummysh) {
- bace.loc = 3;
- tsbond(bace, cbesh);
- }
if (cadsh.sh != dummysh) {
abcd.loc = 3;
tsbond(abcd, cadsh);
}
+ if (baesh.sh != dummysh) {
+ bace.loc = 1;
+ tsbond(bace, baesh);
+ }
+ if (cbesh.sh != dummysh) {
+ bace.loc = 3;
+ tsbond(bace, cbesh);
+ }
if (acesh.sh != dummysh) {
bace.loc = 2;
tsbond(bace, acesh);
}
+ } else if (checksubsegs) {
+ for (i = 0; i < 6; i++) {
+ abcd.tet[8 + i] = (tetrahedron) dummysh;
+ }
+ for (i = 0; i < 6; i++) {
+ bace.tet[8 + i] = (tetrahedron) dummysh;
+ }
+ abcd.loc = abcd.ver = 0;
+ bace.loc = bace.ver = 0;
+ tssbond1(abcd, abseg); // 1
+ enext(abcd, worktet);
+ tssbond1(worktet, bcseg); // 2
+ enext2(abcd, worktet);
+ tssbond1(worktet, caseg); // 3
+ fnext(abcd, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, adseg); // 4
+ enextfnext(abcd, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, bdseg); // 5
+ enext2fnext(abcd, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, cdseg); // 6
+ tssbond1(bace, abseg);
+ enext2(bace, worktet);
+ tssbond1(worktet, bcseg);
+ enext(bace, worktet);
+ tssbond1(worktet, caseg);
+ fnext(bace, worktet);
+ enextself(worktet);
+ tssbond1(worktet, aeseg); // 7
+ enext2fnext(bace, worktet);
+ enextself(worktet);
+ tssbond1(worktet, beseg); // 8
+ enextfnext(bace, worktet);
+ enextself(worktet);
+ tssbond1(worktet, ceseg); // 9
}
abcd.loc = 0;
@@ -10084,10 +10569,14 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
triface bacf, abdf;
triface oldacf, oldcbf, oldbdf, olddaf;
triface acfcasing, cbfcasing, bdfcasing, dafcasing;
+ triface worktet;
face acfsh, cbfsh, bdfsh, dafsh;
face abc, bad;
+ face adseg, dbseg, bcseg, caseg; // Coplanar segs.
+ face aeseg, deseg, beseg, ceseg; // Above segs.
+ face afseg, dfseg, bfseg, cfseg; // Below segs.
point pa, pb, pc, pd, pe, pf;
- int mirrorflag;
+ int mirrorflag, i;
adjustedgering(*flipface, CCW); // 'flipface' is bae.
fnext(*flipface, abce);
@@ -10109,12 +10598,20 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
sym(abce, bacf);
mirrorflag = bacf.tet != dummytet;
if (mirrorflag) {
- findedge(&bacf, pb, pa);
+ // findedge(&bacf, pb, pa);
+ bacf.ver = 0;
+ for (i = 0; (i < 3) && (org(bacf) != pb); i++) {
+ enextself(bacf);
+ }
sym(bade, abdf);
#ifdef SELF_CHECK
assert(abdf.tet != dummytet);
#endif
- findedge(&abdf, pa, pb);
+ // findedge(&abdf, pa, pb);
+ abdf.ver = 0;
+ for (i = 0; (i < 3) && (org(abdf) != pa); i++) {
+ enextself(abdf);
+ }
pf = oppo(bacf);
#ifdef SELF_CHECK
assert(oppo(abdf) == pf);
@@ -10127,12 +10624,6 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
}
mirrorflag ? flip44s++ : flip22s++;
-#ifdef SELF_CHECK
- // The quadrilateral formed by a, b, c, and d must be convex.
- assert(orient3d(pc, pd, pe, pa) <= 0.0);
- assert(orient3d(pd, pc, pe, pb) <= 0.0);
-#endif
-
// Save the old configuration at the convex hull.
enextfnext(abce, oldbce);
enext2fnext(abce, oldcae);
@@ -10149,6 +10640,29 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
tspivot(olddbe, dbesh);
tspivot(abce, abc);
tspivot(bade, bad);
+ } else if (checksubsegs) {
+ // Coplanar segs: a->d->b->c.
+ enext(bade, worktet);
+ tsspivot1(worktet, adseg);
+ enext2(bade, worktet);
+ tsspivot1(worktet, dbseg);
+ enext(abce, worktet);
+ tsspivot1(worktet, bcseg);
+ enext2(abce, worktet);
+ tsspivot1(worktet, caseg);
+ // Above segs: a->e, d->e, b->e, c->e.
+ fnext(bade, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, aeseg);
+ enextfnext(bade, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, deseg);
+ enext2fnext(bade, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, beseg);
+ enextfnext(abce, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, ceseg);
}
if (mirrorflag) {
enextfnext(bacf, oldacf);
@@ -10164,6 +10678,20 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
tspivot(oldcbf, cbfsh);
tspivot(oldbdf, bdfsh);
tspivot(olddaf, dafsh);
+ } else if (checksubsegs) {
+ // Below segs: a->f, d->f, b->f, c->f.
+ fnext(abdf, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, afseg);
+ enext2fnext(abdf, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, dfseg);
+ enextfnext(abdf, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, bfseg);
+ enextfnext(bacf, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, cfseg);
}
}
@@ -10194,6 +10722,75 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
} else {
tsbond(olddbe, bcesh);
}
+ } else if (checksubsegs) {
+ // 5 edges in abce are changed.
+ enext(abce, worktet); // fit b->c into c->a.
+ if (caseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, caseg);
+ }
+ enext2(abce, worktet); // fit c->a into a->d.
+ if (adseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, adseg);
+ }
+ fnext(abce, worktet); // fit b->e into c->e.
+ enextself(worktet);
+ if (ceseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, ceseg);
+ }
+ enextfnext(abce, worktet); // fit c->e into a->e.
+ enextself(worktet);
+ if (aeseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, aeseg);
+ }
+ enext2fnext(abce, worktet); // fit a->e into d->e.
+ enextself(worktet);
+ if (deseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, deseg);
+ }
+ // 5 edges in bade are changed.
+ enext(bade, worktet); // fit a->d into d->b.
+ if (dbseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, dbseg);
+ }
+ enext2(bade, worktet); // fit d->b into b->c.
+ if (bcseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, bcseg);
+ }
+ fnext(bade, worktet); // fit a->e into d->e.
+ enextself(worktet);
+ if (deseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, deseg);
+ }
+ enextfnext(bade, worktet); // fit d->e into b->e.
+ enextself(worktet);
+ if (beseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, beseg);
+ }
+ enext2fnext(bade, worktet); // fit b->e into c->e.
+ enextself(worktet);
+ if (ceseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, ceseg);
+ }
}
if (mirrorflag) {
// Rotate bacf, abdf one-quarter turn counterclockwise.
@@ -10223,6 +10820,75 @@ void tetgenmesh::flip22(triface* flipface, queue* flipqueue)
} else {
tsbond(oldbdf, cbfsh);
}
+ } else if (checksubsegs) {
+ // 5 edges in bacf are changed.
+ enext2(bacf, worktet); // fit b->c into c->a.
+ if (caseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, caseg);
+ }
+ enext(bacf, worktet); // fit c->a into a->d.
+ if (adseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, adseg);
+ }
+ fnext(bacf, worktet); // fit b->f into c->f.
+ enext2self(worktet);
+ if (cfseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, cfseg);
+ }
+ enext2fnext(bacf, worktet); // fit c->f into a->f.
+ enext2self(worktet);
+ if (afseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, afseg);
+ }
+ enextfnext(bacf, worktet); // fit a->f into d->f.
+ enext2self(worktet);
+ if (dfseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, dfseg);
+ }
+ // 5 edges in abdf are changed.
+ enext2(abdf, worktet); // fit a->d into d->b.
+ if (dbseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, dbseg);
+ }
+ enext(abdf, worktet); // fit d->b into b->c.
+ if (bcseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, bcseg);
+ }
+ fnext(abdf, worktet); // fit a->f into d->f.
+ enext2self(worktet);
+ if (dfseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, dfseg);
+ }
+ enext2fnext(abdf, worktet); // fit d->f into b->f.
+ enext2self(worktet);
+ if (bfseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, bfseg);
+ }
+ enextfnext(abdf, worktet); // fit b->f into c->f.
+ enext2self(worktet);
+ if (cfseg.sh == dummysh) {
+ tssdissolve1(worktet);
+ } else {
+ tssbond1(worktet, cfseg);
+ }
}
}
@@ -10553,15 +11219,10 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
while (!flipqueue->empty()) {
qface = (badface *) flipqueue->pop();
flipface = qface->tt;
- // Check the validity of this face.
- if (isdead(&flipface) || flipface.tet == dummytet ||
- (org(flipface) != qface->forg) ||
- (dest(flipface) != qface->fdest) ||
- (apex(flipface) != qface->fapex) ||
- (oppo(flipface) == (point) NULL)) continue;
+ if (isdead(&flipface)) continue;
sym(flipface, symface);
// Only do check when the adjacent tet exists and it's not a "fake" tet.
- if (symface.tet != dummytet && oppo(symface) != (point) NULL) {
+ if ((symface.tet != dummytet) && (oppo(symface) == qface->foppo)) {
// For positive orientation that insphere() test requires.
adjustedgering(flipface, CW);
pa = org(flipface);
@@ -10569,7 +11230,7 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
pc = apex(flipface);
pd = oppo(flipface);
pe = oppo(symface);
- // if (symbolic) {
+ if (symbolic) {
ia = pointmark(pa);
ib = pointmark(pb);
ic = pointmark(pc);
@@ -10577,9 +11238,9 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
ie = pointmark(pe);
sign = insphere_sos(pa, pb, pc, pd, pe, ia, ib, ic, id, ie);
assert(sign != 0.0);
- // } else {
- // sign = insphere(pa, pb, pc, pd, pe);
- // }
+ } else {
+ sign = insphere(pa, pb, pc, pd, pe);
+ }
} else {
sign = -1.0; // A hull face is locally Delaunay.
}
@@ -10591,7 +11252,7 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
epscount = 0;
while (epscount < 32) {
fc = categorizeface(flipface);
- if (fc == NONCONVEX) {
+ if (fc == N40) {
b->epsilon *= 1e-1;
epscount++;
continue;
@@ -10603,12 +11264,12 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
if (b->verbose > 0) {
printf("Warning: Can't flip a degenerate tetrahedron.\n");
}
- fc = NONCONVEX;
+ fc = N40;
}
} else {
fc = categorizeface(flipface);
#ifdef SELF_CHECK
- assert(fc != NONCONVEX);
+ assert(fc != N40);
#endif
}
switch (fc) {
@@ -10624,14 +11285,14 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
flip32(&flipface, flipqueue);
break;
// The following face types are unflipable.
- case UNFLIPABLE:
+ case N32:
break;
case FORBIDDENFACE:
break;
case FORBIDDENEDGE:
break;
// This case is only possible when the domain is nonconvex.
- case NONCONVEX:
+ case N40:
// assert(nonconvex);
break;
}
@@ -10659,6 +11320,233 @@ long tetgenmesh::flip(queue* flipqueue, badface **plastflip)
return flipcount;
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// lawson() Flip locally non-Delaunay faces by Lawson's algorithm. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+long tetgenmesh::lawson(list *misseglist, queue* flipqueue)
+{
+ badface *qface, *misseg;
+ triface flipface, symface;
+ triface starttet, spintet;
+ face checksh, checkseg;
+ point pa, pb, pc, pd, pe;
+ point swappt;
+ REAL sign, ori;
+ long flipcount;
+ int ia, ib, ic, id, ie;
+ int hitbdry, i;
+
+ if (b->verbose > 1) {
+ printf(" Do flipface queue: %ld faces.\n", flipqueue->len());
+ }
+ flipcount = flip23s + flip32s + flip22s + flip44s;
+
+ // Go through the stack of possible flips and decide whether to do them.
+ // Note that during the loop new possible flips will be pushed onto
+ // this stack, while they popped in this loop.
+ while (!flipqueue->empty()) {
+ qface = (badface *) flipqueue->pop();
+ flipface = qface->tt;
+ // Check if tet has already been flipped out of existence.
+ if (!isdead(&flipface)) {
+ sym(flipface, symface);
+ // Check if this tet is the same as the one which was stacked.
+ if ((symface.tet != dummytet) && (oppo(symface) == qface->foppo)) {
+ flipface.ver = 0; // Select the CCW ring.
+ pa = org(flipface);
+ pb = dest(flipface);
+ pc = apex(flipface);
+ pd = oppo(flipface);
+ pe = oppo(symface);
+ if (symbolic) {
+ ia = pointmark(pa);
+ ib = pointmark(pb);
+ ic = pointmark(pc);
+ id = pointmark(pd);
+ ie = pointmark(pe);
+ sign = insphere_sos(pb, pa, pc, pd, pe, ib, ia, ic, id, ie);
+ } else {
+ sign = insphere(pb, pa, pc, pd, pe);
+ }
+ if (sign > 0.0) {
+ for (i = 0; i < 3; i++) {
+ ori = orient3d(pa, pb, pd, pe);
+ if (ori > 0.0) {
+ // Goto and check the next edge.
+ swappt = pa;
+ pa = pb;
+ pb = pc;
+ pc = swappt;
+ enextself(flipface);
+ } else {
+ break; // either (ori < 0.0) or (ori == 0.0)
+ }
+ } // for (i = 0; ....)
+ if (ori > 0.0) {
+ // All three edges are convex, a 2-3 flip is possible.
+ if (checksubfaces) {
+ tspivot(flipface, checksh);
+ if (checksh.sh != dummysh) {
+ // A subface is not flipable.
+ continue;
+ }
+ }
+ flip23(&flipface, flipqueue);
+ } else if (ori < 0.0) {
+ // The edge (a, b) is non-convex, check for a 3-2 flip.
+ fnext(flipface, symface);
+ symself(symface);
+ if (oppo(symface) == pe) {
+ // Only three tets adjoining this edge.
+ if (checksubfaces) {
+ tsspivot(&flipface, &checkseg);
+ if (checkseg.sh != dummysh) {
+ // A subsegment is not flipable.
+ continue;
+ }
+ } else if (checksubsegs) {
+ tsspivot1(flipface, checkseg);
+ if (checkseg.sh != dummysh) {
+ if (b->verbose > 2) {
+ printf(" Queuing missing segment (%d, %d).\n",
+ pointmark(org(flipface)), pointmark(dest(flipface)));
+ }
+ misseg = (badface *) misseglist->append(NULL);
+ misseg->ss = checkseg;
+ misseg->forg = sorg(checkseg);
+ misseg->fdest = sdest(checkseg);
+ // Detach all tets having this seg.
+ starttet = flipface;
+ adjustedgering(starttet, CCW);
+ fnextself(starttet);
+ spintet = starttet;
+ hitbdry = 0;
+ do {
+ tssdissolve1(spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(starttet, spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ }
+ }
+ }
+ } while ((apex(spintet) != apex(starttet)) && (hitbdry < 2));
+ }
+ } // if (checksubfaces)
+ flip32(&flipface, flipqueue);
+ }
+ } else {
+ // Four points (a, b, d, e) are coplanar.
+ fnext(flipface, symface);
+ if (fnextself(symface)) {
+ // Check for a 4-4 flip.
+ fnextself(symface);
+ if (apex(symface) == pe) {
+ if (checksubfaces) {
+ tsspivot(&flipface, &checkseg);
+ if (checkseg.sh != dummysh) {
+ // A subsegment is not flippable.
+ continue;
+ }
+ } else if (checksubsegs) {
+ tsspivot1(flipface, checkseg);
+ if (checkseg.sh != dummysh) {
+ if (b->verbose > 2) {
+ printf(" Queuing missing segment (%d, %d).\n",
+ pointmark(org(flipface)), pointmark(dest(flipface)));
+ }
+ misseg = (badface *) misseglist->append(NULL);
+ misseg->ss = checkseg;
+ misseg->forg = sorg(checkseg);
+ misseg->fdest = sdest(checkseg);
+ // Detach all tets having this seg.
+ starttet = flipface;
+ adjustedgering(starttet, CCW);
+ fnextself(starttet);
+ spintet = starttet;
+ hitbdry = 0;
+ do {
+ tssdissolve1(spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(starttet, spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ }
+ }
+ }
+ } while ((apex(spintet) != apex(starttet)) &&
+ (hitbdry < 2));
+ }
+ } // if (checksubfaces)
+ flip22(&flipface, flipqueue);
+ }
+ } else {
+ // Check for a 2-2 flip.
+ esym(flipface, symface);
+ fnextself(symface);
+ symself(symface);
+ if (symface.tet == dummytet) {
+ if (checksubfaces) {
+ tsspivot(&flipface, &checkseg);
+ if (checkseg.sh != dummysh) {
+ // A subsegment is not flipable.
+ continue;
+ }
+ } else if (checksubsegs) {
+ tsspivot1(flipface, checkseg);
+ if (checkseg.sh != dummysh) {
+ if (b->verbose > 2) {
+ printf(" Queuing missing segment (%d, %d).\n",
+ pointmark(org(flipface)), pointmark(dest(flipface)));
+ }
+ misseg = (badface *) misseglist->append(NULL);
+ misseg->ss = checkseg;
+ misseg->forg = sorg(checkseg);
+ misseg->fdest = sdest(checkseg);
+ // Detach all tets having this seg.
+ starttet = flipface;
+ adjustedgering(starttet, CCW);
+ fnextself(starttet);
+ spintet = starttet;
+ hitbdry = 0;
+ do {
+ tssdissolve1(spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(starttet, spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ }
+ }
+ }
+ } while ((apex(spintet) != apex(starttet)) &&
+ (hitbdry < 2));
+ }
+ } // if (checksubfaces)
+ flip22(&flipface, flipqueue);
+ }
+ }
+ } // if (ori > 0.0)
+ } // if (sign > 0.0)
+ }
+ } // !isdead(&qface->tt)
+ } // while (!flipqueue->empty())
+
+ flipcount = flip23s + flip32s + flip22s + flip44s - flipcount;
+ if (b->verbose > 1) {
+ printf(" %ld flips.\n", flipcount);
+ }
+ return flipcount;
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// undoflip() Undo the most recent flip sequence induced by flip(). //
@@ -10727,7 +11615,8 @@ long tetgenmesh::flipsub(queue* flipqueue)
edgeflips = 0;
- while ((qedge = (badface *) flipqueue->pop()) != NULL) {
+ while (!flipqueue->empty()) {
+ qedge = (badface *) flipqueue->pop();
flipedge = qedge->ss;
if (flipedge.sh == dummysh) continue;
if ((sorg(flipedge) != qedge->forg) ||
@@ -10786,46 +11675,1131 @@ long tetgenmesh::flipsub(queue* flipqueue)
///////////////////////////////////////////////////////////////////////////////
// //
-// splittetrahedron() Insert a point into a tetrahedron, split it into //
-// four tetrahedra. //
+// removetetbypeeloff() Remove a boundary tet by peeling it off. //
// //
-// The tetrahedron is given by 'splittet'. Let it is abcd. The inserting //
-// point 'newpoint' v should lie strictly inside abcd. //
+// 'striptet' (abcd) is on boundary and can be removed by stripping it off. //
+// Let abc and bad are the external boundary faces. //
// //
-// Splitting a tetrahedron is to shrink abcd to abcv, and create three new //
-// tetrahedra badv, cbdv, and acdv. //
+// To strip 'abcd' from the mesh is to detach its two interal faces (dca and //
+// cdb) from their adjoining tets together with a 2-to-2 flip to transform //
+// two subfaces (abc and bad) into another two (dca and cdb). //
// //
-// On completion, 'splittet' returns abcv. If 'flipqueue' is not NULL, it //
-// contains all possibly non-locally Delaunay faces. //
+// In mesh optimization. It is possible that ab is a segment and abcd is a //
+// sliver on the hull. Strip abcd will also delete the segment ab. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::
-splittetrahedron(point newpoint, triface* splittet, queue* flipqueue)
+bool tetgenmesh::removetetbypeeloff(triface *striptet)
{
- triface oldabd, oldbcd, oldcad; // Old configuration.
- triface abdcasing, bcdcasing, cadcasing;
- face abdsh, bcdsh, cadsh;
- triface abcv, badv, cbdv, acdv; // New configuration.
- point pa, pb, pc, pd;
- REAL attrib, volume;
- int i;
-
- abcv = *splittet;
- abcv.ver = 0;
- // Set the changed vertices and new tetrahedron.
- pa = org(abcv);
- pb = dest(abcv);
- pc = apex(abcv);
- pd = oppo(abcv);
-
- if (b->verbose > 1) {
- printf(" Inserting point %d in tetrahedron (%d, %d, %d, %d).\n",
- pointmark(newpoint), pointmark(pa), pointmark(pb), pointmark(pc),
- pointmark(pd));
+ triface abcd, badc;
+ triface dcacasing, cdbcasing;
+ face abc, bad;
+ face abseg;
+ REAL ang;
+
+ abcd = *striptet;
+ adjustedgering(abcd, CCW);
+ // Get the casing tets at the internal sides.
+ enextfnext(abcd, cdbcasing);
+ enext2fnext(abcd, dcacasing);
+ symself(cdbcasing);
+ symself(dcacasing);
+ // Do the neighboring tets exist? During optimization. It is possible
+ // that the neighboring tets are already dead.
+ if ((cdbcasing.tet == dummytet) || (dcacasing.tet == dummytet)) {
+ // Do not strip this tet.
+ return false;
}
- fnext(abcv, oldabd);
+ // Are there subfaces?
+ if (checksubfaces) {
+ // Get the external subfaces abc, bad.
+ fnext(abcd, badc);
+ esymself(badc);
+ tspivot(abcd, abc);
+ tspivot(badc, bad);
+ if (abc.sh != dummysh) {
+ assert(bad.sh != dummysh);
+ findedge(&abc, org(abcd), dest(abcd));
+ findedge(&bad, org(badc), dest(badc));
+ // Is ab a segment?
+ sspivot(abc, abseg);
+ if (abseg.sh != dummysh) {
+ // Does a segment allow to be removed?
+ if ((b->optlevel > 3) && (b->nobisect == 0)) {
+ // Only remove this segment if the dihedal angle at ab is between
+ // [b->maxdihedral-9, 180] (deg). This avoids mistakely fliping
+ // ab when it has actually no big dihedral angle while cd has.
+ ang = facedihedral(org(abcd), dest(abcd), apex(abcd), oppo(abcd));
+ ang = ang * 180.0 / PI;
+ if ((ang + 9.0) > b->maxdihedral) {
+ if (b->verbose > 1) {
+ printf(" Remove a segment during peeling.\n");
+ }
+ face prevseg, nextseg;
+ // It is only shared by abc and bad (abcd is a tet).
+ ssdissolve(abc);
+ ssdissolve(bad);
+ abseg.shver = 0;
+ senext(abseg, nextseg);
+ spivotself(nextseg);
+ if (nextseg.sh != dummysh) {
+ ssdissolve(nextseg);
+ }
+ senext2(abseg, prevseg);
+ spivotself(prevseg);
+ if (prevseg.sh != dummysh) {
+ ssdissolve(prevseg);
+ }
+ shellfacedealloc(subsegs, abseg.sh);
+ optcount[1]++;
+ } else {
+ return false;
+ }
+ } else {
+ return false;
+ }
+ }
+ // Do a 2-to-2 flip on abc and bad, transform abc->dca, bad->cdb.
+ flip22sub(&abc, NULL);
+ // The two internal faces become boundary faces.
+ tsbond(cdbcasing, bad);
+ tsbond(dcacasing, abc);
+ }
+ }
+
+ // Detach abcd from the two internal faces.
+ dissolve(cdbcasing);
+ dissolve(dcacasing);
+ // Delete abcd.
+ tetrahedrondealloc(abcd.tet);
+ return true;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// removeedgebyflip22() Remove an edge by a 2-to-2 (or 4-to-4) flip. //
+// //
+// 'abtetlist' contains n tets (n is 2 or 4) sharing edge ab, abtetlist[0] //
+// and abtetlist[1] are tets abec and abde, respectively (NOTE, both are in //
+// CW edge ring), where a, b, c, and d are coplanar. If n = 4, abtetlist[2] //
+// and abtetlist[3] are tets abfd and abcf, respectively. This routine uses //
+// flip22() to replace edge ab with cd, the surrounding tets are rotated. //
+// //
+// If 'key' != NULL. The old tets are replaced by the new tets only if the //
+// local mesh quality is improved. Current 'key' = cos(\theta), where \theta //
+// is the maximum dihedral angle in the old tets. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::removeedgebyflip22(REAL *key, int n, triface *abtetlist,
+ queue *flipque)
+{
+ point pa, pb, pc, pd, pe, pf;
+ REAL cosmaxd, d1, d2, d3;
+ bool doflip;
+
+ doflip = true;
+ adjustedgering(abtetlist[0], CW);
+ pa = org(abtetlist[0]);
+ pb = dest(abtetlist[0]);
+ pe = apex(abtetlist[0]);
+ pc = oppo(abtetlist[0]);
+ pd = apex(abtetlist[1]);
+ if (n == 4) {
+ pf = apex(abtetlist[2]);
+ }
+ if (key && (*key > -1.0)) {
+ tetalldihedral(pc, pd, pe, pa, NULL, &d1, NULL);
+ tetalldihedral(pd, pc, pe, pb, NULL, &d2, NULL);
+ cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
+ if (n == 4) {
+ tetalldihedral(pd, pc, pf, pa, NULL, &d1, NULL);
+ tetalldihedral(pc, pd, pf, pb, NULL, &d2, NULL);
+ d3 = d1 < d2 ? d1 : d2; // Choose the bigger angle.
+ cosmaxd = cosmaxd < d3 ? cosmaxd : d3; // Choose the bigger angle.
+ }
+ doflip = (*key < cosmaxd); // Can local quality be improved?
+ }
+
+ if (doflip) {
+ flip22(&abtetlist[0], NULL);
+ // Return the improved quality value.
+ if (key) *key = cosmaxd;
+ }
+
+ return doflip;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// removefacebyflip23() Remove a face by a 2-to-3 flip. //
+// //
+// 'abctetlist' contains 2 tets sharing abc, which are [0]abcd and [1]bace. //
+// This routine forms three new tets that abc is not a face anymore. Save //
+// them in 'newtetlist': [0]edab, [1]edbc, and [2]edca. Note that the new //
+// tets may not valid if one of them get inverted. return false if so. //
+// //
+// If 'key' != NULL. The old tets are replaced by the new tets only if the //
+// local mesh quality is improved. Current 'key' = cos(\theta), where \theta //
+// is the maximum dihedral angle in the old tets. //
+// //
+// If the face is flipped, 'newtetlist' returns the three new tets. The two //
+// tets in 'abctetlist' are NOT deleted. The caller has the right to either //
+// delete them or reverse the operation. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::removefacebyflip23(REAL *key, triface *abctetlist,
+ triface *newtetlist, queue *flipque)
+{
+ triface edab, edbc, edca; // new configuration.
+ triface newfront, oldfront, adjfront;
+ face checksh;
+ point pa, pb, pc, pd, pe;
+ REAL ori, cosmaxd, d1, d2, d3;
+ REAL attrib, volume;
+ bool doflip;
+ int i;
+
+ adjustedgering(abctetlist[0], CCW);
+ pa = org(abctetlist[0]);
+ pb = dest(abctetlist[0]);
+ pc = apex(abctetlist[0]);
+ pd = oppo(abctetlist[0]);
+ pe = oppo(abctetlist[1]);
+
+ // Check if the flip creates valid new tets.
+ ori = orient3d(pe, pd, pa, pb);
+ if (ori < 0.0) {
+ ori = orient3d(pe, pd, pb, pc);
+ if (ori < 0.0) {
+ ori = orient3d(pe, pd, pc, pa);
+ }
+ }
+ doflip = (ori < 0.0); // Can abc be flipped away?
+ if (doflip && (key != (REAL *) NULL)) {
+ if (*key > -1.0) {
+ // Test if the new tets reduce the maximal dihedral angle.
+ tetalldihedral(pe, pd, pa, pb, NULL, &d1, NULL);
+ tetalldihedral(pe, pd, pb, pc, NULL, &d2, NULL);
+ tetalldihedral(pe, pd, pc, pa, NULL, &d3, NULL);
+ cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
+ cosmaxd = cosmaxd < d3 ? cosmaxd : d3; // Choose the bigger angle.
+ doflip = (*key < cosmaxd); // Can local quality be improved?
+ }
+ }
+
+ if (doflip) {
+ // A valid (2-to-3) flip is found.
+ flip23s++;
+ // Create the new tets.
+ maketetrahedron(&edab);
+ setorg(edab, pe);
+ setdest(edab, pd);
+ setapex(edab, pa);
+ setoppo(edab, pb);
+ maketetrahedron(&edbc);
+ setorg(edbc, pe);
+ setdest(edbc, pd);
+ setapex(edbc, pb);
+ setoppo(edbc, pc);
+ maketetrahedron(&edca);
+ setorg(edca, pe);
+ setdest(edca, pd);
+ setapex(edca, pc);
+ setoppo(edca, pa);
+ // Transfer the element attributes.
+ for (i = 0; i < in->numberoftetrahedronattributes; i++) {
+ attrib = elemattribute(abctetlist[0].tet, i);
+ setelemattribute(edab.tet, i, attrib);
+ setelemattribute(edbc.tet, i, attrib);
+ setelemattribute(edca.tet, i, attrib);
+ }
+ // Transfer the volume constraints.
+ if (b->varvolume && !b->refine) {
+ volume = volumebound(abctetlist[0].tet);
+ setvolumebound(edab.tet, volume);
+ setvolumebound(edbc.tet, volume);
+ setvolumebound(edca.tet, volume);
+ }
+ // Return two new tets.
+ newtetlist[0] = edab;
+ newtetlist[1] = edbc;
+ newtetlist[2] = edca;
+ // Glue the three new tets.
+ for (i = 0; i < 3; i++) {
+ fnext(newtetlist[i], newfront);
+ bond(newfront, newtetlist[(i + 1) % 3]);
+ }
+ // Substitute the three new tets into the old cavity.
+ for (i = 0; i < 3; i++) {
+ fnext(abctetlist[0], oldfront);
+ sym(oldfront, adjfront); // may be outside.
+ enextfnext(newtetlist[i], newfront);
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ if (flipque != (queue *) NULL) {
+ enqueueflipface(newfront, flipque);
+ }
+ enextself(abctetlist[0]);
+ }
+ findedge(&(abctetlist[1]), pb, pa);
+ for (i = 0; i < 3; i++) {
+ fnext(abctetlist[1], oldfront);
+ sym(oldfront, adjfront); // may be outside.
+ enext2fnext(newtetlist[i], newfront);
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ if (flipque != (queue *) NULL) {
+ enqueueflipface(newfront, flipque);
+ }
+ enext2self(abctetlist[1]);
+ }
+ // Do not delete the old tets.
+ // for (i = 0; i < 2; i++) {
+ // tetrahedrondealloc(abctetlist[i].tet);
+ // }
+ // Return the improved quality value.
+ if (key != (REAL *) NULL) *key = cosmaxd;
+ return true;
+ }
+
+ return false;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// removeedgebyflip32() Remove an edge by a 3-to-2 flip. //
+// //
+// 'abtetlist' contains 3 tets sharing ab. Imaging that ab is perpendicular //
+// to the screen, where a lies in front of and b lies behind it. The 3 tets //
+// of the list are: [0]abce, [1]abdc, and [2]abed, respectively. //
+// //
+// This routine forms two new tets that ab is not an edge of them. Save them //
+// in 'newtetlist', [0]dcea, [1]cdeb. Note that the new tets may not valid //
+// if one of them get inverted. return false if so. //
+// //
+// If 'key' != NULL. The old tets are replaced by the new tets only if the //
+// local mesh quality is improved. Current 'key' = cos(\theta), where \theta //
+// is the maximum dihedral angle in the old tets. //
+// //
+// If the edge is flipped, 'newtetlist' returns the two new tets. The three //
+// tets in 'abtetlist' are NOT deleted. The caller has the right to either //
+// delete them or reverse the operation. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::removeedgebyflip32(REAL *key, triface *abtetlist,
+ triface *newtetlist, queue *flipque)
+{
+ triface dcea, cdeb; // new configuration.
+ triface newfront, oldfront, adjfront;
+ face checksh;
+ point pa, pb, pc, pd, pe;
+ REAL ori, cosmaxd, d1, d2;
+ REAL attrib, volume;
+ bool doflip;
+ int i;
+
+ pa = org(abtetlist[0]);
+ pb = dest(abtetlist[0]);
+ pc = apex(abtetlist[0]);
+ pd = apex(abtetlist[1]);
+ pe = apex(abtetlist[2]);
+
+ ori = orient3d(pd, pc, pe, pa);
+ if (ori < 0.0) {
+ ori = orient3d(pc, pd, pe, pb);
+ }
+ doflip = (ori < 0.0); // Can ab be flipped away?
+
+ // Does the caller ensure a valid configuration?
+ if (doflip && (key != (REAL *) NULL)) {
+ if (*key > -1.0) {
+ // Test if the new tets reduce the maximal dihedral angle.
+ tetalldihedral(pd, pc, pe, pa, NULL, &d1, NULL);
+ tetalldihedral(pc, pd, pe, pb, NULL, &d2, NULL);
+ cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
+ doflip = (*key < cosmaxd); // Can local quality be improved?
+ // Return the key
+ *key = cosmaxd;
+ }
+ }
+
+ if (doflip) {
+ // Create the new tets.
+ maketetrahedron(&dcea);
+ setorg(dcea, pd);
+ setdest(dcea, pc);
+ setapex(dcea, pe);
+ setoppo(dcea, pa);
+ maketetrahedron(&cdeb);
+ setorg(cdeb, pc);
+ setdest(cdeb, pd);
+ setapex(cdeb, pe);
+ setoppo(cdeb, pb);
+ // Transfer the element attributes.
+ for (i = 0; i < in->numberoftetrahedronattributes; i++) {
+ attrib = elemattribute(abtetlist[0].tet, i);
+ setelemattribute(dcea.tet, i, attrib);
+ setelemattribute(cdeb.tet, i, attrib);
+ }
+ // Transfer the volume constraints.
+ if (b->varvolume && !b->refine) {
+ volume = volumebound(abtetlist[0].tet);
+ setvolumebound(dcea.tet, volume);
+ setvolumebound(cdeb.tet, volume);
+ }
+ // Return two new tets.
+ newtetlist[0] = dcea;
+ newtetlist[1] = cdeb;
+ // Glue the two new tets.
+ bond(dcea, cdeb);
+ // Substitute the two new tets into the old three-tets cavity.
+ for (i = 0; i < 3; i++) {
+ fnext(dcea, newfront); // face dca, cea, eda.
+ esym(abtetlist[(i + 1) % 3], oldfront);
+ enextfnextself(oldfront);
+ // Get the adjacent tet at the face (may be a dummytet).
+ sym(oldfront, adjfront);
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ if (flipque != (queue *) NULL) {
+ enqueueflipface(newfront, flipque);
+ }
+ enext2self(dcea);
+ }
+ for (i = 0; i < 3; i++) {
+ fnext(cdeb, newfront); // face cdb, deb, ecb.
+ esym(abtetlist[(i + 1) % 3], oldfront);
+ enext2fnextself(oldfront);
+ // Get the adjacent tet at the face (may be a dummytet).
+ sym(oldfront, adjfront);
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ if (flipque != (queue *) NULL) {
+ enqueueflipface(newfront, flipque);
+ }
+ enextself(cdeb);
+ }
+ // Do not delete the old tets.
+ // for (i = 0; i < 3; i++) {
+ // tetrahedrondealloc(abtetlist[i].tet);
+ // }
+ return true;
+ } // if (doflip)
+
+ return false;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// removeedgebytranNM() Remove an edge by transforming n-to-m tets. //
+// //
+// This routine attempts to remove a given edge (ab) by transforming the set //
+// T of tets surrounding ab into another set T' of tets. T and T' have the //
+// same outer faces and ab is not an edge of T' anymore. Let |T|=n, and |T'| //
+// =m, it is actually a n-to-m flip for n > 3. The relation between n and m //
+// depends on the method, ours is found below. //
+// //
+// 'abtetlist' contains n tets sharing ab. Imaging that ab is perpendicular //
+// to the screen, where a lies in front of and b lies behind it. Let the //
+// projections of the n apexes onto screen in clockwise order are: p_0, ... //
+// p_n-1, respectively. The tets in the list are: [0]abp_0p_n-1,[1]abp_1p_0, //
+// ..., [n-1]abp_n-1p_n-2, respectively. //
+// //
+// The principle of the approach is: Recursively reduce the link of ab by //
+// using flip23 until only three faces remain, hence a flip32 can be applied //
+// to remove ab. For a given face a.b.p_0, check a flip23 can be applied on //
+// it, i.e, edge p_1.p_n-1 crosses it. NOTE*** We do the flip even p_1.p_n-1 //
+// intersects with a.b (they are coplanar). If so, a degenerate tet (a.b.p_1.//
+// p_n-1) is temporarily created, but it will be eventually removed by the //
+// final flip32. This relaxation splits a flip44 into flip23 + flip32. *NOTE //
+// Now suppose a.b.p_0 gets flipped, p_0 is not on the link of ab anymore. //
+// The link is then reduced (by 1). 2 of the 3 new tets, p_n-1.p_1.p_0.a and //
+// p_1.p_n-1.p_0.b, will be part of the new configuration. The left new tet,//
+// a.b.p_1.p_n-1, goes into the new link of ab. A recurrence can be applied. //
+// //
+// If 'e1' and 'e2' are not NULLs, they specify an wanted edge to appear in //
+// the new tet configuration. In such case, only do flip23 if edge e1<->e2 //
+// can be recovered. It is used in removeedgebycombNM(). //
+// //
+// If ab gets removed. 'newtetlist' contains m new tets. By using the above //
+// approach, the pairs (n, m) can be easily enumerated. For example, (3, 2),//
+// (4, 4), (5, 6), (6, 8), (7, 10), (8, 12), (9, 14), (10, 16), and so on. //
+// It is easy to deduce, that m = (n - 2) * 2, when n >= 3. The n tets in //
+// 'abtetlist' are NOT deleted in this routine. The caller has the right to //
+// either delete them or reverse this operation. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::removeedgebytranNM(REAL *key, int n, triface *abtetlist,
+ triface *newtetlist, point e1, point e2, queue *flipque)
+{
+ triface tmpabtetlist[9]; // Temporary max 9 tets configuration.
+ triface newfront, oldfront, adjfront;
+ face checksh;
+ point pa, pb, p[10];
+ REAL ori, cosmaxd, d1, d2;
+ REAL tmpkey;
+ REAL attrib, volume;
+ bool doflip, copflag, success;
+ int i, j, k;
+
+ // Maximum 10 tets.
+ assert(n <= 10);
+ // Two points a and b are fixed.
+ pa = org(abtetlist[0]);
+ pb = dest(abtetlist[0]);
+ // The points p_0, p_1, ..., p_n-1 are permuted in each new configuration.
+ // These permutations can be easily done in the following loop.
+ // Loop through all the possible new tets configurations. Stop on finding
+ // a valid new tet configuration which also immproves the quality value.
+ for (i = 0; i < n; i++) {
+ // Get other n points for the current configuration.
+ for (j = 0; j < n; j++) {
+ p[j] = apex(abtetlist[(i + j) % n]);
+ }
+ // Is there a wanted edge?
+ if ((e1 != (point) NULL) && (e2 != (point) NULL)) {
+ // Yes. Skip this face if p[1]<->p[n-1] is not the edge.
+ if (!(((p[1] == e1) && (p[n - 1] == e2)) ||
+ ((p[1] == e2) && (p[n - 1] == e1)))) continue;
+ }
+ // Test if face a.b.p_0 can be flipped (by flip23), ie, to check if the
+ // edge p_n-1.p_1 crosses face a.b.p_0 properly.
+ // Note. It is possible that face a.b.p_0 has type flip44, ie, a,b,p_1,
+ // and p_n-1 are coplanar. A trick is to split the flip44 into two
+ // steps: frist a flip23, then a flip32. The first step creates a
+ // degenerate tet (vol=0) which will be removed by the second flip.
+ ori = orient3d(pa, pb, p[1], p[n - 1]);
+ copflag = (ori == 0.0); // Are they coplanar?
+ if (ori >= 0.0) {
+ // Accept the coplanar case which supports flip44.
+ ori = orient3d(pb, p[0], p[1], p[n - 1]);
+ if (ori > 0.0) {
+ ori = orient3d(p[0], pa, p[1], p[n - 1]);
+ }
+ }
+ // Is face abc flipable?
+ if (ori > 0.0) {
+ // A valid (2-to-3) flip (or 4-to-4 flip) is found.
+ copflag ? flip44s++ : flip23s++;
+ doflip = true;
+ if (key != (REAL *) NULL) {
+ if (*key > -1.0) {
+ // Test if the new tets reduce the maximal dihedral angle. Only 2
+ // tets, p_n-1.p_1.p_0.a and p_1.p_n-1.p_0.b, need to be tested
+ // The left one a.b.p_n-1.p_1 goes into the new link of ab.
+ tetalldihedral(p[n - 1], p[1], p[0], pa, NULL, &d1, NULL);
+ tetalldihedral(p[1], p[n - 1], p[0], pb, NULL, &d2, NULL);
+ cosmaxd = d1 < d2 ? d1 : d2; // Choose the bigger angle.
+ doflip = *key < cosmaxd; // Can the local quality be improved?
+ }
+ }
+ if (doflip) {
+ tmpkey = key != NULL ? *key : -1.0;
+ // Create the two new tets.
+ maketetrahedron(&(newtetlist[0]));
+ setorg(newtetlist[0], p[n - 1]);
+ setdest(newtetlist[0], p[1]);
+ setapex(newtetlist[0], p[0]);
+ setoppo(newtetlist[0], pa);
+ maketetrahedron(&(newtetlist[1]));
+ setorg(newtetlist[1], p[1]);
+ setdest(newtetlist[1], p[n - 1]);
+ setapex(newtetlist[1], p[0]);
+ setoppo(newtetlist[1], pb);
+ // Create the n - 1 temporary new tets (the new Star(ab)).
+ maketetrahedron(&(tmpabtetlist[0]));
+ setorg(tmpabtetlist[0], pa);
+ setdest(tmpabtetlist[0], pb);
+ setapex(tmpabtetlist[0], p[n - 1]);
+ setoppo(tmpabtetlist[0], p[1]);
+ for (j = 1; j < n - 1; j++) {
+ maketetrahedron(&(tmpabtetlist[j]));
+ setorg(tmpabtetlist[j], pa);
+ setdest(tmpabtetlist[j], pb);
+ setapex(tmpabtetlist[j], p[j]);
+ setoppo(tmpabtetlist[j], p[j + 1]);
+ }
+ // Transfer the element attributes.
+ for (j = 0; j < in->numberoftetrahedronattributes; j++) {
+ attrib = elemattribute(abtetlist[0].tet, j);
+ setelemattribute(newtetlist[0].tet, j, attrib);
+ setelemattribute(newtetlist[1].tet, j, attrib);
+ for (k = 0; k < n - 1; k++) {
+ setelemattribute(tmpabtetlist[k].tet, j, attrib);
+ }
+ }
+ // Transfer the volume constraints.
+ if (b->varvolume && !b->refine) {
+ volume = volumebound(abtetlist[0].tet);
+ setvolumebound(newtetlist[0].tet, volume);
+ setvolumebound(newtetlist[1].tet, volume);
+ for (k = 0; k < n - 1; k++) {
+ setvolumebound(tmpabtetlist[k].tet, volume);
+ }
+ }
+ // Glue the new tets at their internal faces: 2 + (n - 1).
+ bond(newtetlist[0], newtetlist[1]); // p_n-1.p_1.p_0.
+ fnext(newtetlist[0], newfront);
+ enext2fnext(tmpabtetlist[0], adjfront);
+ bond(newfront, adjfront); // p_n-1.p_1.a.
+ fnext(newtetlist[1], newfront);
+ enextfnext(tmpabtetlist[0], adjfront);
+ bond(newfront, adjfront); // p_n-1.p_1.b.
+ // Glue n - 1 internal faces around ab.
+ for (j = 0; j < n - 1; j++) {
+ fnext(tmpabtetlist[j], newfront);
+ bond(newfront, tmpabtetlist[(j + 1) % (n - 1)]); // a.b.p_j+1
+ }
+ // Substitute the old tets with the new tets by connecting the new
+ // tets to the adjacent tets in the mesh. There are n * 2 (outer)
+ // faces of the new tets need to be operated.
+ // Note, after the substitution, the old tets still have pointers to
+ // their adjacent tets in the mesh. These pointers can be re-used
+ // to inverse the substitution.
+ for (j = 0; j < n; j++) {
+ // Get an old tet: [0]a.b.p_0.p_n-1 or [j]a.b.p_j.p_j-1, (j > 0).
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enextfnextself(oldfront);
+ // Get an adjacent tet at face: [0]a.p_0.p_n-1 or [j]a.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ // Get the corresponding face from the new tets.
+ if (j == 0) {
+ enext2fnext(newtetlist[0], newfront); // a.p_0.n_n-1
+ } else if (j == 1) {
+ enextfnext(newtetlist[0], newfront); // a.p_1.p_0
+ } else { // j >= 2.
+ enext2fnext(tmpabtetlist[j - 1], newfront); // a.p_j.p_j-1
+ }
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ if (flipque != (queue *) NULL) {
+ // Only queue the faces of the two new tets.
+ if (j < 2) enqueueflipface(newfront, flipque);
+ }
+ }
+ for (j = 0; j < n; j++) {
+ // Get an old tet: [0]a.b.p_0.p_n-1 or [j]a.b.p_j.p_j-1, (j > 0).
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enext2fnextself(oldfront);
+ // Get an adjacent tet at face: [0]b.p_0.p_n-1 or [j]b.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ // Get the corresponding face from the new tets.
+ if (j == 0) {
+ enextfnext(newtetlist[1], newfront); // b.p_0.n_n-1
+ } else if (j == 1) {
+ enext2fnext(newtetlist[1], newfront); // b.p_1.p_0
+ } else { // j >= 2.
+ enextfnext(tmpabtetlist[j - 1], newfront); // b.p_j.p_j-1
+ }
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ if (flipque != (queue *) NULL) {
+ // Only queue the faces of the two new tets.
+ if (j < 2) enqueueflipface(newfront, flipque);
+ }
+ }
+ // Adjust the faces in the temporary new tets at ab for recursively
+ // processing on the n-1 tets.(See the description at beginning)
+ for (j = 0; j < n - 1; j++) {
+ fnextself(tmpabtetlist[j]);
+ }
+ if (n > 4) {
+ success = removeedgebytranNM(&tmpkey, n-1, tmpabtetlist,
+ &(newtetlist[2]), NULL, NULL, flipque);
+ } else { // assert(n == 4);
+ success = removeedgebyflip32(&tmpkey, tmpabtetlist,
+ &(newtetlist[2]), flipque);
+ }
+ // No matter it was success or not, delete the temporary tets.
+ for (j = 0; j < n - 1; j++) {
+ tetrahedrondealloc(tmpabtetlist[j].tet);
+ }
+ if (success) {
+ // The new configuration is good.
+ // Do not delete the old tets.
+ // for (j = 0; j < n; j++) {
+ // tetrahedrondealloc(abtetlist[j].tet);
+ // }
+ // Save the minimal improved quality value.
+ if (key != (REAL *) NULL) {
+ *key = (tmpkey < cosmaxd ? tmpkey : cosmaxd);
+ }
+ return true;
+ } else {
+ // The new configuration is bad, substitue back the old tets.
+ for (j = 0; j < n; j++) {
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enextfnextself(oldfront); // [0]a.p_0.p_n-1, [j]a.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ bond(oldfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(oldfront, checksh);
+ }
+ }
+ }
+ for (j = 0; j < n; j++) {
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enext2fnextself(oldfront); // [0]b.p_0.p_n-1, [j]b.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy
+ bond(oldfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(oldfront, checksh);
+ }
+ }
+ }
+ // Delete the new tets.
+ tetrahedrondealloc(newtetlist[0].tet);
+ tetrahedrondealloc(newtetlist[1].tet);
+ // If tmpkey has been modified, then the failure was not due to
+ // unflipable configuration, but the non-improvement.
+ if (key && (tmpkey < *key)) {
+ *key = tmpkey;
+ return false;
+ }
+ } // if (success)
+ } // if (doflip)
+ } // if (ori > 0.0)
+ } // for (i = 0; i < n; i++)
+
+ return false;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// removeedgebycombNM() Remove an edge by combining two flipNMs. //
+// //
+// Given a set T of tets surrounding edge ab. The premise is that ab can not //
+// be removed by a flipNM. This routine attempts to remove ab by two flipNMs,//
+// i.e., first find and flip an edge af (or bf) by flipNM, then flip ab by //
+// flipNM. If it succeeds, two sets T(ab) and T(af) of tets are replaced by //
+// a new set T' and both ab and af are not edges in T' anymore. //
+// //
+// 'abtetlist' contains n tets sharing ab. Imaging that ab is perpendicular //
+// to the screen, such that a lies in front of and b lies behind it. Let the //
+// projections of the n apexes on the screen in clockwise order are: p_0,...,//
+// p_n-1, respectively. So the list of tets are: [0]abp_0p_n-1, [1]abp_1p_0, //
+// ..., [n-1]abp_n-1p_n-2, respectively. //
+// //
+// The principle of the approach is: for a face a.b.p_0, check if edge b.p_0 //
+// is of type N32 (or N44). If it is, then try to do a flipNM on it. If the //
+// flip is successful, then try to do another flipNM on a.b. If one of the //
+// two flipNMs fails, restore the old tets as they have never been flipped. //
+// Then try the next face a.b.p_1. The process can be looped for all faces //
+// having ab. Stop if ab is removed or all faces have been visited. Note in //
+// the above description only b.p_0 is considered, a.p_0 is done by swapping //
+// the position of a and b. //
+// //
+// Similar operations have been described in [Joe,1995]. My approach checks //
+// more cases for finding flips than Joe's. For instance, the cases (1)-(7) //
+// of Joe only consider abf for finding a flip (T23/T32). My approach looks //
+// all faces at ab for finding flips. Moreover, the flipNM can flip an edge //
+// whose star may have more than 3 tets while Joe's only works on 3-tet case.//
+// //
+// If ab is removed, 'newtetlist' contains the new tets. Two sets 'abtetlist'//
+// (n tets) and 'bftetlist' (n1 tets) have been replaced. The number of new //
+// tets can be calculated by follows: the 1st flip transforms n1 tets into //
+// (n1 - 2) * 2 new tets, however,one of the new tets goes into the new link //
+// of ab, i.e., the reduced tet number in Star(ab) is n - 1; the 2nd flip //
+// transforms n - 1 tets into (n - 3) * 2 new tets. Hence the number of new //
+// tets are: m = ((n1 - 2) * 2 - 1) + (n - 3) * 2. The old tets are NOT del-//
+// eted. The caller has the right to delete them or reverse the operation. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::removeedgebycombNM(REAL *key, int n, triface *abtetlist,
+ int *n1, triface *bftetlist, triface *newtetlist, queue *flipque)
+{
+ triface tmpabtetlist[11];
+ triface newfront, oldfront, adjfront;
+ face checksh;
+ point pa, pb, p[10];
+ REAL ori, tmpkey, tmpkey2;
+ REAL attrib, volume;
+ bool doflip, success;
+ int twice, count;
+ int i, j, k, m;
+
+ // Maximal 10 tets in Star(ab).
+ assert(n <= 10);
+
+ // Do the following procedure twice, one for flipping edge b.p_0 and the
+ // other for p_0.a which is symmetric to the first.
+ twice = 0;
+ do {
+ // Two points a and b are fixed.
+ pa = org(abtetlist[0]);
+ pb = dest(abtetlist[0]);
+ // The points p_0, ..., p_n-1 are permuted in the following loop.
+ for (i = 0; i < n; i++) {
+ // Get the n points for the current configuration.
+ for (j = 0; j < n; j++) {
+ p[j] = apex(abtetlist[(i + j) % n]);
+ }
+ // Check if b.p_0 is of type N32 or N44.
+ ori = orient3d(pb, p[0], p[1], p[n - 1]);
+ if ((ori > 0) && (key != (REAL *) NULL)) {
+ // b.p_0 is not N32. However, it is possible that the tet b.p_0.p_1.
+ // p_n-1 has worse quality value than the key. In such case, also
+ // try to flip b.p_0.
+ tetalldihedral(pb, p[0], p[n - 1], p[1], NULL, &tmpkey, NULL);
+ if (tmpkey < *key) ori = 0.0;
+ }
+ if (ori <= 0.0) {
+ // b.p_0 is either N32 or N44. Try the 1st flipNM.
+ bftetlist[0] = abtetlist[i];
+ enextself(bftetlist[0]);// go to edge b.p_0.
+ adjustedgering(bftetlist[0], CW); // edge p_0.b.
+ assert(apex(bftetlist[0]) == pa);
+ // Form Star(b.p_0).
+ doflip = true;
+ *n1 = 0;
+ do {
+ // Is the list full?
+ if (*n1 == 10) break;
+ if (checksubfaces) {
+ // Stop if a subface appears.
+ tspivot(bftetlist[*n1], checksh);
+ if (checksh.sh != dummysh) {
+ doflip = false; break;
+ }
+ }
+ // Get the next tet at p_0.b.
+ fnext(bftetlist[*n1], bftetlist[(*n1) + 1]);
+ (*n1)++;
+ } while (apex(bftetlist[*n1]) != pa);
+ // 2 <= n1 <= 10.
+ if (doflip) {
+ success = false;
+ tmpkey = -1.0; // = acos(pi).
+ if (key != (REAL *) NULL) tmpkey = *key;
+ m = 0;
+ if (*n1 == 3) {
+ // Three tets case. Try flip32.
+ success = removeedgebyflip32(&tmpkey,bftetlist,newtetlist,flipque);
+ m = 2;
+ } else if ((*n1 > 3) && (*n1 < 7)) {
+ // Four or more tets case. Try flipNM.
+ success = removeedgebytranNM(&tmpkey, *n1, bftetlist, newtetlist,
+ p[1], p[n - 1], flipque);
+ // If success, the number of new tets.
+ m = ((*n1) - 2) * 2;
+ } else {
+ if (b->verbose > 1) {
+ printf(" !! Unhandled case: n1 = %d.\n", *n1);
+ }
+ }
+ if (success) {
+ // b.p_0 is flipped. The link of ab is reduced (by 1), i.e., p_0
+ // is not on the link of ab. Two old tets a.b.p_0.p_n-1 and
+ // a.b.p_1.p_0 have been removed from the Star(ab) and one new
+ // tet t = a.b.p_1.p_n-1 belongs to Star(ab).
+ // Find t in the 'newtetlist' and remove it from the list.
+ setpointmark(pa, -pointmark(pa) - 1);
+ setpointmark(pb, -pointmark(pb) - 1);
+ assert(m > 0);
+ for (j = 0; j < m; j++) {
+ tmpabtetlist[0] = newtetlist[j];
+ // Does it has ab?
+ count = 0;
+ for (k = 0; k < 4; k++) {
+ if (pointmark((point)(tmpabtetlist[0].tet[4+k])) < 0) count++;
+ }
+ if (count == 2) {
+ // It is. Adjust t to be the edge ab.
+ for (tmpabtetlist[0].loc = 0; tmpabtetlist[0].loc < 4;
+ tmpabtetlist[0].loc++) {
+ if ((oppo(tmpabtetlist[0]) != pa) &&
+ (oppo(tmpabtetlist[0]) != pb)) break;
+ }
+ // The face of t must contain ab.
+ assert(tmpabtetlist[0].loc < 4);
+ findedge(&(tmpabtetlist[0]), pa, pb);
+ break;
+ }
+ }
+ assert(j < m); // The tet must exist.
+ // Remove t from list. Fill t's position by the last tet.
+ newtetlist[j] = newtetlist[m - 1];
+ setpointmark(pa, -(pointmark(pa) + 1));
+ setpointmark(pb, -(pointmark(pb) + 1));
+ // Create the temporary Star(ab) for the next flipNM.
+ adjustedgering(tmpabtetlist[0], CCW);
+ if (org(tmpabtetlist[0]) != pa) {
+ fnextself(tmpabtetlist[0]);
+ esymself(tmpabtetlist[0]);
+ }
+#ifdef SELF_CHECK
+ // Make sure current edge is a->b.
+ assert(org(tmpabtetlist[0]) == pa);
+ assert(dest(tmpabtetlist[0]) == pb);
+ assert(apex(tmpabtetlist[0]) == p[n - 1]);
+ assert(oppo(tmpabtetlist[0]) == p[1]);
+#endif // SELF_CHECK
+ // There are n - 2 left temporary tets.
+ for (j = 1; j < n - 1; j++) {
+ maketetrahedron(&(tmpabtetlist[j]));
+ setorg(tmpabtetlist[j], pa);
+ setdest(tmpabtetlist[j], pb);
+ setapex(tmpabtetlist[j], p[j]);
+ setoppo(tmpabtetlist[j], p[j + 1]);
+ }
+ // Transfer the element attributes.
+ for (j = 0; j < in->numberoftetrahedronattributes; j++) {
+ attrib = elemattribute(abtetlist[0].tet, j);
+ for (k = 0; k < n - 1; k++) {
+ setelemattribute(tmpabtetlist[k].tet, j, attrib);
+ }
+ }
+ // Transfer the volume constraints.
+ if (b->varvolume && !b->refine) {
+ volume = volumebound(abtetlist[0].tet);
+ for (k = 0; k < n - 1; k++) {
+ setvolumebound(tmpabtetlist[k].tet, volume);
+ }
+ }
+ // Glue n - 1 internal faces of Star(ab).
+ for (j = 0; j < n - 1; j++) {
+ fnext(tmpabtetlist[j], newfront);
+ bond(newfront, tmpabtetlist[(j + 1) % (n - 1)]); // a.b.p_j+1
+ }
+ // Substitute the old tets with the new tets by connecting the
+ // new tets to the adjacent tets in the mesh. There are (n-2)
+ // * 2 (outer) faces of the new tets need to be operated.
+ // Note that the old tets still have the pointers to their
+ // adjacent tets in the mesh. These pointers can be re-used
+ // to inverse the substitution.
+ for (j = 2; j < n; j++) {
+ // Get an old tet: [j]a.b.p_j.p_j-1, (j > 1).
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enextfnextself(oldfront);
+ // Get an adjacent tet at face: [j]a.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ // Get the corresponding face from the new tets.
+ // j >= 2.
+ enext2fnext(tmpabtetlist[j - 1], newfront); // a.p_j.p_j-1
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ }
+ for (j = 2; j < n; j++) {
+ // Get an old tet: [j]a.b.p_j.p_j-1, (j > 2).
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enext2fnextself(oldfront);
+ // Get an adjacent tet at face: [j]b.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ // Get the corresponding face from the new tets.
+ // j >= 2.
+ enextfnext(tmpabtetlist[j - 1], newfront); // b.p_j.p_j-1
+ bond(newfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(newfront, checksh);
+ }
+ }
+ }
+ // Adjust the faces in the temporary new tets at ab for
+ // recursively processing on the n-1 tets.
+ for (j = 0; j < n - 1; j++) {
+ fnextself(tmpabtetlist[j]);
+ }
+ tmpkey2 = -1;
+ if (key) tmpkey2 = *key;
+ if ((n - 1) == 3) {
+ success = removeedgebyflip32(&tmpkey2, tmpabtetlist,
+ &(newtetlist[m - 1]), flipque);
+ } else { // assert((n - 1) >= 4);
+ success = removeedgebytranNM(&tmpkey2, n - 1, tmpabtetlist,
+ &(newtetlist[m - 1]), NULL, NULL, flipque);
+ }
+ // No matter it was success or not, delete the temporary tets.
+ for (j = 0; j < n - 1; j++) {
+ tetrahedrondealloc(tmpabtetlist[j].tet);
+ }
+ if (success) {
+ // The new configuration is good.
+ // Do not delete the old tets.
+ // for (j = 0; j < n; j++) {
+ // tetrahedrondealloc(abtetlist[j].tet);
+ // }
+ // Return the bigger dihedral in the two sets of new tets.
+ if (key != (REAL *) NULL) {
+ *key = tmpkey2 < tmpkey ? tmpkey2 : tmpkey;
+ }
+ return true;
+ } else {
+ // The new configuration is bad, substitue back the old tets.
+ for (j = 0; j < n; j++) {
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enextfnextself(oldfront); // [0]a.p_0.p_n-1, [j]a.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ bond(oldfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(oldfront, checksh);
+ }
+ }
+ }
+ for (j = 0; j < n; j++) {
+ oldfront = abtetlist[(i + j) % n];
+ esymself(oldfront);
+ enext2fnextself(oldfront); // [0]b.p_0.p_n-1, [j]b.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy
+ bond(oldfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(oldfront, checksh);
+ }
+ }
+ }
+ // Substitute back the old tets of the first flip.
+ for (j = 0; j < *n1; j++) {
+ oldfront = bftetlist[j];
+ esymself(oldfront);
+ enextfnextself(oldfront);
+ sym(oldfront, adjfront); // adjfront may be dummy.
+ bond(oldfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(oldfront, checksh);
+ }
+ }
+ }
+ for (j = 0; j < *n1; j++) {
+ oldfront = bftetlist[j];
+ esymself(oldfront);
+ enext2fnextself(oldfront); // [0]b.p_0.p_n-1, [j]b.p_j.p_j-1.
+ sym(oldfront, adjfront); // adjfront may be dummy
+ bond(oldfront, adjfront);
+ if (checksubfaces) {
+ tspivot(oldfront, checksh);
+ if (checksh.sh != dummysh) {
+ tsbond(oldfront, checksh);
+ }
+ }
+ }
+ // Delete the new tets of the first flip. Note that one new
+ // tet has already been removed from the list.
+ for (j = 0; j < m - 1; j++) {
+ tetrahedrondealloc(newtetlist[j].tet);
+ }
+ } // if (success)
+ } // if (success)
+ } // if (doflip)
+ } // if (ori <= 0.0)
+ } // for (i = 0; i < n; i++)
+ // Inverse a and b and the tets configuration.
+ for (i = 0; i < n; i++) newtetlist[i] = abtetlist[i];
+ for (i = 0; i < n; i++) {
+ oldfront = newtetlist[n - i - 1];
+ esymself(oldfront);
+ fnextself(oldfront);
+ abtetlist[i] = oldfront;
+ }
+ twice++;
+ } while (twice < 2);
+
+ return false;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// splittetrahedron() Insert a point into a tetrahedron, split it into //
+// four tetrahedra. //
+// //
+// The tetrahedron is given by 'splittet'. Let it is abcd. The inserting //
+// point 'newpoint' v should lie strictly inside abcd. //
+// //
+// Splitting a tetrahedron is to shrink abcd to abcv, and create three new //
+// tetrahedra badv, cbdv, and acdv. //
+// //
+// On completion, 'splittet' returns abcv. If 'flipqueue' is not NULL, it //
+// contains all possibly non-locally Delaunay faces. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::splittetrahedron(point newpoint, triface* splittet,
+ queue* flipqueue)
+{
+ triface oldabd, oldbcd, oldcad; // Old configuration.
+ triface abdcasing, bcdcasing, cadcasing;
+ face abdsh, bcdsh, cadsh;
+ triface abcv, badv, cbdv, acdv; // New configuration.
+ triface worktet;
+ face abseg, bcseg, caseg;
+ face adseg, bdseg, cdseg;
+ point pa, pb, pc, pd;
+ REAL attrib, volume;
+ int i;
+
+ abcv = *splittet;
+ abcv.ver = 0;
+ // Set the changed vertices and new tetrahedron.
+ pa = org(abcv);
+ pb = dest(abcv);
+ pc = apex(abcv);
+ pd = oppo(abcv);
+
+ if (b->verbose > 1) {
+ printf(" Inserting point %d in tetrahedron (%d, %d, %d, %d).\n",
+ pointmark(newpoint), pointmark(pa), pointmark(pb), pointmark(pc),
+ pointmark(pd));
+ }
+
+ fnext(abcv, oldabd);
enextfnext(abcv, oldbcd);
enext2fnext(abcv, oldcad);
sym(oldabd, abdcasing);
@@ -10889,6 +12863,51 @@ splittetrahedron(point newpoint, triface* splittet, queue* flipqueue)
tsdissolve(oldcad);
tsbond(acdv, cadsh);
}
+ } else if (checksubsegs) {
+ tsspivot1(abcv, abseg);
+ if (abseg.sh != dummysh) {
+ tssbond1(badv, abseg);
+ }
+ enext(abcv, worktet);
+ tsspivot1(worktet, bcseg);
+ if (bcseg.sh != dummysh) {
+ tssbond1(cbdv, bcseg);
+ }
+ enext2(abcv, worktet);
+ tsspivot1(worktet, caseg);
+ if (caseg.sh != dummysh) {
+ tssbond1(acdv, caseg);
+ }
+ fnext(abcv, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, adseg);
+ if (adseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ enext(badv, worktet);
+ tssbond1(worktet, adseg);
+ enext2(acdv, worktet);
+ tssbond1(worktet, adseg);
+ }
+ enextfnext(abcv, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, bdseg);
+ if (bdseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ enext(cbdv, worktet);
+ tssbond1(worktet, bdseg);
+ enext2(badv, worktet);
+ tssbond1(worktet, bdseg);
+ }
+ enext2fnext(abcv, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, cdseg);
+ if (cdseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ enext(acdv, worktet);
+ tssbond1(worktet, cdseg);
+ enext2(cbdv, worktet);
+ tssbond1(worktet, cdseg);
+ }
}
badv.loc = 3;
cbdv.loc = 2;
@@ -11022,14 +13041,18 @@ void tetgenmesh::unsplittetrahedron(triface* splittet)
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::
-splittetface(point newpoint, triface* splittet, queue* flipqueue)
+void tetgenmesh::splittetface(point newpoint, triface* splittet,
+ queue* flipqueue)
{
triface abcd, bace; // Old configuration.
triface oldbcd, oldcad, oldace, oldcbe;
triface bcdcasing, cadcasing, acecasing, cbecasing;
face abcsh, bcdsh, cadsh, acesh, cbesh;
triface abvd, bcvd, cavd, bave, cbve, acve; // New configuration.
+ triface worktet;
+ face bcseg, caseg;
+ face adseg, bdseg, cdseg;
+ face aeseg, beseg, ceseg;
point pa, pb, pc, pd, pe;
REAL attrib, volume;
bool mirrorflag;
@@ -11065,13 +13088,6 @@ splittetface(point newpoint, triface* splittet, queue* flipqueue)
pointmark(pa), pointmark(pb), pointmark(pc));
}
-#ifdef SELF_CHECK
- // Make sure no inversed tetrahedron has been created.
- assert(orient3d(pa, pb, pd, newpoint) >= 0.0);
- assert(orient3d(pb, pc, pd, newpoint) >= 0.0);
- assert(orient3d(pc, pa, pd, newpoint) >= 0.0);
-#endif
-
// Save the old configuration at faces bcd and cad.
enextfnext(abcd, oldbcd);
enext2fnext(abcd, oldcad);
@@ -11208,6 +13224,95 @@ splittetface(point newpoint, triface* splittet, queue* flipqueue)
// Split this subface 'abc' into three i.e, abv, bcv, cav.
splitsubface(newpoint, &abcsh, (queue *) NULL);
}
+ } else if (checksubsegs) {
+ // abvd.loc = abvd.ver = 0;
+ bcvd.loc = bcvd.ver = 0;
+ cavd.loc = cavd.ver = 0;
+ if (mirrorflag) {
+ // bave.loc = bave.ver = 0;
+ cbve.loc = cbve.ver = 0;
+ acve.loc = acve.ver = 0;
+ }
+ enext(abvd, worktet);
+ tsspivot1(worktet, bcseg);
+ if (bcseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ tssbond1(bcvd, bcseg);
+ if (mirrorflag) {
+ enext2(bave, worktet);
+ tssdissolve1(worktet);
+ tssbond1(cbve, bcseg);
+ }
+ }
+ enext2(abvd, worktet);
+ tsspivot1(worktet, caseg);
+ if (caseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ tssbond1(cavd, caseg);
+ if (mirrorflag) {
+ enext(bave, worktet);
+ tssdissolve1(worktet);
+ tssbond1(acve, caseg);
+ }
+ }
+ fnext(abvd, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, adseg);
+ if (adseg.sh != dummysh) {
+ fnext(cavd, worktet);
+ enextself(worktet);
+ tssbond1(worktet, adseg);
+ }
+ fnext(abvd, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, bdseg);
+ if (bdseg.sh != dummysh) {
+ fnext(bcvd, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, bdseg);
+ }
+ enextfnext(abvd, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, cdseg);
+ if (cdseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ fnext(bcvd, worktet);
+ enextself(worktet);
+ tssbond1(worktet, cdseg);
+ fnext(cavd, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, cdseg);
+ }
+ if (mirrorflag) {
+ fnext(bave, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, aeseg);
+ if (aeseg.sh != dummysh) {
+ fnext(acve, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, aeseg);
+ }
+ fnext(bave, worktet);
+ enext2self(worktet);
+ tsspivot1(worktet, beseg);
+ if (beseg.sh != dummysh) {
+ fnext(cbve, worktet);
+ enextself(worktet);
+ tssbond1(worktet, beseg);
+ }
+ enextfnext(bave, worktet);
+ enextself(worktet);
+ tsspivot1(worktet, ceseg);
+ if (ceseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ fnext(cbve, worktet);
+ enext2self(worktet);
+ tssbond1(worktet, ceseg);
+ fnext(acve, worktet);
+ enextself(worktet);
+ tssbond1(worktet, ceseg);
+ }
+ }
}
// Save a handle for quick point location.
@@ -11400,8 +13505,8 @@ void tetgenmesh::unsplittetface(triface* splittet)
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::
-splitsubface(point newpoint, face* splitface, queue* flipqueue)
+void tetgenmesh::splitsubface(point newpoint, face* splitface,
+ queue* flipqueue)
{
triface abvd, bcvd, cavd, bave, cbve, acve;
face abc, oldbc, oldca, bc, ca, spinsh;
@@ -11706,13 +13811,15 @@ void tetgenmesh::unsplitsubface(face* splitsh)
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::
-splittetedge(point newpoint, triface* splittet, queue* flipqueue)
+void tetgenmesh::splittetedge(point newpoint, triface* splittet,
+ queue* flipqueue)
{
triface *bots, *newtops;
triface oldtop, topcasing;
triface spintet, tmpbond0, tmpbond1;
face abseg, splitsh, topsh, spinsh;
+ triface worktet;
+ face n1n2seg, n2vseg, n1vseg;
point pa, pb, n1, n2;
REAL attrib, volume;
int wrapcount, hitbdry;
@@ -11855,14 +13962,14 @@ splittetedge(point newpoint, triface* splittet, queue* flipqueue)
}
#ifdef SELF_CHECK
// Make sure no inversed tetrahedron has been created.
- volume = orient3d(pa, n1, n2, newpoint);
- if (volume >= 0.0) {
- printf("Internal error in splittetedge(): volume = %.12g.\n", volume);
- }
- volume = orient3d(pb, n2, n1, newpoint);
- if (volume >= 0.0) {
- printf("Internal error in splittetedge(): volume = %.12g.\n", volume);
- }
+ // volume = orient3d(pa, n1, n2, newpoint);
+ // if (volume >= 0.0) {
+ // printf("Internal error in splittetedge(): volume = %.12g.\n", volume);
+ // }
+ // volume = orient3d(pb, n2, n1, newpoint);
+ // if (volume >= 0.0) {
+ // printf("Internal error in splittetedge(): volume = %.12g.\n", volume);
+ // }
#endif
}
@@ -11898,6 +14005,29 @@ splittetedge(point newpoint, triface* splittet, queue* flipqueue)
enext2fnext(newtops[0], tmpbond1);
bond(tmpbond0, tmpbond1);
}
+ if (checksubsegs) {
+ for (i = 0; i < wrapcount; i++) {
+ enextfnext(bots[i], worktet); // edge n1->n2.
+ tsspivot1(worktet, n1n2seg);
+ if (n1n2seg.sh != dummysh) {
+ enext(newtops[i], tmpbond0);
+ tssbond1(tmpbond0, n1n2seg);
+ }
+ enextself(worktet); // edge n2->v ==> n2->b
+ tsspivot1(worktet, n2vseg);
+ if (n2vseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ tssbond1(newtops[i], n2vseg);
+ }
+ enextself(worktet); // edge v->n1 ==> b->n1
+ tsspivot1(worktet, n1vseg);
+ if (n1vseg.sh != dummysh) {
+ tssdissolve1(worktet);
+ enext2(newtops[i], tmpbond0);
+ tssbond1(tmpbond0, n1vseg);
+ }
+ }
+ }
// Is there exist subfaces and subsegment need to be split?
if (checksubfaces) {
@@ -12308,6 +14438,7 @@ void tetgenmesh::splitsubedge(point newpoint, face* splitsh, queue* flipqueue)
// There is a subsegment connecting with ab at b. It will connect
// to vb at b after splitting.
bccasout.shver = 0;
+ if (sorg(bccasout) != pb) sesymself(bccasout);
#ifdef SELF_CHECK
assert(sorg(bccasout) == pb);
#endif
@@ -12584,8 +14715,8 @@ void tetgenmesh::unsplitsubedge(face* splitsh)
// //
///////////////////////////////////////////////////////////////////////////////
-enum tetgenmesh::insertsiteresult tetgenmesh::
-insertsite(point newpoint, triface* searchtet, bool approx, queue* flipqueue)
+enum tetgenmesh::insertsiteresult tetgenmesh::insertsite(point newpoint,
+ triface* searchtet, bool approx, queue* flipqueue)
{
enum locateresult intersect, exactloc;
point checkpt;
@@ -12677,38 +14808,176 @@ insertsite(point newpoint, triface* searchtet, bool approx, queue* flipqueue)
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::
-undosite(enum insertsiteresult insresult, triface* splittet, point torg,
- point tdest, point tapex, point toppo)
+void tetgenmesh::undosite(enum insertsiteresult insresult, triface* splittet,
+ point torg, point tdest, point tapex, point toppo)
+{
+ // Set the four corners of 'splittet' exactly be 'torg', ... 'toppo'.
+ findface(splittet, torg, tdest, tapex);
+ if (oppo(*splittet) != toppo) {
+ symself(*splittet);
+#ifdef SELF_CHECK
+ assert(oppo(*splittet) == toppo);
+#endif
+ // The sym() operation may inverse the edge, correct it if so.
+ findedge(splittet, torg, tdest);
+ }
+
+ // Unsplit the tetrahedron according to 'insresult'.
+ switch (insresult) {
+ case SUCCESSINTET:
+ // 'splittet' should be the face with 'newpoint' as its opposite.
+ unsplittetrahedron(splittet);
+ break;
+ case SUCCESSONFACE:
+ // 'splittet' should be the one of three splitted face with 'newpoint'
+ // as its apex.
+ unsplittetface(splittet);
+ break;
+ case SUCCESSONEDGE:
+ // 'splittet' should be the tet with destination is 'newpoint'.
+ unsplittetedge(splittet);
+ break;
+ default: // To omit compile warnings.
+ break;
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// closeopenface() Close "open" faces recursively. //
+// //
+// This is the support routine of inserthullsite(). A point p which lies out-//
+// side of CH(T). p is inserted to T by forming a tet t from p and a visible //
+// CH face f. The three sides of f which have p as a vertex is called "open" //
+// face. Each open face will be closed by either creating a tet on top of it //
+// or become a new CH face. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::closeopenface(triface* openface, queue* flipque)
+{
+ triface newtet, oldhull;
+ triface newopenface, closeface;
+ point inspoint, pa, pb, pc;
+ REAL attrib, volume;
+ int i;
+
+ // Get the new point p.
+ inspoint = apex(*openface);
+ // Find the old CH face f_o (f and f_o share the same edge).
+ esym(*openface, oldhull);
+ while (fnextself(oldhull)) ;
+ if (apex(oldhull) != inspoint) {
+ // Is f_o visible by p?
+ pa = org(oldhull);
+ pb = dest(oldhull);
+ pc = apex(oldhull);
+ if (orient3d(pa, pb, pc, inspoint) < 0.0) {
+ // Yes. Create a new tet t above f_o.
+ maketetrahedron(&newtet);
+ setorg(newtet, pa);
+ setdest(newtet, pb);
+ setapex(newtet, pc);
+ setoppo(newtet, inspoint);
+ for (i = 0; i < in->numberoftetrahedronattributes; i++) {
+ attrib = elemattribute(oldhull.tet, i);
+ setelemattribute(newtet.tet, i, attrib);
+ }
+ if (b->varvolume) {
+ volume = volumebound(oldhull.tet);
+ setvolumebound(newtet.tet, volume);
+ }
+ // Connect t to T.
+ bond(newtet, oldhull);
+ // Close f.
+ fnext(newtet, newopenface);
+ bond(newopenface, *openface);
+ // f_o becomes an interior face.
+ enqueueflipface(oldhull, flipque);
+ // Hull face number decreases.
+ hullsize--;
+ // Two faces of t become open face.
+ enextself(newtet);
+ for (i = 0; i < 2; i++) {
+ fnext(newtet, newopenface);
+ sym(newopenface, closeface);
+ if (closeface.tet == dummytet) {
+ closeopenface(&newopenface, flipque);
+ }
+ enextself(newtet);
+ }
+ } else {
+ // Inivisible. f becomes a new CH face.
+ hullsize++;
+ // Let 'dummytet' holds f for the next point location.
+ dummytet[0] = encode(*openface);
+ }
+ } else {
+ // f_o is co-incident with f --> f is closed by f_o.
+ bond(*openface, oldhull);
+ // f is an interior face.
+ enqueueflipface(*openface, flipque);
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// inserthullsite() Insert a point which lies outside the convex hull. //
+// //
+// The 'inspoint' p lies outside the tetrahedralization T. The 'horiz' f is //
+// on the convex hull of T, CH(T), which is visible by p (Imagine f is para- //
+// llel to the horizon). To insert p into T we have to enlarge the CH(T) and //
+// update T so that p is on the new CH(T). //
+// //
+// To enlarge the CH(T). We need to find the set F of faces which are on CH //
+// (T) and visible by p (F can be formed by a depth-first search from f). p //
+// is then inserted into T by mounting new tets formed by p and these faces. //
+// Faces of F become interior faces and may non-locally Delaunay. They are //
+// queued in 'flipqueue' for flip tests. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::inserthullsite(point inspoint, triface* horiz, queue* flipque)
{
- // Set the four corners of 'splittet' exactly be 'torg', ... 'toppo'.
- findface(splittet, torg, tdest, tapex);
- if (oppo(*splittet) != toppo) {
- symself(*splittet);
-#ifdef SELF_CHECK
- assert(oppo(*splittet) == toppo);
-#endif
- // The sym() operation may inverse the edge, correct it if so.
- findedge(splittet, torg, tdest);
+ triface firstnewtet;
+ triface openface, closeface;
+ REAL attrib, volume;
+ int i;
+
+ // Let f face to p.
+ adjustedgering(*horiz, CW);
+ // Create the first tet t (from f and p).
+ maketetrahedron(&firstnewtet);
+ setorg (firstnewtet, org(*horiz));
+ setdest(firstnewtet, dest(*horiz));
+ setapex(firstnewtet, apex(*horiz));
+ setoppo(firstnewtet, inspoint);
+ for (i = 0; i < in->numberoftetrahedronattributes; i++) {
+ attrib = elemattribute(horiz->tet, i);
+ setelemattribute(firstnewtet.tet, i, attrib);
}
-
- // Unsplit the tetrahedron according to 'insresult'.
- switch (insresult) {
- case SUCCESSINTET:
- // 'splittet' should be the face with 'newpoint' as its opposite.
- unsplittetrahedron(splittet);
- break;
- case SUCCESSONFACE:
- // 'splittet' should be the one of three splitted face with 'newpoint'
- // as its apex.
- unsplittetface(splittet);
- break;
- case SUCCESSONEDGE:
- // 'splittet' should be the tet with destination is 'newpoint'.
- unsplittetedge(splittet);
- break;
- default: // To omit compile warnings.
- break;
+ if (b->varvolume) {
+ volume = volumebound(horiz->tet);
+ setvolumebound(firstnewtet.tet, volume);
+ }
+ // Connect t to T.
+ bond(firstnewtet, *horiz);
+ // f is not on CH(T) anymore.
+ enqueueflipface(*horiz, flipque);
+ // Hull face number decreases.
+ hullsize--;
+
+ // Call the faces of t which have p as a vertex "open" face.
+ for (i = 0; i < 3; i++) {
+ // Get an open face f_i of t.
+ fnext(firstnewtet, openface);
+ // Close f_i if it is still open.
+ sym(openface, closeface);
+ if (closeface.tet == dummytet) {
+ closeopenface(&openface, flipque);
+ }
+ // Go to the next open face of t.
+ enextself(firstnewtet);
}
}
@@ -13925,17 +16194,7 @@ void tetgenmesh::bowatinsertsite(point bp,face* splitseg,int n,list** sublists,
if (chkencseg) {
// Check if a->p and p->b are encroached by other vertices.
checkseg4encroach(&apseg, NULL, NULL, true);
- if (!shell2badface(apseg)) {
- if (varconstraint && (areabound(apseg) > 0.0)) {
- checkseg4badqual(&apseg, true);
- }
- }
checkseg4encroach(&pbseg, NULL, NULL, true);
- if (!shell2badface(pbseg)) {
- if (varconstraint && (areabound(pbseg) > 0.0)) {
- checkseg4badqual(&pbseg, true);
- }
- }
// Check if the adjacent segments are encroached by p.
tallencsegs(bp, n, ceillists);
}
@@ -13962,11 +16221,6 @@ void tetgenmesh::bowatinsertsite(point bp,face* splitseg,int n,list** sublists,
for (i = 0; i < subceillist->len(); i++) {
newsh = * (face *)(* subceillist)[i];
checksub4encroach(&newsh, NULL, true);
- if (!shell2badface(newsh)) {
- if (varconstraint && (areabound(newsh) > 0.0)) {
- checksub4badqual(&newsh, true);
- }
- }
}
// Only do once if p is on a facet.
if (splitseg == (face *) NULL) break;
@@ -14046,15 +16300,17 @@ void tetgenmesh::formstarpolyhedron(point pt, list* tetlist, list* verlist,
// Add t into T.
* (triface *)(* tetlist)[0] = starttet;
infect(starttet);
- // Add three verts of t into V.
- ver[0] = org(starttet);
- ver[1] = dest(starttet);
- ver[2] = apex(starttet);
- for (i = 0; i < 3; i++) {
- // Mark the vert by inversing the index of the vert.
- idx = pointmark(ver[i]);
- setpointmark(ver[i], -idx - 1); // -1 to distinguish the zero.
- verlist->append(&(ver[i]));
+ if (verlist != (list *) NULL) {
+ // Add three verts of t into V.
+ ver[0] = org(starttet);
+ ver[1] = dest(starttet);
+ ver[2] = apex(starttet);
+ for (i = 0; i < 3; i++) {
+ // Mark the vert by inversing the index of the vert.
+ idx = pointmark(ver[i]);
+ setpointmark(ver[i], -idx - 1); // -1 to distinguish the zero.
+ verlist->append(&(ver[i]));
+ }
}
// Find other tets by a broadth-first search.
@@ -14077,14 +16333,17 @@ void tetgenmesh::formstarpolyhedron(point pt, list* tetlist, list* verlist,
// Add n into T.
infect(neightet);
tetlist->append(&neightet);
- ver[0] = org(starttet);
- ver[1] = dest(starttet);
- findedge(&neightet, ver[0], ver[1]);
- ver[2] = apex(neightet);
- idx = pointmark(ver[2]);
- if (idx >= 0) {
- setpointmark(ver[2], -idx - 1);
- verlist->append(&(ver[2]));
+ if (verlist != (list *) NULL) {
+ // Add the apex vertex in n into V.
+ ver[0] = org(starttet);
+ ver[1] = dest(starttet);
+ findedge(&neightet, ver[0], ver[1]);
+ ver[2] = apex(neightet);
+ idx = pointmark(ver[2]);
+ if (idx >= 0) {
+ setpointmark(ver[2], -idx - 1);
+ verlist->append(&(ver[2]));
+ }
}
}
}
@@ -14097,11 +16356,13 @@ void tetgenmesh::formstarpolyhedron(point pt, list* tetlist, list* verlist,
starttet = * (triface *)(* tetlist)[i];
uninfect(starttet);
}
- // Uninfect vertices.
- for (i = 0; i < verlist->len(); i++) {
- ver[0] = * (point *)(* verlist)[i];
- idx = pointmark(ver[0]);
- setpointmark(ver[0], -(idx + 1));
+ if (verlist != (list *) NULL) {
+ // Uninfect vertices.
+ for (i = 0; i < verlist->len(); i++) {
+ ver[0] = * (point *)(* verlist)[i];
+ idx = pointmark(ver[0]);
+ setpointmark(ver[0], -(idx + 1));
+ }
}
}
@@ -14200,145 +16461,6 @@ bool tetgenmesh::unifypoint(point testpt, triface *starttet, enum locateresult
return merged;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// closeopenface() Close "open" faces recursively. //
-// //
-// This is the support routine of inserthullsite(). A point p which lies out-//
-// side of CH(T). p is inserted to T by forming a tet t from p and a visible //
-// CH face f. The three sides of f which have p as a vertex is called "open" //
-// face. Each open face will be closed by either creating a tet on top of it //
-// or become a new CH face. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::closeopenface(triface* openface, queue* flipque)
-{
- triface newtet, oldhull;
- triface newopenface, closeface;
- point inspoint, pa, pb, pc;
- REAL attrib, volume;
- int i;
-
- // Get the new point p.
- inspoint = apex(*openface);
- // Find the old CH face f_o (f and f_o share the same edge).
- esym(*openface, oldhull);
- while (fnextself(oldhull)) ;
- if (apex(oldhull) != inspoint) {
- // Is f_o visible by p?
- pa = org(oldhull);
- pb = dest(oldhull);
- pc = apex(oldhull);
- if (orient3d(pa, pb, pc, inspoint) < 0.0) {
- // Yes. Create a new tet t above f_o.
- maketetrahedron(&newtet);
- setorg(newtet, pa);
- setdest(newtet, pb);
- setapex(newtet, pc);
- setoppo(newtet, inspoint);
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(oldhull.tet, i);
- setelemattribute(newtet.tet, i, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(oldhull.tet);
- setvolumebound(newtet.tet, volume);
- }
- // Connect t to T.
- bond(newtet, oldhull);
- // Close f.
- fnext(newtet, newopenface);
- bond(newopenface, *openface);
- // f_o becomes an interior face.
- enqueueflipface(oldhull, flipque);
- // Hull face number decreases.
- hullsize--;
- // Two faces of t become open face.
- enextself(newtet);
- for (i = 0; i < 2; i++) {
- fnext(newtet, newopenface);
- sym(newopenface, closeface);
- if (closeface.tet == dummytet) {
- closeopenface(&newopenface, flipque);
- }
- enextself(newtet);
- }
- } else {
- // Inivisible. f becomes a new CH face.
- hullsize++;
- // Let 'dummytet' holds f for the next point location.
- dummytet[0] = encode(*openface);
- }
- } else {
- // f_o is co-incident with f --> f is closed by f_o.
- bond(*openface, oldhull);
- // f is an interior face.
- enqueueflipface(*openface, flipque);
- }
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// inserthullsite() Insert a point which lies outside the convex hull. //
-// //
-// The 'inspoint' p lies outside the tetrahedralization T. The 'horiz' f is //
-// on the convex hull of T, CH(T), which is visible by p (Imagine f is para- //
-// llel to the horizon). To insert p into T we have to enlarge the CH(T) and //
-// update T so that p is on the new CH(T). //
-// //
-// To enlarge the CH(T). We need to find the set F of faces which are on CH //
-// (T) and visible by p (F can be formed by a depth-first search from f). p //
-// is then inserted into T by mounting new tets formed by p and these faces. //
-// Faces of F become interior faces and may non-locally Delaunay. They are //
-// queued in 'flipqueue' for flip tests. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::inserthullsite(point inspoint, triface* horiz, queue* flipque)
-{
- triface firstnewtet;
- triface openface, closeface;
- REAL attrib, volume;
- int i;
-
- // Let f face to p.
- adjustedgering(*horiz, CW);
- // Create the first tet t (from f and p).
- maketetrahedron(&firstnewtet);
- setorg (firstnewtet, org(*horiz));
- setdest(firstnewtet, dest(*horiz));
- setapex(firstnewtet, apex(*horiz));
- setoppo(firstnewtet, inspoint);
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(horiz->tet, i);
- setelemattribute(firstnewtet.tet, i, attrib);
- }
- if (b->varvolume) {
- volume = volumebound(horiz->tet);
- setvolumebound(firstnewtet.tet, volume);
- }
- // Connect t to T.
- bond(firstnewtet, *horiz);
- // f is not on CH(T) anymore.
- enqueueflipface(*horiz, flipque);
- // Hull face number decreases.
- hullsize--;
-
- // Call the faces of t which have p as a vertex "open" face.
- for (i = 0; i < 3; i++) {
- // Get an open face f_i of t.
- fnext(firstnewtet, openface);
- // Close f_i if it is still open.
- sym(openface, closeface);
- if (closeface.tet == dummytet) {
- closeopenface(&openface, flipque);
- }
- // Go to the next open face of t.
- enextself(firstnewtet);
- }
-}
-
///////////////////////////////////////////////////////////////////////////////
// //
// incrflipdelaunay() Construct a delaunay tetrahedrization from a set of //
@@ -14367,6 +16489,7 @@ void tetgenmesh::incrflipdelaunay(triface* oldtet, point* insertarray,
REAL det, n[3];
REAL attrib, volume;
int i, j;
+ clock_t loc_start, loc_end;
if (b->verbose > 0) {
printf(" Creating initial tetrahedralization.\n");
@@ -14451,6 +16574,11 @@ void tetgenmesh::incrflipdelaunay(triface* oldtet, point* insertarray,
insertarray[0] = insertarray[1];
insertarray[1] = swappt;
}
+ if (b->verbose > 2) {
+ printf(" Create the first tet (%d, %d, %d, %d).\n",
+ pointmark(insertarray[0]), pointmark(insertarray[1]),
+ pointmark(insertarray[2]), pointmark(lastpt));
+ }
setorg(newtet, insertarray[0]);
setdest(newtet, insertarray[1]);
setapex(newtet, insertarray[2]);
@@ -14465,18 +16593,18 @@ void tetgenmesh::incrflipdelaunay(triface* oldtet, point* insertarray,
setvolumebound(newtet.tet, volume);
}
}
- // Set vertex type be VOLVERTEX if it has no type yet.
+ // Set vertex type be FREEVOLVERTEX if it has no type yet.
if (pointtype(insertarray[0]) == UNUSEDVERTEX) {
- setpointtype(insertarray[0], VOLVERTEX);
+ setpointtype(insertarray[0], FREEVOLVERTEX);
}
if (pointtype(insertarray[1]) == UNUSEDVERTEX) {
- setpointtype(insertarray[1], VOLVERTEX);
+ setpointtype(insertarray[1], FREEVOLVERTEX);
}
if (pointtype(insertarray[2]) == UNUSEDVERTEX) {
- setpointtype(insertarray[2], VOLVERTEX);
+ setpointtype(insertarray[2], FREEVOLVERTEX);
}
if (pointtype(lastpt) == UNUSEDVERTEX) {
- setpointtype(lastpt, VOLVERTEX);
+ setpointtype(lastpt, FREEVOLVERTEX);
}
// Bond to 'dummytet' for point location.
dummytet[0] = encode(newtet);
@@ -14497,11 +16625,18 @@ void tetgenmesh::incrflipdelaunay(triface* oldtet, point* insertarray,
// Insert the rest of points, one by one.
for (; i < arraysize; i++) {
// Locate p_i in T.
+#ifdef SELF_CHECK
+ loc_start = clock();
+#endif
if (jump) {
loc = locate(insertarray[i], &searchtet);
} else {
loc = preciselocate(insertarray[i], &searchtet, tetrahedrons->items);
}
+#ifdef SELF_CHECK
+ loc_end = clock();
+ tloctime += ((REAL) (loc_end - loc_start)) / CLOCKS_PER_SEC;
+#endif
// Keep current search state for next searching.
recenttet = searchtet;
if (loc == ONVERTEX) {
@@ -14549,18 +16684,26 @@ void tetgenmesh::incrflipdelaunay(triface* oldtet, point* insertarray,
}
if (pointtype(insertarray[i]) == UNUSEDVERTEX) {
// p_i becomes a (volume) vertex of T.
- setpointtype(insertarray[i], VOLVERTEX);
+ setpointtype(insertarray[i], FREEVOLVERTEX);
}
+#ifdef SELF_CHECK
+ loc_start = clock();
+#endif
if (!b->noflip) {
// Recover Delaunayness of T by flipping.
flip(flipque, NULL);
} else {
+ lawson(NULL, flipque);
// T remains regular.
- flipque->clear();
+ // flipque->clear();
}
+#ifdef SELF_CHECK
+ loc_end = clock();
+ tfliptime += ((REAL) (loc_end - loc_start)) / CLOCKS_PER_SEC;
+#endif
}
- if (!b->noflip && b->verbose > 0) {
+ if (b->verbose > 0) {
printf(" %ld Flips (T23 %ld, T32 %ld, T22 %ld, T44 %ld)\n",
flip23s+flip32s+flip22s+flip44s, flip23s, flip32s, flip22s, flip44s);
}
@@ -14591,23 +16734,29 @@ long tetgenmesh::delaunizevertices()
}
}
+ flipque = new queue(sizeof(badface));
// Prepare the array of points for inserting.
arraysize = points->items;
- insertarray = new point[arraysize];
+ insertarray = new point[arraysize];
+ points->traversalinit();
+
// Randomize the point order.
// randomseed = b->srandseed;
- points->traversalinit();
for (i = 0; i < arraysize; i++) {
j = (int) randomnation(i + 1); // 0 <= j <= i;
insertarray[i] = insertarray[j];
insertarray[j] = pointtraverse();
}
- flipque = new queue(sizeof(badface));
+
+ // Use lawson flip.
+ b->noflip = 1;
// Form the DT by incremental flip Delaunay algorithm.
incrflipdelaunay(NULL, insertarray, arraysize, true, b->plc, b->epsilon,
flipque);
+ b->noflip = 0;
+
delete [] insertarray;
delete flipque;
return hullsize;
@@ -14650,12 +16799,15 @@ void tetgenmesh::formstarpolygon(point pt, list* trilist, list* vertlist)
senextself(steinsh);
}
assert(i < 3);
+ // Add the edge f into list.
* (face *)(* trilist)[0] = steinsh;
- // Add two verts a, b and one edge ab of f into lists,
pa = sorg(steinsh);
pb = sdest(steinsh);
- vertlist->append(&pa);
- vertlist->append(&pb);
+ if (vertlist != (list *) NULL) {
+ // Add two verts a, b into V,
+ vertlist->append(&pa);
+ vertlist->append(&pb);
+ }
// Rotate edge pa to the left (CW) until meet pb or a segment.
lnextsh = steinsh;
@@ -14677,8 +16829,10 @@ void tetgenmesh::formstarpolygon(point pt, list* trilist, list* vertlist)
// Add edge ca to E.
pc = sorg(lnextsh);
if (pc == pb) break; // Rotate back.
- // Add vert c to V.
- vertlist->append(&pc);
+ if (vertlist != (list *) NULL) {
+ // Add vert c into V.
+ vertlist->append(&pc);
+ }
} while (true);
if (pc != pb) {
@@ -14701,8 +16855,10 @@ void tetgenmesh::formstarpolygon(point pt, list* trilist, list* vertlist)
// Add edge bd to E.
pd = sdest(rnextsh);
if (pd == pa) break; // Rotate back.
- // Add vert d to V.
- vertlist->append(&pd);
+ if (vertlist != (list *) NULL) {
+ // Add vert d into V.
+ vertlist->append(&pd);
+ }
} while (true);
}
}
@@ -14729,7 +16885,7 @@ void tetgenmesh::formstarpolygon(point pt, list* trilist, list* vertlist)
// //
// getfacetabovepoint() Get a point above a plane pass through a facet. //
// //
-// The calulcated point is saved in 'facetabovepointarray'. The 'abovepoint' //
+// The calculcated point is saved in 'facetabovepointarray'. The 'abovepoint'//
// is set on return. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -14737,7 +16893,6 @@ void tetgenmesh::formstarpolygon(point pt, list* trilist, list* vertlist)
void tetgenmesh::getfacetabovepoint(face* facetsh)
{
list *verlist, *trilist, *tetlist;
- tetrahedron tetptr;
triface adjtet;
face symsh;
point p1, p2, p3, pa;
@@ -14804,17 +16959,22 @@ void tetgenmesh::getfacetabovepoint(face* facetsh)
stpivot(symsh, adjtet);
}
if (adjtet.tet == dummytet) {
- tetptr = point2tet(p1);
- if (tetptr != (tetrahedron) NULL) {
- decode(tetptr, adjtet);
- if (isdead(&adjtet)) {
+ decode(point2tet(p1), adjtet);
+ if (isdead(&adjtet)) {
+ adjtet.tet = dummytet;
+ } else {
+ if (!findorg(&adjtet, p1)) {
adjtet.tet = dummytet;
}
}
}
if (adjtet.tet == dummytet) {
loc = locate(p1, &adjtet);
- if (loc != ONVERTEX) adjtet.tet = dummytet;
+ if (loc == ONVERTEX) {
+ setpoint2tet(p1, encode(adjtet));
+ } else {
+ adjtet.tet = dummytet;
+ }
}
if (adjtet.tet != dummytet) {
// Get the star polyhedron of p1.
@@ -15088,6 +17248,7 @@ void tetgenmesh::incrflipdelaunaysub(int shmark, REAL eps, list* ptlist,
REAL det, area;
bool aboveflag;
int arraysize;
+ int epscount;
int fmarker;
int idx, i, j, k;
@@ -15103,6 +17264,8 @@ void tetgenmesh::incrflipdelaunaysub(int shmark, REAL eps, list* ptlist,
// cillinear points of the set V = 'insertarray'. The first point:
// a = insertarray[0].
+ epscount = 0;
+ while (true) {
for (i = 1; i < arraysize; i++) {
det = distance(insertarray[0], insertarray[i]);
if (det > (longest * eps)) break;
@@ -15128,22 +17291,23 @@ void tetgenmesh::incrflipdelaunaysub(int shmark, REAL eps, list* ptlist,
// The set of vertices is not good (or nearly degenerate). However,
// a trivial triangulation can be formed (using 3 vertices). It may
// be corrected (or deleted) by mergefacet().
- if (eps == 0.0) {
- if (!b->quiet) {
- printf("Warning: Facet %d (%d, %d, %d", shmark,
- pointmark(insertarray[0]), pointmark(insertarray[1]),
- pointmark(insertarray[2]));
- if (ptlist->len() > 3) {
- printf(", ...");
- }
- printf(") is not a valid polygon.\n");
+ if ((eps == 0.0) || (epscount > 16)) {
+ printf("Error: Invalid PLC.\n");
+ printf(" Facet (%d, %d, %d", pointmark(insertarray[0]),
+ pointmark(insertarray[1]), pointmark(insertarray[2]));
+ if (ptlist->len() > 3) {
+ printf(", ...");
}
+ printf(") (%d) is not a valid polygon.\n", shmark);
+ terminatetetgen(1);
}
- // Only use the first three points.
- i = arraysize;
- // Don't do calculation of abovepoint.
- aboveflag = false;
+ // Decrease the eps, and continue to try.
+ eps *= 1e-2;
+ epscount++;
+ continue;
}
+ break;
+ } // while (true);
// Create the initial triangle.
makeshellface(subfaces, &newsh);
@@ -15152,15 +17316,15 @@ void tetgenmesh::incrflipdelaunaysub(int shmark, REAL eps, list* ptlist,
setsapex(newsh, insertarray[2]);
// Remeber the facet it belongs to.
setshellmark(newsh, shmark);
- // Set vertex type be FACETVERTEX if it has no type yet.
- if (pointtype(insertarray[0]) == VOLVERTEX) {
- setpointtype(insertarray[0], FACETVERTEX);
+ // Set vertex type be FREESUBVERTEX if it has no type yet.
+ if (pointtype(insertarray[0]) == FREEVOLVERTEX) {
+ setpointtype(insertarray[0], FREESUBVERTEX);
}
- if (pointtype(insertarray[1]) == VOLVERTEX) {
- setpointtype(insertarray[1], FACETVERTEX);
+ if (pointtype(insertarray[1]) == FREEVOLVERTEX) {
+ setpointtype(insertarray[1], FREESUBVERTEX);
}
- if (pointtype(insertarray[2]) == VOLVERTEX) {
- setpointtype(insertarray[2], FACETVERTEX);
+ if (pointtype(insertarray[2]) == FREEVOLVERTEX) {
+ setpointtype(insertarray[2], FREESUBVERTEX);
}
// Let 'dummysh' point to it (for point location).
dummysh[0] = sencode(newsh);
@@ -15224,9 +17388,9 @@ void tetgenmesh::incrflipdelaunaysub(int shmark, REAL eps, list* ptlist,
} else if (loc == ONVERTEX) {
// !should not happen!
}
- // Set p_i's type FACETVERTEX if it has no type yet.
- if (pointtype(insertarray[i]) == VOLVERTEX) {
- setpointtype(insertarray[i], FACETVERTEX);
+ // Set p_i's type FREESUBVERTEX if it has no type yet.
+ if (pointtype(insertarray[i]) == FREEVOLVERTEX) {
+ setpointtype(insertarray[i], FREESUBVERTEX);
}
flipsub(flipque);
}
@@ -15847,6 +18011,14 @@ void tetgenmesh::triangulate(int shmark, REAL eps, list* ptlist, list* conlist,
insertsubseg(&newsh);
senextself(newsh);
}
+ } else if (ptlist->len() == 2) {
+ // This facet is actually a segment. It is not support by the mesh data
+ // strcuture. Hence the segment will not be maintained in the mesh.
+ // However, during segment recovery, the segment can be processed.
+ cons = (point *)(* conlist)[0];
+ makeshellface(subsegs, &newsh);
+ setsorg(newsh, cons[0]);
+ setsdest(newsh, cons[1]);
}
}
@@ -16068,8 +18240,8 @@ void tetgenmesh::unifysegments()
// //
// Segments between two merged facets will be removed from the mesh. If all //
// segments around a vertex have been removed, change its vertex type to be //
-// FACETVERTEX. Edge flips will be performed to ensure the Delaunay criteria //
-// of the triangulation of merged facets. //
+// FREESUBVERTEX. Edge flips will be performed to ensure the Delaunayness of //
+// the triangulation of merged facets. //
// //
///////////////////////////////////////////////////////////////////////////////
@@ -16146,12 +18318,12 @@ void tetgenmesh::mergefacets(queue* flipqueue)
j = pointmark(eorg);
segspernodelist[j]--;
if (segspernodelist[j] == 0) {
- setpointtype(eorg, FACETVERTEX);
+ setpointtype(eorg, FREESUBVERTEX);
}
j = pointmark(edest);
segspernodelist[j]--;
if (segspernodelist[j] == 0) {
- setpointtype(edest, FACETVERTEX);
+ setpointtype(edest, FREESUBVERTEX);
}
// Add 'parentsh' to queue checking for flip.
enqueueflipedge(parentsh, flipqueue);
@@ -16345,6 +18517,8 @@ long tetgenmesh::meshsurface()
// Unify segments in 'subsegs', remove redundant segments. Face links
// of segments are also built.
unifysegments();
+ // Remember the number of input segments (for output).
+ insegments = subsegs->items;
if (checkpbcs) {
// Create the global array 'segpbcgrouptable'.
@@ -16356,7 +18530,7 @@ long tetgenmesh::meshsurface()
jettisonnodes();
}
- if (!b->nomerge && !checkpbcs) {
+ if (!b->nomerge && !b->nobisect && !checkpbcs) {
// No '-M' switch - merge adjacent facets if they are coplanar.
mergefacets(flipqueue);
}
@@ -16835,13 +19009,15 @@ enum tetgenmesh::locateresult tetgenmesh:: getsubpbcsympoint(point newpoint,
void tetgenmesh::createsegpbcgrouptable()
{
- pbcdata *pd, *pd1, *pd2;
+ shellface** segsperverlist;
+ pbcdata *pd, *ppd, pd1, pd2;
face segloop, symseg;
face startsh, spinsh, symsh;
- point pa, pb;
+ point pa, pb, syma, symb;
enum locateresult symloc;
REAL testpt[3], sympt[3];
bool inflag;
+ int *idx2seglist;
int segid1, segid2;
int f1, f2;
int i, j, k, l;
@@ -16849,6 +19025,11 @@ void tetgenmesh::createsegpbcgrouptable()
// Allocate memory for 'subpbcgrouptable'.
segpbcgrouptable = new list(sizeof(pbcdata), NULL, 256);
+ if (b->refine) {
+ // Create a point-to-seg map for quickly finding PBC seg pairs.
+ makesegmentmap(idx2seglist, segsperverlist);
+ }
+
// Loop through the segment list.
subsegs->traversalinit();
segloop.sh = shellfacetraverse(subsegs);
@@ -16867,13 +19048,52 @@ void tetgenmesh::createsegpbcgrouptable()
// Does spinsh belong to a pbcgroup?
if (shellpbcgroup(spinsh) != -1) {
// Yes! There exists a segment cd. ab and cd form a pbcgroup.
- // 'testpt' is the midpoint of ab used to find cd.
- for (i = 0; i < 3; i++) testpt[i] = 0.5 * (pa[i] + pb[i]);
- symloc = getsubpbcsympoint(testpt, &spinsh, sympt, &symsh);
+ if (b->refine) {
+ getsubpbcgroup(&spinsh, &pd, &f1, &f2);
+ // Transform pa from f1 -> f2.
+ for (i = 0; i < 3; i++) {
+ sympt[i] = pd->transmat[f1][i][0] * pa[0]
+ + pd->transmat[f1][i][1] * pa[1]
+ + pd->transmat[f1][i][2] * pa[2]
+ + pd->transmat[f1][i][3] * 1.0;
+ }
+ syma = point2pbcpt(pa);
+ // Is 'sympt == syma'?
+ if (distance(sympt, syma) > (longest * b->epsilon)) {
+ // No. Search the symmetric vertex of pa.
+ symloc = getsubpbcsympoint(pa, &spinsh, sympt, &symsh);
+ syma = sorg(symsh);
+ if (symloc != ONVERTEX) {
+ // Do a brute force search. Not done yet.
+ assert(0);
+ }
+ }
+ // Transform pb from f1 -> f2.
+ for (i = 0; i < 3; i++) {
+ sympt[i] = pd->transmat[f1][i][0] * pb[0]
+ + pd->transmat[f1][i][1] * pb[1]
+ + pd->transmat[f1][i][2] * pb[2]
+ + pd->transmat[f1][i][3] * 1.0;
+ }
+ // Search sym subface from the point-to-subface map.
+ symseg.shver = 0;
+ j = pointmark(syma) - in->firstnumber;
+ for (i = idx2seglist[j]; i < idx2seglist[j + 1]; i++) {
+ symseg.sh = segsperverlist[i];
+ if (sorg(symseg) == syma) symb = sdest(symseg);
+ else symb = sorg(symseg);
+ if (distance(sympt, symb) <= (longest * b->epsilon)) break;
+ }
+ assert(i < idx2seglist[j + 1]);
+ } else {
+ // 'testpt' is the midpoint of ab used to find cd.
+ for (i = 0; i < 3; i++) testpt[i] = 0.5 * (pa[i] + pb[i]);
+ symloc = getsubpbcsympoint(testpt, &spinsh, sympt, &symsh);
#ifdef SELF_CHECK
- assert(symloc == ONEDGE);
+ assert(symloc == ONEDGE);
#endif
- sspivot(symsh, symseg);
+ sspivot(symsh, symseg);
+ }
#ifdef SELF_CHECK
assert(symseg.sh != dummysh);
#endif
@@ -16898,19 +19118,19 @@ void tetgenmesh::createsegpbcgrouptable()
pd->ss[0] = segloop;
pd->ss[1] = symseg;
// Find the map from ab to cd.
- getsubpbcgroup(&spinsh, &pd1, &f1, &f2);
- pd->fmark[0] = pd1->fmark[f1];
- pd->fmark[1] = pd1->fmark[f2];
+ getsubpbcgroup(&spinsh, &ppd, &f1, &f2);
+ pd->fmark[0] = ppd->fmark[f1];
+ pd->fmark[1] = ppd->fmark[f2];
// Set the map from ab to cd.
for (i = 0; i < 4; i++) {
for (j = 0; j < 4; j++) {
- pd->transmat[0][i][j] = pd1->transmat[f1][i][j];
+ pd->transmat[0][i][j] = ppd->transmat[f1][i][j];
}
}
// Set the map from cd to ab.
for (i = 0; i < 4; i++) {
for (j = 0; j < 4; j++) {
- pd->transmat[1][i][j] = pd1->transmat[f2][i][j];
+ pd->transmat[1][i][j] = ppd->transmat[f2][i][j];
}
}
}
@@ -16920,27 +19140,35 @@ void tetgenmesh::createsegpbcgrouptable()
} while (spinsh.sh != startsh.sh);
segloop.sh = shellfacetraverse(subsegs);
}
+
+ if (b->refine) {
+ delete [] segsperverlist;
+ delete [] idx2seglist;
+ }
// Create the indirect segment pbcgroups.
+ // Bug-fixed (08 Sept. 2006). The total size of 'segpbcgrouptable' may get
+ // increased. Do not use pointers for 'pd1' and 'pd2'. The addresses may
+ // be invaild after realloc().
for (i = 0; i < segpbcgrouptable->len(); i++) {
- pd1 = (pbcdata *)(* segpbcgrouptable)[i];
+ pd1 = * (pbcdata *)(* segpbcgrouptable)[i];
for (f1 = 0; f1 < 2; f1++) {
- // Search for a group (except i) contains pd1->segid[f1].
+ // Search for a group (except i) contains pd1.segid[f1].
for (j = 0; j < segpbcgrouptable->len(); j++) {
if (j == i) continue;
- pd2 = (pbcdata *)(* segpbcgrouptable)[j];
+ pd2 = * (pbcdata *)(* segpbcgrouptable)[j];
f2 = -1;
- if (pd1->segid[f1] == pd2->segid[0]) {
+ if (pd1.segid[f1] == pd2.segid[0]) {
f2 = 0;
- } else if (pd1->segid[f1] == pd2->segid[1]) {
+ } else if (pd1.segid[f1] == pd2.segid[1]) {
f2 = 1;
}
if (f2 != -1) {
#ifdef SELF_CHECK
- assert(pd1->segid[f1] == pd2->segid[f2]);
+ assert(pd1.segid[f1] == pd2.segid[f2]);
#endif
- segid1 = pd1->segid[1 - f1];
- segid2 = pd2->segid[1 - f2];
+ segid1 = pd1.segid[1 - f1];
+ segid2 = pd2.segid[1 - f2];
// Search for the existence of segment pbcgroup (segid1, segid2).
inflag = false;
for (k = 0; k < segpbcgrouptable->len() && !inflag; k++) {
@@ -16953,28 +19181,28 @@ void tetgenmesh::createsegpbcgrouptable()
}
if (!inflag) {
pd = (pbcdata *) segpbcgrouptable->append(NULL);
- pd->segid[0] = pd1->segid[1 - f1];
- pd->segid[1] = pd2->segid[1 - f2];
- pd->ss[0] = pd1->ss[1 - f1];
- pd->ss[1] = pd2->ss[1 - f2];
+ pd->segid[0] = pd1.segid[1 - f1];
+ pd->segid[1] = pd2.segid[1 - f2];
+ pd->ss[0] = pd1.ss[1 - f1];
+ pd->ss[1] = pd2.ss[1 - f2];
// Invalid the fmark[0] == fmark[1].
pd->fmark[0] = pd->fmark[1] = 0;
// Translate matrix pd->transmat[0] = m2 * m1, where m1 =
- // pd1->transmat[1 - f1], m2 = pd2->transmat[f2].
+ // pd1.transmat[1 - f1], m2 = pd2.transmat[f2].
for (k = 0; k < 4; k++) {
for (l = 0; l < 4; l++) {
- pd->transmat[0][k][l] = pd2->transmat[f2][k][l];
+ pd->transmat[0][k][l] = pd2.transmat[f2][k][l];
}
}
- m4xm4(pd->transmat[0], pd1->transmat[1 - f1]);
+ m4xm4(pd->transmat[0], pd1.transmat[1 - f1]);
// Translate matrix pd->transmat[1] = m4 * m3, where m3 =
- // pd2->transmat[1 - f2], m4 = pd1->transmat[f1].
+ // pd2.transmat[1 - f2], m4 = pd1.transmat[f1].
for (k = 0; k < 4; k++) {
for (l = 0; l < 4; l++) {
- pd->transmat[1][k][l] = pd1->transmat[f1][k][l];
+ pd->transmat[1][k][l] = pd1.transmat[f1][k][l];
}
}
- m4xm4(pd->transmat[1], pd2->transmat[1 - f2]);
+ m4xm4(pd->transmat[1], pd2.transmat[1 - f2]);
}
}
}
@@ -17812,92 +20040,93 @@ void tetgenmesh::incrperturbvertices(REAL eps)
///////////////////////////////////////////////////////////////////////////////
// //
-// markacutevertices() Mark each vertex to be ACUTE or NACUTE. //
+// markacutevertices() Mark acute vertices. //
// //
-// A vertex is acute if at least two segments incident at it with an angle //
-// smaller than a given angle bound (e.g. 90 degree). //
+// A vertex v is called acute if there are two segments sharing at v forming //
+// an acute angle (i.e. smaller than 90 degree). //
+// //
+// This routine finds all acute vertices in the PLC and marks them as point- //
+// type ACUTEVERTEX. The other vertices of segments which are non-acute will //
+// be marked as NACUTEVERTEX. Vertices which are not endpoints of segments //
+// (such as DUPLICATEDVERTEX, UNUSEDVERTEX, etc) are not infected. //
+// //
+// NOTE: This routine should be called before Steiner points are introduced. //
+// That is, no point has type like FREESEGVERTEX, etc. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::markacutevertices(REAL acuteangle)
{
shellface **segsperverlist;
- face segloop, workseg, inciseg;
- point eorg, edest, eapex;
+ face segloop, nextseg;
+ point pointloop, edest, eapex;
REAL cosbound, anglearc;
REAL v1[3], v2[3], L, D;
bool isacute;
int *idx2seglist;
+ int acutecount;
int idx, i, j, k;
if (b->verbose > 0) {
- printf(" Marking segments have acute corners.\n");
+ printf(" Marking acute vertices.\n");
}
anglearc = acuteangle * PI / 180.0;
cosbound = cos(anglearc);
+ acutecount = 0;
// Constructing a map from vertex to segments.
makesegmentmap(idx2seglist, segsperverlist);
-
- // Loop over the set of subsegments.
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while (segloop.sh != (shellface *) NULL) {
- // Check and set types for the two ends of this segment.
- for (segloop.shver = 0; segloop.shver < 2; segloop.shver++) {
- eorg = sorg(segloop);
- if ((pointtype(eorg) != ACUTEVERTEX) &&
- (pointtype(eorg) != NACUTEVERTEX) &&
- (pointtype(eorg) != FREESEGVERTEX)) {
- // This vertex has no type be set yet.
- idx = pointmark(eorg) - in->firstnumber;
- isacute = false;
- for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isacute; i++) {
- workseg.sh = segsperverlist[i];
- workseg.shver = 0;
- if (sorg(workseg) != eorg) sesymself(workseg);
-#ifdef SELF_CHECK
- assert(sorg(workseg) == eorg);
-#endif
- edest = sdest(workseg);
- for (j = i + 1; j < idx2seglist[idx + 1] && !isacute; j++) {
- inciseg.sh = segsperverlist[j];
- inciseg.shver = 0;
-#ifdef SELF_CHECK
- assert(inciseg.sh != workseg.sh);
-#endif
- if (sorg(inciseg) != eorg) sesymself(inciseg);
-#ifdef SELF_CHECK
- assert(sorg(inciseg) == eorg);
-#endif
- eapex = sdest(inciseg);
- // Check angles between segs (eorg, edest) and (eorg, eapex).
- for (k = 0; k < 3; k++) {
- v1[k] = edest[k] - eorg[k];
- v2[k] = eapex[k] - eorg[k];
- }
- L = sqrt(v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2]);
- for (k = 0; k < 3; k++) v1[k] /= L;
- L = sqrt(v2[0] * v2[0] + v2[1] * v2[1] + v2[2] * v2[2]);
- for (k = 0; k < 3; k++) v2[k] /= L;
- D = v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
- if (D >= cosbound) {
- isacute = true;
- }
+
+ // Loop over the set of vertices.
+ points->traversalinit();
+ pointloop = pointtraverse();
+ while (pointloop != (point) NULL) {
+ idx = pointmark(pointloop) - in->firstnumber;
+ // Only do test if p is an endpoint of some segments.
+ if (idx2seglist[idx + 1] > idx2seglist[idx]) {
+ // Init p to be non-acute.
+ setpointtype(pointloop, NACUTEVERTEX);
+ isacute = false;
+ // Loop through all segments sharing at p.
+ for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isacute; i++) {
+ segloop.sh = segsperverlist[i];
+ // segloop.shver = 0;
+ if (sorg(segloop) != pointloop) sesymself(segloop);
+ edest = sdest(segloop);
+ for (j = i + 1; j < idx2seglist[idx + 1] && !isacute; j++) {
+ nextseg.sh = segsperverlist[j];
+ // nextseg.shver = 0;
+ if (sorg(nextseg) != pointloop) sesymself(nextseg);
+ eapex = sdest(nextseg);
+ // Check the angle formed by segs (p, edest) and (p, eapex).
+ for (k = 0; k < 3; k++) {
+ v1[k] = edest[k] - pointloop[k];
+ v2[k] = eapex[k] - pointloop[k];
}
+ L = sqrt(v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2]);
+ for (k = 0; k < 3; k++) v1[k] /= L;
+ L = sqrt(v2[0] * v2[0] + v2[1] * v2[1] + v2[2] * v2[2]);
+ for (k = 0; k < 3; k++) v2[k] /= L;
+ D = v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
+ // Is D acute?
+ isacute = (D >= cosbound);
}
- if (isacute) {
- setpointtype(eorg, ACUTEVERTEX);
- } else {
- setpointtype(eorg, NACUTEVERTEX);
- }
+ }
+ if (isacute) {
+ // Mark p to be acute.
+ setpointtype(pointloop, ACUTEVERTEX);
+ acutecount++;
}
}
- segloop.sh = shellfacetraverse(subsegs);
+ pointloop = pointtraverse();
}
delete [] idx2seglist;
delete [] segsperverlist;
+
+ if ((b->verbose > 0) && (acutecount > 0)) {
+ printf(" %d acute vertices.\n", acutecount);
+ }
}
///////////////////////////////////////////////////////////////////////////////
@@ -18426,7 +20655,7 @@ tetgenmesh::point tetgenmesh::getsplitpoint(face* splitseg, point refpoint)
point farorg, fardest;
point ei, ej, ek, c;
REAL v[3], r, split;
- REAL d1, ps, rs;
+ REAL d1, d2, ps, rs;
bool acuteorg, acutedest;
int stype, rule;
int i;
@@ -18536,7 +20765,6 @@ tetgenmesh::point tetgenmesh::getsplitpoint(face* splitseg, point refpoint)
if (rule == 1) r1count++;
else if (rule == 2) r2count++;
else if (rule == 3) r3count++;
- else if (rule == 4) r4count++;
if (b->verbose > 1) {
if (stype == 2) {
@@ -18550,12 +20778,13 @@ tetgenmesh::point tetgenmesh::getsplitpoint(face* splitseg, point refpoint)
makepoint(&splitpoint);
// Add a random perturbation on splitpoint.
d1 = distance(c, v);
+ d2 = distance(refpoint, v);
if (stype == 1 || stype == 3) {
ps = randgenerator(d1 * 1.0e-3);
} else {
// For type-2 segment, add a smaller perturbation.
// ps = randgenerator(d1 * 1.0e-5);
- REAL d2 = distance(refpoint, v);
+ // REAL d2 = distance(refpoint, v);
ps = randgenerator(d2 * 1.0e-5);
}
rs = ps / d1;
@@ -18578,6 +20807,100 @@ tetgenmesh::point tetgenmesh::getsplitpoint(face* splitseg, point refpoint)
return splitpoint;
}
+///////////////////////////////////////////////////////////////////////////////
+// //
+// insertsegment() Insert segment into DT. Queue it if it does not exist. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+bool tetgenmesh::insertsegment(face *insseg, list *misseglist)
+{
+ badface *misseg;
+ triface searchtet, spintet;
+ point tend, checkpoint;
+ point p1, p2;
+ enum finddirectionresult collinear;
+ int hitbdry;
+
+ // Search segment ab in DT.
+ p1 = (point) insseg->sh[3];
+ p2 = (point) insseg->sh[4];
+ getsearchtet(p1, p2, &searchtet, &tend);
+ collinear = finddirection(&searchtet, tend, tetrahedrons->items);
+ if (collinear == LEFTCOLLINEAR) {
+ checkpoint = apex(searchtet);
+ enext2self(searchtet);
+ esymself(searchtet);
+ } else if (collinear == RIGHTCOLLINEAR) {
+ checkpoint = dest(searchtet);
+ } else if (collinear == TOPCOLLINEAR) {
+ checkpoint = oppo(searchtet);
+ fnextself(searchtet);
+ enext2self(searchtet);
+ esymself(searchtet);
+ } else {
+ // assert(collinear == ACROSSFACE || collinear == ACROSSEDGE);
+ checkpoint = (point) NULL;
+ }
+ if (checkpoint == tend) {
+ // Segment exist. Bond it to all tets containing it.
+ hitbdry = 0;
+ adjustedgering(searchtet, CCW);
+ fnextself(searchtet);
+ spintet = searchtet;
+ do {
+ tssbond1(spintet, *insseg);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(searchtet, spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ }
+ }
+ }
+ } while ((apex(spintet) != apex(searchtet)) && (hitbdry < 2));
+ return true;
+ } else {
+ // Segment is missing.
+ if (misseglist != (list *) NULL) {
+ if (b->verbose > 2) {
+ printf(" Queuing missing segment (%d, %d).\n", pointmark(p1),
+ pointmark(p2));
+ }
+ misseg = (badface *) misseglist->append(NULL);
+ misseg->ss = *insseg;
+ misseg->forg = p1;
+ misseg->fdest = p2;
+ misseg->foppo = (point) NULL; // Not used.
+ // setshell2badface(misseg->ss, misseg);
+ }
+ return false;
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// tallmissegs() Find and queue all missing segments in DT. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::tallmissegs(list *misseglist)
+{
+ face segloop;
+
+ if (b->verbose) {
+ printf(" Queuing missing segments.\n");
+ }
+
+ subsegs->traversalinit();
+ segloop.sh = shellfacetraverse(subsegs);
+ while (segloop.sh != (shellface *) NULL) {
+ insertsegment(&segloop, misseglist);
+ segloop.sh = shellfacetraverse(subsegs);
+ }
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// delaunizesegments() Split segments repeatedly until they appear in a //
@@ -18617,19 +20940,20 @@ tetgenmesh::point tetgenmesh::getsplitpoint(face* splitseg, point refpoint)
void tetgenmesh::delaunizesegments()
{
+ list *misseglist;
queue *flipqueue;
+ badface *misloop;
tetrahedron encodedtet;
triface searchtet, splittet;
face splitsh, symsplitsub;
face segloop, symsplitseg;
- face lastsplit;
point refpoint, splitpoint, sympoint;
point tend, checkpoint;
point p1, p2, pa;
enum finddirectionresult collinear;
enum insertsiteresult success;
enum locateresult symloc;
- bool finish, coll;
+ bool coll;
long vertcount;
int i, j;
@@ -18637,30 +20961,35 @@ void tetgenmesh::delaunizesegments()
printf("Delaunizing segments.\n");
}
- // Mark segment vertices (acute or not) for determining segment types.
- markacutevertices(89.0);
- // Construct a map from points to tetrahedra for speeding point location.
- // makepoint2tetmap(); // This is done in above routine.
- // Initialize a queue for returning non-Delaunay faces and edges.
+ // Construct a map from points to tets for speeding point location.
+ makepoint2tetmap();
+ // Initialize a flipqueue.
flipqueue = new queue(sizeof(badface));
- // 'lastsplit' is the last segment be split in one loop, all segments
- // after it are existing. At first, set it be NULL;
- lastsplit.sh = (shellface *) NULL;
+ // Initialize the pool of missing segments.
+ misseglist = new list(sizeof(badface), NULL, SUBPERBLOCK);
+ // Looking for missing segments.
+ tallmissegs(misseglist);
+ // The DT contains segments now.
+ checksubsegs = 1;
// Remember the current number of points.
vertcount = points->items;
// Initialize the counters.
- r1count = r2count = r3count = r4count = 0l;
-
- finish = false;
- while (!finish && (steinerleft != 0)) {
- subsegs->traversalinit();
- segloop.sh = shellfacetraverse(subsegs);
- while ((segloop.sh != (shellface *) NULL) && (steinerleft != 0)) {
- // Search segment ab in DT.
- p1 = sorg(segloop); // p1 = a;
- p2 = sdest(segloop); // p2 = b;
- if (b->verbose > 2) {
- printf(" Checking segment (%d, %d).\n", pointmark(p1), pointmark(p2));
+ r1count = r2count = r3count = 0l;
+
+ // Loop until 'misseglist' is empty.
+ while (misseglist->items > 0) {
+ // Randomly pick a missing segment to recover.
+ i = randomnation(misseglist->items);
+ misloop = (badface *)(* misseglist)[i];
+ segloop = misloop->ss;
+ // Fill the "hole" in the list by filling the last one.
+ *misloop = *(badface *)(* misseglist)[misseglist->items - 1];
+ misseglist->items--;
+ // Now recover the segment.
+ p1 = (point) segloop.sh[3];
+ p2 = (point) segloop.sh[4];
+ if (b->verbose > 1) {
+ printf(" Recover segment (%d, %d).\n", pointmark(p1), pointmark(p2));
}
getsearchtet(p1, p2, &searchtet, &tend);
collinear = finddirection(&searchtet, tend, tetrahedrons->items);
@@ -18684,7 +21013,7 @@ void tetgenmesh::delaunizesegments()
// ab is defined by a long segment with c inside it. Use c to
// split ab. No new point is created.
splitpoint = checkpoint;
- if (pointtype(checkpoint) == VOLVERTEX) {
+ if (pointtype(checkpoint) == FREEVOLVERTEX) {
// c is not a segment vertex yet. It becomes NACUTEVERTEX.
setpointtype(splitpoint, NACUTEVERTEX);
} else if (pointtype(checkpoint) == ACUTEVERTEX) {
@@ -18697,7 +21026,7 @@ void tetgenmesh::delaunizesegments()
} else {
// Find a reference point p of ab.
refpoint = scoutrefpoint(&searchtet, tend);
- if (pointtype(refpoint) == VOLVERTEX) {
+ if (pointtype(refpoint) == FREEVOLVERTEX) {
// p is an input point, check if it is nearly collinear with ab.
coll = iscollinear(p1, p2, refpoint, b->epsilon);
if (coll) {
@@ -18751,7 +21080,7 @@ void tetgenmesh::delaunizesegments()
// Let sympoint remember splittet.
setpoint2tet(sympoint, encode(splittet));
// Do flip in DT.
- flip(flipqueue, NULL);
+ lawson(misseglist, flipqueue);
// Insert sympoint into F.
symsplitseg.shver = 0;
spivot(symsplitseg, symsplitsub);
@@ -18759,6 +21088,13 @@ void tetgenmesh::delaunizesegments()
splitsubedge(sympoint, &symsplitsub, flipqueue);
// Do flip in facet.
flipsub(flipqueue);
+ // Insert the two subsegments.
+ symsplitseg.shver = 0;
+ insertsegment(&symsplitseg, misseglist);
+ senextself(symsplitseg);
+ spivotself(symsplitseg);
+ symsplitseg.shver = 0;
+ insertsegment(&symsplitseg, misseglist);
} else { // if (symloc == ONVERTEX) {
// The sympoint already exists. It is possible when two
// pbc groups are exactly the same. Omit this point.
@@ -18781,35 +21117,42 @@ void tetgenmesh::delaunizesegments()
// consequent point location.
setpoint2tet(splitpoint, encode(searchtet));
// Maintain Delaunayness in DT.
- flip(flipqueue, NULL);
+ lawson(misseglist, flipqueue);
}
}
// Insert 'splitpoint' into F.
spivot(segloop, splitsh);
splitsubedge(splitpoint, &splitsh, flipqueue);
flipsub(flipqueue);
- // Remember 'segloop'.
- lastsplit = segloop;
- } else {
- // ab exists. Is it the last one we've checked?
- if (segloop.sh == lastsplit.sh) {
- finish = true;
- break;
- }
+ // Insert the two subsegments.
+ segloop.shver = 0;
+ insertsegment(&segloop, misseglist);
+ senextself(segloop);
+ spivotself(segloop);
+ segloop.shver = 0;
+ insertsegment(&segloop, misseglist);
}
- segloop.sh = shellfacetraverse(subsegs);
- }
- if (lastsplit.sh == (shellface *) NULL) {
- // No missing segment!
- finish = true;
+ }
+
+ // Detach all segments from tets.
+ tetrahedrons->traversalinit();
+ searchtet.tet = tetrahedrontraverse();
+ while (searchtet.tet != (tetrahedron *) NULL) {
+ for (i = 0; i < 6; i++) {
+ searchtet.tet[8 + i] = (tetrahedron) dummysh;
}
+ searchtet.tet = tetrahedrontraverse();
}
+ // No segments now.
+ checksubsegs = 0;
if (b->verbose > 0) {
printf(" %ld protect points.\n", points->items - vertcount);
+ printf(" R1: %ld, R2: %ld, R3: %ld.\n", r1count, r2count, r3count);
}
delete flipqueue;
+ delete misseglist;
}
//
@@ -21110,6 +23453,8 @@ void tetgenmesh::plague(memorypool *viri)
if (shellmark(neighsh) == 0) {
setshellmark(neighsh, 1);
}
+ // This side becomes hull. Update the handle in dummytet.
+ dummytet[0] = encode(neighbor);
}
}
}
@@ -21260,9 +23605,8 @@ void tetgenmesh::removeholetets(memorypool* viri)
j = pointmark(checkpt);
tetspernodelist[j]--;
if (tetspernodelist[j] == 0) {
- // If it is a volume vertex, mark to delete it.
- if ((pointtype(checkpt) == VOLVERTEX) ||
- (pointtype(checkpt) == FREEVOLVERTEX)) {
+ // If it is added volume vertex or '-j' is not used, delete it.
+ if ((pointtype(checkpt) == FREEVOLVERTEX) || !b->nojettison) {
setpointtype(checkpt, UNUSEDVERTEX);
unuverts++;
}
@@ -21831,7 +24175,7 @@ bool tetgenmesh::constrainedflip(triface* flipface, triface* front,
flip22(flipface, flipque);
return true;
}
- } else if (fc == UNFLIPABLE) {
+ } else if (fc == N32) {
// Is f a crossface?
if (front != (triface *) NULL) {
// (6) Is any obstacle face (abd, or abe, ...) flipable?
@@ -22269,7 +24613,7 @@ bool tetgenmesh::constrainedcavity(triface* oldtet, list* floorlist,
floorlist->len(), ceillist->len(), ptlist->len());
}
- symbolic = 1;
+ // symbolic = 1;
// Initialize the cavity C.
initializecavity(floorlist, ceillist, frontlist);
@@ -22310,7 +24654,7 @@ bool tetgenmesh::constrainedcavity(triface* oldtet, list* floorlist,
retrievenewtets(newtetlist);
}
- symbolic = 0;
+ // symbolic = 0;
if (misfrontlist->len() == 0) {
// All fronts have identified in D. Get the shape of C by removing out
@@ -22855,8 +25199,8 @@ void tetgenmesh::collapseedge(point suppt, point conpt, list* oldtetlist,
// Loop in B(p), replace p with np, queue dead tets, uninfect old tets.
for (i = 0; i < oldtetlist->len(); i++) {
- oldtet = * (triface *)(* oldtetlist)[i];
- assert(!infected(oldtet));
+ oldtet = * (triface *)(* oldtetlist)[i]; // assert(infected(oldtet));
+ uninfect(oldtet);
pa = org(oldtet);
pb = dest(oldtet);
pc = apex(oldtet);
@@ -22945,8 +25289,12 @@ void tetgenmesh::deallocfaketets(list* frontlist)
}
// Dealloc the 'fake' tet.
tetrahedrondealloc(front.tet);
- // This side (neightet) is a boundary face, let 'dummytet' bond to it.
- dummytet[0] = encode(neightet);
+ // If 'neightet' is a hull face, let 'dummytet' bond to it. It is
+ // a 'dummytet' when this front was created from a new subface.
+ // In such case, it should not be bounded.
+ if (neightet.tet != dummytet) {
+ dummytet[0] = encode(neightet);
+ }
}
}
}
@@ -23012,11 +25360,14 @@ void tetgenmesh::restorepolyhedron(list* oldtetlist)
// 'supsh' is a subface f of F, and p = sapex(f); the other parameters are //
// working lists which are empty at the beginning and the end. //
// //
+// 'optflag' is used for mesh optimization. If it is set, after removing p, //
+// test the object function on each new tet, queue bad tets. //
+// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::suppressfacetpoint(face* supsh, list* frontlist,
list* misfrontlist, list* ptlist, list* conlist, memorypool* viri,
- queue* flipque)
+ queue* flipque, bool noreloc, bool optflag)
{
list *oldtetlist[2], *newtetlist[2];
list *oldshlist, *newshlist;
@@ -23090,12 +25441,17 @@ bool tetgenmesh::suppressfacetpoint(face* supsh, list* frontlist,
// Preparation for re-tetrahedralzing old B_i(p).
orientnewsubs(newshlist, supsh, norm);
// Tetrahedralize old B_i(p).
- if (!constrainedcavity(&oldtet, newshlist, oldtetlist[i], ptlist,
- frontlist, misfrontlist, newtetlist[i], flipque)) {
- // Unable to mesh old B_i(p), try to relocate p into it.
+ success = constrainedcavity(&oldtet, newshlist, oldtetlist[i], ptlist,
+ frontlist, misfrontlist, newtetlist[i], flipque);
+ // If p is not suppressed, do relocation if 'noreloc' is not set.
+ if (!success && !noreloc) {
+ // Try to relocate p into the old B_i(p).
makepoint(&(newpt[i]));
success = findrelocatepoint(suppt, newpt[i], norm, frontlist,
oldtetlist[i]);
+ // Initialize newpt = suppt.
+ // for (j = 0; j < 3; j++) newpt[i][j] = suppt[j];
+ // success = smoothvolpoint(newpt[i], frontlist, true);
if (success) {
// p is relocated by newpt[i]. Now insert it. Don't do flip since
// the new tets may get deleted again.
@@ -23110,6 +25466,10 @@ bool tetgenmesh::suppressfacetpoint(face* supsh, list* frontlist,
assert(newtetlist[i]->len() == 0);
}
}
+ if (!success && noreloc) {
+ // Failed and no point relocation. Clean fake tets.
+ deallocfaketets(frontlist);
+ }
// Clear work lists.
ptlist->clear();
frontlist->clear();
@@ -23151,6 +25511,17 @@ bool tetgenmesh::suppressfacetpoint(face* supsh, list* frontlist,
}
}
}
+ if (optflag) {
+ // Check for new bad-quality tets.
+ for (i = 0; i < 2; i++) {
+ if (newtetlist[i] != (list *) NULL) {
+ for (j = 0; j < newtetlist[i]->len(); j++) {
+ newtet = * (triface *)(* (newtetlist[i]))[j];
+ if (!isdead(&newtet)) checktet4opt(&newtet, true);
+ }
+ }
+ }
+ }
} else {
// p is not suppressed. Recover the original state.
unsupverts++;
@@ -23219,7 +25590,7 @@ bool tetgenmesh::suppressfacetpoint(face* supsh, list* frontlist,
bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
list* newsegshlist, list* frontlist, list* misfrontlist, list* ptlist,
- list* conlist, memorypool* viri, queue* flipque)
+ list* conlist, memorypool* viri, queue* flipque, bool noreloc, bool optflag)
{
list **oldtetlist, **newtetlist;
list **oldshlist, **newshlist;
@@ -23230,19 +25601,20 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
face nsupseg, newseg, prevseg, nextseg;
point suppt, *newpt;
point pa, pb, *cons;
- REAL norm[3], pnorm[2][3];
+ REAL pnorm[2][3], norm[3];
bool success;
int shmark;
int n, i, j, k;
// Get the Steiner point p.
- assert(supseg->shver == 0);
+ assert(supseg->shver < 2);
suppt = sdest(*supseg);
// Find the segment ab split by p.
senext(*supseg, nsupseg);
spivotself(nsupseg);
assert(nsupseg.sh != dummysh);
nsupseg.shver = 0;
+ if (sorg(nsupseg) != suppt) sesymself(nsupseg);
assert(sorg(nsupseg) == suppt);
pa = sorg(*supseg);
pb = sdest(nsupseg);
@@ -23300,6 +25672,7 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
spivotself(prevseg);
if (prevseg.sh != dummysh) {
prevseg.shver = 0;
+ if (sdest(prevseg) != pa) sesymself(prevseg);
assert(sdest(prevseg) == pa);
senextself(prevseg);
senext2self(newseg);
@@ -23311,6 +25684,7 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
spivotself(nextseg);
if (nextseg.sh != dummysh) {
nextseg.shver = 0;
+ if (sorg(nextseg) != pb) sesymself(nextseg);
assert(sorg(nextseg) == pb);
senext2self(nextseg);
senextself(newseg);
@@ -23427,13 +25801,16 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
}
}
// Tetrahedralize B_i(p).
- if (!constrainedcavity(&oldtet, dnewshlist, oldtetlist[i], ptlist,
- frontlist, misfrontlist, newtetlist[i], flipque)) {
+ success = constrainedcavity(&oldtet, dnewshlist, oldtetlist[i], ptlist,
+ frontlist, misfrontlist, newtetlist[i], flipque);
+ if (!success && !noreloc) {
// C must be finished by re-locating the steiner point.
makepoint(&(newpt[i]));
for (j = 0; j < 3; j++) norm[j] = 0.5 * (pnorm[0][j] + pnorm[1][j]);
success = findrelocatepoint(suppt, newpt[i], norm, frontlist,
oldtetlist[i]);
+ // for (j = 0; j < 3; j++) newpt[i][j] = suppt[j];
+ // success = smoothvolpoint(newpt[i], frontlist, true);
if (success) {
// p is relocated by newpt[i]. Now insert it. Don't do flip since
// the new tets may get deleted again.
@@ -23448,6 +25825,10 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
assert(newtetlist[i]->len() == 0);
}
}
+ if (!success && noreloc) {
+ // Failed and no point relocation. Clean fake tets.
+ deallocfaketets(frontlist);
+ }
// Clear work lists.
dnewshlist->clear();
ptlist->clear();
@@ -23460,6 +25841,9 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
// p has been suppressed. (Still in the pool).
setpointtype(suppt, UNUSEDVERTEX);
unuverts++;
+ // Update the segmnet pointers saved in a and b.
+ setpoint2sh(pa, sencode(newseg));
+ setpoint2sh(pb, sencode(newseg));
// Delete old segments ap, pb.
shellfacedealloc(subsegs, supseg->sh);
shellfacedealloc(subsegs, nsupseg.sh);
@@ -23495,6 +25879,17 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
}
}
}
+ if (optflag) {
+ for (i = 0; i < spinshlist->len(); i++) {
+ // Check for new bad-quality tets.
+ if (newtetlist[i] != (list *) NULL) {
+ for (j = 0; j < newtetlist[i]->len(); j++) {
+ newtet = * (triface *)(* (newtetlist[i]))[j];
+ if (!isdead(&newtet)) checktet4opt(&newtet, true);
+ }
+ }
+ }
+ }
} else {
// p is not suppressed. Recover the original state.
unsupverts++;
@@ -23503,22 +25898,27 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
spivotself(prevseg);
if (prevseg.sh != dummysh) {
prevseg.shver = 0;
+ if (sdest(prevseg) != pa) sesymself(prevseg);
assert(sdest(prevseg) == pa);
senextself(prevseg);
senext2self(*supseg);
sbond(*supseg, prevseg);
- supseg->shver = 0;
+ senextself(*supseg); // Restore original state.
+ assert(supseg->shver < 2);
}
// Restore old connection at b.
senext(nsupseg, nextseg);
spivotself(nextseg);
if (nextseg.sh != dummysh) {
nextseg.shver = 0;
+ if (sorg(nextseg) != pb) sesymself(nextseg);
assert(sorg(nextseg) == pb);
senext2self(nextseg);
senextself(nsupseg);
sbond(nsupseg, nextseg);
- nsupseg.shver = 0;
+ // nsupseg.shver = 0;
+ senext2self(nsupseg); // Restore original state
+ assert(nsupseg.shver < 2);
}
// Delete the new segment ab.
shellfacedealloc(subsegs, newseg.sh);
@@ -23589,52 +25989,52 @@ bool tetgenmesh::suppresssegpoint(face* supseg, list* spinshlist,
// //
// suppressvolpoint() Suppress a point inside mesh. //
// //
-// The point p inside the mesh will be suppressed by being deleted from the //
-// mesh. p may not be suppressed. //
+// The point p = org(suptet) is inside the mesh and will be suppressed from //
+// the mesh. Note that p may not be suppressed. //
+// //
+// 'optflag' is used for mesh optimization. If it is set, after removing p, //
+// test the object function on each new tet, queue bad tets. //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::suppressvolpoint(point suppt, list* frontlist,
- list* misfrontlist, list* ptlist, queue* flipque)
+bool tetgenmesh::suppressvolpoint(triface* suptet, list* frontlist,
+ list* misfrontlist, list* ptlist, queue* flipque, bool optflag)
{
+ list *myfrontlist, *mymisfrontlist, *myptlist;
list *oldtetlist, *newtetlist;
list *newshlist; // a dummy list.
- tetrahedron tetptr;
+ queue *myflipque;
triface oldtet, newtet;
+ point suppt, conpt;
bool success;
int j;
- if (b->verbose > 1) {
- printf(" Remove point %d in mesh.\n", pointmark(suppt));
- }
-
- // Get a tet with p as a vertex.
- oldtet.tet = (tetrahedron *) NULL;
- tetptr = point2tet(suppt);
- if (tetptr != (tetrahedron) NULL) {
- decode(tetptr, oldtet);
- }
- // Make sure oldtet contains p.
- if (isdead(&oldtet) || !findorg(&oldtet, suppt)) {
- // The pointer is invalid. Recreate the map.
- makepoint2tetmap();
- tetptr = point2tet(suppt);
- decode(tetptr, oldtet);
- if (isdead(&oldtet)) {
- // There is no tet contain p, it is indeed an unused point.
- // expandsteinercavity() deleted all tets of p.
- setpointtype(suppt, UNUSEDVERTEX);
- unuverts++;
- return true;
- }
- }
-
// Allocate spaces for storing (old and new) B(p).
oldtetlist = new list(sizeof(triface), NULL, 256);
newtetlist = new list(sizeof(triface), NULL, 256);
newshlist = new list(sizeof(face), NULL, 256);
+ // Allocate work lists if user doesn't supply them.
+ myfrontlist = mymisfrontlist = myptlist = (list *) NULL;
+ myflipque = (queue *) NULL;
+ if (frontlist == (list *) NULL) {
+ myfrontlist = new list(sizeof(triface), NULL, 256);
+ frontlist = myfrontlist;
+ mymisfrontlist = new list(sizeof(triface), NULL, 256);
+ misfrontlist = mymisfrontlist;
+ myptlist = new list(sizeof(point *), NULL, 256);
+ ptlist = myptlist;
+ myflipque = new queue(sizeof(badface));
+ flipque = myflipque;
+ }
+
+ suppt = org(*suptet);
+ oldtet = *suptet;
success = true; // Assume p can be suppressed.
+ if (b->verbose > 1) {
+ printf(" Remove point %d in mesh.\n", pointmark(suppt));
+ }
+
// Form old B(p) in oldtetlist.
oldtetlist->append(&oldtet);
formstarpolyhedron(suppt, oldtetlist, ptlist, false);
@@ -23644,20 +26044,30 @@ bool tetgenmesh::suppressvolpoint(point suppt, list* frontlist,
infect(oldtet);
}
// Tetrahedralize old B(p).
- if (!constrainedcavity(&oldtet, newshlist, oldtetlist, ptlist, frontlist,
- misfrontlist, newtetlist, flipque)) {
- // Unable to suppress p.
- success = false;
- // Clean fake tets and quit this option.
+ success = constrainedcavity(&oldtet, newshlist, oldtetlist, ptlist,
+ frontlist, misfrontlist, newtetlist, flipque);
+ if (!success) {
+ // Unable to suppress p.
deallocfaketets(frontlist);
+ // Try to collapse an edge at p.
+ conpt = (point) NULL;
assert(newtetlist->len() == 0);
+ if (findcollapseedge(suppt, &conpt, oldtetlist, ptlist)) {
+ // Collapse the edge suppt->conpt. Re-use newtetlist.
+ collapseedge(suppt, conpt, oldtetlist, newtetlist);
+ // The oldtetlist contains newtetlist.
+ if (optflag) {
+ assert(newtetlist->len() == 0);
+ for (j = 0; j < oldtetlist->len(); j++) {
+ newtet = * (triface *)(* oldtetlist)[j];
+ newtetlist->append(&newtet);
+ }
+ }
+ oldtetlist->clear(); // Do not delete them.
+ collapverts++;
+ success = true;
+ }
}
- // Clear work lists.
- ptlist->clear();
- frontlist->clear();
- misfrontlist->clear();
- flipque->clear();
-
if (success) {
// p has been removed! (Still in the pool).
setpointtype(suppt, UNUSEDVERTEX);
@@ -23669,6 +26079,13 @@ bool tetgenmesh::suppressvolpoint(point suppt, list* frontlist,
assert(!isdead(&oldtet));
tetrahedrondealloc(oldtet.tet);
}
+ if (optflag) {
+ // Check for new bad tets.
+ for (j = 0; j < newtetlist->len(); j++) {
+ newtet = * (triface *)(* newtetlist)[j];
+ if (!isdead(&newtet)) checktet4opt(&newtet, true);
+ }
+ }
} else {
// p is not suppressed. Recover the original state.
// Uninfect tets of old B(p).
@@ -23679,6 +26096,18 @@ bool tetgenmesh::suppressvolpoint(point suppt, list* frontlist,
}
}
+ // Clear work lists.
+ ptlist->clear();
+ frontlist->clear();
+ misfrontlist->clear();
+ flipque->clear();
+ // Deallocate work lists.
+ if (myfrontlist != (list *) NULL) {
+ delete myfrontlist;
+ delete mymisfrontlist;
+ delete myptlist;
+ delete myflipque;
+ }
delete oldtetlist;
delete newtetlist;
delete newshlist;
@@ -23688,61 +26117,177 @@ bool tetgenmesh::suppressvolpoint(point suppt, list* frontlist,
///////////////////////////////////////////////////////////////////////////////
// //
-// collapseedgepoint() Delete a point by edge collapse. //
+// smoothpoint() Smooth a volume/segment point. //
+// //
+// 'smthpt' (p) is inside the polyhedron (C) bounded by faces in 'starlist'. //
+// This routine moves p inside C until an object function is maximized. //
+// //
+// Default, the CCW edge ring of the faces on C points to p. If 'invtori' is //
+// TRUE, the orientation is inversed. //
+// //
+// If 'key' != NULL, it contains an object value to be improved. Current it //
+// means the cosine of the largest dihedral angle. In such case, the point //
+// is smoothed only if the final configuration improves the object value, it //
+// is returned by the 'key'. //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::collapseedgepoint(point colpt, list *oldtetlist,
- list* deadtetlist, list *ptlist)
+bool tetgenmesh::smoothpoint(point smthpt, point e1, point e2, list *starlist,
+ bool invtori, REAL *key)
{
- tetrahedron tetptr;
- triface oldtet, newtet;
- point conpt;
- bool success;
+ triface starttet;
+ point pa, pb, pc;
+ REAL fcent[3], startpt[3], nextpt[3], bestpt[3];
+ REAL iniTmax, oldTmax, newTmax;
+ REAL ori, aspT, aspTmax, imprate;
+ REAL cosd, maxcosd;
+ bool segflag, randflag; //, subflag;
+ int numdirs;
+ int iter, i, j;
+
+ // Is p a segment vertex?
+ segflag = (e1 != (point) NULL);
+ // Decide the number of moving directions.
+ numdirs = segflag ? 2 : starlist->len();
+ randflag = numdirs > 10;
+ if (randflag) {
+ numdirs = 10; // Maximum 10 directions.
+ }
+
+ // Calculate the initial object value (the largest aspect ratio).
+ for (i = 0; i < starlist->len(); i++) {
+ starttet = * (triface *)(* starlist)[i];
+ adjustedgering(starttet, !invtori ? CCW : CW);
+ pa = org(starttet);
+ pb = dest(starttet);
+ pc = apex(starttet);
+ aspT = tetaspectratio(pa, pb, pc, smthpt);
+ if (i == 0) {
+ aspTmax = aspT;
+ } else {
+ aspTmax = aspT > aspTmax ? aspT : aspTmax;
+ }
+ }
+ iniTmax = aspTmax;
if (b->verbose > 1) {
- printf(" Collapse point %d.\n", pointmark(colpt));
- }
-
- // Get a tet with p as a vertex.
- oldtet.tet = (tetrahedron *) NULL;
- tetptr = point2tet(colpt);
- if (tetptr != (tetrahedron) NULL) {
- decode(tetptr, oldtet);
- }
- // Make sure oldtet contains p.
- if (isdead(&oldtet) || !findorg(&oldtet, colpt)) {
- // The pointer is invalid. Recreate the map.
- makepoint2tetmap();
- tetptr = point2tet(colpt);
- decode(tetptr, oldtet);
- if (isdead(&oldtet)) {
- // There is no tet contain p, it is indeed an unused point.
- // expandsteinercavity() deleted all tets of p.
- setpointtype(colpt, UNUSEDVERTEX);
- unuverts++;
- return true;
- }
+ printf(" Smooth %s point %d (%g, %g, %g).\n", segflag ? "seg" : "vol",
+ pointmark(smthpt), smthpt[0], smthpt[1], smthpt[2]);
+ printf(" Initial max L/h = %g.\n", iniTmax);
+ }
+ for (i = 0; i < 3; i++) {
+ bestpt[i] = startpt[i] = smthpt[i];
}
- // Form old B(p) in oldtetlist.
- oldtetlist->append(&oldtet);
- formstarpolyhedron(colpt, oldtetlist, ptlist, false);
- // Try to collapse p.
- success = findcollapseedge(colpt, &conpt, oldtetlist, ptlist);
- if (success) {
- // Collapse p by edge contraction.
- collapseedge(colpt, conpt, oldtetlist, deadtetlist);
- collapverts++;
- // p has been removed! (Still in the pool).
- setpointtype(colpt, UNUSEDVERTEX);
- unuverts++;
- deadtetlist->clear();
+ // Do iteration until the new aspTmax does not decrease.
+ newTmax = iniTmax;
+ iter = 0;
+ while (true) {
+ // Find the best next location.
+ oldTmax = newTmax;
+ for (i = 0; i < numdirs; i++) {
+ // Calculate the moved point (saved in 'nextpt').
+ if (!segflag) {
+ if (randflag) {
+ // Randomly pick a direction.
+ j = (int) randomnation(starlist->len());
+ } else {
+ j = i;
+ }
+ starttet = * (triface *)(* starlist)[j];
+ adjustedgering(starttet, !invtori ? CCW : CW);
+ pa = org(starttet);
+ pb = dest(starttet);
+ pc = apex(starttet);
+ for (j = 0; j < 3; j++) {
+ fcent[j] = (pa[j] + pb[j] + pc[j]) / 3.0;
+ }
+ } else {
+ for (j = 0; j < 3; j++) {
+ fcent[j] = (i == 0 ? e1[j] : e2[j]);
+ }
+ }
+ for (j = 0; j < 3; j++) {
+ nextpt[j] = startpt[j] + 0.01 * (fcent[j] - startpt[j]);
+ }
+ // Get the largest object value for the new location.
+ for (j = 0; j < starlist->len(); j++) {
+ starttet = * (triface *)(* starlist)[j];
+ adjustedgering(starttet, !invtori ? CCW : CW);
+ pa = org(starttet);
+ pb = dest(starttet);
+ pc = apex(starttet);
+ ori = orient3d(pa, pb, pc, nextpt);
+ if (ori < 0.0) {
+ aspT = tetaspectratio(pa, pb, pc, nextpt);
+ if (j == 0) {
+ aspTmax = aspT;
+ } else {
+ aspTmax = aspT > aspTmax ? aspT : aspTmax;
+ }
+ } else {
+ // An invalid new tet. Discard this point.
+ aspTmax = newTmax;
+ } // if (ori < 0.0)
+ // Stop looping when the object value is bigger than before.
+ if (aspTmax >= newTmax) break;
+ } // for (j = 0; j < starlist->len(); j++)
+ if (aspTmax < newTmax) {
+ // Save the improved object value and the location.
+ newTmax = aspTmax;
+ for (j = 0; j < 3; j++) bestpt[j] = nextpt[j];
+ }
+ } // for (i = 0; i < starlist->len(); i++)
+ // Does the object value improved much?
+ imprate = fabs(oldTmax - newTmax) / oldTmax;
+ if (imprate < 1e-3) break;
+ // Yes, move p to the new location and continue.
+ for (j = 0; j < 3; j++) startpt[j] = bestpt[j];
+ iter++;
+ } // while (true)
+
+ if (iter > 0) {
+ // The point is moved.
+ if (key) {
+ // Check if the quality is improved by the smoothed point.
+ maxcosd = 0.0; // = cos(90).
+ for (j = 0; j < starlist->len(); j++) {
+ starttet = * (triface *)(* starlist)[j];
+ adjustedgering(starttet, !invtori ? CCW : CW);
+ pa = org(starttet);
+ pb = dest(starttet);
+ pc = apex(starttet);
+ tetalldihedral(pa, pb, pc, startpt, NULL, &cosd, NULL);
+ if (cosd < *key) {
+ // This quality will not be improved. Stop.
+ iter = 0; break;
+ } else {
+ // Remeber the worst quality value (of the new configuration).
+ maxcosd = maxcosd < cosd ? maxcosd : cosd;
+ }
+ }
+ if (iter > 0) *key = maxcosd;
+ }
}
- oldtetlist->clear();
- ptlist->clear();
- return success;
+ if (iter > 0) {
+ segflag ? smoothsegverts++ : smoothvolverts++;
+ for (i = 0; i < 3; i++) smthpt[i] = startpt[i];
+ if (b->verbose > 1) {
+ printf(" Move to new location (%g, %g, %g).\n", smthpt[0], smthpt[1],
+ smthpt[2]);
+ printf(" Final max L/h = %g. (%d iterations)\n", newTmax, iter);
+ if (key) {
+ printf(" Max. dihed = %g (degree).\n", acos(*key) / PI * 180.0);
+ }
+ }
+ return true;
+ } else {
+ if (b->verbose > 1) {
+ printf(" Not smoothed.\n");
+ }
+ return false;
+ }
}
///////////////////////////////////////////////////////////////////////////////
@@ -23751,7 +26296,7 @@ bool tetgenmesh::collapseedgepoint(point colpt, list *oldtetlist,
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::removesteiners()
+void tetgenmesh::removesteiners(bool coarseflag)
{
list *frontlist, *misfrontlist;
list *spinshlist, *newsegshlist;
@@ -23761,12 +26306,22 @@ void tetgenmesh::removesteiners()
triface checktet;
face shloop;
face segloop, nextseg;
- point pa;
+ point pa, neipt;
+ REAL len;
bool remflag;
+ int *worklist;
int oldnum, rmstein;
- int i;
+ int i, j;
+
+ if (!b->quiet) {
+ if (!coarseflag) {
+ printf("Removing Steiner points.\n");
+ } else {
+ printf("Coarsening mesh.\n");
+ }
+ }
- // Initiliaze work lists.
+ // Initialize work lists.
frontlist = new list(sizeof(triface), NULL);
misfrontlist = new list(sizeof(triface), NULL);
spinshlist = new list(sizeof(face), NULL);
@@ -23776,13 +26331,10 @@ void tetgenmesh::removesteiners()
flipque = new queue(sizeof(badface));
viri = new memorypool(sizeof(shellface *), 1024, POINTER, 0);
oldnum = unuverts;
- relverts = suprelverts = collapverts = unsupverts = 0;
+ relverts = suprelverts = collapverts = unsupverts;
+ smoothvolverts = 0;
expcavcount = 0;
- if (!b->quiet) {
- printf("Removing Steiner points.\n");
- }
-
// Suppress Steiner points inside facets.
do {
rmstein = unuverts;
@@ -23795,32 +26347,115 @@ void tetgenmesh::removesteiners()
for (i = 0; i < 3; i++) {
pa = sapex(shloop);
if (pointtype(pa) == FREESUBVERTEX) {
- // Find a Steiner point p.
- if (b->nobisect == 1) {
- // '-Y'. Remove p if s is a hull face.
- stpivot(shloop, checktet);
- if (checktet.tet != dummytet) {
- sesymself(shloop);
- stpivot(shloop, checktet);
+ if (!coarseflag) {
+ // Remove it if it is not an input point.
+ j = pointmark(pa) - in->firstnumber;
+ if (j >= in->numberofpoints) {
+ if (b->nobisect == 1) {
+ // '-Y'. Remove p if s is a hull face.
+ stpivot(shloop, checktet);
+ if (checktet.tet != dummytet) {
+ sesymself(shloop);
+ stpivot(shloop, checktet);
+ }
+ remflag = (checktet.tet == dummytet);
+ } else {
+ // '-YY'. Remove p whatever s is a hull face or not.
+ remflag = true;
+ }
}
- remflag = (checktet.tet == dummytet);
} else {
- // '-YY'. Remove p whatever s is a hull face or not.
- remflag = true;
- }
- break;
- }
+ // Check if this vertex can be coarsed.
+ if (b->nobisect == 0) {
+ // Is a background mesh available?
+ if (b->metric) {
+ // assert(pa[pointmtrindex] > 0.0);
+ // Form the star of pa.
+ spinshlist->append(&shloop);
+ formstarpolygon(pa, spinshlist, ptlist);
+ len = 0.0;
+ for (j = 0; j < ptlist->len(); j++) {
+ neipt = * (point *)(* ptlist)[j];
+ len += distance(pa, neipt);
+ }
+ len /= ptlist->len();
+ // Carse it if the average edge length is small.
+ remflag = len < pa[pointmtrindex];
+ spinshlist->clear();
+ ptlist->clear();
+ } else {
+ // Coarse it if (1) it is an input point and its pointmarker
+ // is zero, or (2) it is a Steiner point.
+ remflag = true;
+ j = pointmark(pa) - in->firstnumber;
+ if (j < in->numberofpoints) {
+ remflag = (in->pointmarkerlist[j] == 0);
+ }
+ } // if (b->metric)
+ } // if (b->nobisect == 0)
+ } // if (!coarseflag)
+ if (remflag) break;
+ } // if (pointtype(pa) == FREESUBVERTEX)
senextself(shloop);
- }
+ } // for (i = 0; i < 3; i++)
if (remflag) {
suppressfacetpoint(&shloop, frontlist, misfrontlist, ptlist, conlist,
- viri, flipque);
+ viri, flipque, coarseflag, false);
}
shloop.sh = shellfacetraverse(subfaces);
}
// Continue if any Steiner point has been removed.
} while (unuverts > rmstein);
+ if (coarseflag) {
+ shellface **segsperverlist;
+ int *idx2seglist;
+ face seg1, seg2;
+ point e1, e2;
+ // Connecting collinear segments. Hence the segment vertices may be
+ // removed. In fact, this should be done by reconstructmesh().
+ makesegmentmap(idx2seglist, segsperverlist);
+ subsegs->traversalinit();
+ segloop.sh = shellfacetraverse(subsegs);
+ while (segloop.sh != (shellface *) NULL) {
+ for (i = 0; i < 2; i++) {
+ segloop.shver = i;
+ senext(segloop, nextseg);
+ spivotself(nextseg);
+ if ((nextseg.sh == dummysh) || (nextseg.sh > segloop.sh)) {
+ // No neighbor segment connection or haven't been processed yet.
+ pa = sdest(segloop);
+ j = pointmark(pa) - in->firstnumber;
+ if (idx2seglist[j + 1] - idx2seglist[j] == 2) {
+ // pa is shared by only two segments. Get the other one.
+ nextseg.sh = segsperverlist[idx2seglist[j]];
+ if (nextseg.sh == segloop.sh) {
+ nextseg.sh = segsperverlist[idx2seglist[j] + 1];
+ }
+ nextseg.shver = 0;
+ if (sorg(nextseg) != pa) sesymself(nextseg);
+ // Check if the two segments are collinear.
+ e1 = sorg(segloop);
+ e2 = sdest(nextseg);
+ if (iscollinear(e1, pa, e2, b->epsilon)) {
+ // Connect the two segments together.
+ if (b->verbose > 1) {
+ printf(" Glue two insegs (%d, %d) at %d.\n", pointmark(e1),
+ pointmark(e2), pointmark(pa));
+ }
+ senext(segloop, seg1);
+ senext2(nextseg, seg2);
+ sbond(seg1, seg2);
+ }
+ }
+ } // if (nextseg.sh == dummysh)
+ } // for (i = 0;
+ segloop.sh = shellfacetraverse(subsegs);
+ }
+ delete [] segsperverlist;
+ delete [] idx2seglist;
+ }
+
// Suppress Steiner points on segments.
do {
rmstein = unuverts;
@@ -23828,95 +26463,202 @@ void tetgenmesh::removesteiners()
segloop.sh = shellfacetraverse(subsegs);
while (segloop.sh != (shellface *) NULL) {
remflag = false;
- // Don't check the poinytype of pa, it may be a Steiner point but has
- // type NACUTEVERTEX due to splitting a type-3 segment.
- // if (pointtype(pa) == FREESEGVERTEX) {
- segloop.shver = 0;
- senext(segloop, nextseg);
- spivotself(nextseg);
- if (nextseg.sh != dummysh) {
- // Find a Steiner point p.
- pa = sdest(segloop); // For checking.
- nextseg.shver = 0;
- assert(sorg(nextseg) == pa);
- if (b->nobisect == 1) {
- // '-Y'. Remove p if it is on the hull.
- sstpivot(&segloop, &checktet);
- assert(checktet.tet != dummytet);
- pa = apex(checktet);
- do {
- if (!fnextself(checktet)) {
- // Meet a boundary face - p is on the hull.
- remflag = true; break;
+ // for (i = 0; i < 2; i++) {
+ // Don't check the poinytype of pa, it may be a Steiner point but
+ // has type NACUTEVERTEX due to splitting a type-3 segment.
+ segloop.shver = 0; // segloop.shver = i;
+ senext(segloop, nextseg);
+ spivotself(nextseg);
+ if (nextseg.sh != dummysh) {
+ pa = sdest(segloop); // p is going to be checked for removal.
+ nextseg.shver = 0;
+ if (sorg(nextseg) != pa) sesymself(nextseg);
+ assert(sorg(nextseg) == pa);
+ if (!coarseflag) {
+ // try to remove it if it is not an input point.
+ j = pointmark(pa) - in->firstnumber;
+ if (j >= in->numberofpoints) {
+ if (b->nobisect == 1) {
+ // '-Y'. Remove p if it is on the hull.
+ sstpivot(&segloop, &checktet);
+ assert(checktet.tet != dummytet);
+ pa = apex(checktet);
+ do {
+ if (!fnextself(checktet)) {
+ // Meet a boundary face - p is on the hull.
+ remflag = true; break;
+ }
+ } while (pa != apex(checktet));
+ } else {
+ // '-YY'. Remove p whatever it is on the hull or not.
+ remflag = true;
+ }
}
- } while (pa != apex(checktet));
- } else {
- // '-YY'. Remove p whatever it is on the hull or not.
- remflag = true;
- }
- }
+ } else {
+ // Check if this vertex can be coarsed.
+ if (b->nobisect == 0) {
+ if (b->metric) {
+ // assert(pa[pointmtrindex] > 0.0);
+ len = 0.0;
+ neipt = sorg(segloop);
+ for (j = 0; j < 2; j++) {
+ len += distance(pa, neipt);
+ /*// Is neipt inside the sparse ball of pa?
+ if (len < pa[pointmtrindex]) {
+ // Yes, the local of pa is too dense, corse it.
+ remflag = true; break;
+ } */
+ neipt = sdest(nextseg);
+ }
+ len /= 2.0;
+ // Carse it if the average edge lengh is small.
+ remflag = len < pa[pointmtrindex];
+ } else {
+ // Coarse it if (1) it is an input point and its pointmarker
+ // is zero, or (2) it is a Steiner point.
+ remflag = true;
+ j = pointmark(pa) - in->firstnumber;
+ if (j < in->numberofpoints) {
+ remflag = (in->pointmarkerlist[j] == 0);
+ }
+ } // if (b->metric)
+ } // if (b->nobisect == 0)
+ } // if (!coarseflag)
+ } // if (nextseg.sh != dummysh)
+ // if (remflag) break;
+ // } // for (i = 0; i < 2; i++)
if (remflag) {
suppresssegpoint(&segloop, spinshlist, newsegshlist, frontlist,
- misfrontlist, ptlist, conlist, viri, flipque);
+ misfrontlist, ptlist, conlist, viri, flipque, coarseflag, false);
}
segloop.sh = shellfacetraverse(subsegs);
}
// Continue if any Steiner point has been removed.
} while (unuverts > rmstein);
- if (relverts > 0) {
- // Suppress relocated points.
+ if ((relverts > 0) || coarseflag) {
+ worklist = new int[points->items + 1];
+ // Suppress relocated points & coarse free mesh points.
do {
+ // Initialize the work list. Each entry of the list counts how many
+ // times the point has been processed.
+ for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
rmstein = unuverts;
- points->traversalinit();
- pa = pointtraverse();
- while (pa != (point) NULL) {
- remflag = (pointtype(pa) == FREEVOLVERTEX);
+ tetrahedrons->traversalinit();
+ checktet.tet = tetrahedrontraverse();
+ while (checktet.tet != (tetrahedron *) NULL) {
+ remflag = false;
+ for (i = 0; i < 4; i++) {
+ pa = (point) checktet.tet[4 + i];
+ if (pointtype(pa) == FREEVOLVERTEX) {
+ // NOTE. Chenge the number 3 will change the number n of removed
+ // Steiner points. In my test, n is larger when it is 1. 3
+ // reduces n in a reasonable way (see example, mech_part,
+ // thepart), 5 results a larger n than 3 does. While the best
+ // result is no limit of this number, but it makes the code
+ // extremely slow.
+ if (worklist[pointmark(pa)] < 3) {
+ worklist[pointmark(pa)]++;
+ if (!coarseflag) {
+ // Remove p if it is a Steiner point.
+ if (pointmark(pa) >= (in->numberofpoints + in->firstnumber)) {
+ remflag = true;
+ }
+ } else {
+ if (b->metric) {
+ // assert(pa[pointmtrindex] > 0.0);
+ // Form the star of pa.
+ frontlist->append(&checktet);
+ formstarpolyhedron(pa, frontlist, ptlist, true);
+ len = 0.0;
+ for (j = 0; j < ptlist->len(); j++) {
+ neipt = * (point *)(* ptlist)[j];
+ len += distance(pa, neipt);
+ }
+ len /= ptlist->len();
+ // Carse it if the average edge length is small.
+ remflag = len < pa[pointmtrindex];
+ frontlist->clear();
+ ptlist->clear();
+ } else {
+ // Coarse it if (1) it is an input point and its pointmarker
+ // is zero, or (2) it is a Steiner point.
+ remflag = true;
+ j = pointmark(pa) - in->firstnumber;
+ if (j < in->numberofpoints) {
+ remflag = (in->pointmarkerlist[j] == 0);
+ }
+ } // if (b->metric)
+ } // if (!coarseflag)
+ if (remflag) break;
+ } // if (worklist[pointmark(pa)] == 0)
+ } // if (pointtype(pa) == FREEVOLVERTEX)
+ } // for (i = 0; i < 4; i++)
if (remflag) {
- suppressvolpoint(pa, frontlist, misfrontlist, ptlist, flipque);
+ findorg(&checktet, pa);
+ assert(org(checktet) == pa);
+ suppressvolpoint(&checktet, frontlist, misfrontlist, ptlist, flipque,
+ false);
}
- pa = pointtraverse();
+ checktet.tet = tetrahedrontraverse();
}
// Continue if any relocated point has been suppressed.
} while (unuverts > rmstein);
- }
- /* if ((relverts - suprelverts) > 0) {
- // Try to collapse relocated points.
- do {
- rmstein = unuverts;
- points->traversalinit();
- pa = pointtraverse();
- while (pa != (point) NULL) {
- remflag = (pointtype(pa) == FREEVOLVERTEX);
- if (remflag) {
- collapseedgepoint(pa, frontlist, misfrontlist, ptlist);
- }
- pa = pointtraverse();
+
+ // Smooth the unsuppressed points if it is not coarse mesh.
+ if (!coarseflag && (relverts > suprelverts)) {
+ if (b->verbose) {
+ printf(" Smoothing relocated points.\n");
}
- // Continue if any relocated point has been suppressed.
- } while (unuverts > rmstein);
- } */
+ for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
+ tetrahedrons->traversalinit();
+ checktet.tet = tetrahedrontraverse();
+ while (checktet.tet != (tetrahedron *) NULL) {
+ for (i = 0; i < 4; i++) {
+ pa = (point) checktet.tet[4 + i];
+ if (pointtype(pa) == FREEVOLVERTEX) {
+ if (worklist[pointmark(pa)] == 0) {
+ worklist[pointmark(pa)] = 1;
+ if (pointmark(pa) >= (in->numberofpoints + in->firstnumber)) {
+ // Smooth pa.
+ findorg(&checktet, pa);
+ frontlist->append(&checktet);
+ formstarpolyhedron(pa, frontlist, NULL, false);
+ smoothpoint(pa, NULL, NULL, frontlist, false, NULL);
+ frontlist->clear();
+ }
+ } // if (worklist[pointmark(pa)] == 0)
+ } // if (pointtype(pa) == FREEVOLVERTEX)
+ } // for (i = 0; i < 4; i++)
+ checktet.tet = tetrahedrontraverse();
+ }
+ }
+ delete [] worklist;
+ }
if (b->verbose > 0) {
- printf(" %d points removed from boundary.\n", unuverts - oldnum);
- if (relverts > 0) {
- printf(" %d points relocated into volume.\n", relverts);
- }
- if (suprelverts > 0) {
- printf(" %d relocated points are suppressed.\n", suprelverts);
- }
- if (collapverts > 0) {
- printf(" %d relocated points are collapsed.\n", collapverts);
- }
- if (unsupverts > 0) {
- printf(" %d points are unsuppressed.\n", unsupverts);
- }
- if (expcavcount > 0) {
- printf(" %d cavity corrections.\n", expcavcount);
+ if (!coarseflag) {
+ printf(" %d points removed from boundary", unuverts - oldnum);
+ if (expcavcount > 0) {
+ printf(" (%d cavity corrections)", expcavcount);
+ }
+ printf("\n");
+ if (relverts > 0) {
+ printf(" %d points relocated (%d suppressed, %d collapsed).\n",
+ relverts, suprelverts - collapverts, collapverts);
+ if (smoothvolverts > 0) {
+ printf(" %d points are smoothed.\n", smoothvolverts);
+ }
+ }
+ if (unsupverts > 0) {
+ printf(" !! %d points are unsuppressed.\n", unsupverts);
+ }
+ } else {
+ printf(" %d points are removed.\n", unuverts - oldnum);
}
}
-
+
// Delete work lists.
delete frontlist;
delete misfrontlist;
@@ -23932,10 +26674,6 @@ void tetgenmesh::removesteiners()
// End of boundary Steiner points removing routines
//
-//
-// Begin of mesh reconstruction routines
-//
-
///////////////////////////////////////////////////////////////////////////////
// //
// reconstructmesh() Reconstruct a tetrahedral mesh from a list of //
@@ -24029,12 +26767,12 @@ long tetgenmesh::reconstructmesh()
setdest(tetloop, tdest);
setapex(tetloop, tapex);
setoppo(tetloop, toppo);
- // Temporarily set the vertices be type VOLVERTEX, to indicate that
+ // Temporarily set the vertices be type FREEVOLVERTEX, to indicate that
// they belong to the mesh. These types may be changed later.
- setpointtype(torg, VOLVERTEX);
- setpointtype(tdest, VOLVERTEX);
- setpointtype(tapex, VOLVERTEX);
- setpointtype(toppo, VOLVERTEX);
+ setpointtype(torg, FREEVOLVERTEX);
+ setpointtype(tdest, FREEVOLVERTEX);
+ setpointtype(tapex, FREEVOLVERTEX);
+ setpointtype(toppo, FREEVOLVERTEX);
// Set element attributes if they exist.
for (j = 0; j < in->numberoftetrahedronattributes; j++) {
index = i * in->numberoftetrahedronattributes;
@@ -24106,7 +26844,7 @@ long tetgenmesh::reconstructmesh()
hullsize++; // It's a hull face.
// Bond this side to outer space.
dummytet[0] = encode(tetloop);
- if (in->pointmarkerlist != (int *) NULL) {
+ if ((in->pointmarkerlist != (int *) NULL) && !b->coarse) {
// Set its three corners's markers be boundary (hull) vertices.
if (in->pointmarkerlist[iorg] == 0) {
in->pointmarkerlist[iorg] = 1;
@@ -24231,11 +26969,11 @@ long tetgenmesh::reconstructmesh()
setsorg(subloop, torg);
setsdest(subloop, tdest);
setsapex(subloop, tapex);
- // Set the vertices be FACETVERTEX to indicate they belong to a
+ // Set the vertices be FREESUBVERTEX to indicate they belong to a
// facet of the domain. They may be changed later.
- setpointtype(torg, FACETVERTEX);
- setpointtype(tdest, FACETVERTEX);
- setpointtype(tapex, FACETVERTEX);
+ setpointtype(torg, FREESUBVERTEX);
+ setpointtype(tdest, FREESUBVERTEX);
+ setpointtype(tapex, FREESUBVERTEX);
tsbond(tetloop, subloop);
if (neightet.tet != dummytet) {
sesymself(subloop);
@@ -24353,11 +27091,10 @@ long tetgenmesh::reconstructmesh()
makeshellface(subsegs, &subseg);
setsorg(subseg, torg);
setsdest(subseg, tdest);
- // At the moment, all segment vertices have type FACETVERTEX.
- // They will be set to type ACUTEVERTEX or NACUTEVERTEX by
- // routine markacutevertices() later.
- // setpointtype(torg, SEGMENTVERTEX);
- // setpointtype(tdest, SEGMENTVERTEX);
+ // The two vertices have been marked as FREESUBVERTEX. Now mark
+ // them as NACUTEVERTEX.
+ setpointtype(torg, NACUTEVERTEX);
+ setpointtype(tdest, NACUTEVERTEX);
setshellmark(subseg, marker);
marker++;
// Bond all subfaces to this subsegment.
@@ -24483,24 +27220,6 @@ long tetgenmesh::reconstructmesh()
createsegpbcgrouptable();
}
- // if (b->quality && varconstraint) {
- // // Assign constraints on facets, segments, and nodes.
- // assignvarconstraints(idx2verlist);
- // }
-
- /*
- if (b->quality) {
- // Check and recover the Delaunay property.
- queue* flipqueue = new queue(sizeof(badface));
- checkdelaunay(0.0, flipqueue);
- if (!flipqueue->empty()) {
- // Call flip algorithm to recover Delaunayness.
- flip(flipqueue, NULL);
- }
- delete flipqueue;
- }
- */
-
delete markerlist;
delete neighshlist;
delete [] worklist;
@@ -24515,54 +27234,11 @@ long tetgenmesh::reconstructmesh()
///////////////////////////////////////////////////////////////////////////////
// //
-// intettest() Test if a point is inside (or on) a tetrahedron. //
-// //
-// Return TRUE if the point p and the tet t has one of the relations: (1) p //
-// is inside t; (2) p is on a faces of t; (3) p is on an edge of t; (4) p is //
-// a vertex of t. Otherwise, return FALSE. //
-// //
-// An relative tolerance is used to determine coplanar case when a face of t //
-// is on the hull. To bring back a boundary point inside the mesh. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::intettest(point testpt, triface* testtet, REAL eps)
-{
- triface checktet;
- point p1, p2, p3;
- REAL ori;
-
- testtet->ver = 0;
- for (testtet->loc = 0; testtet->loc < 4; testtet->loc++) {
- // Get points of the side f.
- p1 = org(*testtet);
- p2 = dest(*testtet);
- p3 = apex(*testtet);
- ori = orient3d(p1, p2, p3, testpt);
- if (ori > 0.0) {
- if (eps > 0.0) {
- // Is f on the hull.
- sym(*testtet, checktet);
- if (checktet.tet == dummytet) {
- if (iscoplanar(p1, p2, p3, testpt, ori, eps)) continue;
- }
- }
- // p is below f. outside.
- return false;
- }
- }
- testtet->loc = 0;
-
- return true;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// insertaddpoints() Insert additional points in 'in->addpointlist'. //
+// insertconstrainedpoints() Insert a list of constrained points. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::insertaddpoints()
+void tetgenmesh::insertconstrainedpoints(tetgenio *addio)
{
queue *flipqueue;
triface searchtet;
@@ -24570,6 +27246,8 @@ void tetgenmesh::insertaddpoints()
point newpoint;
enum locateresult loc;
REAL *attr;
+ bool insertflag;
+ int covertices, outvertices;
int index;
int i, j;
@@ -24579,117 +27257,134 @@ void tetgenmesh::insertaddpoints()
// Initialize 'flipqueue'.
flipqueue = new queue(sizeof(badface));
recenttet.tet = dummytet;
+ covertices = outvertices = 0;
index = 0;
- for (i = 0; i < in->numberofaddpoints; i++) {
+ for (i = 0; i < addio->numberofpoints; i++) {
// Create a newpoint.
makepoint(&newpoint);
- newpoint[0] = in->addpointlist[index++];
- newpoint[1] = in->addpointlist[index++];
- newpoint[2] = in->addpointlist[index++];
- // Copy new attributes (if available).
- if(in->addpointattributelist != (REAL *) NULL) {
- attr = in->addpointattributelist + in->numberofpointattributes * i;
- for (j = 0; j < in->numberofpointattributes; j++)
- newpoint[3 + j] = attr[j];
+ newpoint[0] = addio->pointlist[index++];
+ newpoint[1] = addio->pointlist[index++];
+ newpoint[2] = addio->pointlist[index++];
+ // 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) {
+ newpoint[3 + j] = attr[j];
+ }
+ }
}
// Find the location of the inserted point.
searchtet = recenttet;
loc = locate(newpoint, &searchtet);
- if (loc != OUTSIDE) {
- if (loc != ONVERTEX) {
- loc = adjustlocate(newpoint, &searchtet, loc, b->epsilon);
- }
+ if (loc != ONVERTEX) {
+ loc = adjustlocate(newpoint, &searchtet, loc, b->epsilon2);
}
if (loc == OUTSIDE) {
- // Perform a brute-force search.
- tetrahedrons->traversalinit();
- searchtet.tet = tetrahedrontraverse();
- while (searchtet.tet != (tetrahedron *) NULL) {
- if (intettest(newpoint, &searchtet, b->epsilon)) {
- loc = adjustlocate(newpoint, &searchtet, OUTSIDE, b->epsilon);
- assert(loc != OUTSIDE);
- break;
- }
+ loc = hullwalk(newpoint, &searchtet);
+ if (loc == OUTSIDE) {
+ // Perform a brute-force search.
+ tetrahedrons->traversalinit();
searchtet.tet = tetrahedrontraverse();
+ while (searchtet.tet != (tetrahedron *) NULL) {
+ loc = adjustlocate(newpoint, &searchtet, OUTSIDE, b->epsilon2);
+ if (loc != OUTSIDE) break;
+ searchtet.tet = tetrahedrontraverse();
+ }
}
}
// Insert the point if it not lies outside or on a vertex.
+ insertflag = true;
switch (loc) {
case INTETRAHEDRON:
- setpointtype(newpoint, VOLVERTEX);
+ setpointtype(newpoint, FREEVOLVERTEX);
splittetrahedron(newpoint, &searchtet, flipqueue);
break;
case ONFACE:
tspivot(searchtet, checksh);
if (checksh.sh != dummysh) {
- setpointtype(newpoint, FREESUBVERTEX);
+ // It is a boundary face. Don't insert it if -Y option is used.
+ if (b->nobisect) {
+ insertflag = false;
+ } else {
+ setpointtype(newpoint, FREESUBVERTEX);
+ }
} else {
setpointtype(newpoint, FREEVOLVERTEX);
}
- splittetface(newpoint, &searchtet, flipqueue);
+ if (insertflag) {
+ splittetface(newpoint, &searchtet, flipqueue);
+ }
break;
case ONEDGE:
tsspivot(&searchtet, &checkseg);
if (checkseg.sh != dummysh) {
- setpointtype(newpoint, FREESEGVERTEX);
- setpoint2sh(newpoint, sencode(checkseg));
+ if (b->nobisect) {
+ insertflag = false;
+ } else {
+ setpointtype(newpoint, FREESEGVERTEX);
+ setpoint2sh(newpoint, sencode(checkseg));
+ }
} else {
tspivot(searchtet, checksh);
if (checksh.sh != dummysh) {
- setpointtype(newpoint, FREESUBVERTEX);
+ if (b->nobisect) {
+ insertflag = false;
+ } else {
+ setpointtype(newpoint, FREESUBVERTEX);
+ }
} else {
- setpointtype(newpoint, VOLVERTEX);
+ setpointtype(newpoint, FREEVOLVERTEX);
}
}
- splittetedge(newpoint, &searchtet, flipqueue);
+ if (insertflag) {
+ splittetedge(newpoint, &searchtet, flipqueue);
+ }
break;
case ONVERTEX:
- if (!b->quiet) {
- printf("Warning: Point (%.17g, %.17g, %.17g) falls on a vertex.\n",
- newpoint[0], newpoint[1], newpoint[2]);
- }
+ insertflag = false;
+ covertices++;
break;
case OUTSIDE:
- if (!b->quiet) {
- printf("Warning: Point (%.17g, %.17g, %.17g) lies outside the mesh.\n",
- newpoint[0], newpoint[1], newpoint[2]);
- }
+ insertflag = false;
+ outvertices++;
break;
}
// Remember the tetrahedron for next point searching.
recenttet = searchtet;
- if (loc == ONVERTEX || loc == OUTSIDE) {
+ if (!insertflag) {
pointdealloc(newpoint);
} else {
flip(flipqueue, NULL);
}
}
+ if (b->verbose) {
+ if (covertices > 0) {
+ printf(" %d constrained points already exist.\n", covertices);
+ }
+ if (outvertices > 0) {
+ printf(" %d constrained points lie outside the mesh.\n", outvertices);
+ }
+ printf(" %d constrained points have been inserted.\n",
+ addio->numberofpoints - covertices - outvertices);
+ }
+
delete flipqueue;
}
-//
-// End of mesh reconstruction routines
-//
-
-//
-// Begin of background mesh routines
-//
-
///////////////////////////////////////////////////////////////////////////////
// //
-// interpolatepointsize() Set a point size by interpolating in bgmesh. //
-// //
-// This function first finds the tet t in background mesh contains 'pt, then //
-// set the size of 'pt' by interpolating the sizes of the corners of t. //
+// p1interpolatebgm() Set pt size by p^1 interpolation in background mesh.//
// //
-// 'bgmtet' is a suggesting tet in background mesh for locating 'pt' in it. //
-// It returns the tet containing 'pt'. //
+// On input, 'bgmtet' is a suggesting tet in background mesh for searching //
+// 'pt'. It returns the tet containing 'pt'. //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::interpolatepointsize(point pt, triface* bgmtet, long *scount)
+bool tetgenmesh::p1interpolatebgm(point pt, triface* bgmtet, long *scount)
{
point bgmpt[4];
enum locateresult loc;
@@ -24698,23 +27393,25 @@ bool tetgenmesh::interpolatepointsize(point pt, triface* bgmtet, long *scount)
loc = bgm->preciselocate(pt, bgmtet, bgm->tetrahedrons->items);
if (loc == OUTSIDE) {
- // Perform a brute-force search.
- if (scount) (*scount)++;
- bgm->tetrahedrons->traversalinit(); // in bgm
- bgmtet->tet = bgm->tetrahedrontraverse(); // in bgm
- while (bgmtet->tet != (tetrahedron *) NULL) {
- if (bgm->intettest(pt, bgmtet, b->epsilon)) {
- loc = bgm->adjustlocate(pt, bgmtet, OUTSIDE, b->epsilon);
- assert(loc != OUTSIDE);
- break;
+ loc = bgm->hullwalk(pt, bgmtet);
+ if (loc == OUTSIDE) {
+ // Perform a brute-force search.
+ if (b->verbose) {
+ printf("Warning: Global point location.\n");
}
+ if (scount) (*scount)++;
+ bgm->tetrahedrons->traversalinit(); // in bgm
bgmtet->tet = bgm->tetrahedrontraverse(); // in bgm
+ while (bgmtet->tet != (tetrahedron *) NULL) {
+ loc = bgm->adjustlocate(pt, bgmtet, OUTSIDE, b->epsilon);
+ if (loc != OUTSIDE) break;
+ bgmtet->tet = bgm->tetrahedrontraverse(); // in bgm
+ }
}
}
if (loc != OUTSIDE) {
// Let p remember t.
setpoint2bgmtet(pt, encode(*bgmtet)); // in m
- // Interpolate the point size.
// get the corners of t.
for (i = 0; i < 4; i++) bgmpt[i] = (point) bgmtet->tet[4 + i];
// Calculate the weighted coordinates of p in t.
@@ -24725,11 +27422,11 @@ bool tetgenmesh::interpolatepointsize(point pt, triface* bgmtet, long *scount)
volpt[3] = orient3d(bgmpt[0], bgmpt[1], bgmpt[2], pt);
for (i = 0; i < 4; i++) weights[i] = fabs(volpt[i] / vol);
// Interpolate the solution for p.
- for (i = 0; i < bgm->in->numberofpointattributes; i++) {
- pt[3 + i] = weights[0] * bgmpt[0][3 + i]
- + weights[1] * bgmpt[1][3 + i]
- + weights[2] * bgmpt[2][3 + i]
- + weights[3] * bgmpt[3][3 + i];
+ for (i = 0; i < bgm->in->numberofpointmtrs; i++) {
+ pt[pointmtrindex + i] = weights[0] * bgmpt[0][bgm->pointmtrindex + i]
+ + weights[1] * bgmpt[1][bgm->pointmtrindex + i]
+ + weights[2] * bgmpt[2][bgm->pointmtrindex + i]
+ + weights[3] * bgmpt[3][bgm->pointmtrindex + i];
}
} else {
setpoint2bgmtet(pt, (tetrahedron) NULL); // in m
@@ -24737,45 +27434,6 @@ bool tetgenmesh::interpolatepointsize(point pt, triface* bgmtet, long *scount)
return loc != OUTSIDE;
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// searchpointrecursive() Search point in background mesh recursively. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::searchpointrecursive(triface *curtet, long *scount)
-{
- triface searchtet, bgmtet;
- point searchpt;
- int idx, i;
-
- // Mark t as proceed.
- infect(*curtet);
- // Get the opposite point of t.
- searchpt = oppo(*curtet);
- // Has p already been processed?
- if (pointmark(searchpt) >= 0) {
- // Find the location of p.
- bgmtet = bgm->recenttet;
- if (interpolatepointsize(searchpt, &bgmtet, scount)) {
- bgm->recenttet = bgmtet; // in bgm
- }
- // Mark p as processed.
- idx = pointmark(searchpt);
- setpointmark(searchpt, -idx - 1);
- }
- // Recursively do the above searching.
- adjustedgering(*curtet, CCW);
- for (i = 0; i < 3; i++) {
- fnext(*curtet, searchtet);
- symself(searchtet);
- if ((searchtet.tet != dummytet) && (!infected(searchtet))) {
- searchpointrecursive(&searchtet, scount);
- }
- enextself(*curtet);
- }
-}
-
///////////////////////////////////////////////////////////////////////////////
// //
// interpolatesizemap() Interpolate the point sizes in the given size map.//
@@ -24791,46 +27449,78 @@ void tetgenmesh::searchpointrecursive(triface *curtet, long *scount)
void tetgenmesh::interpolatesizemap()
{
- triface tetloop, bgmtet;
+ list *adjtetlist;
+ triface tetloop, neightet, bgmtet;
point searchpt;
long scount;
- int idx, i;
+ int *worklist;
+ int sepcount;
+ int i;
if (b->verbose) {
printf(" Interpolating size map.\n");
}
+
+ worklist = new int[points->items + 1];
+ for (i = 0; i < points->items + 1; i++) worklist[i] = 0;
+ sepcount = 0;
scount = 0l;
tetrahedrons->traversalinit();
tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
if (!infected(tetloop)) {
- // Found an traversed tet t.
- tetloop.loc = 0;
- tetloop.ver = 0;
- // Locate the three vertices of current face of t.
- for (i = 0; i < 3; i++) {
- searchpt = org(tetloop);
- // Has p already been processed?
- if (pointmark(searchpt) >= 0) {
- // Interpolate p in background mesh.
+ // Find a new subdomain.
+ adjtetlist = new list(sizeof(triface), NULL, 1024);
+ infect(tetloop);
+ // Search the four corners in background mesh.
+ for (i = 0; i < 4; i++) {
+ searchpt = (point) tetloop.tet[4 + i];
+ // Mark the point for avoiding multiple searchings.
+ // assert(worklist[pointmark(searchpt)] == 0);
+ worklist[pointmark(searchpt)] = 1;
+ // Does it contain a pointer to bgm tet?
+ bgm->decode(point2bgmtet(searchpt), bgmtet);
+ if (bgm->isdead(&bgmtet)) {
bgmtet = bgm->recenttet;
- if (interpolatepointsize(searchpt, &bgmtet, &scount)) {
- bgm->recenttet = bgmtet;
+ }
+ if (p1interpolatebgm(searchpt, &bgmtet, &scount)) {
+ bgm->recenttet = bgmtet;
+ }
+ } // for (i = 0; i < 4; i++)
+ // Collect all tets in this region.
+ adjtetlist->append(&tetloop);
+ // Collect the tets in the subdomain.
+ for (i = 0; i < adjtetlist->len(); i++) {
+ tetloop = * (triface *)(* adjtetlist)[i];
+ for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
+ sym(tetloop, neightet);
+ if ((neightet.tet != dummytet) && !infected(neightet)) {
+ // Only need to search for the opposite point.
+ searchpt = oppo(neightet);
+ if (worklist[pointmark(searchpt)] == 0) {
+ worklist[pointmark(searchpt)] = 1;
+ decode(point2bgmtet(searchpt), bgmtet);
+ if (bgm->isdead(&bgmtet)) {
+ bgmtet = bgm->recenttet;
+ }
+ if (p1interpolatebgm(searchpt, &bgmtet, &scount)) {
+ bgm->recenttet = bgmtet;
+ }
+ }
+ infect(neightet);
+ adjtetlist->append(&neightet);
}
- // Mark p as processed.
- idx = pointmark(searchpt);
- setpointmark(searchpt, -idx - 1);
}
- enextself(tetloop);
}
- // Recursively do the above searching in the neighbring tets of t.
- searchpointrecursive(&tetloop, &scount);
- }
+ // Increase the number of separated domains.
+ sepcount++;
+ delete adjtetlist;
+ } // if (!infect())
tetloop.tet = tetrahedrontraverse();
}
- // Have searched all points. Unmark tets.
+ // Unmark all tets.
tetrahedrons->traversalinit();
tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
@@ -24838,390 +27528,653 @@ void tetgenmesh::interpolatesizemap()
uninfect(tetloop);
tetloop.tet = tetrahedrontraverse();
}
- // Unmark points.
- points->traversalinit(); // in m
- searchpt = pointtraverse(); // in m
- while (searchpt != (point) NULL) {
- idx = pointmark(searchpt);
- assert(idx < 0);
- setpointmark(searchpt, -(idx + 1));
- searchpt = pointtraverse(); // in m
- }
+ delete [] worklist;
#ifdef SELF_CHECK
- if (b->verbose) {
+ if (b->verbose && scount > 0l) {
printf(" %ld brute-force searches.\n", scount);
}
+ if (b->verbose && sepcount > 0) {
+ printf(" %d separate domains.\n", sepcount);
+ }
#endif
}
-//
-// End of of background mesh routines
-//
-
-//
-// Begin of Delaunay refinement routines
-//
-
///////////////////////////////////////////////////////////////////////////////
// //
-// calclocalfeaturesizes() Calculate local feature sizes of all points. //
+// duplicatebgmesh() Duplicate current mesh to background mesh. //
// //
-// Given a PLC X, the local feature size, lfs_d(x), of any point x in X is //
-// defined as the distance from x to two features of X which are of dim no //
-// large than d. For example, lfs_0(x) is the distance from x to the second //
-// nearest point of X. Let lfs(x) = lfs_2(x). //
+// Current mesh 'this' is copied into 'this->bgm'.Both meshes share the same //
+// input tetgenio object, 'this->in', same tetgenbehavior object 'this->b'. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::calclocalfeaturesizes()
+void tetgenmesh::duplicatebgmesh()
{
- list *tetlist, *verlist;
- tetrahedron tetptr;
- triface starttet;
- face checksh, checkseg;
- point ploop, ver[3];
- point ptlfslarge, ptlfssmall;
- enum locateresult loc;
- REAL prj[3], lfs[3], len;
- REAL lfslarge, lfssmall;
- int i, j;
+ triface tetloop, btetloop;
+ triface symtet, bsymtet;
+ face bhullsh, bneighsh;
+ point *idx2bplist, *tetptbaklist;
+ point ploop, bploop;
+ int idx, i;
- if (b->verbose > 0) {
- printf(" Calculating local feature sizes.\n");
+ if (!b->quiet) {
+ printf("Duplicating background mesh.\n");
}
- // Construct a map from points to tetrahedra.
- makepoint2tetmap();
- // Initialize working lists.
- tetlist = new list(sizeof(triface), NULL, 256);
- verlist = new list(sizeof(point *), NULL, 256);
- // Initialize bookkeeping variables.
- ptlfslarge = ptlfssmall = (point) NULL;
- lfslarge = lfssmall = 0.0;
+ // The background mesh itself has no background mesh.
+ // assert(bgm->bgm == (tetgenmesh *) NULL);
+ // The space for metric tensor should be allocated.
+ // assert(bgm->sizeoftensor > 0);
+ // Copy point list.
+ idx2bplist = new point[points->items + 1];
+ idx = in->firstnumber;
points->traversalinit();
ploop = pointtraverse();
while (ploop != (point) NULL) {
- tetptr = point2tet(ploop);
- // Only calculate lfs(p) if it is in the mesh.
- if (tetptr != (tetrahedron) NULL) {
- decode(tetptr, starttet);
- tetlist->append(&starttet);
- formstarpolyhedron(ploop, tetlist, verlist, true); // Form star(p).
- lfs[0] = lfs[1] = lfs[2] = longest;
- // Calculate lfs_0(p).
- for (i = 0; i < verlist->len(); i++) {
- ver[0] = * (point *)(* verlist)[i];
- len = distance(ploop, ver[0]);
- if (lfs[0] > len) lfs[0] = len;
- }
- // Claculate lfs_1(p).
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- starttet.ver = 0;
- for (j = 0; j < 3; j++) {
- tsspivot(&starttet, &checkseg);
- if (checkseg.sh != dummysh) {
- checkseg.shver = 0;
- ver[0] = sorg(checkseg);
- ver[1] = sdest(checkseg);
- projpt2edge(ploop, ver[0], ver[1], prj);
- loc = locateseg(prj, &checkseg);
- if (loc != OUTSIDE) {
- len = distance(ploop, prj);
- if (lfs[1] > len) lfs[1] = len;
- }
- }
- enextself(starttet);
- }
- }
- // Claculate lfs_2(p).
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- tspivot(starttet, checksh);
- if (checksh.sh != dummysh) {
- ver[0] = sorg(checksh);
- ver[1] = sdest(checksh);
- ver[2] = sapex(checksh);
- projpt2face(ploop, ver[0], ver[1], ver[2], prj);
- abovepoint = facetabovepointarray[shellmark(checksh)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(&checksh);
- }
- loc = locatesub(prj, &checksh, 1, b->epsilon);
- if (loc != OUTSIDE) {
- len = distance(ploop, prj);
- if (lfs[2] > len) lfs[2] = len;
- }
- }
- }
- // Decide lfs(p).
- ploop[pointlfsindex] = lfs[0];
- if (ploop[pointlfsindex] > lfs[1]) ploop[pointlfsindex] = lfs[1];
- if (ploop[pointlfsindex] > lfs[2]) ploop[pointlfsindex] = lfs[2];
- // Update statistics.
- if (ptlfslarge == (point) NULL) {
- ptlfslarge = ptlfssmall = ploop;
- lfslarge = lfssmall = ploop[pointlfsindex];
- } else {
- if (lfslarge < ploop[pointlfsindex]) {
- lfslarge = ploop[pointlfsindex];
- ptlfslarge = ploop;
- }
- if (lfssmall > ploop[pointlfsindex]) {
- lfssmall = ploop[pointlfsindex];
- ptlfssmall = ploop;
- }
+ bgm->makepoint(&bploop);
+ // Copy coordinates, attributes.
+ for (i = 0; i < 3 + in->numberofpointattributes; i++) {
+ bploop[i] = ploop[i];
+ }
+ // Transfer the metric tensor.
+ for (i = 0; i < bgm->sizeoftensor; i++) {
+ bploop[bgm->pointmtrindex + i] = ploop[pointmtrindex + i];
+ // Metric tensor should have a positive value.
+ if (bploop[bgm->pointmtrindex + i] <= 0.0) {
+ printf("Error: Point %d has non-positive size %g (-m option).\n",
+ bgm->pointmark(bploop), bploop[bgm->pointmtrindex + i]);
+ terminatetetgen(1);
}
- // Clear working lists.
- tetlist->clear();
- verlist->clear();
}
+ // Remember the point for searching.
+ idx2bplist[idx++] = bploop;
ploop = pointtraverse();
}
- if (b->verbose > 1) {
- printf(" smallest lfs = %g (%d).\n", lfssmall, pointmark(ptlfssmall));
- printf(" largest lfs = %g (%d).\n", lfslarge, pointmark(ptlfslarge));
+ // Copy tetrahedra list.
+ tetptbaklist = new point[tetrahedrons->items + 1];
+ idx = in->firstnumber;
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ bgm->maketetrahedron(&btetloop);
+ // Set the four corners.
+ for (i = 0; i < 4; i++) {
+ ploop = (point) tetloop.tet[4 + i];
+ bploop = idx2bplist[pointmark(ploop)];
+ btetloop.tet[4 + i] = (tetrahedron) bploop;
+ }
+ // Remember the tet for setting neighbor connections.
+ tetptbaklist[idx++] = (point) tetloop.tet[4];
+ tetloop.tet[4] = (tetrahedron) btetloop.tet;
+ tetloop.tet = tetrahedrontraverse();
}
- delete tetlist;
- delete verlist;
+ // Set the connections between background tetrahedra. Create background
+ // hull subfaces. Create the map of point-to-bgmtet.
+ idx = in->firstnumber;
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ // Get the corresponding background tet.
+ btetloop.tet = (tetrahedron *) tetloop.tet[4];
+ // Set the four neighbors.
+ for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
+ btetloop.loc = tetloop.loc;
+ sym(tetloop, symtet);
+ if ((symtet.tet != dummytet) && (symtet.tet > tetloop.tet)) {
+ // Operate on the un-connected interior face.
+ bsymtet.tet = (tetrahedron *) symtet.tet[4]; // The saved bgm tet.
+ bsymtet.loc = symtet.loc;
+ bgm->bond(btetloop, bsymtet);
+ } else if (symtet.tet == dummytet) {
+ // Create a subface in background mesh.
+ bgm->makeshellface(bgm->subfaces, &bhullsh);
+ bgm->adjustedgering(btetloop, CCW); // face to inside.
+ bgm->setsorg(bhullsh, bgm->org(btetloop));
+ bgm->setsdest(bhullsh, bgm->dest(btetloop));
+ bgm->setsapex(bhullsh, bgm->apex(btetloop));
+ bgm->tsbond(btetloop, bhullsh);
+ // Remember a hull face for point location.
+ bgm->dummytet[0] = bgm->encode(btetloop);
+ }
+ }
+ // Restore the backup tet point.
+ tetloop.tet[4] = (tetrahedron) tetptbaklist[idx++];
+ // Make the point-to-bgmtet map for size interpolation.
+ btetloop.loc = 0;
+ for (i = 0; i < 4; i++) {
+ ploop = (point) tetloop.tet[4 + i];
+ setpoint2bgmtet(ploop, bgm->encode(btetloop));
+ }
+ // Go to the next tet, btet.
+ tetloop.tet = tetrahedrontraverse();
+ }
+
+ // Connect bgm hull subfaces. Note: all hull subfaces form a 2-manifold.
+ bgm->subfaces->traversalinit();
+ bhullsh.sh = bgm->shellfacetraverse(bgm->subfaces);
+ while (bhullsh.sh != (shellface *) NULL) {
+ bhullsh.shver = 0;
+ bgm->stpivot(bhullsh, btetloop);
+ assert(btetloop.tet != bgm->dummytet);
+ bgm->adjustedgering(btetloop, CCW);
+ for (i = 0; i < 3; i++) {
+ bgm->spivot(bhullsh, bneighsh);
+ if (bneighsh.sh == bgm->dummysh) {
+ // This side is open, operate on it.
+ bsymtet = btetloop;
+ while (bgm->fnextself(bsymtet));
+ bgm->tspivot(bsymtet, bneighsh);
+ bgm->findedge(&bneighsh, bgm->sdest(bhullsh), bgm->sorg(bhullsh));
+ bgm->sbond(bhullsh, bneighsh);
+ }
+ bgm->enextself(btetloop);
+ bgm->senextself(bhullsh);
+ }
+ bhullsh.sh = bgm->shellfacetraverse(bgm->subfaces);
+ }
+
+ delete [] tetptbaklist;
+ delete [] idx2bplist;
}
+//
+// Begin of Delaunay refinement routines
+//
+
///////////////////////////////////////////////////////////////////////////////
// //
-// marksharpsubsegs() Mark all sharp subsegments. //
+// marksharpsegments() Mark sharp segments. //
+// //
+// A segment s is called sharp if it is in one of the two cases: //
+// (1) There is a segment s' intersecting with s. The internal angle (*) //
+// between s and s' is acute. //
+// (2) There are two facets f1 and f2 intersecting at s. The internal //
+// dihedral angle (*) between f1 and f2 is acute. //
+// This routine finds the sharp segments and marked them as type SHARP. //
+// The minimum angle between segments (minfaceang) and the minimum dihedral //
+// angle between facets (minfacetdihed) are calulcated. //
// //
-// A segment is sharp if it is between two facets that form a small dihedral //
-// angle (< 'dihedbound', given in degrees). It is marked as SHARP. //
+// (*) The internal angle (or dihedral) bewteen two features means the angle //
+// inside the mesh domain. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::marksharpsubsegs(REAL dihedbound)
+void tetgenmesh::marksharpsegments(REAL sharpangle)
{
- list *spinshlist;
triface adjtet;
face startsh, spinsh, neighsh;
face segloop, prevseg, nextseg;
point eorg, edest;
- enum shestype stype;
- REAL angle, smallang;
+ REAL ang, smallang;
bool issharp;
- int scount;
- int i;
+ int sharpsegcount;
if (b->verbose > 0) {
- printf(" Marking sharp subsegments.\n");
+ printf(" Marking sharp segments.\n");
+ }
+
+ smallang = sharpangle * PI / 180.;
+ sharpsegcount = 0;
+ eorg = edest = (point) NULL; // To avoid compiler warnings.
+
+ // A segment s may have been split into many subsegments. Operate the one
+ // which contains the origin of s. Then mark the rest of subsegments.
+ subsegs->traversalinit();
+ segloop.sh = shellfacetraverse(subsegs);
+ while (segloop.sh != (shellface *) NULL) {
+ segloop.shver = 0;
+ senext2(segloop, prevseg);
+ spivotself(prevseg);
+ if (prevseg.sh == dummysh) {
+ // Operate on this seg s.
+ assert(shelltype(segloop) != SHARP); // It should be unmarked.
+ issharp = false;
+ spivot(segloop, startsh);
+ if (startsh.sh != dummysh) {
+ // First check if two facets form an acute dihedral angle at s.
+ eorg = sorg(segloop);
+ edest = sdest(segloop);
+ spinsh = startsh;
+ do {
+ if (sorg(spinsh) != eorg) {
+ sesymself(spinsh);
+ }
+ // Only do test when the spinsh is faceing inward.
+ stpivot(spinsh, adjtet);
+ if (adjtet.tet != dummytet) {
+ // Get the subface on the adjacent facet.
+ spivot(spinsh, neighsh);
+ // Do not calculate if it is self-bonded.
+ if (neighsh.sh != spinsh.sh) {
+ // Calculate the dihedral angle between the two subfaces.
+ ang = facedihedral(eorg, edest, sapex(spinsh), sapex(neighsh));
+ // Only do check if a sharp angle has not been found.
+ if (!issharp) issharp = (ang < smallang);
+ // Remember the smallest facet dihedral angle.
+ minfacetdihed = minfacetdihed < ang ? minfacetdihed : ang;
+ }
+ }
+ // Go to the next facet.
+ spivotself(spinsh);
+ } while (spinsh.sh != startsh.sh);
+ // if (!issharp) {
+ // Second check if s forms an acute angle with another seg.
+ spinsh = startsh;
+ do {
+ if (sorg(spinsh) != eorg) {
+ sesymself(spinsh);
+ }
+ // Calculate the angle between s and s' of this facet.
+ neighsh = spinsh;
+ // Rotate edges around 'eorg' until meeting another seg s'. Such
+ // seg (s') must exist since the facet is segment-bounded.
+ // The sum of the angles of faces at 'eorg' gives the internal
+ // angle between the two segments.
+ ang = 0.0;
+ do {
+ ang += interiorangle(eorg, sdest(neighsh), sapex(neighsh), NULL);
+ senext2self(neighsh);
+ sspivot(neighsh, nextseg);
+ if (nextseg.sh != dummysh) break;
+ // Go to the next coplanar subface.
+ spivotself(neighsh);
+ assert(neighsh.sh != dummysh);
+ if (sorg(neighsh) != eorg) {
+ sesymself(neighsh);
+ }
+ } while (true);
+ // Only do check if a sharp angle has not been found.
+ if (!issharp) issharp = (ang < smallang);
+ // Remember the smallest input face angle.
+ minfaceang = minfaceang < ang ? minfaceang : ang;
+ // Go to the next facet.
+ spivotself(spinsh);
+ } while (spinsh.sh != startsh.sh);
+ // }
+ }
+ if (issharp) {
+ setshelltype(segloop, SHARP);
+ // Set the type for all subsegments at forwards.
+ senext(segloop, nextseg);
+ spivotself(nextseg);
+ while (nextseg.sh != dummysh) {
+ nextseg.shver = 0;
+ setshelltype(nextseg, SHARP);
+ senextself(nextseg);
+ spivotself(nextseg);
+ }
+ sharpsegcount++;
+ }
+ }
+ segloop.sh = shellfacetraverse(subsegs);
}
- smallang = dihedbound * PI / 180.;
- scount = 0;
- eorg = edest = (point) NULL; // avoid compilation warnings.
- // Initial working list.
- spinshlist = new list(sizeof(face), NULL, 256);
-
- // A segment s may be split into many subsegments. Operate the one which
- // contains the origin of s. Then mark the rest of subsegments.
+ // So far we have marked all segments which have an acute dihedral angle
+ // or whose ORIGINs have an acute angle. In the un-marked subsegments,
+ // there are possible ones whose DESTINATIONs have an acute angle.
subsegs->traversalinit();
segloop.sh = shellfacetraverse(subsegs);
while (segloop.sh != (shellface *) NULL) {
+ // Only operate if s is non-sharp and contains the dest.
segloop.shver = 0;
- senext2(segloop, prevseg);
- spivotself(prevseg);
- if (prevseg.sh == dummysh) {
- // Operate on this seg.
- issharp = false;
- segloop.shver = 0;
+ senext(segloop, nextseg);
+ spivotself(nextseg);
+ // if ((nextseg.sh == dummysh) && (shelltype(segloop) != SHARP)) {
+ if (nextseg.sh == dummysh) {
+ // issharp = false;
+ issharp = (shelltype(segloop) == SHARP);
spivot(segloop, startsh);
if (startsh.sh != dummysh) {
- spivot(startsh, spinsh);
- if (spinsh.sh != startsh.sh) {
- // This subface is not self-bonded.
- eorg = sorg(segloop);
- edest = sdest(segloop);
- // Get all incident subfaces around the seg.
- spinsh = startsh;
+ // Check if s forms an acute angle with another seg.
+ eorg = sdest(segloop);
+ spinsh = startsh;
+ do {
+ if (sorg(spinsh) != eorg) {
+ sesymself(spinsh);
+ }
+ // Calculate the angle between s and s' of this facet.
+ neighsh = spinsh;
+ ang = 0.0;
do {
- if (sorg(spinsh) != eorg) {
- sesymself(spinsh);
+ ang += interiorangle(eorg, sdest(neighsh), sapex(neighsh), NULL);
+ senext2self(neighsh);
+ sspivot(neighsh, nextseg);
+ if (nextseg.sh != dummysh) break;
+ // Go to the next coplanar subface.
+ spivotself(neighsh);
+ assert(neighsh.sh != dummysh);
+ if (sorg(neighsh) != eorg) {
+ sesymself(neighsh);
}
- spinshlist->append(&spinsh);
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
+ } while (true);
+ // Only do check if a sharp angle has not been found.
+ if (!issharp) issharp = (ang < smallang);
+ // Remember the smallest input face angle.
+ minfaceang = minfaceang < ang ? minfaceang : ang;
+ // Go to the next facet.
+ spivotself(spinsh);
+ } while (spinsh.sh != startsh.sh);
+ }
+ if (issharp) {
+ setshelltype(segloop, SHARP);
+ // Set the type for all subsegments at backwards.
+ senext2(segloop, prevseg);
+ spivotself(prevseg);
+ while (prevseg.sh != dummysh) {
+ prevseg.shver = 0;
+ setshelltype(prevseg, SHARP);
+ senext2self(prevseg);
+ spivotself(prevseg);
}
- // Check the pair of adjacent subfaces for small angle.
- spinsh = * (face *)(* spinshlist)[0];
- for (i = 1; i <= spinshlist->len() && !issharp; i++) {
- if (i == spinshlist->len()) {
- neighsh = * (face *)(* spinshlist)[0];
- } else {
- neighsh = * (face *)(* spinshlist)[i];
- }
- // Only do test when the spinsh is faceing inward.
- stpivot(spinsh, adjtet);
- if (adjtet.tet != dummytet) {
- angle = facedihedral(eorg, edest, sapex(spinsh), sapex(neighsh));
- issharp = angle < smallang;
- }
- spinsh = neighsh;
- }
- spinshlist->clear();
- }
- // Set type for this segment (inclusing subsegments).
- stype = issharp ? SHARP : NSHARPNSKINNY;
- scount += issharp ? 1 : 0;
- setshelltype(segloop, stype);
- senext(segloop, nextseg);
- spivotself(nextseg);
- while (nextseg.sh != dummysh) {
- nextseg.shver = 0;
- setshelltype(nextseg, stype);
- senextself(nextseg);
- spivotself(nextseg);
+ sharpsegcount++;
}
}
segloop.sh = shellfacetraverse(subsegs);
- }
+ }
- if (b->verbose > 0) {
- printf(" %d sharp segments.\n", scount);
+ if ((b->verbose > 0) && (sharpsegcount > 0)) {
+ printf(" %d sharp segments.\n", sharpsegcount);
}
- delete spinshlist;
}
///////////////////////////////////////////////////////////////////////////////
// //
-// markskinnysubfaces() Mark all skinny subfaces. //
+// decidefeaturepointsizes() Decide the sizes for all feature points. //
// //
-// A subface is skinny if it has an angle smaller than 'anglebound' and the //
-// two edges form the angle are both segments. Such subface is not be able //
-// to refine. It will be marked as type SKINNY. //
+// A feature point is a point on a sharp segment. Every feature point p will //
+// be assigned a positive size which is the radius of the protecting ball. //
// //
-// This procedure operates in two phases. The first phase finds some skinny //
-// subfaces by checking the angles of subfaces. The second phase finds all //
-// skinny subfaces by a neighbor-first search. //
+// The size of a feature point may be specified by one of the following ways://
+// (1) directly specifying on an input vertex (by using .mtr file); //
+// (2) imposing a fixed maximal volume constraint ('-a__' option); //
+// (3) imposing a maximal volume constraint in a region ('-a' option); //
+// (4) imposing a maximal area constraint on a facet (in .var file); //
+// (5) imposing a maximal length constraint on a segment (in .var file); //
+// (6) combining (1) - (5). //
+// (7) automatically deriving a size if none of (1) - (6) is available. //
+// In case (7),the size of p is set to be the smallest edge length among all //
+// edges connecting at p. The final size of p is the minimum of (1) - (7). //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::markskinnysubfaces(REAL anglebound)
+void tetgenmesh::decidefeaturepointsizes()
{
- list *skinnyshlist;
- face subloop, checksub;
- face startsh, neighsh;
- face seg1, seg2, checkseg;
- point pa, pb, pc;
- enum shestype shty;
- REAL smallang, angle;
- int i, j;
+ list *tetlist, *verlist;
+ shellface **segsperverlist;
+ triface starttet;
+ face shloop;
+ face checkseg, prevseg, nextseg, testseg;
+ point ploop, adjpt, e1, e2;
+ REAL lfs_0, len, vol, maxlen, varlen;
+ bool isfeature;
+ int *idx2seglist;
+ int featurecount;
+ int idx, i, j;
if (b->verbose > 0) {
- printf(" Marking skinny subfaces.\n");
+ printf(" Deciding feature-point sizes.\n");
}
- smallang = anglebound * PI / 180.;
- // Initial working list.
- skinnyshlist = new list(sizeof(face), NULL, subfaces->items);
+ // Constructing a map from vertices to segments.
+ makesegmentmap(idx2seglist, segsperverlist);
+ // Initialize working lists.
+ tetlist = new list(sizeof(triface), NULL, 256);
+ verlist = new list(sizeof(point *), NULL, 256);
- // Loop the set of subfaces, collect some skinny ones.
- subfaces->traversalinit();
- subloop.sh = shellfacetraverse(subfaces);
- while (subloop.sh != (shellface *) NULL) {
- // Check the three angles of subloop;
- for (i = 0; i < 3; i++) {
- sspivot(subloop, seg1);
- if (seg1.sh != dummysh) {
- senext2(subloop, checksub);
- sspivot(checksub, seg2);
- if (seg2.sh != dummysh) {
- pa = sorg(subloop);
- pb = sdest(subloop);
- pc = sapex(subloop);
- angle = interiorangle(pa, pb, pc, NULL);
- if (angle < smallang) {
- // It is skinny!
- setshelltype(subloop, SKINNY);
- skinnyshlist->append(&subloop);
- break;
- }
+ if (b->fixedvolume) {
+ // A fixed volume constraint is imposed. This gives an upper bound of
+ // the maximal radius of the protect ball of a vertex.
+ maxlen = pow(6.0 * b->maxvolume, 1.0/3.0);
+ }
+
+ if (!b->refine) {
+ // Initially correct types for Steiner points.
+ featurecount = 0;
+ points->traversalinit();
+ ploop = pointtraverse();
+ while (ploop != (point) NULL) {
+ if (pointtype(ploop) == NACUTEVERTEX) {
+ if (point2sh(ploop) != (shellface) NULL) {
+ setpointtype(ploop, FREESEGVERTEX);
+ featurecount++;
}
}
- senextself(subloop);
+ ploop = pointtraverse();
}
- subloop.sh = shellfacetraverse(subfaces);
+#ifdef SELF_CHECK
+ if ((b->verbose > 0) && (featurecount > 0)) {
+ printf(" %d Steiner points correction.\n", featurecount);
+ }
+#endif
}
- // Next finds all skinny subfaces.
- for (i = 0; i < skinnyshlist->len(); i++) {
- startsh = * (face *)(* skinnyshlist)[i];
- shty = shelltype(startsh);
- for (j = 0; j < 3; j++) {
- sspivot(startsh, checkseg);
- if (checkseg.sh == dummysh) {
- spivot(startsh, neighsh);
- if (shelltype(neighsh) != shty) {
- setshelltype(neighsh, shty);
- skinnyshlist->append(&neighsh);
+ // 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.
+ featurecount = 0;
+ points->traversalinit();
+ ploop = pointtraverse();
+ while (ploop != (point) NULL) {
+ if (pointtype(ploop) != FREESEGVERTEX) {
+ // Is p a feature point?
+ isfeature = false;
+ idx = pointmark(ploop) - in->firstnumber;
+ for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isfeature; i++) {
+ checkseg.sh = segsperverlist[i];
+ isfeature = (shelltype(checkseg) == SHARP);
+ }
+ // Decide the size of p if it is on a sharp segment.
+ if (isfeature) {
+ // Find a tet containing p (checkseg is a sharp seg which contains p).
+ sstpivot(&checkseg, &starttet);
+ // Form star(p).
+ tetlist->append(&starttet);
+ formstarpolyhedron(ploop, tetlist, verlist, true);
+ // Decide the size for p if no input size is given on input.
+ if (ploop[pointmtrindex] == 0.0) {
+ // Calculate lfs_0(p).
+ lfs_0 = longest;
+ for (i = 0; i < verlist->len(); i++) {
+ adjpt = * (point *)(* verlist)[i];
+ if (pointtype(adjpt) == FREESEGVERTEX) {
+ // A Steiner point q. Find the seg it lies on.
+ sdecode(point2sh(adjpt), checkseg);
+ assert(checkseg.sh != dummysh);
+ checkseg.shver = 0;
+ // Find the origin of this seg.
+ prevseg = checkseg;
+ do {
+ senext2(prevseg, testseg);
+ spivotself(testseg);
+ if (testseg.sh == dummysh) break;
+ prevseg = testseg; // Go to the previous subseg.
+ prevseg.shver = 0;
+ } while (true);
+ // Find the dest of this seg.
+ nextseg = checkseg;
+ do {
+ senext(nextseg, testseg);
+ spivotself(testseg);
+ if (testseg.sh == dummysh) break;
+ nextseg = testseg; // Go to the next subseg.
+ nextseg.shver = 0;
+ } while (true);
+ e1 = sorg(prevseg);
+ e2 = sdest(nextseg);
+ // Check if p is the origin or the dest of this seg.
+ if (ploop == e1) {
+ // Set q to be the dest of this seg.
+ adjpt = e2;
+ } else if (ploop == e2) {
+ // Set q to be the org of this seg.
+ adjpt = e1;
+ }
+ }
+ len = distance(ploop, adjpt);
+ if (lfs_0 > len) lfs_0 = len;
+ }
+ ploop[pointmtrindex] = lfs_0;
+ }
+ if (b->fixedvolume) {
+ // A fixed volume constraint is imposed. Adjust H(p) <= maxlen.
+ if (ploop[pointmtrindex] > maxlen) {
+ ploop[pointmtrindex] = maxlen;
+ }
+ }
+ if (b->varvolume) {
+ // Variant volume constraints are imposed. Adjust H(p) <= varlen.
+ for (i = 0; i < tetlist->len(); i++) {
+ starttet = * (triface *)(* tetlist)[i];
+ vol = volumebound(starttet.tet);
+ if (vol > 0.0) {
+ varlen = pow(6 * vol, 1.0/3.0);
+ if (ploop[pointmtrindex] > varlen) {
+ ploop[pointmtrindex] = varlen;
+ }
+ }
+ }
}
+ // Clear working lists.
+ tetlist->clear();
+ verlist->clear();
+ featurecount++;
+ } else {
+ // NO feature point, set the size of p be zero.
+ ploop[pointmtrindex] = 0.0;
}
- senextself(startsh);
- }
+ } // if (pointtype(ploop) != FREESEGVERTEX) {
+ ploop = pointtraverse();
}
if (b->verbose > 0) {
- printf(" %d skinny subfaces.\n", skinnyshlist->len());
+ printf(" %d feature points.\n", featurecount);
}
- delete skinnyshlist;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// enqueuebadtet() Add a tetrahedron into the queue. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::enqueuebadtet(triface* testtet, REAL ratio2, REAL* cent)
-{
- badface *newbadtet;
- int queuenumber;
- int i;
- // Allocate space for the bad tetrahedron.
- newbadtet = (badface *) badtetrahedrons->alloc();
- newbadtet->tt = *testtet;
- newbadtet->key = ratio2;
- if (cent != NULL) {
- for (i = 0; i < 3; i++) newbadtet->cent[i] = cent[i];
- } else {
- for (i = 0; i < 3; i++) newbadtet->cent[i] = 0.0;
- }
- newbadtet->forg = org(*testtet);
- newbadtet->fdest = dest(*testtet);
- newbadtet->fapex = apex(*testtet);
- newbadtet->foppo = oppo(*testtet);
- newbadtet->nextitem = (badface *) NULL;
- // Determine the appropriate queue to put the bad tetrahedron into.
- if (ratio2 > b->goodratio) {
- queuenumber = (int) ((ratio2 - b->goodratio) / 0.5);
- // 'queuenumber' may overflow (negative) caused by a very large ratio.
- if ((queuenumber > 63) || (queuenumber < 0)) {
- queuenumber = 63;
+ if (!b->refine) {
+ // 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.
+ featurecount = 0;
+ points->traversalinit();
+ ploop = pointtraverse();
+ while (ploop != (point) NULL) {
+ if (pointtype(ploop) == FREESEGVERTEX) {
+ if (ploop[pointmtrindex] == 0.0) {
+ sdecode(point2sh(ploop), checkseg);
+ assert(checkseg.sh != dummysh);
+ if (shelltype(checkseg) == SHARP) {
+ checkseg.shver = 0;
+ // Find the origin of this seg.
+ prevseg = checkseg;
+ do {
+ senext2(prevseg, testseg);
+ spivotself(testseg);
+ if (testseg.sh == dummysh) break;
+ prevseg = testseg; // Go the previous subseg.
+ prevseg.shver = 0;
+ } while (true);
+ // Find the dest of this seg.
+ nextseg = checkseg;
+ do {
+ senext(nextseg, testseg);
+ spivotself(testseg);
+ if (testseg.sh == dummysh) break;
+ nextseg = testseg; // Go the next subseg.
+ nextseg.shver = 0;
+ } while (true);
+ e1 = sorg(prevseg);
+ e2 = sdest(nextseg);
+ len = distance(e1, e2);
+ lfs_0 = distance(e1, ploop);
+ // The following assert() happens when -Y option is used.
+ if (b->nobisect == 0) {
+ assert(lfs_0 < len);
+ }
+ ploop[pointmtrindex] = e1[pointmtrindex]
+ + (lfs_0 / len) * (e2[pointmtrindex] - e1[pointmtrindex]);
+ featurecount++;
+ } else {
+ // NO feature point, set the size of p be zero.
+ ploop[pointmtrindex] = 0.0;
+ } // if (shelltype(checkseg) == SHARP)
+ } // if (ploop[pointmtrindex] == 0.0)
+ } // if (pointtype(ploop) != FREESEGVERTEX)
+ ploop = pointtraverse();
+ }
+ if ((b->verbose > 0) && (featurecount > 0)) {
+ printf(" %d Steiner feature points.\n", featurecount);
}
- } else {
- // It's not a bad ratio; put the tet in the lowest-priority queue.
- queuenumber = 0;
- }
- // Add the tetrahedron to the end of a queue.
- *tetquetail[queuenumber] = newbadtet;
- // Maintain a pointer to the NULL pointer at the end of the queue.
- tetquetail[queuenumber] = &newbadtet->nextitem;
- if (b->verbose > 2) {
- printf(" Queueing bad tet: (%d, %d, %d, %d), ratio %g, qnum %d.\n",
- pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
- pointmark(newbadtet->fapex), pointmark(newbadtet->foppo),
- sqrt(ratio2), queuenumber);
}
+
+ if (varconstraint) {
+ // A .var file exists. Adjust feature sizes.
+ if (in->facetconstraintlist) {
+ // Have facet area constrains.
+ subfaces->traversalinit();
+ shloop.sh = shellfacetraverse(subfaces);
+ while (shloop.sh != (shellface *) NULL) {
+ varlen = areabound(shloop);
+ if (varlen > 0.0) {
+ // Check if the three corners are feature points.
+ varlen = sqrt(varlen);
+ for (j = 0; j < 3; j++) {
+ ploop = (point) shloop.sh[3 + j];
+ isfeature = false;
+ idx = pointmark(ploop) - in->firstnumber;
+ for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isfeature;
+ i++) {
+ checkseg.sh = segsperverlist[i];
+ isfeature = (shelltype(checkseg) == SHARP);
+ }
+ if (isfeature) {
+ assert(ploop[pointmtrindex] > 0.0);
+ if (ploop[pointmtrindex] > varlen) {
+ ploop[pointmtrindex] = varlen;
+ }
+ }
+ } // for (j = 0; j < 3; j++)
+ }
+ shloop.sh = shellfacetraverse(subfaces);
+ }
+ }
+ if (in->segmentconstraintlist) {
+ // Have facet area constrains.
+ subsegs->traversalinit();
+ shloop.sh = shellfacetraverse(subsegs);
+ while (shloop.sh != (shellface *) NULL) {
+ varlen = areabound(shloop);
+ if (varlen > 0.0) {
+ // Check if the two endpoints are feature points.
+ for (j = 0; j < 2; j++) {
+ ploop = (point) shloop.sh[3 + j];
+ isfeature = false;
+ idx = pointmark(ploop) - in->firstnumber;
+ for (i = idx2seglist[idx]; i < idx2seglist[idx + 1] && !isfeature;
+ i++) {
+ checkseg.sh = segsperverlist[i];
+ isfeature = (shelltype(checkseg) == SHARP);
+ }
+ if (isfeature) {
+ assert(ploop[pointmtrindex] > 0.0);
+ if (ploop[pointmtrindex] > varlen) {
+ ploop[pointmtrindex] = varlen;
+ }
+ }
+ } // for (j = 0; j < 2; j++)
+ }
+ shloop.sh = shellfacetraverse(subsegs);
+ }
+ }
+ } // if (varconstraint)
+
+ delete [] segsperverlist;
+ delete [] idx2seglist;
+ delete tetlist;
+ delete verlist;
}
///////////////////////////////////////////////////////////////////////////////
@@ -25242,11 +28195,7 @@ void tetgenmesh::enqueueencsub(face* testsub, point encpt, int quenumber,
encsub->fdest = sdest(*testsub);
encsub->fapex = sapex(*testsub);
encsub->foppo = (point) encpt;
- if (quenumber == 2) {
- for (i = 0; i < 3; i++) encsub->cent[i] = 0.0;
- } else {
- for (i = 0; i < 3; i++) encsub->cent[i] = cent[i];
- }
+ for (i = 0; i < 3; i++) encsub->cent[i] = cent[i];
encsub->nextitem = (badface *) NULL;
// Set the pointer of 'encsubseg' into 'testsub'. It has two purposes:
// (1) We can regonize it is encroached; (2) It is uniquely queued.
@@ -25263,25 +28212,26 @@ void tetgenmesh::enqueueencsub(face* testsub, point encpt, int quenumber,
///////////////////////////////////////////////////////////////////////////////
// //
-// dequeuebadtet() Remove a tetrahedron from the front of the queue. //
+// dequeueencsub() Remove an enc-subface from the front of the queue. //
// //
///////////////////////////////////////////////////////////////////////////////
-tetgenmesh::badface* tetgenmesh::dequeuebadtet()
+tetgenmesh::badface* tetgenmesh::dequeueencsub(int* pquenumber)
{
badface *result;
- int queuenumber;
+ int quenumber;
// Look for a nonempty queue.
- for (queuenumber = 63; queuenumber >= 0; queuenumber--) {
- result = tetquefront[queuenumber];
+ for (quenumber = 2; quenumber >= 0; quenumber--) {
+ result = subquefront[quenumber];
if (result != (badface *) NULL) {
- // Remove the tetrahedron from the queue.
- tetquefront[queuenumber] = result->nextitem;
+ // Remove the badface from the queue.
+ subquefront[quenumber] = result->nextitem;
// Maintain a pointer to the NULL pointer at the end of the queue.
- if (tetquefront[queuenumber] == (badface *) NULL) {
- tetquetail[queuenumber] = &tetquefront[queuenumber];
+ if (subquefront[quenumber] == (badface *) NULL) {
+ subquetail[quenumber] = &subquefront[quenumber];
}
+ *pquenumber = quenumber;
return result;
}
}
@@ -25290,30 +28240,126 @@ tetgenmesh::badface* tetgenmesh::dequeuebadtet()
///////////////////////////////////////////////////////////////////////////////
// //
-// dequeueencsub() Remove an enc-subface from the front of the queue. //
+// enqueuebadtet() Add a tetrahedron into the queue. //
// //
///////////////////////////////////////////////////////////////////////////////
-tetgenmesh::badface* tetgenmesh::dequeueencsub(int* pquenumber)
+void tetgenmesh::enqueuebadtet(triface* testtet, REAL ratio2, REAL* cent)
{
- badface *result;
- int quenumber;
+ badface *newbadtet;
+ int queuenumber;
+ int i;
- // Look for a nonempty queue.
- for (quenumber = 2; quenumber >= 0; quenumber--) {
- result = subquefront[quenumber];
- if (result != (badface *) NULL) {
- // Remove the badface from the queue.
- subquefront[quenumber] = result->nextitem;
- // Maintain a pointer to the NULL pointer at the end of the queue.
- if (subquefront[quenumber] == (badface *) NULL) {
- subquetail[quenumber] = &subquefront[quenumber];
+ // Allocate space for the bad tetrahedron.
+ newbadtet = (badface *) badtetrahedrons->alloc();
+ newbadtet->tt = *testtet;
+ newbadtet->key = ratio2;
+ if (cent != NULL) {
+ for (i = 0; i < 3; i++) newbadtet->cent[i] = cent[i];
+ } else {
+ for (i = 0; i < 3; i++) newbadtet->cent[i] = 0.0;
+ }
+ newbadtet->forg = org(*testtet);
+ newbadtet->fdest = dest(*testtet);
+ newbadtet->fapex = apex(*testtet);
+ newbadtet->foppo = oppo(*testtet);
+ newbadtet->nextitem = (badface *) NULL;
+ // Determine the appropriate queue to put the bad tetrahedron into.
+ if (ratio2 > b->goodratio) {
+ // queuenumber = (int) ((ratio2 - b->goodratio) / 0.5);
+ queuenumber = (int) (64.0 - 64.0 / ratio2);
+ // 'queuenumber' may overflow (negative) caused by a very large ratio.
+ if ((queuenumber > 63) || (queuenumber < 0)) {
+ queuenumber = 63;
+ }
+ } else {
+ // It's not a bad ratio; put the tet in the lowest-priority queue.
+ queuenumber = 0;
+ }
+
+ // Are we inserting into an empty queue?
+ if (tetquefront[queuenumber] == (badface *) NULL) {
+ // Yes. Will this become the highest-priority queue?
+ if (queuenumber > firstnonemptyq) {
+ // Yes, this is the highest-priority queue.
+ nextnonemptyq[queuenumber] = firstnonemptyq;
+ firstnonemptyq = queuenumber;
+ } else {
+ // No. Find the queue with next higher priority.
+ i = queuenumber + 1;
+ while (tetquefront[i] == (badface *) NULL) {
+ i++;
}
- *pquenumber = quenumber;
- return result;
+ // Mark the newly nonempty queue as following a higher-priority queue.
+ nextnonemptyq[queuenumber] = nextnonemptyq[i];
+ nextnonemptyq[i] = queuenumber;
}
+ // Put the bad tetrahedron at the beginning of the (empty) queue.
+ tetquefront[queuenumber] = newbadtet;
+ } else {
+ // Add the bad tetrahedron to the end of an already nonempty queue.
+ tetquetail[queuenumber]->nextitem = newbadtet;
+ }
+ // Maintain a pointer to the last tetrahedron of the queue.
+ tetquetail[queuenumber] = newbadtet;
+
+ if (b->verbose > 2) {
+ printf(" Queueing bad tet: (%d, %d, %d, %d), ratio %g, qnum %d.\n",
+ pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
+ pointmark(newbadtet->fapex), pointmark(newbadtet->foppo),
+ sqrt(ratio2), queuenumber);
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// dequeuebadtet() Remove a tetrahedron from the front of the queue. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+tetgenmesh::badface* tetgenmesh::topbadtetra()
+{
+ // Keep a record of which queue was accessed in case dequeuebadtetra()
+ // is called later.
+ recentq = firstnonemptyq;
+ // If no queues are nonempty, return NULL.
+ if (firstnonemptyq < 0) {
+ return (badface *) NULL;
+ } else {
+ // Return the first tetrahedron of the highest-priority queue.
+ return tetquefront[firstnonemptyq];
+ }
+}
+
+void tetgenmesh::dequeuebadtet()
+{
+ badface *deadbadtet;
+ int i;
+
+ // If queues were empty last time topbadtetra() was called, do nothing.
+ if (recentq >= 0) {
+ // Find the tetrahedron last returned by topbadtetra().
+ deadbadtet = tetquefront[recentq];
+ // Remove the tetrahedron from the queue.
+ tetquefront[recentq] = deadbadtet->nextitem;
+ // If this queue is now empty, update the list of nonempty queues.
+ if (deadbadtet == tetquetail[recentq]) {
+ // Was this the highest-priority queue?
+ if (firstnonemptyq == recentq) {
+ // Yes; find the queue with next lower priority.
+ firstnonemptyq = nextnonemptyq[firstnonemptyq];
+ } else {
+ // No; find the queue with next higher priority.
+ i = recentq + 1;
+ while (tetquefront[i] == (badface *) NULL) {
+ i++;
+ }
+ nextnonemptyq[i] = nextnonemptyq[recentq];
+ }
+ }
+ // Return the bad tetrahedron to the pool.
+ badfacedealloc(badtetrahedrons, deadbadtet);
}
- return (badface *) NULL;
}
///////////////////////////////////////////////////////////////////////////////
@@ -25343,6 +28389,7 @@ bool tetgenmesh::checkseg4encroach(face* testseg, point testpt, point* prefpt,
bool enq;
int hitbdry;
+ enq = false;
eorg = sorg(*testseg);
edest = sdest(*testseg);
cent[0] = 0.5 * (eorg[0] + edest[0]);
@@ -25350,50 +28397,55 @@ bool tetgenmesh::checkseg4encroach(face* testseg, point testpt, point* prefpt,
cent[2] = 0.5 * (eorg[2] + edest[2]);
radius = distance(cent, eorg);
- enq = false;
- maxradius = 0.0;
- if (testpt == (point) NULL) {
- // Check if it is encroached by traversing all faces containing it.
- sstpivot(testseg, &starttet);
- eapex = apex(starttet);
- spintet = starttet;
- hitbdry = 0;
- do {
- dist = distance(cent, apex(spintet));
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- if (diff <= 0.0) {
- // s is encroached.
- enq = true;
- if (prefpt != (point *) NULL) {
- // Find the reference point.
- encpt = apex(spintet);
- circumsphere(eorg, edest, encpt, NULL, NULL, &dist);
- if (dist > maxradius) {
- // Rememebr this point.
- *prefpt = encpt;
- maxradius = dist;
+ if (varconstraint && (areabound(*testseg) > 0.0)) {
+ enq = (2.0 * radius) > areabound(*testseg);
+ }
+
+ if (!enq) {
+ maxradius = 0.0;
+ if (testpt == (point) NULL) {
+ // Check if it is encroached by traversing all faces containing it.
+ sstpivot(testseg, &starttet);
+ eapex = apex(starttet);
+ spintet = starttet;
+ hitbdry = 0;
+ do {
+ dist = distance(cent, apex(spintet));
+ diff = dist - radius;
+ if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
+ if (diff <= 0.0) {
+ // s is encroached.
+ enq = true;
+ if (prefpt != (point *) NULL) {
+ // Find the reference point.
+ encpt = apex(spintet);
+ circumsphere(eorg, edest, encpt, NULL, NULL, &dist);
+ if (dist > maxradius) {
+ // Rememebr this point.
+ *prefpt = encpt;
+ maxradius = dist;
+ }
+ } else {
+ break;
}
- } else {
- break;
}
- }
- if (!fnextself(spintet)) {
- hitbdry++;
- if (hitbdry < 2) {
- esym(starttet, spintet);
- if (!fnextself(spintet)) {
- hitbdry++;
- }
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(starttet, spintet);
+ if (!fnextself(spintet)) {
+ hitbdry++;
+ }
+ }
}
- }
- } while (apex(spintet) != eapex && (hitbdry < 2));
- } else {
- // Only check if 'testseg' is encroached by 'testpt'.
- dist = distance(cent, testpt);
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
+ } while (apex(spintet) != eapex && (hitbdry < 2));
+ } else {
+ // Only check if 'testseg' is encroached by 'testpt'.
+ dist = distance(cent, testpt);
+ diff = dist - radius;
+ if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
+ enq = (diff <= 0.0);
+ }
}
if (enq && enqflag) {
@@ -25430,31 +28482,57 @@ bool tetgenmesh::checkseg4encroach(face* testseg, point testpt, point* prefpt,
bool tetgenmesh::checksub4encroach(face* testsub, point testpt, bool enqflag)
{
triface abuttet;
- point forg, fdest, fapex, encpt;
- REAL cent[3];
+ point pa, pb, pc, encpt;
+ REAL A[4][4], rhs[4], D;
+ REAL cent[3], area;
REAL radius, dist, diff;
- bool enq, ncollinear;
+ bool enq;
+ int indx[4];
int quenumber;
- forg = sorg(*testsub);
- fdest = sdest(*testsub);
- fapex = sapex(*testsub);
- ncollinear = circumsphere(forg, fdest, fapex, NULL, cent, &radius);
- if (!ncollinear) return false; // Not a valid subface.
-
enq = false;
- encpt = (point) NULL;
- if (testpt == (point) NULL) {
- stpivot(*testsub, abuttet);
- if (abuttet.tet != dummytet) {
- dist = distance(cent, oppo(abuttet));
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
- if (enq) encpt = oppo(abuttet);
+ radius = 0.0;
+ encpt = (point) NULL;
+
+ pa = sorg(*testsub);
+ pb = sdest(*testsub);
+ pc = sapex(*testsub);
+
+ // Compute the coefficient matrix A (3x3).
+ A[0][0] = pb[0] - pa[0];
+ A[0][1] = pb[1] - pa[1];
+ A[0][2] = pb[2] - pa[2]; // vector V1 (pa->pb)
+ A[1][0] = pc[0] - pa[0];
+ A[1][1] = pc[1] - pa[1];
+ A[1][2] = pc[2] - pa[2]; // vector V2 (pa->pc)
+ cross(A[0], A[1], A[2]); // vector V3 (V1 X V2)
+
+ if (varconstraint && (areabound(*testsub) > 0.0)) {
+ // Check if the subface has too big area.
+ area = 0.5 * sqrt(dot(A[2], A[2]));
+ enq = area > areabound(*testsub);
+ if (enq) {
+ quenumber = 2; // A queue of subfaces having too big area.
}
- if (!enq) {
- sesymself(*testsub);
+ }
+
+ // Compute the right hand side vector b (3x1).
+ rhs[0] = 0.5 * dot(A[0], A[0]);
+ rhs[1] = 0.5 * dot(A[1], A[1]);
+ 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];
+ radius = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]);
+ }
+
+ if (!enq) {
+ // Check if the subface is encroached.
+ if (testpt == (point) NULL) {
stpivot(*testsub, abuttet);
if (abuttet.tet != dummytet) {
dist = distance(cent, oppo(abuttet));
@@ -25463,190 +28541,30 @@ bool tetgenmesh::checksub4encroach(face* testsub, point testpt, bool enqflag)
enq = (diff <= 0.0);
if (enq) encpt = oppo(abuttet);
}
- }
- } else {
- dist = distance(cent, testpt);
- diff = dist - radius;
- if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
- enq = (diff <= 0.0);
- }
-
- if (enq && enqflag) {
- /* REAL prj[3], ori1, ori2, ori3;
- bool inflag;
- // Test if encpt is inside the face.
- if (encpt) {
- projpt2face(encpt, forg, fdest, fapex, prj);
+ if (!enq) {
+ sesymself(*testsub);
+ stpivot(*testsub, abuttet);
+ if (abuttet.tet != dummytet) {
+ dist = distance(cent, oppo(abuttet));
+ diff = dist - radius;
+ if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
+ enq = (diff <= 0.0);
+ if (enq) encpt = oppo(abuttet);
+ }
+ }
} else {
- assert(testpt);
- projpt2face(testpt, forg, fdest, fapex, prj);
+ dist = distance(cent, testpt);
+ diff = dist - radius;
+ if (fabs(diff) / radius <= b->epsilon) diff = 0.0; // Rounding.
+ enq = (diff <= 0.0);
}
- abovepoint = facetabovepointarray[shellmark(*testsub)];
- if (abovepoint == (point) NULL) {
- getfacetabovepoint(testsub);
- }
- ori1 = orient3d(forg, fdest, abovepoint, prj);
- ori2 = orient3d(fdest, fapex, abovepoint, prj);
- inflag = (ori1 * ori2 >= 0.0);
- if (inflag) {
- ori3 = orient3d(fapex, forg, abovepoint, prj);
- inflag = (ori2 * ori3 >= 0.0);
- }
- // Decide which queue (1 or 0) to put s (1 has higher priority).
- quenumber = (inflag ? 1 : 0); */
- quenumber = 0;
- enqueueencsub(testsub, encpt, quenumber, cent);
- }
-
- return enq;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkseg4badqual() Check if a segment is longer than it is allowed. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checkseg4badqual(face* testseg, bool enqflag)
-{
- badface *encsubseg;
- point eorg, edest;
- REAL dist;
- bool enq;
-
- eorg = sorg(*testseg);
- edest = sdest(*testseg);
- dist = distance(eorg, edest);
-
- enq = dist > areabound(*testseg);
-
- if (enq && enqflag) {
- if (b->verbose > 2) {
- printf(" Queuing badqual subsegment (%d, %d).\n",
- pointmark(eorg), pointmark(edest));
+ if (enq) {
+ quenumber = 0; // A queue of encroached subfaces.
}
- encsubseg = (badface *) badsubsegs->alloc();
- encsubseg->ss = *testseg;
- encsubseg->forg = eorg;
- encsubseg->fdest = edest;
- encsubseg->foppo = NULL;
- // Set the pointer of 'encsubseg' into 'testseg'. It has two purposes:
- // (1) We can regonize it is encroached; (2) It is uniquely queued.
- setshell2badface(encsubseg->ss, encsubseg);
- }
-
- return enq;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checksub4badqual() Test if the quality of a subface is bad. //
-// //
-// A subface has bad quality if: (1) its minimum internal angle is smaller //
-// than 20 degree; or (2) its area is larger than a maximum area condition. //
-// Return TRUE if it is bad. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-bool tetgenmesh::checksub4badqual(face* testsub, bool enqflag)
-{
- face sametestsub;
- face subseg1, subseg2;
- point torg, tdest, tapex;
- point anglevertex;
- REAL dxod, dyod, dzod;
- REAL dxda, dyda, dzda;
- REAL dxao, dyao, dzao;
- REAL dxod2, dyod2, dzod2;
- REAL dxda2, dyda2, dzda2;
- REAL dxao2, dyao2, dzao2;
- REAL apexlen, orglen, destlen;
- REAL angle, area;
- bool enq;
-
- enq = false;
- torg = sorg(*testsub);
- tdest = sdest(*testsub);
- tapex = sapex(*testsub);
- dxod = torg[0] - tdest[0];
- dyod = torg[1] - tdest[1];
- dzod = torg[2] - tdest[2];
- dxda = tdest[0] - tapex[0];
- dyda = tdest[1] - tapex[1];
- dzda = tdest[2] - tapex[2];
- dxao = tapex[0] - torg[0];
- dyao = tapex[1] - torg[1];
- dzao = tapex[2] - torg[2];
- dxod2 = dxod * dxod;
- dyod2 = dyod * dyod;
- dzod2 = dzod * dzod;
- dxda2 = dxda * dxda;
- dyda2 = dyda * dyda;
- dzda2 = dzda * dzda;
- dxao2 = dxao * dxao;
- dyao2 = dyao * dyao;
- dzao2 = dzao * dzao;
- // Find the lengths of the triangle's three edges.
- apexlen = dxod2 + dyod2 + dzod2;
- orglen = dxda2 + dyda2 + dzda2;
- destlen = dxao2 + dyao2 + dzao2;
- if ((apexlen < orglen) && (apexlen < destlen)) {
- // The edge opposite the apex is shortest.
- // Find the square of the cosine of the angle at the apex.
- angle = dxda * dxao + dyda * dyao + dzda * dzao;
- angle = angle * angle / (orglen * destlen);
- anglevertex = tapex;
- senext(*testsub, sametestsub);
- sspivot(sametestsub, subseg1);
- senext2(*testsub, sametestsub);
- sspivot(sametestsub, subseg2);
- } else if (orglen < destlen) {
- // The edge opposite the origin is shortest.
- // Find the square of the cosine of the angle at the origin.
- angle = dxod * dxao + dyod * dyao + dzod * dzao;
- angle = angle * angle / (apexlen * destlen);
- anglevertex = torg;
- sspivot(*testsub, subseg1);
- senext2(*testsub, sametestsub);
- sspivot(sametestsub, subseg2);
- } else {
- // The edge opposite the destination is shortest.
- // Find the square of the cosine of the angle at the destination.
- angle = dxod * dxda + dyod * dyda + dzod * dzda;
- angle = angle * angle / (apexlen * orglen);
- anglevertex = tdest;
- sspivot(*testsub, subseg1);
- senext(*testsub, sametestsub);
- sspivot(sametestsub, subseg2);
- }
-
- // Check if both edges that form the angle are segments.
- // if ((subseg1.sh != dummysh) && (subseg2.sh != dummysh)) {
- if (shelltype(*testsub) == SKINNY) {
- // The angle is a segment intersection. Don't add this bad subface to
- // the list; there's nothing that can be done about a small angle
- // between two segments.
- angle = 0.0;
- }
-
- // Check whether the angle is smaller than permitted.
- if (angle > b->goodangle) {
- enq = true;
- }
-
- if (!enq && varconstraint && areabound(*testsub) > 0.0) {
- // Check whether the area is larger than desired. A variation form of
- // Heron's formula which only uses the squares of the edge lengthes
- // is used to calculated the area of a 3D triangle.
- area = apexlen + orglen - destlen;
- area = area * area;
- area = 4 * apexlen * orglen - area;
- area = 0.25 * sqrt(fabs(area));
- enq = area > areabound(*testsub);
}
- if (enq && enqflag) {
- enqueueencsub(testsub, NULL, 2, NULL);
+ if (enq && enqflag) {
+ enqueueencsub(testsub, encpt, quenumber, cent);
}
return enq;
@@ -25664,19 +28582,17 @@ bool tetgenmesh::checksub4badqual(face* testsub, bool enqflag)
bool tetgenmesh::checktet4badqual(triface* testtet, bool enqflag)
{
- badface *newbadtet;
point pa, pb, pc, pd, pe1, pe2;
REAL vda[3], vdb[3], vdc[3];
REAL vab[3], vbc[3], vca[3];
REAL N[4][3], A[4][4], rhs[4], D;
REAL elen[6], circumcent[3];
REAL bicent[3], offcent[3];
- REAL volume, L, q, cosd;
+ REAL volume, L, cosd;
REAL radius2, smlen2, ratio2;
REAL dist, sdist, split;
bool enq;
int indx[4];
- int queuenumber;
int sidx, i, j;
pa = (point) testtet->tet[4];
@@ -25684,10 +28600,6 @@ bool tetgenmesh::checktet4badqual(triface* testtet, bool enqflag)
pc = (point) testtet->tet[6];
pd = (point) testtet->tet[7];
- // Avoid compile warnings.
- pe1 = pe2 = (point) NULL;
- radius2 = 0.0;
-
// 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];
@@ -25703,135 +28615,118 @@ bool tetgenmesh::checktet4badqual(triface* testtet, bool enqflag)
// Get the volume of abcd.
volume = (A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2]) / 6.0;
if (volume < 0.0) volume = -volume;
- // Compare the volume to average edge length of abcd.
+ // Check the radiu-edge ratio of the tet.
+ rhs[0] = 0.5 * dot(vda, vda);
+ rhs[1] = 0.5 * dot(vdb, vdb);
+ rhs[2] = 0.5 * dot(vdc, vdc);
+ lu_solve(A, 3, indx, rhs, 0);
+ // Get the circumcenter.
+ for (i = 0; i < 3; i++) circumcent[i] = pd[i] + rhs[i];
+ // Get the square of the circumradius.
+ radius2 = dot(rhs, rhs);
+ // Find the square of the shortest edge length.
elen[0] = dot(vda, vda);
elen[1] = dot(vdb, vdb);
elen[2] = dot(vdc, vdc);
elen[3] = dot(vab, vab);
elen[4] = dot(vbc, vbc);
elen[5] = dot(vca, vca);
-
- enq = false;
- if (b->offcenter) {
- // Check if the tet is very flat.
- L = 0.0;
- for (i = 0; i < 6; i++) L += sqrt(elen[i]);
- L /= 6.0;
- q = volume / (L * L * L);
- enq = (q < b->epsilon * 1e+2);
- }
-
- // Is abcd very flat?
+ smlen2 = elen[0]; sidx = 0;
+ for (i = 1; i < 6; i++) {
+ if (smlen2 > elen[i]) { smlen2 = elen[i]; sidx = i; }
+ }
+ // Calculate the square of radius-edge ratio.
+ ratio2 = radius2 / smlen2;
+ // Check whether the ratio is smaller than permitted.
+ enq = ratio2 > b->goodratio;
if (!enq) {
- rhs[0] = 0.5 * dot(vda, vda);
- rhs[1] = 0.5 * dot(vdb, vdb);
- rhs[2] = 0.5 * dot(vdc, vdc);
- lu_solve(A, 3, indx, rhs, 0);
- // Get the circumcenter.
- for (i = 0; i < 3; i++) circumcent[i] = pd[i] + rhs[i];
- // Get the square of the circumradius.
- radius2 = dot(rhs, rhs);
- // Find the square of the shortest edge length.
- smlen2 = elen[0]; sidx = 0;
- for (i = 1; i < 6; i++) {
- if (smlen2 > elen[i]) { smlen2 = elen[i]; sidx = i; }
- }
- // Calculate the square of radius-edge ratio.
- ratio2 = radius2 / smlen2;
- // Check whether the ratio is smaller than permitted.
- enq = ratio2 > b->goodratio;
- if (!enq) {
- // abcd has good ratio.
- if (b->offcenter) {
- // Test if it is a sliver.
- // Compute the 4 face normals (N[0], ..., N[3]).
- for (j = 0; j < 3; j++) {
- for (i = 0; i < 3; i++) rhs[i] = 0.0;
- rhs[j] = 1.0; // Positive means the inside direction
- lu_solve(A, 3, indx, rhs, 0);
- for (i = 0; i < 3; i++) N[j][i] = rhs[i];
- }
- // Get the fourth normal by summing up the first three.
- for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
- // Normalized the normals.
- for (i = 0; i < 4; i++) {
- L = sqrt(dot(N[i], N[i]));
- if (L > 0.0) {
- for (j = 0; j < 3; j++) N[i][j] /= L;
- }
+ // abcd has good ratio.
+ // ratio2 = 0.0;
+ // if (b->offcenter) {
+ // Test if it is a sliver.
+ // Compute the 4 face normals (N[0], ..., N[3]).
+ for (j = 0; j < 3; j++) {
+ for (i = 0; i < 3; i++) rhs[i] = 0.0;
+ rhs[j] = 1.0; // Positive means the inside direction
+ lu_solve(A, 3, indx, rhs, 0);
+ for (i = 0; i < 3; i++) N[j][i] = rhs[i];
+ }
+ // Get the fourth normal by summing up the first three.
+ for (i = 0; i < 3; i++) N[3][i] = - N[0][i] - N[1][i] - N[2][i];
+ // Normalized the normals.
+ for (i = 0; i < 4; i++) {
+ L = sqrt(dot(N[i], N[i]));
+ if (L > 0.0) {
+ for (j = 0; j < 3; j++) N[i][j] /= L;
}
- // N[0] is the normal of face bcd. Test the dihedral angles at edge
- // cd, bd, and bc to see if they are too small or too big.
- for (i = 1; i < 4 && !enq; i++) {
- cosd = -dot(N[0], N[i]); // Edge cd, bd, bc.
- enq = ((cosd > cosmindihed) || ((cosd < cosmaxdihed)));
+ }
+ // N[0] is the normal of face bcd. Test the dihedral angles at edge
+ // cd, bd, and bc to see if they are too small or too big.
+ for (i = 1; i < 4 && !enq; i++) {
+ cosd = -dot(N[0], N[i]); // Edge cd, bd, bc.
+ enq = cosd > cosmindihed;
+ }
+ if (!enq) {
+ for (i = 2; i < 4 && !enq; i++) {
+ cosd = -dot(N[1], N[i]); // Edge ad, ac
+ enq = cosd > cosmindihed;
+ }
+ if (!enq) {
+ cosd = -dot(N[2], N[3]); // Edge ab
+ enq = cosd > cosmindihed;
}
- if (enq) {
- // A sliver! Split it at the barycenter.
- for (i = 0; i < 3; i++) {
- circumcent[i] = 0.25 * (pa[i] + pb[i] + pc[i] + pd[i]);
- }
- ratio2 = 0.0;
- }
- }
- } else if (b->offcenter) {
- // abcd has bad-quality. Use off-center instead of circumcenter.
- switch (sidx) {
- case 0: // edge da.
- pe1 = pd; pe2 = pa; break;
- case 1: // edge db.
- pe1 = pd; pe2 = pb; break;
- case 2: // edge dc.
- pe1 = pd; pe2 = pc; break;
- case 3: // edge ab.
- pe1 = pa; pe2 = pb; break;
- case 4: // edge bc.
- pe1 = pb; pe2 = pc; break;
- case 5: // edge ca.
- pe1 = pc; pe2 = pa; break;
- default: break;
- }
- // The shortest edge is e1->e2.
- for (i = 0; i < 3; i++) bicent[i] = 0.5 * (pe1[i] + pe2[i]);
- dist = distance(bicent, circumcent);
- // sdist = sqrt(smlen2) * sin(PI / 3.0); // A icoso-triangle.
- // The following formulae is from
- sdist = b->alpha3 * (b->minratio + sqrt(b->goodratio - 0.25))
- * sqrt(smlen2);
- split = sdist / dist;
- if (split > 1.0) split = 1.0;
- // Get the off-center.
- for (i = 0; i < 3; i++) {
- offcent[i] = bicent[i] + split * (circumcent[i] - bicent[i]);
}
- }
- } else {
- // A fat tet. Split it at the centroid.
+ // }
+ } else if (b->offcenter) {
+ // abcd has bad-quality. Use off-center instead of circumcenter.
+ switch (sidx) {
+ case 0: // edge da.
+ pe1 = pd; pe2 = pa; break;
+ case 1: // edge db.
+ pe1 = pd; pe2 = pb; break;
+ case 2: // edge dc.
+ pe1 = pd; pe2 = pc; break;
+ case 3: // edge ab.
+ pe1 = pa; pe2 = pb; break;
+ case 4: // edge bc.
+ pe1 = pb; pe2 = pc; break;
+ case 5: // edge ca.
+ pe1 = pc; pe2 = pa; break;
+ default:
+ pe1 = pe2 = (point) NULL; // Avoid a compile warning.
+ }
+ // The shortest edge is e1->e2.
+ for (i = 0; i < 3; i++) bicent[i] = 0.5 * (pe1[i] + pe2[i]);
+ dist = distance(bicent, circumcent);
+ // sdist = sqrt(smlen2) * sin(PI / 3.0); // A icoso-triangle.
+ // The following formulae is from
+ sdist = b->alpha3 * (b->minratio+sqrt(b->goodratio-0.25))* sqrt(smlen2);
+ split = sdist / dist;
+ if (split > 1.0) split = 1.0;
+ // Get the off-center.
for (i = 0; i < 3; i++) {
- circumcent[i] = 0.25 * (pa[i] + pb[i] + pc[i] + pd[i]);
+ offcent[i] = bicent[i] + split * (circumcent[i] - bicent[i]);
}
- ratio2 = 0.0;
}
if (!enq && (b->varvolume || b->fixedvolume)) {
- // The tet is in good shape.
- ratio2 = 0.0;
+ // Check if the tet has too big volume.
enq = b->fixedvolume && (volume > b->maxvolume);
if (!enq && b->varvolume) {
enq = (volume > volumebound(testtet->tet)) &&
(volumebound(testtet->tet) > 0.0);
}
}
+
if (!enq) {
- // The tet is in good shape.
- ratio2 = 0.0;
- if (b->bgmesh && (b->alpha1 > 0.0)) {
+ // Check if the user-defined sizing function is satisfied.
+ if (b->metric) {
+ // assert(b->alpha1 > 0.0);
sdist = sqrt(radius2) / b->alpha1;
- // Check if the nodal size map is satisfied.
for (i = 0; i < 4; i++) {
pa = (point) testtet->tet[4 + i];
// Get the indicated size of p.
- dist = pa[3]; // dist = b->alpha1 * pa[pointlfsindex];
+ dist = pa[pointmtrindex]; // dist = b->alpha1 * pa[pointmtrindex];
enq = ((dist < sdist) && (dist > 0.0));
if (enq) break; // It is bad wrt. a node constraint.
// *** Experiment ! Stop test if c is inside H(a).
@@ -25839,44 +28734,14 @@ bool tetgenmesh::checktet4badqual(triface* testtet, bool enqflag)
}
// *** Experiment !
// enq = (i == 4); // Does c lies outside all sparse-ball?
- }
+ } // if (b->metric)
}
if (enq && enqflag) {
- // Allocate space for the bad tetrahedron.
- newbadtet = (badface *) badtetrahedrons->alloc();
- newbadtet->tt = *testtet;
- newbadtet->key = ratio2;
- if ((ratio2 != 0) && b->offcenter) {
- for (i = 0; i < 3; i++) newbadtet->cent[i] = offcent[i];
- } else {
- for (i = 0; i < 3; i++) newbadtet->cent[i] = circumcent[i];
- }
- newbadtet->forg = org(*testtet);
- newbadtet->fdest = dest(*testtet);
- newbadtet->fapex = apex(*testtet);
- newbadtet->foppo = oppo(*testtet);
- newbadtet->nextitem = (badface *) NULL;
- // Determine the appropriate queue to put the bad tetrahedron into.
- if (ratio2 > b->goodratio) {
- queuenumber = (int) ((ratio2 - b->goodratio) / 0.5);
- // 'queuenumber' may overflow (negative) caused by a very large ratio.
- if ((queuenumber > 63) || (queuenumber < 0)) {
- queuenumber = 63;
- }
- } else {
- // It's not a bad ratio; put the tet in the lowest-priority queue.
- queuenumber = 0;
- }
- // Add the tetrahedron to the end of a queue.
- *tetquetail[queuenumber] = newbadtet;
- // Maintain a pointer to the NULL pointer at the end of the queue.
- tetquetail[queuenumber] = &newbadtet->nextitem;
- if (b->verbose > 2) {
- printf(" Queueing bad tet: (%d, %d, %d, %d), ratio %g, qnum %d.\n",
- pointmark(pa), pointmark(pb), pointmark(pc), pointmark(pd),
- sqrt(ratio2), queuenumber);
+ if (b->offcenter && (ratio2 > b->goodratio)) {
+ for (i = 0; i < 3; i++) circumcent[i] = offcent[i];
}
+ enqueuebadtet(testtet, ratio2, circumcent);
}
return enq;
@@ -25892,28 +28757,23 @@ bool tetgenmesh::checktet4badqual(triface* testtet, bool enqflag)
// p can not be inserted either the '-Y' option is used and ab is a hull //
// segment or '-YY' option is used. //
// //
-// p can be inserted if it is in one of the following cases (L = |a - b|): //
-// (1) if ab is too long wrt the edge constraint (bad-quality); or //
-// (2) if a subface having ab has max. area constraint A, and L^2 > 2 * A, //
-// (3) if a tet having ab has maximal volume constraint V, and L^3 > 6 * V.//
-// (4) if |a - p| > \alpha_2 H(a) and |p - b| > \alpha_2 H(b). //
-// (5) if 'refpt' != NULL. //
-// //
-// The purpose of using L instead of area and volume is to avoid resulting //
-// too skinny triangles and tetrahedron. //
+// p can be inserted if it is in one of the following cases: //
+// (1) if L = |a - b| is too long wrt the edge constraint; or //
+// (2) if |x - p| > \alpha_2 H(x) for x = a, b; or //
+// (3) if 'refpt' != NULL. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::acceptsegpt(point segpt, point refpt, face* splitseg)
{
- triface spintet;
- face parentsh, spinsh;
- point pa, pb, pc;
- REAL ablen, palen, pblen;
- REAL V, A;
+ point p[2];
+ REAL L, lfs;
+ int i, j;
if (b->nobisect == 1) {
// '-Y'. It can not be split if it is on the hull.
+ triface spintet;
+ point pc;
sstpivot(splitseg, &spintet);
assert(spintet.tet != dummytet);
pc = apex(spintet);
@@ -25928,73 +28788,26 @@ bool tetgenmesh::acceptsegpt(point segpt, point refpt, face* splitseg)
return false;
}
- pa = sorg(*splitseg);
- pb = sdest(*splitseg);
- ablen = distance(pa, pb);
- if (varconstraint) {
- A = areabound(*splitseg);
- if ((A > 0.0) && (ablen > A)) {
+ p[0] = sorg(*splitseg);
+ p[1] = sdest(*splitseg);
+ if (varconstraint && (areabound(*splitseg) > 0)) {
+ lfs = areabound(*splitseg);
+ L = distance(p[0], p[1]);
+ if (L > lfs) {
return true; // case (1)
}
}
- if (varconstraint && in->facetconstraintlist) {
- A = ablen * ablen / 2.0;
- spinsh = parentsh;
- do {
- if ((A > areabound(spinsh)) && (areabound(spinsh) > 0.0)) {
- return true; // case (2)
- }
- spivotself(spinsh);
- } while (spinsh.sh != parentsh.sh);
- }
-
- if (b->varvolume || b->fixedvolume) {
- V = ablen * ablen * ablen / 6.0;
- if (b->fixedvolume && (V > b->maxvolume)) {
- return true; // case (3)
- }
- if (b->varvolume) {
- spivot(*splitseg, parentsh);
- if (sorg(parentsh) != pa) sesymself(parentsh);
- stpivot(parentsh, spintet);
- if (spintet.tet == dummytet) {
- sesymself(parentsh);
- stpivot(parentsh, spintet);
- }
- findedge(&spintet, pa, pb);
- pc = apex(spintet);
- while (true) {
- if (!fnextself(spintet)) {
- // Meet a boundary, walk through it.
- tspivot(spintet, spinsh);
- findedge(&spinsh, pa, pb);
- sfnextself(spinsh);
- stpivot(spinsh, spintet);
- findedge(&spintet, pa, pb);
- }
- if ((V > volumebound(spintet.tet)) &&
- (volumebound(spintet.tet) > 0.0)) {
- return true; // case (3)
- }
- if (apex(spintet) == pc) break;
- }
- }
- }
-
- // If p is outside both protect balls of a and b.
- palen = distance(segpt, pa);
- pblen = distance(segpt, pb);
- if (!b->bgmesh) {
- if ((palen > (b->alpha2 * pa[pointlfsindex])) &&
- (pblen > (b->alpha2 * pb[pointlfsindex]))) {
- return true; // case (4)
- }
- } else {
- if ((palen > b->alpha2 * pa[3]) && (pblen > b->alpha2 * pb[3])) {
- return true; // case (4)
+ j = 0; // Use j to count the number of inside balls.
+ for (i = 0; i < 2; i++) {
+ // Check if p is inside the protect ball of q.
+ if (p[i][pointmtrindex] > 0.0) {
+ lfs = b->alpha2 * p[i][pointmtrindex];
+ L = distance(p[i], segpt);
+ if (L < lfs) j++; // p is inside ball.
}
}
+ if (j == 0) return true; // case (3).
// If 'refpt' != NULL, force p to be inserted.
if (refpt != (point) NULL) {
@@ -26017,26 +28830,20 @@ bool tetgenmesh::acceptsegpt(point segpt, point refpt, face* splitseg)
// p can not be inserted either the '-Y' option is used and the facet is on //
// the hull or '-YY' option is used. //
// //
-// p can be inserted if it is in one of the following cases (f is a subface //
-// of CBC(p), L = max{|p - v|, v \in V}): //
-// (1) if f has maximal area constraints A, and L^2 > 2 * A. //
-// (2) if a tet having f has max. volume constraint V, and L^3 > 6 * V. //
-// (3) if |p - v| > \alpha_2 H(v), for all v \in V. //
-// //
-// The purpose of using L^3 is to avoid resulting too skinny tetrahedron. //
+// p can be inserted if |p - v| > \alpha_2 H(v), for all v \in V. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::acceptfacpt(point facpt, list* subceillist, list* verlist)
{
- triface testtet;
face *testsh;
- point p[3];
- REAL L, L2, L3, lfs;
+ point p[2], ploop;
+ REAL L, lfs;
int idx, i, j;
if (b->nobisect == 1) {
// '-Y'. p can not be inserted if CBC(p) is on the hull.
+ triface testtet;
testsh = (face *)(* subceillist)[0];
stpivot(*testsh, testtet);
if (testtet.tet != dummytet) {
@@ -26062,76 +28869,23 @@ bool tetgenmesh::acceptfacpt(point facpt, list* subceillist, list* verlist)
}
}
}
- // Uninfect collected vertices.
- for (i = 0; i < verlist->len(); i++) {
- p[0] = * (point *)(* verlist)[i];
- idx = pointmark(p[0]);
- setpointmark(p[0], -(idx + 1));
- }
-
- if (varconstraint && in->facetconstraintlist) {
- for (i = 0; i < subceillist->len(); i++) {
- testsh = (face *)(* subceillist)[i];
- if (areabound(*testsh) > 0.0) {
- // Get the longest edge length of testsh = L.
- for (j = 0; j < 3; j++) p[j] = (point) testsh->sh[j + 3];
- L = distance(p[0], p[1]);
- L2 = distance(p[1], p[2]);
- L = (L >= L2 ? L : L2);
- L2 = distance(p[2], p[0]);
- L = (L >= L2 ? L : L2);
- L2 = L * L / 2.0;
- if (L2 > areabound(*testsh)) {
- return true; // case (1)
- }
- }
- }
- }
-
- // Check if it is in case (2).
- if (b->varvolume || b->fixedvolume) {
- for (i = 0; i < subceillist->len(); i++) {
- testsh = (face *)(* subceillist)[i];
- // Get the longest edge length of testsh = L.
- for (j = 0; j < 3; j++) p[j] = (point) testsh->sh[j + 3];
- L = distance(p[0], p[1]);
- L3 = distance(p[1], p[2]);
- L = (L >= L3 ? L : L3);
- L3 = distance(p[2], p[0]);
- L = (L >= L3 ? L : L3);
- L3 = L * L * L / 6.0;
- if (b->fixedvolume && (L3 > b->maxvolume)) {
- // This face is too large wrt. the maximum volume bound. Split it.
- return true; // case (2)
- }
- if (b->varvolume) {
- for (j = 0; j < 2; j ++) {
- stpivot(*testsh, testtet);
- if (testtet.tet != dummytet) {
- if ((L3 > volumebound(testtet.tet)) &&
- (volumebound(testtet.tet) > 0.0)) {
- // This face is too large wrt the maximum volume bound.
- return true; // case (2)
- }
- }
- sesymself(*testsh);
- }
- }
- }
- }
- // Check if p is inside the protect balls of vertices of V.
+ j = 0; // Use j to count the number of inside balls.
for (i = 0; i < verlist->len(); i++) {
- p[0] = * (point *)(* verlist)[i];
- if (!b->bgmesh) {
- lfs = b->alpha2 * p[0][pointlfsindex];
- } else {
- lfs = b->alpha2 * p[0][3];
+ ploop = * (point *)(* verlist)[i];
+ // Uninfect q.
+ idx = pointmark(ploop);
+ setpointmark(ploop, -(idx + 1));
+ // Check if p is inside the protect ball of q.
+ if (ploop[pointmtrindex] > 0.0) {
+ lfs = b->alpha2 * ploop[pointmtrindex];
+ L = distance(ploop, facpt);
+ if (L < lfs) j++; // p is inside ball.
}
- L = distance(p[0], facpt);
- if (L < lfs) break; // p is inside ball.
}
- if (i == verlist->len()) return true; // case (3).
+ verlist->clear();
+
+ if (j == 0) return true; // case (3).
rejsubpts++;
return false;
@@ -26144,17 +28898,15 @@ bool tetgenmesh::acceptfacpt(point facpt, list* subceillist, list* verlist)
// 'ceillist' is B(p). 'verlist' (V) is empty on input, it returns the set //
// of vertices of B(p). //
// //
-// p can be split if it is in one of the following cases: //
-// (1) if the t \in B(p) has maximal volume constraint V, and vol(t) < V. //
-// (2) if |p - v| > \alpha_2 H(v), for all v \in V. //
+// p can be split if |p - v| > \alpha_2 H(v), for all v \in V. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::acceptvolpt(point volpt, list* ceillist, list* verlist)
{
triface* testtet;
- point p[4];
- REAL L, vol, lfs;
+ point p[3], ploop;
+ REAL L, lfs;
int idx, i, j;
// Collect the vertices of CBC(p), save them in V.
@@ -26171,45 +28923,23 @@ bool tetgenmesh::acceptvolpt(point volpt, list* ceillist, list* verlist)
}
}
}
- // Uninfect collected vertices.
- for (i = 0; i < verlist->len(); i++) {
- p[0] = * (point *)(* verlist)[i];
- idx = pointmark(p[0]);
- setpointmark(p[0], -(idx + 1));
- }
-
- if (b->varvolume || b->fixedvolume) {
- for (i = 0; i < ceillist->len(); i++) {
- testtet = (triface *)(* ceillist)[i];
- for (j = 0; j < 4; j++) p[j] = (point) testtet->tet[4 + j];
- vol = orient3d(p[0], p[1], p[2], p[3]) / 6.0;
- if (vol < 0) vol = -vol;
- if (b->fixedvolume && (vol > b->maxvolume)) {
- // This tet is too large wrt. the maximum volume bound. Split it.
- return true; // case (1)
- }
- if (b->varvolume) {
- if ((vol > volumebound(testtet->tet)) &&
- (volumebound(testtet->tet) > 0.0)) {
- // This tet is too large wrt the maximum volume bound.
- return true; // case (1)
- }
- }
- }
- }
- // Check if p is inside the protect balls of vertices of V.
+ j = 0; // Use j to counte the number of inside balls.
for (i = 0; i < verlist->len(); i++) {
- p[0] = * (point *)(* verlist)[i];
- if (!b->bgmesh) {
- lfs = b->alpha2 * p[0][pointlfsindex];
- } else {
- lfs = b->alpha2 * p[0][3];
+ ploop = * (point *)(* verlist)[i];
+ // Uninfect q.
+ idx = pointmark(ploop);
+ setpointmark(ploop, -(idx + 1));
+ // Check if p is inside the protect ball of q.
+ if (ploop[pointmtrindex] > 0.0) {
+ lfs = b->alpha2 * ploop[pointmtrindex];
+ L = distance(ploop, volpt);
+ if (L < lfs) j++; // p is inside the protect ball.
}
- L = distance(p[0], volpt);
- if (L < lfs) break; // p is inside ball.
}
- if (i == verlist->len()) return true; // case (2).
+ verlist->clear();
+
+ if (j == 0) return true; // case (2).
rejtetpts++;
return false;
@@ -26267,17 +28997,27 @@ void tetgenmesh::getsplitpoint(point e1, point e2, point refpt, point newpt)
// Add a random perturbation on newpt.
d1 = distance(ei, newpt);
d2 = distance(newpt, refpt);
- ps = randgenerator(d2 * b->epsilon2);
+ ps = randgenerator(d2 * b->epsilon2 * 1e+2);
rs = ps / d1;
// Perturb newpt away from ei.
for (i = 0; i < 3; i++) newpt[i] = ei[i] + (1.0+rs) * (newpt[i] - ei[i]);
} else {
// Both endpoints are acute or not. Split it at the middle.
for (i = 0; i < 3; i++) newpt[i] = 0.5 * (e1[i] + e2[i]);
+ // Add a random perturbation on newpt.
+ d1 = 0.5 * distance(e1, e2);
+ ps = randgenerator(d1 * b->epsilon2 * 1e+2);
+ rs = ps / d1;
+ for (i = 0; i < 3; i++) newpt[i] = e1[i] + (1.0+rs) * (newpt[i] - e1[i]);
}
} else {
// Split the segment at its midpoint.
for (i = 0; i < 3; i++) newpt[i] = 0.5 * (e1[i] + e2[i]);
+ // Add a random perturbation on newpt.
+ d1 = 0.5 * distance(e1, e2);
+ ps = randgenerator(d1 * b->epsilon2 * 1e+2);
+ rs = ps / d1;
+ for (i = 0; i < 3; i++) newpt[i] = e1[i] + (1.0+rs) * (newpt[i] - e1[i]);
}
}
@@ -26310,10 +29050,10 @@ void tetgenmesh::shepardinterpolate(point newpt, list *verlist)
sumweight += weights[i];
}
// Interpolate.
- newpt[pointlfsindex] = 0.0;
+ newpt[pointmtrindex] = 0.0;
for (i = 0; i < verlist->len(); i++) {
neipt = * (point *)(* verlist)[i];
- newpt[pointlfsindex] += (weights[i] * neipt[pointlfsindex]) / sumweight;
+ newpt[pointmtrindex] += (weights[i] * neipt[pointmtrindex]) / sumweight;
}
delete [] weights;
@@ -26324,22 +29064,33 @@ void tetgenmesh::shepardinterpolate(point newpt, list *verlist)
// setnewpointsize() Set the size for a new point. //
// //
// The size of the new point p is interpolated either from a background mesh //
-// (b->bgmesh) or from the sizes of the adjacent vertices of p. //
+// (b->bgmesh) or from the two input endpoints. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::setnewpointsize(point newpt, list* verlist)
+void tetgenmesh::setnewpointsize(point newpt, point e1, point e2)
{
- if (b->bgmesh) {
+ if (b->metric) {
+ // Interpolate the point size in a background mesh.
triface bgmtet;
- point pa;
// Get a tet in background mesh for locating p.
- pa = * (point *)(* verlist)[0];
- decode(point2bgmtet(pa), bgmtet);
- interpolatepointsize(newpt, &bgmtet, NULL);
+ decode(point2bgmtet(e1), bgmtet);
+ p1interpolatebgm(newpt, &bgmtet, NULL);
} else {
- // Interpolate a local size for p using Shepard interpolation.
- shepardinterpolate(newpt, verlist);
+ if (e2 != (point) NULL) {
+ // Interpolate the size between the two endpoints.
+ REAL split, l, d;
+ l = distance(e1, e2);
+ d = distance(e1, newpt);
+ split = d / l;
+#ifdef SELF_CHECK
+ // Check if e1 and e2 are endpoints of a sharp segment.
+ assert(e1[pointmtrindex] > 0.0);
+ assert(e2[pointmtrindex] > 0.0);
+#endif
+ newpt[pointmtrindex] = (1.0 - split) * e1[pointmtrindex]
+ + split * e2[pointmtrindex];
+ }
}
}
@@ -26350,82 +29101,93 @@ void tetgenmesh::setnewpointsize(point newpt, list* verlist)
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::splitencseg(point newpt, face* splitseg, list* tetlist,
- list* sublist, list* verlist, queue* flipque, bool chkencsub, bool chkbadtet)
+ list* sublist, list* verlist, queue* flipque, bool chkencsub, bool chkbadtet,
+ bool optflag)
{
+ list *mytetlist;
+ queue *myflipque;
triface starttet;
face startsh, spinsh, checksh;
int i;
+ if (optflag) {
+ mytetlist = new list(sizeof(triface), NULL, 1024);
+ myflipque = new queue(sizeof(badface));
+ tetlist = mytetlist;
+ flipque = myflipque;
+ }
+
// Use the base orientation (important in this routine).
splitseg->shver = 0;
// Insert p, this should always success.
sstpivot(splitseg, &starttet);
splittetedge(newpt, &starttet, flipque);
- if (steinerleft > 0) steinerleft--;
// Remove locally non-Delaunay faces by flipping.
- flip(flipque, NULL);
+ flip(flipque, NULL); // lawson(NULL, flipque);
- // Check the two new subsegs to see if they're encroached (not by p).
- for (i = 0; i < 2; i++) {
- if (!shell2badface(*splitseg)) {
- checkseg4encroach(splitseg, NULL, NULL, true);
+ if (!optflag) {
+ // Check the two new subsegs to see if they're encroached (not by p).
+ for (i = 0; i < 2; i++) {
if (!shell2badface(*splitseg)) {
- if (varconstraint && (areabound(*splitseg) > 0.0)) {
- checkseg4badqual(splitseg, true);
- }
+ checkseg4encroach(splitseg, NULL, NULL, true);
}
- }
- if (i == 1) break; // Two new segs have been checked.
- senextself(*splitseg);
- spivotself(*splitseg);
+ if (i == 1) break; // Two new segs have been checked.
+ senextself(*splitseg);
+ spivotself(*splitseg);
#ifdef SELF_CHECK
- assert(splitseg->sh != (shellface *) NULL);
+ assert(splitseg->sh != (shellface *) NULL);
#endif
- splitseg->shver = 0;
- }
- // Check the new subfaces to see if they're encroached (not by p).
- if (chkencsub) {
- spivot(*splitseg, startsh);
- spinsh = startsh;
- do {
- sublist->append(&spinsh);
- formstarpolygon(newpt, sublist, verlist);
- for (i = 0; i < sublist->len(); i++) {
- checksh = * (face *)(* sublist)[i];
- if (!shell2badface(checksh)) {
- checksub4encroach(&checksh, NULL, true);
+ splitseg->shver = 0;
+ }
+ // Check the new subfaces to see if they're encroached (not by p).
+ if (chkencsub) {
+ spivot(*splitseg, startsh);
+ spinsh = startsh;
+ do {
+ sublist->append(&spinsh);
+ formstarpolygon(newpt, sublist, verlist);
+ for (i = 0; i < sublist->len(); i++) {
+ checksh = * (face *)(* sublist)[i];
if (!shell2badface(checksh)) {
- if (varconstraint && (areabound(checksh) > 0.0)) {
- checksub4badqual(&checksh, true);
- }
+ checksub4encroach(&checksh, NULL, true);
}
}
- }
- sublist->clear();
- verlist->clear();
- spivotself(spinsh);
- } while (spinsh.sh != startsh.sh);
- }
-
+ sublist->clear();
+ if (verlist) verlist->clear();
+ spivotself(spinsh);
+ } while (spinsh.sh != startsh.sh);
+ }
+ } // if (!optflag)
+
// Collect the new tets connecting at p.
sstpivot(splitseg, &starttet);
tetlist->append(&starttet);
formstarpolyhedron(newpt, tetlist, verlist, true);
- // Check if p encroaches adjacent segments.
- tallencsegs(newpt, 1, &tetlist);
- if (chkencsub) {
- // Check if p encroaches adjacent subfaces.
- tallencsubs(newpt, 1, &tetlist);
- }
- if (chkbadtet) {
- // Check if there are new bad quality tets at p.
+ if (!optflag) {
+ // Check if p encroaches adjacent segments.
+ tallencsegs(newpt, 1, &tetlist);
+ if (chkencsub) {
+ // Check if p encroaches adjacent subfaces.
+ tallencsubs(newpt, 1, &tetlist);
+ }
+ if (chkbadtet) {
+ // Check if there are new bad quality tets at p.
+ for (i = 0; i < tetlist->len(); i++) {
+ starttet = * (triface *)(* tetlist)[i];
+ checktet4badqual(&starttet, true);
+ }
+ }
+ tetlist->clear();
+ } else {
+ // Check if new tets are non-optimal.
for (i = 0; i < tetlist->len(); i++) {
starttet = * (triface *)(* tetlist)[i];
- checktet4badqual(&starttet, true);
+ checktet4opt(&starttet, true);
}
+ delete mytetlist;
+ delete myflipque;
}
- tetlist->clear();
}
///////////////////////////////////////////////////////////////////////////////
@@ -26465,11 +29227,6 @@ bool tetgenmesh::tallencsegs(point testpt, int n, list **ceillists)
// Found a segment. Test it if it isn't in enc-list.
if (!shell2badface(checkseg)) {
checkseg4encroach(&checkseg, testpt, NULL, true);
- if (!shell2badface(checkseg)) {
- if (varconstraint && (areabound(checkseg) > 0.0)) {
- checkseg4badqual(&checkseg, true);
- }
- }
}
}
enextself(ceiltet);
@@ -26484,11 +29241,6 @@ bool tetgenmesh::tallencsegs(point testpt, int n, list **ceillists)
// Test it if it isn't in enc-list.
if (!shell2badface(checkseg)) {
checkseg4encroach(&checkseg, testpt, NULL, true);
- if (!shell2badface(checkseg)) {
- if (varconstraint && (areabound(checkseg) > 0.0)) {
- checkseg4badqual(&checkseg, true);
- }
- }
}
checkseg.sh = shellfacetraverse(subsegs);
}
@@ -26532,11 +29284,6 @@ bool tetgenmesh::tallencsubs(point testpt, int n, list** ceillists)
// Found a subface. Test it if it isn't in enc-list.
if (!shell2badface(checksh)) {
checksub4encroach(&checksh, testpt, true);
- if (!shell2badface(checksh)) {
- if (varconstraint && (areabound(checksh) > 0.0)) {
- checksub4badqual(&checksh, true);
- }
- }
}
}
}
@@ -26549,11 +29296,6 @@ bool tetgenmesh::tallencsubs(point testpt, int n, list** ceillists)
// Test it if it isn't in enc-list.
if (!shell2badface(checksh)) {
checksub4encroach(&checksh, testpt, true);
- if (!shell2badface(checksh)) {
- if (varconstraint && (areabound(checksh) > 0.0)) {
- checksub4badqual(&checksh, true);
- }
- }
}
checksh.sh = shellfacetraverse(subfaces);
}
@@ -26598,18 +29340,17 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
{
list **tetlists, **ceillists;
list **sublists, **subceillists;
- list *tetlist, *sublist, *verlist;
+ list *tetlist, *sublist;
queue *flipque;
badface *encloop;
face splitseg, symsplitseg;
point newpt, sympt, refpt;
+ point e1, e2;
enum locateresult symloc;
int nmax, n, i, j;
n = 0;
nmax = 128;
- tetlist = (list *) NULL;
- flipque = (queue *) NULL;
if (!b->fliprepair) {
tetlists = new list*[nmax];
ceillists = new list*[nmax];
@@ -26618,9 +29359,6 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
} else {
tetlist = new list(sizeof(triface), NULL, 1024);
sublist = new list(sizeof(face), NULL, 256);
- }
- verlist = new list(sizeof(point *), NULL, 256);
- if (b->fliprepair) {
flipque = new queue(sizeof(badface));
}
@@ -26647,9 +29385,6 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
}
// Create the new point p (at the middle of s).
makepoint(&newpt);
- // for (i = 0; i < 3; i++) {
- // newpt[i] = 0.5 * (encloop->forg[i] + encloop->fdest[i]);
- // }
getsplitpoint(encloop->forg, encloop->fdest, refpt, newpt);
setpointtype(newpt, FREESEGVERTEX);
setpoint2sh(newpt, sencode(splitseg));
@@ -26668,6 +29403,13 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
// Insert sympt.
setpointtype(sympt, FREESEGVERTEX);
setpoint2sh(sympt, sencode(symsplitseg));
+ // Save the endpoints of the seg for size interpolation.
+ e1 = sorg(symsplitseg);
+ if (shelltype(symsplitseg) == SHARP) {
+ e2 = sdest(symsplitseg);
+ } else {
+ e2 = (point) NULL; // No need to do size interpolation.
+ }
if (!b->fliprepair) {
// Form BC(symp), B(symp), CBC(symp)s, C(symp)s.
formbowatcavity(sympt, &symsplitseg, NULL, &n, &nmax,
@@ -26676,9 +29418,9 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
if (trimbowatcavity(sympt, &symsplitseg, n, sublists,
subceillists, tetlists, ceillists, -1.0)) {
bowatinsertsite(sympt, &symsplitseg, n, sublists,
- subceillists, tetlists, ceillists, verlist, flipque,
+ subceillists, tetlists, ceillists, NULL, flipque,
true, chkencsub, chkbadtet);
- setnewpointsize(sympt, verlist);
+ setnewpointsize(sympt, e1, e2);
if (steinerleft > 0) steinerleft--;
} else {
// p did not insert for invalid BC(symp).
@@ -26688,12 +29430,11 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
releasebowatcavity(&symsplitseg, n, sublists, subceillists,
tetlists, ceillists);
} else {
- splitencseg(sympt, &symsplitseg, tetlist, sublist, verlist,
- flipque, chkencsub, chkbadtet);
- setnewpointsize(sympt, verlist);
+ splitencseg(sympt, &symsplitseg, tetlist, sublist, NULL,
+ flipque, chkencsub, chkbadtet, false);
+ setnewpointsize(sympt, e1, e2);
if (steinerleft > 0) steinerleft--;
}
- verlist->clear();
} else {
// The sympt are on the same segment. It is possible when
// splitseg is the symmetric rotating axes.
@@ -26710,6 +29451,13 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
}
} // for (j = idx2segpglist[i]; j < idx2segpglist[i + 1]; j++)
} // if (checkpbcs)
+ // Save the endpoints of the seg for size interpolation.
+ e1 = sorg(splitseg);
+ if (shelltype(splitseg) == SHARP) {
+ e2 = sdest(splitseg);
+ } else {
+ e2 = (point) NULL; // No need to do size interoplation.
+ }
if (!b->fliprepair) {
// Form BC(p), B(p), CBC(p)s, and C(p)s.
formbowatcavity(newpt, &splitseg, NULL, &n, &nmax, sublists,
@@ -26718,9 +29466,9 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
if (trimbowatcavity(newpt, &splitseg, n, sublists, subceillists,
tetlists, ceillists, -1.0)) {
bowatinsertsite(newpt, &splitseg, n, sublists, subceillists,
- tetlists, ceillists, verlist, flipque, true,
+ tetlists, ceillists, NULL, flipque, true,
chkencsub, chkbadtet);
- setnewpointsize(newpt, verlist);
+ setnewpointsize(newpt, e1, e2);
if (steinerleft > 0) steinerleft--;
} else {
// p did not insert for invalid B(p).
@@ -26730,12 +29478,11 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
releasebowatcavity(&splitseg, n, sublists, subceillists, tetlists,
ceillists);
} else {
- splitencseg(newpt, &splitseg, tetlist, sublist, verlist, flipque,
- chkencsub, chkbadtet);
- setnewpointsize(newpt, verlist);
+ splitencseg(newpt, &splitseg, tetlist, sublist, NULL, flipque,
+ chkencsub, chkbadtet, false);
+ setnewpointsize(newpt, e1, e2);
if (steinerleft > 0) steinerleft--;
}
- verlist->clear();
} else {
// p did not accept for insertion.
pointdealloc(newpt);
@@ -26754,9 +29501,6 @@ void tetgenmesh::repairencsegs(bool chkencsub, bool chkbadtet)
} else {
delete tetlist;
delete sublist;
- }
- delete verlist;
- if (b->fliprepair) {
delete flipque;
}
}
@@ -26781,7 +29525,7 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
list *verlist;
badface *encloop;
face splitsub, symsplitsub;
- point newpt, sympt;
+ point newpt, sympt, e1;
enum locateresult loc, symloc;
bool reject;
long oldptnum;
@@ -26801,21 +29545,17 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
// Clear the in-queue flag of f.
setshell2badface(splitsub, NULL);
// f may not be the same one when it was determined to be encroached.
- if (!isdead(&splitsub) && (sorg(splitsub) == encloop->forg) &&
- (sdest(splitsub) == encloop->fdest) &&
- (sapex(splitsub) == encloop->fapex)) {
+ if (!isdead(&splitsub)
+ && (sorg(splitsub) == encloop->forg)
+ && (sdest(splitsub) == encloop->fdest)
+ && (sapex(splitsub) == encloop->fapex)) {
if (b->verbose > 1) {
printf(" Dequeuing ensub (%d, %d, %d) [%d].\n",
pointmark(encloop->forg), pointmark(encloop->fdest),
pointmark(encloop->fapex), quenumber);
}
- // Create a new point p.
+ // Create a new point p at the circumcenter of f.
makepoint(&newpt);
- // If f was added by checksub4badqual(), calculate its circumcenter.
- if (quenumber == 2) {
- circumsphere(encloop->forg, encloop->fdest, encloop->fapex, NULL,
- encloop->cent, NULL);
- }
for (i = 0; i < 3; i++) newpt[i] = encloop->cent[i];
setpointtype(newpt, FREESUBVERTEX);
setpoint2sh(newpt, sencode(splitsub));
@@ -26831,12 +29571,11 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
// Form BC(p), B(p), CBC(p) and C(p).
formbowatcavity(newpt, NULL, &splitsub, &n, NULL, &sublist,
&subceillist, tetlists, ceillists);
- // Check for encroaching subsegments (on B(p)).
+ // Check for encroached subsegments (on B(p)).
reject = tallencsegs(newpt, 2, ceillists);
+ // Execute point accept rule if p does not encroach upon any segment.
if (!reject) {
- // Decide whether f is allowed to be split or not?
reject = !acceptfacpt(newpt, subceillist, verlist);
- verlist->clear();
}
if (!reject) {
// Validate/update cavity.
@@ -26866,7 +29605,6 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
reject = tallencsegs(sympt, 2, ceillists);
if (!reject) {
reject = !acceptfacpt(sympt, subceillist, verlist);
- verlist->clear();
}
if (!reject) {
reject = !trimbowatcavity(sympt,NULL,n,&sublist,&subceillist,
@@ -26878,21 +29616,23 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
setpoint2pbcpt(sympt, newpt);
setpointtype(sympt, FREESUBVERTEX);
setpoint2sh(sympt, sencode(symsplitsub));
+ // Save a point for size interpolation.
+ e1 = sorg(symsplitsub);
bowatinsertsite(sympt, NULL, n, &sublist, &subceillist,
- tetlists,ceillists,verlist,NULL,false,true,chkbadtet);
- setnewpointsize(sympt, verlist);
- verlist->clear();
+ tetlists,ceillists,NULL,NULL,false,true,chkbadtet);
+ setnewpointsize(sympt, e1, NULL);
if (steinerleft > 0) steinerleft--;
+ // Release CBC(symp) and BC(symp) and free the memory..
+ releasebowatcavity(NULL, n, &sublist, &subceillist, tetlists,
+ ceillists);
} else {
// symp is rejected for one of the following reasons:
// (1) BC(symp) is not valid; or
// (2) symp encroaches upon some subsegments (queued); or
// (3) symp is rejected by point accepting rule.
pointdealloc(sympt);
+ // Cavity will be released by the following code.
}
- // Release CBC(symp) and BC(symp) and free the memory..
- releasebowatcavity(NULL, n, &sublist, &subceillist, tetlists,
- ceillists);
} else {
// Do not insert sympt for invalid PBC data.
pointdealloc(sympt);
@@ -26913,10 +29653,11 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
ceillists, -1.0);
}
}
+ // Save a point for size interpolation.
+ e1 = sorg(splitsub);
bowatinsertsite(newpt, NULL, n, &sublist, &subceillist, tetlists,
- ceillists, verlist, NULL, true, true, chkbadtet);
- setnewpointsize(newpt, verlist);
- verlist->clear();
+ ceillists, NULL, NULL, true, true, chkbadtet);
+ setnewpointsize(newpt, e1, NULL);
if (steinerleft > 0) steinerleft--;
} else {
// p is rejected for the one of the following reasons:
@@ -26928,8 +29669,7 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
pointdealloc(newpt);
} // if (!reject)
// Release the cavity and free the memory.
- releasebowatcavity(NULL, n, &sublist, &subceillist, tetlists,
- ceillists);
+ releasebowatcavity(NULL,n,&sublist,&subceillist,tetlists,ceillists);
if (reject) {
// Are there queued encroached subsegments.
if (badsubsegs->items > 0) {
@@ -26942,11 +29682,6 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
if (!isdead(&splitsub)) {
if (!shell2badface(splitsub)) {
checksub4encroach(&splitsub, NULL, true);
- if (!shell2badface(splitsub)) {
- if (varconstraint && (areabound(splitsub) > 0.0)) {
- checksub4badqual(&splitsub, true);
- }
- }
}
}
}
@@ -26980,11 +29715,6 @@ void tetgenmesh::repairencsubs(bool chkbadtet)
if (!isdead(&splitsub)) {
// The subface has been changed, re-check it.
checksub4encroach(&splitsub, NULL, true);
- if (!shell2badface(splitsub)) {
- if (varconstraint && (areabound(splitsub) > 0.0)) {
- checksub4badqual(&splitsub, true);
- }
- }
}
} // if (!isdead(&splitsub) && (sorg(splitsub) == encloop->forg) &&
// Remove this entry from list.
@@ -27012,7 +29742,7 @@ void tetgenmesh::repairbadtets()
list *verlist;
badface *badtet;
triface starttet;
- point newpt;
+ point newpt, e1;
enum locateresult loc;
bool reject;
long oldptnum;
@@ -27026,14 +29756,20 @@ void tetgenmesh::repairbadtets()
// if an unlimited number of Steiner points is allowed.
while ((badtetrahedrons->items > 0) && (steinerleft != 0)) {
// Get a bad-quality tet t.
- badtet = dequeuebadtet();
+ badtet = topbadtetra();
// Make sure that the tet is still the same one when it was tested.
// Subsequent transformations may have made it a different tet.
- if (!isdead(&badtet->tt) && org(badtet->tt) == badtet->forg &&
- dest(badtet->tt) == badtet->fdest &&
- apex(badtet->tt) == badtet->fapex &&
- oppo(badtet->tt) == badtet->foppo) {
- // Create the new point p.
+ if ((badtet != (badface *) NULL) && !isdead(&badtet->tt)
+ && org(badtet->tt) == badtet->forg
+ && dest(badtet->tt) == badtet->fdest
+ && apex(badtet->tt) == badtet->fapex
+ && oppo(badtet->tt) == badtet->foppo) {
+ if (b->verbose > 1) {
+ printf(" Dequeuing btet (%d, %d, %d, %d).\n",
+ pointmark(badtet->forg), pointmark(badtet->fdest),
+ pointmark(badtet->fapex), pointmark(badtet->foppo));
+ }
+ // Create the new point p (at the circumcenter of t).
makepoint(&newpt);
for (i = 0; i < 3; i++) newpt[i] = badtet->cent[i];
setpointtype(newpt, FREEVOLVERTEX);
@@ -27051,8 +29787,9 @@ void tetgenmesh::repairbadtets()
// Check for encroached subfaces.
reject = tallencsubs(newpt, 1, &ceillist);
}
+ // Execute point accepting rule if p does not encroach upon any
+ // subsegment and subface.
if (!reject) {
- // Does p allowed to be inseted?
reject = !acceptvolpt(newpt, ceillist, verlist);
}
if (!reject) {
@@ -27068,10 +29805,12 @@ void tetgenmesh::repairbadtets()
if (reject) outbowatcircumcount++;
}
if (!reject) {
+ // Save a point for size interpolation.
+ e1 = org(starttet);
// Insert p.
bowatinsertsite(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist,
NULL, NULL, false, false, true);
- setnewpointsize(newpt, verlist);
+ setnewpointsize(newpt, e1, NULL);
if (steinerleft > 0) steinerleft--;
} else {
// p is rejected for one of the following reasons:
@@ -27089,7 +29828,6 @@ void tetgenmesh::repairbadtets()
}
tetlist->clear();
ceillist->clear();
- verlist->clear();
// Split encroached subsegments/subfaces if there are.
if (reject) {
oldptnum = points->items;
@@ -27100,7 +29838,8 @@ void tetgenmesh::repairbadtets()
repairencsubs(true);
}
if (points->items > oldptnum) {
- // Some encroaching subsegments/subfaces have been split.
+ // Some encroaching subsegments/subfaces got split. Re-queue the
+ // tet if it is still alive.
starttet = badtet->tt;
if (!isdead(&starttet)) {
checktet4badqual(&starttet, true);
@@ -27133,8 +29872,8 @@ void tetgenmesh::repairbadtets()
pointdealloc(newpt);
} // if ((loc != ONVERTEX) && (loc != OUTSIDE))
} // if (!isdead(&badtet->tt) && org(badtet->tt) == badtet->forg &&
- // Remove the tet from the pool.
- badfacedealloc(badtetrahedrons, badtet);
+ // Remove the tet from the queue.
+ dequeuebadtet();
} // while ((badtetrahedrons->items > 0) && (steinerleft != 0))
delete tetlist;
@@ -27162,18 +29901,17 @@ void tetgenmesh::enforcequality()
r2count = r3count = 0l;
}
- if (b->refine) {
- // Mark segment vertices (acute or not).
- markacutevertices(89.0);
+ // If both '-D' and '-r' options are used.
+ if (b->conformdel && b->refine) {
+ markacutevertices(65.0);
}
- if (!b->bgmesh) {
- // Calculate the node local feature sizes.
- calclocalfeaturesizes();
+ // If '-m' is not used.
+ if (!b->metric) {
+ // Find and mark all sharp segments.
+ marksharpsegments(65.0);
+ // Decide the sizes for feature points.
+ decidefeaturepointsizes();
}
- // Mark sharp subfaces (for termination).
- marksharpsubsegs(89.0);
- // Mark skinny subfaces (for reducing Steiner points).
- markskinnysubfaces(19.0);
// Initialize the pool of encroached subsegments.
badsubsegs = new memorypool(sizeof(badface), SUBPERBLOCK, POINTER, 0);
@@ -27216,8 +29954,11 @@ void tetgenmesh::enforcequality()
badtetrahedrons = new memorypool(sizeof(badface), ELEPERBLOCK, POINTER, 0);
// Initialize the priority queues of bad tets.
for (i = 0; i < 64; i++) tetquefront[i] = (badface *) NULL;
- for (i = 0; i < 64; i++) tetquetail[i] = &tetquefront[i];
+ firstnonemptyq = -1;
+ recentq = -1;
// Looking for bad quality tets.
+ cosmaxdihed = cos(b->maxdihedral * PI / 180.0);
+ cosmindihed = cos(b->mindihedral * PI / 180.0);
tallbadtetrahedrons();
if (b->verbose && badtetrahedrons->items > 0) {
printf(" Splitting bad tetrahedra.\n");
@@ -27244,9 +29985,36 @@ void tetgenmesh::enforcequality()
//
//
-// Begin of mesh smoothing routines
+// Begin of mesh optimization routines
//
+void tetgenmesh::dumpbadtets()
+{
+ FILE *fout;
+ badface *remtet;
+
+ // Write out a file of remaining bad tets.
+ printf(" Writing bad tets to file bad-dump.lua.\n");
+ fout = fopen("bad-dump.lua", "w");
+ fprintf(fout, "-- %ld remaining bad tets (> %g degree).\n",
+ badtetrahedrons->items, b->maxdihedral);
+ badtetrahedrons->traversalinit();
+ remtet = badfacetraverse(badtetrahedrons);
+ while (remtet != (badface *) NULL) {
+ if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
+ dest(remtet->tt) == remtet->fdest &&
+ apex(remtet->tt) == remtet->fapex &&
+ oppo(remtet->tt) == remtet->foppo) {
+ fprintf(fout, "p:draw_tet(%d, %d, %d, %d) -- %g\n",
+ pointmark(remtet->forg), pointmark(remtet->fdest),
+ pointmark(remtet->fapex), pointmark(remtet->foppo),
+ acos(remtet->key) * 180.0 / PI);
+ }
+ remtet = badfacetraverse(badtetrahedrons);
+ }
+ fclose(fout);
+}
+
///////////////////////////////////////////////////////////////////////////////
// //
// checktet4ill() Check a tet to see if it is illegal. //
@@ -27278,10 +30046,15 @@ bool tetgenmesh::checktet4ill(triface* testtet, bool enqflag)
fnext(*testtet, checktet);
tspivot(checktet, checksh2);
if (checksh2.sh != dummysh) {
- // Two subfaces share this edge. It should be a segment.
+ // Two subfaces share this edge.
sspivot(checksh1, checkseg);
if (checkseg.sh == dummysh) {
- illflag = true; break;
+ // The four corners of the tet are on one facet. Illegal! Try to
+ // flip the opposite edge of the current one.
+ enextfnextself(*testtet);
+ enextself(*testtet);
+ illflag = true;
+ break;
}
}
enextself(*testtet);
@@ -27295,7 +30068,7 @@ bool tetgenmesh::checktet4ill(triface* testtet, bool enqflag)
// Allocate space for the bad tetrahedron.
newbadtet = (badface *) badtetrahedrons->alloc();
newbadtet->tt = *testtet;
- newbadtet->key = 0.0;
+ newbadtet->key = -1.0; // = 180 degree.
for (i = 0; i < 3; i++) newbadtet->cent[i] = 0.0;
newbadtet->forg = org(*testtet);
newbadtet->fdest = dest(*testtet);
@@ -27314,38 +30087,38 @@ bool tetgenmesh::checktet4ill(triface* testtet, bool enqflag)
///////////////////////////////////////////////////////////////////////////////
// //
-// checktet4sliver() Check a tet to see if it is a sliver. //
+// checktet4opt() Check a tet to see if it needs to be optimized. //
// //
-// A sliver is a tet has no small edges, but has a nearly zero volume. When //
-// the mesh quality is measured by radios-edge ratio, slivers can have rela- //
-// tively small value and are not classified as bad quality. //
+// A tet t needs to be optimized if it fails to certain quality measures. //
+// The only quality measure currently used is the maximal dihedral angle at //
+// edges. The desired maximal dihedral angle is b->maxdihed (set by the '-s' //
+// option. //
// //
-// This routine finds whether a tet is a sliver or not by checking the bigg- //
-// est dihedral angle of the tet. It is a sliver if the angle is larger than //
-// 'maxdihed' (default is 170 degree, can be adjusted by '-s' option). //
-// //
-// If the flag 'chkill' is set, only check the volume of tet. It is a sliver //
-// if it has a zero or negative volume. //
+// A tet may have one, two, or three big dihedral angles. Examples: Let the //
+// tet t = abcd, and its four corners are nearly co-planar. Then t has one //
+// big dihedral angle if d is very close to the edge ab; t has three big //
+// dihedral angles if d's projection on the face abc is also inside abc, i.e.//
+// the shape of t likes a hat; finally, t has two big dihedral angles if d's //
+// projection onto abc is outside abc. //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::checktet4sliver(triface* testtet, bool chkill, bool enqflag)
+bool tetgenmesh::checktet4opt(triface* testtet, bool enqflag)
{
badface *newbadtet;
point pa, pb, pc, pd;
- REAL N[4][3], volume, len;
- REAL cosd, smallcosd;
+ REAL N[4][3], len;
+ REAL cosd;
bool enq;
- int edgeno, i, j;
+ int i, j;
enq = false;
-
pa = (point) testtet->tet[4];
pb = (point) testtet->tet[5];
pc = (point) testtet->tet[6];
pd = (point) testtet->tet[7];
- // Compute the 4 face normals (N[0], ..., N[3]).
- tetallnormal(pa, pb, pc, pd, N, &volume);
+ // Compute the 4 face normals: N[0] cbd, N[1] acd, N[2] bad, N[3] abc.
+ tetallnormal(pa, pb, pc, pd, N, NULL);
// Normalize the normals.
for (i = 0; i < 4; i++) {
len = sqrt(dot(N[i], N[i]));
@@ -27353,70 +30126,60 @@ bool tetgenmesh::checktet4sliver(triface* testtet, bool chkill, bool enqflag)
for (j = 0; j < 3; j++) N[i][j] /= len;
}
}
- // Find the largest dihedral and the edge.
- smallcosd = -dot(N[2], N[3]); // Edge ab.
- edgeno = 0;
- for (i = 1; i < 4; i++) {
- cosd = -dot(N[0], N[i]); // Edge cd, bd, bc.
- if (cosd < smallcosd) {
- smallcosd = cosd;
- edgeno = i;
- }
- }
- for (i = 2; i < 4; i++) {
- cosd = -dot(N[1], N[i]); // Edge ad, ac.
- if (cosd < smallcosd) {
- smallcosd = cosd;
- edgeno = i + 2;
- }
- }
- // Check if abcd is sliver.
- if (!chkill) {
- enq = ((smallcosd > cosmindihed) || ((smallcosd < cosmaxdihed)));
- } else {
- enq = (volume <= 0.0);
- }
-
- if (enq && enqflag) {
- // Let t represent the edge having the biggest dihedral angle.
+ // Find all large dihedral angles.
+ for (i = 0; i < 6; i++) {
+ // Locate the edge i and calculate the dihedral angle at the edge.
testtet->loc = 0;
testtet->ver = 0;
- switch (edgeno) {
- case 0: break; // edge ab
+ switch (i) {
+ case 0: // edge ab
+ cosd = -dot(N[2], N[3]);
+ break;
case 1: // edge cd
enextfnextself(*testtet);
enextself(*testtet);
+ cosd = -dot(N[0], N[1]);
break;
case 2: // edge bd
enextfnextself(*testtet);
enext2self(*testtet);
+ cosd = -dot(N[0], N[2]);
break;
case 3: // edge bc
enextself(*testtet);
+ cosd = -dot(N[0], N[3]);
break;
case 4: // edge ad
enext2fnextself(*testtet);
enextself(*testtet);
+ cosd = -dot(N[1], N[2]);
break;
case 5: // edge ac
enext2self(*testtet);
+ cosd = -dot(N[1], N[3]);
break;
}
- // Allocate space for the bad tetrahedron.
- newbadtet = (badface *) badtetrahedrons->alloc();
- newbadtet->tt = *testtet;
- newbadtet->key = smallcosd;
- for (i = 0; i < 3; i++) newbadtet->cent[i] = 0.0;
- newbadtet->forg = org(*testtet);
- newbadtet->fdest = dest(*testtet);
- newbadtet->fapex = apex(*testtet);
- newbadtet->foppo = oppo(*testtet);
- newbadtet->nextitem = (badface *) NULL;
- if (b->verbose > 2) {
- printf(" Queueing sliver: (%d, %d, %d, %d), maxdihed %g (degree).\n",
- pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
- pointmark(newbadtet->fapex), pointmark(newbadtet->foppo),
- acos(smallcosd) * 180.0 / PI);
+ if (cosd < cosmaxdihed) {
+ // A bigger dihedral angle.
+ if (enqflag) {
+ // Allocate space for the bad tetrahedron.
+ newbadtet = (badface *) badtetrahedrons->alloc();
+ newbadtet->tt = *testtet;
+ newbadtet->key = cosd;
+ for (j = 0; j < 3; j++) newbadtet->cent[j] = 0.0;
+ newbadtet->forg = org(*testtet);
+ newbadtet->fdest = dest(*testtet);
+ newbadtet->fapex = apex(*testtet);
+ newbadtet->foppo = oppo(*testtet);
+ newbadtet->nextitem = (badface *) NULL;
+ if (b->verbose > 2) {
+ printf(" Queueing tet: (%d, %d, %d, %d), dihed %g (degree).\n",
+ pointmark(newbadtet->forg), pointmark(newbadtet->fdest),
+ pointmark(newbadtet->fapex), pointmark(newbadtet->foppo),
+ acos(cosd) * 180.0 / PI);
+ }
+ }
+ enq = true;
}
}
@@ -27425,481 +30188,406 @@ bool tetgenmesh::checktet4sliver(triface* testtet, bool chkill, bool enqflag)
///////////////////////////////////////////////////////////////////////////////
// //
-// removetetbystripoff() Remove a boundary tet by stripping it off. //
-// //
-// 'striptet' (abcd) is on boundary and can be removed by stripping it off. //
-// Let abc and bad are the external boundary faces. //
-// //
-// To strip 'abcd' from the mesh is to detach its two interal faces (dca and //
-// cdb) from their adjoining tets together with a 2-to-2 flip to transform //
-// two subfaces (abc and bad) into another two (dca and cdb). //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::removetetbystripoff(triface *striptet)
-{
- triface abcd, badc;
- triface dcacasing, cdbcasing;
- face abc, bad;
-
- if (b->verbose > 1) {
- printf(" by stripping it off.\n");
- }
-
- striptetcount++;
-
- abcd = *striptet;
- adjustedgering(abcd, CCW);
-
- // Get the external subfaces abc, bad.
- fnext(abcd, badc);
- esymself(badc);
- tspivot(abcd, abc);
- tspivot(badc, bad);
-#ifdef SELF_CHECK
- assert((abc.sh != dummysh) && (bad.sh != dummysh));
-#endif
- findedge(&abc, org(abcd), dest(abcd));
- findedge(&bad, org(badc), dest(badc));
-
- // Get the casing tets at the internal sides.
- enextfnext(abcd, cdbcasing);
- enext2fnext(abcd, dcacasing);
- symself(cdbcasing);
- symself(dcacasing);
-#ifdef SELF_CHECK
- assert(cdbcasing.tet != dummytet && dcacasing.tet != dummytet);
-#endif
-
- // Do a 2-to-2 flip on abc and bad, transform abc->dca, bad->cdb.
- flip22sub(&abc, NULL);
- // Detach abcd from the two internal faces.
- dissolve(cdbcasing);
- dissolve(dcacasing);
- // The two internal faces become boundary faces.
- tsbond(cdbcasing, bad);
- tsbond(dcacasing, abc);
- // Delete abcd.
- tetrahedrondealloc(abcd.tet);
-}
-
-///////////////////////////////////////////////////////////////////////////////
+// removeedge() Remove an edge //
// //
-// removetetbyflip32() Remove a tet by a 3-to-2 flip. //
+// 'remedge' is a tet (abcd) having the edge ab wanted to be removed. Local //
+// reconnecting operations are used to remove edge ab. The following opera- //
+// tion will be tryed. //
// //
-// 'fliptet' (abcd) is going to be removed by a 3-to-2 flip. ab is the edge //
-// will be flipped away, i.e., abc, bad, and abe are three internal faces. //
+// If ab is on the hull, and abc and abd are both hull faces. Then ab can be //
+// removed by stripping abcd from the mesh. However, if ab is a segemnt, do //
+// the operation only if 'b->optlevel' > 1 and 'b->nobisect == 0'. //
// //
-// Note: If abc and bad are subfaces(abe must not), a 2-to-2 flip is used to //
-// transform abc, bad into dca, cdb prior to the 3-to-2 flip. //
+// If ab is an internal edge, there are n tets contains it. Then ab can be //
+// removed if there exists another m tets which can replace the n tets with- //
+// out changing the boundary of the n tets. //
// //
-// If 'enq' flag is set, check the two new tets after flip to see if they're //
-// slivers or illegal tets according to the 'chkill' flag. //
+// If 'optflag' is set. The value 'remedge->key' means cos(theta), where //
+// 'theta' is the maximal dishedral angle at ab. In this case, even if the //
+// n-to-m flip exists, it will not be performed if the maximum dihedral of //
+// the new tets is larger than 'theta'. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::removetetbyflip32(triface *fliptet, bool enq, bool chkill)
+bool tetgenmesh::removeedge(badface* remedge, bool optflag)
{
- triface abcd, badc;
- triface cdab, dcba;
+ triface abcd, badc; // Tet configuration at edge ab.
triface baccasing, abdcasing;
- triface dcacasing, cdbcasing;
- face abc, bad;
- REAL attrib, volume;
- int i;
+ triface abtetlist[11]; // Old configuration at ab, save maximum 10 tets.
+ triface bftetlist[11]; // Old configuration at bf, save maximum 10 tets.
+ triface newtetlist[33]; // New configuration after removing ab.
+ face checksh;
+ enum fliptype fty;
+ REAL key;
+ bool remflag, subflag;
+ int n, n1, m, i, j;
+
+ // First try to strip abcd from the mesh. This needs to check either ab
+ // or cd is on the hull. Try to strip it whichever is true.
+ abcd = remedge->tt;
+ adjustedgering(abcd, CCW);
+ i = 0;
+ do {
+ sym(abcd, baccasing);
+ // Is the tet on the hull?
+ if (baccasing.tet == dummytet) {
+ fnext(abcd, badc);
+ sym(badc, abdcasing);
+ if (abdcasing.tet == dummytet) {
+ // Strip the tet from the mesh -> ab is removed as well.
+ if (removetetbypeeloff(&abcd)) {
+ if (b->verbose > 1) {
+ printf(" Stripped tet from the mesh.\n");
+ }
+ optcount[0]++;
+ return true;
+ }
+ }
+ }
+ // Check if the oppsite edge cd is on the hull.
+ enext2fnextself(abcd);
+ enext2self(abcd);
+ esymself(abcd); // --> cdab
+ i++;
+ } while (i < 2);
+
+ // Get the tets configuration at ab. Collect maximum 10 tets.
+ subflag = false;
+ abcd = remedge->tt;
+ adjustedgering(abcd, CW);
+ n = 0;
+ abtetlist[n] = abcd;
+ do {
+ // Is the list full?
+ if (n == 10) break;
+ // Stop if a subface appears.
+ tspivot(abtetlist[n], checksh);
+ if (checksh.sh != dummysh) {
+ // ab is either a segment or a facet edge. The latter case is not
+ // handled yet! An edge flip is needed.
+ subflag = true; break; // return false;
+ }
+ // Get the next tet at ab.
+ fnext(abtetlist[n], abtetlist[n + 1]);
+ n++;
+ } while (apex(abtetlist[n]) != apex(abcd));
- if (b->verbose > 1) {
- printf(" by a 3-to-2 flip.\n");
+ remflag = false;
+ key = remedge->key;
+
+ if (subflag && optflag) {
+ abcd = remedge->tt;
+ adjustedgering(abcd, CCW);
+ // Try to flip face cda or cdb to improve quality.
+ for (j = 0; j < 2; j++) {
+ if (j == 0) {
+ enext2fnext(abcd, abtetlist[0]); // Goto cda.
+ } else {
+ enextfnext(abcd, abtetlist[0]); // Goto cdb.
+ }
+ fty = categorizeface(abtetlist[0]);
+ if (fty == T23) {
+ // A 2-to-3 flip is possible.
+ sym(abtetlist[0], abtetlist[1]);
+ assert(abtetlist[1].tet != dummytet);
+ n = 2;
+ m = 3;
+ remflag = removefacebyflip23(&key, abtetlist, newtetlist, NULL);
+ } else if (fty == T22) {
+ // A 2-to-2 or 4-to-4 flip is possible.
+ n = 2;
+ newtetlist[0] = abtetlist[0];
+ adjustedgering(newtetlist[0], CW);
+ fnext(newtetlist[0], newtetlist[1]);
+ assert(newtetlist[1].tet != dummytet);
+ // May it is 4-to-4 flip.
+ if (fnext(newtetlist[1], newtetlist[2])) {
+ fnext(newtetlist[2], newtetlist[3]);
+ assert(newtetlist[3].tet != dummytet);
+ n = 4;
+ }
+ m = n;
+ remflag = removeedgebyflip22(&key, n, newtetlist, NULL);
+ }
+ // Has quality been improved?
+ if (remflag) {
+ if (b->verbose > 1) {
+ printf(" Done flip %d-to-%d. Qual: %g -> %g.\n", n, m,
+ acos(remedge->key) / PI * 180.0, acos(key) / PI * 180.0);
+ }
+ // Delete the old tets. Note, flip22() does not create new tets.
+ if (m == 3) {
+ for (i = 0; i < n; i++) {
+ tetrahedrondealloc(abtetlist[i].tet);
+ }
+ }
+ for (i = 0; i < m; i++) {
+ checktet4opt(&(newtetlist[i]), true);
+ }
+ optcount[1]++;
+ return true;
+ }
+ } // if (j = 0; j < 2; j++)
+ // Faces are not flipable. Return.
+ return false;
}
- fliptetcount++;
+ // 2 <= n <= 10.
+ if (n == 3) {
+ // There are three tets at ab. Try to do a flip32 at ab.
+ remflag = removeedgebyflip32(&key, abtetlist, newtetlist, NULL);
+ } else if ((n == 4) || (n == 5) || (n == 6)) {
+ // Four tets case. Try to do edge transformation.
+ remflag = removeedgebytranNM(&key,n,abtetlist,newtetlist,NULL,NULL,NULL);
+ } else {
+ if (b->verbose > 1) {
+ printf(" !! Unhandled case: n = %d.\n", n);
+ }
+ }
+ if (remflag) {
+ optcount[n]++;
+ // Delete the old tets.
+ for (i = 0; i < n; i++) {
+ tetrahedrondealloc(abtetlist[i].tet);
+ }
+ m = (n - 2) * 2; // The numebr of new tets.
+ if (b->verbose > 1) {
+ printf(" Done flip %d-to-%d. ", n, m);
+ if (optflag) {
+ printf("Qual: %g -> %g.", acos(remedge->key) / PI * 180.0,
+ acos(key) / PI * 180.0);
+ }
+ printf("\n");
+ }
+ }
- abcd = *fliptet;
- adjustedgering(abcd, CCW);
- fnext(abcd, badc);
- esymself(badc);
- sym(abcd, baccasing);
- sym(badc, abdcasing);
-#ifdef SELF_CHECK
- assert((baccasing.tet != dummytet) && (abdcasing.tet != dummytet));
- assert(oppo(baccasing) == oppo(abdcasing));
-#endif
-
- // Get subfaces abc, bad.
- tspivot(abcd, abc);
- tspivot(badc, bad);
- if (abc.sh != dummysh) {
-#ifdef SELF_CHECK
- // Because ab is not a subsegment.
- assert(bad.sh != dummysh);
-#endif
- // abc and bad are internal subfaces. tets baccasing and abdcasing must
- // have the same attributes (such as the region attribute if the -A
- // switch is in use). But abcd may not be at the same region. After
- // flip32, if abcd is not deleted, it will have the wrong attributes.
- // Set abcd be the same region attributes as baccasing and abdcasing.
- for (i = 0; i < in->numberoftetrahedronattributes; i++) {
- attrib = elemattribute(baccasing.tet, i);
-#ifdef SELF_CHECK
- REAL testattr = elemattribute(abdcasing.tet, i);
- assert(attrib == testattr);
-#endif
- setelemattribute(abcd.tet, i, attrib);
+ if (!remflag && (key == remedge->key) && (n < 7)) {
+ // Try to do a combination of flips.
+ n1 = 0;
+ remflag = removeedgebycombNM(&key, n, abtetlist, &n1, bftetlist,
+ newtetlist, NULL);
+ if (remflag) {
+ optcount[9]++;
+ // Delete the old tets.
+ for (i = 0; i < n; i++) {
+ tetrahedrondealloc(abtetlist[i].tet);
+ }
+ for (i = 0; i < n1; i++) {
+ if (!isdead(&(bftetlist[i]))) {
+ tetrahedrondealloc(bftetlist[i].tet);
+ }
+ }
+ m = ((n1 - 2) * 2 - 1) + (n - 3) * 2; // The number of new tets.
+ if (b->verbose > 1) {
+ printf(" Done flip %d-to-%d (n-1=%d, n1=%d). ", n+n1-2, m, n-1,n1);
+ if (optflag) {
+ printf("Qual: %g -> %g.", acos(remedge->key) / PI * 180.0,
+ acos(key) / PI * 180.0);
+ }
+ printf("\n");
+ }
}
- if (b->varvolume) {
- volume = volumebound(baccasing.tet);
- setvolumebound(abcd.tet, volume);
- }
- findedge(&abc, org(abcd), dest(abcd));
- findedge(&bad, org(badc), dest(badc));
- // Detach abc, bad from the four tets at both sides.
- stdissolve(abc);
- stdissolve(bad);
- sesymself(abc);
- sesymself(bad);
- stdissolve(abc);
- stdissolve(bad);
- sesymself(abc);
- sesymself(bad);
- // Detach the four tets which hold abc and bad.
- tsdissolve(abcd);
- tsdissolve(badc);
- tsdissolve(baccasing);
- tsdissolve(abdcasing);
- // Perform a 2-to-2 flip on abc, bad, transform abc->dca, bad->cdb.
- flip22sub(&abc, NULL);
- // Insert the flipped subfaces abc and bad into tets.
- enextfnext(abcd, dcba); // dcba = bcda
- esymself(dcba); // dcba = cbda
- enext2fnext(abcd, cdab); // cdab = cadb
- esymself(cdab); // cdab = acdb
- findedge(&abc, org(cdab), dest(cdab));
- tsbond(cdab, abc);
- findedge(&bad, org(dcba), dest(dcba));
- tsbond(dcba, bad);
- // Bond the other sides of cdab, dcba, they may outer space.
- sym(cdab, dcacasing);
- sym(dcba, cdbcasing);
- sesymself(abc);
- sesymself(bad);
- tsbond(dcacasing, abc);
- tsbond(cdbcasing, bad);
- }
- // Remove abcd by a 3-to-2 flip.
- flip32(&abcd, NULL);
- // After flip abc is the internal face.
-
- if (enq) {
- // Get the adjtet of abcd (in badc).
- sym(abcd, badc);
- if (chkill) {
- // Test the two new tets to see if they are illegal.
- checktet4ill(&abcd, true);
- checktet4ill(&badc, true);
- } else {
- // Test the two new tets to see if they are sliver.
- checktet4sliver(&abcd, false, true);
- checktet4sliver(&badc, false, true);
+ }
+
+ if (remflag) {
+ // edge is removed. Test new tets for further optimization.
+ for (i = 0; i < m; i++) {
+ if (optflag) {
+ checktet4opt(&(newtetlist[i]), true);
+ } else {
+ checktet4ill(&(newtetlist[i]), true);
+ }
}
}
+
+ return remflag;
}
///////////////////////////////////////////////////////////////////////////////
// //
-// removetetbyrecon() Remove a tet by local reconnection. //
+// smoothsliver() Remove a sliver by smoothing a vertex of it. //
// //
-// 'remtet' (abcd) is wanted to be removed from the mesh. ab is the primary //
-// edge (which is diagonal if a, b, c, and d form a convex quadrilateral). //
-// //
-// abcd is removable if it is not a segment, and either it can be stripped //
-// off or it can be flipped away. //
-// //
-// The return value indicates abcd is remveable or not. Note, although abcd //
-// is removeable but it may not be removed when 'chkill' is FALSE. //
+// The 'slivtet' represents a sliver abcd, and ab is the current edge which //
+// has a large dihedral angle (close to 180 degree). //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::removetetbyrecon(badface* remtet, bool chkill)
+bool tetgenmesh::smoothsliver(badface* remedge, list *starlist)
{
- triface abcd, badc; // Tet configuration at edge ab.
- triface baccasing, abdcasing;
- face abseg;
- point pa, pb, pc, pd, pe;
- REAL ori1, ori2;
- REAL cosmaxd1, cosmaxd2;
- bool remflag;
- int i;
+ triface checktet;
+ point smthpt;
+ bool smthed;
+ int idx, i, j;
- remflag = false;
- // tet 'abcd' is indicated to remove.
- abcd = remtet->tt;
- // Check if abcd is removeable (at edge ab and cd).
- for (i = 0; i < 2; i++) {
- // If ab a segment, it is unremoveable.
- tsspivot(&abcd, &abseg);
- if (abseg.sh == dummysh) {
- adjustedgering(abcd, CCW);
- // Get the tet configuration at edge ab (or cd).
- fnext(abcd, badc);
- esymself(badc);
- sym(abcd, baccasing);
- sym(badc, abdcasing);
- // Can 'abcd' be stripped off?
- if ((baccasing.tet == dummytet) && (abdcasing.tet == dummytet)) {
- removetetbystripoff(&abcd);
- remflag = true;
- break; // abcd has been removed.
- } else if (oppo(baccasing) == oppo(abdcasing)) {
- // Can 'abcd' be flipped away?
- pa = org(abcd);
- pb = dest(abcd);
- pc = apex(abcd);
- pd = oppo(abcd);
- pe = oppo(baccasing);
- // Check if face cde is crossed by ab.
- ori1 = orient3d(pc, pd, pe, pa);
- ori2 = orient3d(pc, pd, pe, pb);
- if (ori1 * ori2 < 0.0) {
- // ab can be flipped away.
- if (!chkill) {
- // Do flip if the maximal dihedrals of the new tets are reduced?
- tetalldihedral(pd, pc, pe, pa, NULL, &cosmaxd1, NULL);
- tetalldihedral(pc, pd, pe, pb, NULL, &cosmaxd2, NULL);
- if ((remtet->key <= cosmaxd1) && (remtet->key <= cosmaxd2)) {
- removetetbyflip32(&abcd, true, chkill);
- remflag = true;
- break; // abcd has been removed.
- }
- } else {
- removetetbyflip32(&abcd, true, chkill);
- remflag = true;
- break; // abcd has been removed.
+ // Find a Steiner volume point and smooth it.
+ smthed = false;
+ for (i = 0; i < 4 && !smthed; i++) {
+ smthpt = (point) remedge->tt.tet[4 + i];
+ // Is it a volume point?
+ if (pointtype(smthpt) == FREEVOLVERTEX) {
+ // Is it a Steiner point?
+ idx = pointmark(smthpt) - in->firstnumber;
+ if (!(idx < in->numberofpoints)) {
+ // Smooth a Steiner volume point.
+ starlist->append(&(remedge->tt.tet));
+ formstarpolyhedron(smthpt, starlist, NULL, false);
+ smthed = smoothpoint(smthpt,NULL,NULL,starlist,false,&remedge->key);
+ // If it is smoothed. Queue new bad tets.
+ if (smthed) {
+ for (j = 0; j < starlist->len(); j++) {
+ checktet = * (triface *)(* starlist)[j];
+ checktet4opt(&checktet, true);
}
}
+ starlist->clear();
}
- } // if (abseg.sh == dummysh)
- // 'abcd' is not removed (although it may be removeable).
- if (i == 1) break; // Stop if both ab and cd have been checked.
- // Go to edge cd, re-use handle abcd.
- enextfnextself(abcd);
- esymself(abcd);
- enext2self(abcd);
- } // for (i = 0; i < 2; i++)
+ }
+ }
- return remflag;
+ /* Omit to smooth segment points. This may cause infinite loop.
+ if (smthed) {
+ return true;
+ }
+ face abseg, nextseg, prevseg;
+ point pt[2];
+ // Check if ab is a segment.
+ tsspivot(slivtet, &abseg);
+ if (abseg.sh == dummysh) {
+ // ab is not a segment. Check if a or b is a Steiner segment point.
+ for (i = 0; i < 2 && !smthed; i++) {
+ smthpt = (i == 0 ? org(*slivtet) : dest(*slivtet));
+ if (pointtype(smthpt) == FREESEGVERTEX) {
+ // Is it a Steiner point?
+ idx = pointmark(smthpt) - in->firstnumber;
+ if (!(idx < in->numberofpoints)) {
+ // Smooth a Steiner segment point. Get the segment.
+ sdecode(point2sh(smthpt), nextseg);
+ locateseg(smthpt, &nextseg);
+ assert(sorg(nextseg) == smthpt);
+ pt[0] = sdest(nextseg);
+ senext2(nextseg, prevseg);
+ spivotself(prevseg);
+ prevseg.shver = 0;
+ if (sorg(prevseg) == smthpt) sesymself(prevseg);
+ assert(sdest(prevseg) == smthpt);
+ pt[1] = sorg(prevseg);
+ starlist->append(slivtet);
+ formstarpolyhedron(smthpt, starlist, NULL, true);
+ smthed = smoothpoint(smthpt, pt[0], pt[1], starlist, false);
+ // If it is smoothed. Check if the tet is still a sliver.
+ if (smthed) checktet4opt(slivtet, true);
+ starlist->clear();
+ }
+ }
+ }
+ }
+ */
+
+ return smthed;
}
///////////////////////////////////////////////////////////////////////////////
// //
-// removetetbysplit() Remove a tet by inserting a point in it. //
+// splitsliver() Remove a sliver by inserting a point. //
+// //
+// The 'remedge->tt' represents a sliver abcd, ab is the current edge which //
+// has a large dihedral angle (close to 180 degree). //
// //
///////////////////////////////////////////////////////////////////////////////
-bool tetgenmesh::removetetbysplit(badface* remtet)
+bool tetgenmesh::splitsliver(badface *remedge, list *tetlist, list *ceillist)
{
- list **tetlists, **ceillists;
- list **sublists, **subceillists;
- list *tetlist, *ceillist, *verlist;
- triface abcd, starttet;
- face abseg, abcsh;
- point newpt, refpt;
- REAL maxcosd;
- int nmax, n;
- int i, j;
-
- // tet 'abcd' is indicated to remove.
- abcd = remtet->tt;
- abseg.sh = dummysh;
- abcsh.sh = dummysh;
-
- // Check if ab or cd is a segment.
- tsspivot(&abcd, &abseg);
- if (abseg.sh == dummysh) {
- adjustedgering(abcd, CCW);
- enextfnextself(abcd);
- enextself(abcd);
- tsspivot(&abcd, &abseg);
- }
- if (abseg.sh == dummysh) {
- abcd = remtet->tt;
- adjustedgering(abcd, CCW);
- // Check if abc is a subface.
- tspivot(abcd, abcsh);
- if (abcsh.sh == dummysh) {
- // Check if bad is a subface.
- fnextself(abcd);
- tspivot(abcd, abcsh);
- if (abcsh.sh == dummysh) {
- // Check if cda is a subface
- abcd = remtet->tt;
- adjustedgering(abcd, CCW);
- enext2fnextself(abcd);
- enext2self(abcd);
- esymself(abcd);
- tspivot(abcd, abcsh);
- if (abcsh.sh == dummysh) {
- // Check if cdb is a subface
- fnextself(abcd);
- tspivot(abcd, abcsh);
- }
- }
- }
- }
-
- if (abseg.sh != dummysh) {
- if (checkpbcs) {
- // Do not split ab if it belongs to any pbcgroup.
- i = shellmark(abseg) - 1;
- if (idx2segpglist[i + 1] > idx2segpglist[i]) {
- return false; // There are pbc facets at ab.
- }
- }
- // Find if segment ab is encroached by an existing point.
- refpt = (point) NULL;
- checkseg4encroach(&abseg, NULL, &refpt, false);
- // Find a point in segment ab.
- makepoint(&newpt);
- getsplitpoint(sorg(abseg), sdest(abseg), refpt, newpt);
- setpointtype(newpt, FREESEGVERTEX);
- setpoint2sh(newpt, sencode(abseg));
- maxcosd = remtet->key;
- if (refpt != (point) NULL) {
- // ab is encroached. Force p to be inserted.
- maxcosd = -1.0; // 180 degree
- }
- n = 0;
- nmax = 128;
- tetlists = new list*[nmax];
- ceillists = new list*[nmax];
- sublists = new list*[nmax];
- subceillists = new list*[nmax];
- verlist = new list(sizeof(point *), NULL, 256);
- // Form BC(p).
- formbowatcavity(newpt, &abseg, NULL, &n, &nmax, sublists, subceillists,
- tetlists, ceillists);
- // Can local maximal dihedral be reduced by inserting p?
- if (trimbowatcavity(newpt, &abseg, n, sublists, subceillists, tetlists,
- ceillists, maxcosd)) {
- // Inserting p. Ignore any new enc-seg, enc-sub, and bad tets.
- bowatinsertsite(newpt, &abseg, n, sublists, subceillists, tetlists,
- ceillists, verlist, NULL, false, false, false);
- setnewpointsize(newpt, verlist);
- // Check if there are new slivers at p.
- for (j = 0; j < n; j++) {
- tetlist = ceillists[j];
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- checktet4sliver(&starttet, false, true);
- }
- }
- refpt != (point) NULL ? smoothcdtsegpt++ : smoothsegpt++;
- } else {
- // The local quality will not be improved. Do not insert p.
- pointdealloc(newpt);
- newpt = (point) NULL;
- refpt != (point) NULL ? unsmoothcdtsegpt++ : unsmoothsegpt++;
- }
- // Free the memory allocated in formbowatcavity().
- releasebowatcavity(&abseg, n, sublists, subceillists, tetlists, ceillists);
- delete [] tetlists;
- delete [] ceillists;
- delete [] sublists;
- delete [] subceillists;
- delete verlist;
- } else if (abcsh.sh != dummysh) {
- if (checkpbcs) {
- // Do not split abc if it belongs to a pbcgroup.
- if (shellpbcgroup(abcsh) >= 0) {
- return false; // It is on a pbc facet.
- }
- }
- // Insert the midpoint of ab which is on a facet.
- makepoint(&newpt);
- getsplitpoint(org(abcd), dest(abcd), NULL, newpt);
- setpointtype(newpt, FREESUBVERTEX);
- setpoint2sh(newpt, sencode(abcsh));
- n = 2;
- tetlists = new list*[2];
- ceillists = new list*[2];
- sublists = new list*[2];
- subceillists = new list*[2];
- verlist = new list(sizeof(point *), NULL, 256);
- // Form BC(p).
- formbowatcavity(newpt, NULL, &abcsh, &n, NULL, sublists, subceillists,
- tetlists, ceillists);
- // Can local maximal dihedral be reduced by inserting p?
- if (trimbowatcavity(newpt, NULL, n, sublists, subceillists, tetlists,
- ceillists, remtet->key)) {
- // Inserting p. Ignore any new enc-seg, enc-sub, and bad tets.
- bowatinsertsite(newpt, NULL, n, sublists, subceillists, tetlists,
- ceillists, verlist, NULL, false, false, false);
- setnewpointsize(newpt, verlist);
- // Check if there are new slivers at p.
- for (j = 0; j < n; j++) {
- tetlist = ceillists[j];
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- checktet4sliver(&starttet, false, true);
- }
+ triface starttet;
+ face checkseg;
+ point newpt, pt[4];
+ bool remflag;
+ int i;
+
+ starttet = remedge->tt;
+
+ // Check if cd is a segment.
+ adjustedgering(starttet, CCW);
+ enextfnextself(starttet);
+ enextself(starttet);
+ tsspivot(&starttet, &checkseg);
+ if (b->nobisect == 0) {
+ if (checkseg.sh != dummysh) {
+ // cd is a segment. The seg will be split. BUT do not flip! Due to the
+ // exact predicates, lot of slivers ay be rsulted and hard to remove.
+ checkseg.shver = 0;
+ pt[0] = sorg(checkseg);
+ pt[1] = sdest(checkseg);
+ makepoint(&newpt);
+ getsplitpoint(pt[0], pt[1], NULL, newpt);
+ setpointtype(newpt, FREESEGVERTEX);
+ setpoint2sh(newpt, sencode(checkseg));
+ // Insert p, this should always success.
+ sstpivot(&checkseg, &starttet);
+ splittetedge(newpt, &starttet, NULL);
+ // Collect the new tets connecting at p.
+ sstpivot(&checkseg, &starttet);
+ ceillist->append(&starttet);
+ formstarpolyhedron(newpt, ceillist, NULL, true);
+ setnewpointsize(newpt, pt[0], NULL);
+ if (steinerleft > 0) steinerleft--;
+ // Smooth p.
+ smoothpoint(newpt, pt[0], pt[1], ceillist, false, NULL);
+ // Queue new slivers.
+ for (i = 0; i < ceillist->len(); i++) {
+ starttet = * (triface *)(* ceillist)[i];
+ checktet4opt(&starttet, true);
}
- smoothsubpt++;
- } else {
- // The local quality will not be improved. Do not insert p.
- pointdealloc(newpt);
- newpt = (point) NULL;
- unsmoothsubpt++;
+ ceillist->clear();
+ return true;
}
- // Free the memory allocated in formbowatcavity().
- releasebowatcavity(NULL, n, sublists, subceillists, tetlists, ceillists);
- delete [] tetlists;
- delete [] ceillists;
- delete [] sublists;
- delete [] subceillists;
- delete verlist;
- } else {
- // Insert the midpoint of the edge having largest dihedral angle.
- abcd = remtet->tt;
- makepoint(&newpt);
- getsplitpoint(org(abcd), dest(abcd), NULL, newpt);
- setpointtype(newpt, FREEVOLVERTEX);
- // Form BC(p).
- tetlist = new list(sizeof(triface), NULL, 1024);
- ceillist = new list(sizeof(triface), NULL, 1024);
- verlist = new list(sizeof(point *), NULL, 256);
- starttet = abcd;
- infect(starttet);
- tetlist->append(&starttet);
- formbowatcavityquad(newpt, tetlist, ceillist);
- // Can local maximal dihedral be reduced by inserting p?
- if (trimbowatcavity(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist,
- remtet->key)) {
- // Inserting p. Ignore any new enc-seg, enc-sub, and bad tets.
- bowatinsertsite(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist, verlist,
+ }
+
+ // Get the four corners.
+ for (i = 0; i < 4; i++) {
+ pt[i] = (point) starttet.tet[4 + i];
+ }
+ // Create the new point p (at the circumcenter of t).
+ makepoint(&newpt);
+ for (i = 0; i < 3; i++) {
+ newpt[i] = 0.25 * (pt[0][i] + pt[1][i] + pt[2][i] + pt[3][i]);
+ }
+ setpointtype(newpt, FREEVOLVERTEX);
+
+ // Form the Bowyer-Watson cavity of p.
+ remflag = false;
+ infect(starttet);
+ tetlist->append(&starttet);
+ formbowatcavityquad(newpt, tetlist, ceillist);
+ if (trimbowatcavity(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist, -1.0)) {
+ // Smooth p.
+ if (smoothpoint( newpt, NULL, NULL, ceillist, false, &remedge->key)) {
+ // Insert p.
+ bowatinsertsite(newpt, NULL, 1, NULL, NULL, &tetlist, &ceillist, NULL,
NULL, false, false, false);
- setnewpointsize(newpt, verlist);
- // Check if there are new slivers at p.
+ setnewpointsize(newpt, pt[0], NULL);
+ if (steinerleft > 0) steinerleft--;
+ // Queue new slivers.
for (i = 0; i < ceillist->len(); i++) {
starttet = * (triface *)(* ceillist)[i];
- checktet4sliver(&starttet, false, true);
- }
- smoothvolpt++;
- } else {
- // The local quality will not be improved. Do not insert p.
- pointdealloc(newpt);
- newpt = (point) NULL;
- // Uninfect tets of BC(p).
- for (i = 0; i < tetlist->len(); i++) {
- starttet = * (triface *)(* tetlist)[i];
- uninfect(starttet);
+ checktet4opt(&starttet, true);
}
- unsmoothvolpt++;
+ remflag = true;
+ } // if (smoothpoint)
+ } // if (trimbowatcavity)
+
+ if (!remflag) {
+ // p is rejected for BC(p) is not valid.
+ pointdealloc(newpt);
+ // Uninfect tets of BC(p).
+ for (i = 0; i < tetlist->len(); i++) {
+ starttet = * (triface *)(* tetlist)[i];
+ uninfect(starttet);
}
- delete tetlist;
- delete ceillist;
- delete verlist;
}
+ tetlist->clear();
+ ceillist->clear();
- return newpt != (point) NULL;
+ return remflag;
}
///////////////////////////////////////////////////////////////////////////////
@@ -27908,19 +30596,17 @@ bool tetgenmesh::removetetbysplit(badface* remtet)
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::tallslivers(bool chkill)
+void tetgenmesh::tallslivers(bool optflag)
{
triface tetloop;
tetrahedrons->traversalinit();
tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
- if (chkill) {
- if (!checktet4sliver(&tetloop, true, true)) {
- checktet4ill(&tetloop, true);
- }
+ if (optflag) {
+ checktet4opt(&tetloop, true);
} else {
- checktet4sliver(&tetloop, false, true);
+ checktet4ill(&tetloop, true);
}
tetloop.tet = tetrahedrontraverse();
}
@@ -27928,26 +30614,62 @@ void tetgenmesh::tallslivers(bool chkill)
///////////////////////////////////////////////////////////////////////////////
// //
-// repairmesh() Remove illegal tets in the mesh. //
+// optimizemesh() Improve mesh quality by mesh optimizations. //
+// //
+// Available mesh optimizing operations are: (1) multiple edge flips (3-to-2,//
+// 4-to-4, 5-to-6, etc), (2) free vertex deletion, (3) new vertex insertion. //
+// (1) is mandatory, while (2) and (3) are optionally. //
+// //
+// The variable 'b->optlevel' (set after '-s') determines the use of these //
+// operations. If it is: 0, do no optimization; 1, only do (1) operation; 2, //
+// do (1) and (2) operations; 3, do all operations. Deault, b->optlvel = 2. //
// //
///////////////////////////////////////////////////////////////////////////////
-void tetgenmesh::repairmesh()
+void tetgenmesh::optimizemesh(bool optflag)
{
- badface *remtet, *lastunrementry;
+ list *splittetlist, *tetlist, *ceillist;
+ badface *remtet, *lastentry;
+ REAL maxdihed, objdihed, curdihed;
+ long oldnum;
+ int iter, i;
if (!b->quiet) {
- printf("Repairing mesh.\n");
+ if (optflag) {
+ printf("Optimizing mesh.\n");
+ } else {
+ printf("Repairing mesh.\n");
+ }
}
- // Initialize the pool of bad tets
- badtetrahedrons = new memorypool(sizeof(badface), ELEPERBLOCK, POINTER, 0);
- lastunrementry = (badface *) NULL;
- striptetcount = fliptetcount = unimprovecount = 0l;
+#ifdef SELF_CHECK
+ if (optflag && (b->verbose)) {
+ printf(" level = %d.\n", b->optlevel);
+ }
+#endif
- // Looking for illegal tets.
- tallslivers(true);
-
+ // Initialize the pool of bad tets.
+ badtetrahedrons = new memorypool(sizeof(badface), ELEPERBLOCK, POINTER, 0);
+ if (optflag) {
+ cosmaxdihed = cos(b->maxdihedral * PI / 180.0);
+ cosmindihed = cos(b->mindihedral * PI / 180.0);
+ // The radian of the maximum dihedral angle.
+ maxdihed = b->maxdihedral / 180.0 * PI;
+ // A sliver has an angle large than 'objdihed' will be split.
+ objdihed = b->maxdihedral + 5.0;
+ if (objdihed < 170.0) objdihed = 170.0;
+ objdihed = objdihed / 180.0 * PI;
+ }
+ // Looking for non-optimal tets.
+ tallslivers(optflag);
+
+ optcount[0] = 0l; // tet strip count.
+ optcount[1] = 0l; // face (2-3) and edge (2-2) flip count.
+ optcount[3] = optcount[4] = optcount[5] = optcount[6] = 0l; // edge flips.
+ optcount[9] = 0l; // combined flip count.
+
+ // Perform edge flip to improve quality.
+ lastentry = (badface *) NULL;
// Loop until pool 'badtetrahedrons' is empty.
while (badtetrahedrons->items > 0) {
badtetrahedrons->traversalinit();
@@ -27960,21 +30682,22 @@ void tetgenmesh::repairmesh()
apex(remtet->tt) == remtet->fapex &&
oppo(remtet->tt) == remtet->foppo) {
if (b->verbose > 1) {
- printf(" Repair tet (%d, %d, %d, %d).\n", pointmark(remtet->forg),
- pointmark(remtet->fdest), pointmark(remtet->fapex),
- pointmark(remtet->foppo));
+ printf(" Repair tet (%d, %d, %d, %d) %g (degree).\n",
+ pointmark(remtet->forg), pointmark(remtet->fdest),
+ pointmark(remtet->fapex), pointmark(remtet->foppo),
+ acos(remtet->key) / PI * 180.0);
}
- if (!removetetbyrecon(remtet, true)) {
+ if (!removeedge(remtet, optflag)) {
// An unremoveable tet. Check if it forms a loop.
- if (lastunrementry != (badface *) NULL) {
- if (remtet == lastunrementry) break;
+ if (lastentry != (badface *) NULL) {
+ if (remtet == lastentry) break;
} else {
// Remember this tet as a breakpoint.
- lastunrementry = remtet;
+ lastentry = remtet;
}
} else {
// Clear the breakpoint.
- lastunrementry = (badface *) NULL;
+ lastentry = (badface *) NULL;
// Remove the entry from the queue.
badfacedealloc(badtetrahedrons, remtet);
}
@@ -27989,153 +30712,97 @@ void tetgenmesh::repairmesh()
}
if (b->verbose) {
- if (striptetcount > 0l) {
- printf(" %ld tets are stripped off.\n", striptetcount);
+ if (optcount[0] > 0l) {
+ printf(" %ld tets are peeled off.\n", optcount[0]);
}
- if (fliptetcount > 0l) {
- printf(" %ld tets are flipped away.\n", fliptetcount);
+ if (optcount[1] > 0l) {
+ printf(" %ld faces are flipped.\n", optcount[1]);
}
- if (badtetrahedrons->items > 0l) {
- printf(" %ld tets are unremoveable.\n", badtetrahedrons->items);
+ if (optcount[3] + optcount[4] + optcount[5] + optcount[6] +
+ optcount[9] > 0l) {
+ printf(" %ld edges are flipped.\n", optcount[3] + optcount[4] +
+ optcount[5] + optcount[6] + optcount[9]);
}
+ // if (badtetrahedrons->items > 0l) {
+ // printf(" %ld edges remain.\n", badtetrahedrons->items);
+ // }
}
- delete badtetrahedrons;
- badtetrahedrons = (memorypool *) NULL;
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// smoothmesh() Smooth the mesh. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::smoothmesh()
-{
- badface *remtet, *lastunrementry;
-
- if (!b->quiet) {
- printf("Smoothing mesh.\n");
- }
+ if ((badtetrahedrons->items > 0l) && optflag && (b->optlevel > 2)) {
+ splittetlist = new list(sizeof(badface), NULL, 256);
+ tetlist = new list(sizeof(triface), NULL, 256);
+ ceillist = new list(sizeof(triface), NULL, 256);
+ oldnum = points->items;
+ smoothsegverts = smoothvolverts = 0;
+ optcount[1] = 0l;
+ optcount[3] = optcount[4] = optcount[5] = optcount[6] = 0l; // edge flips.
+ optcount[9] = 0l; // combined flip count.
+ iter = 0;
- // Initialize the pool of bad tets
- badtetrahedrons = new memorypool(sizeof(badface), ELEPERBLOCK, POINTER, 0);
- cosmaxdihed = cos(b->maxdihedral * PI / 180.0);
- cosmindihed = 1.0;
- striptetcount = fliptetcount = unimprovecount = 0l;
- smoothcdtsegpt = smoothsegpt = smoothsubpt = smoothvolpt = 0l;
- unsmoothcdtsegpt = unsmoothsegpt = unsmoothsubpt = unsmoothvolpt = 0l;
-
- // Looking for bad tets.
- tallslivers(false);
-
- lastunrementry = (badface *) NULL;
- // Loop until pool 'badtetrahedrons' is empty.
- while (badtetrahedrons->items > 0) {
- badtetrahedrons->traversalinit();
- remtet = badfacetraverse(badtetrahedrons);
- while (remtet != (badface *) NULL) {
- // Make sure that the tet is still the same one when it was tested.
- // Subsequent transformations may have made it a different tet.
- if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
- dest(remtet->tt) == remtet->fdest &&
- apex(remtet->tt) == remtet->fapex &&
- oppo(remtet->tt) == remtet->foppo) {
- if (b->verbose > 1) {
- printf(" Repair tet (%d, %d, %d, %d).\n", pointmark(remtet->forg),
- pointmark(remtet->fdest), pointmark(remtet->fapex),
- pointmark(remtet->foppo));
- }
- if (!removetetbyrecon(remtet, false)) {
- // An unremoveable tet. Check if it forms a loop.
- if (lastunrementry != (badface *) NULL) {
- if (remtet == lastunrementry) break;
- } else {
- // Remember this tet as a breakpoint.
- lastunrementry = remtet;
- }
- } else {
- // Clear the breakpoint.
- lastunrementry = (badface *) NULL;
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
- }
- } else {
+ do {
+ // Form a list of slivers to be split and clean the pool.
+ badtetrahedrons->traversalinit();
+ remtet = badfacetraverse(badtetrahedrons);
+ while (remtet != (badface *) NULL) {
+ splittetlist->append(remtet);
// Remove the entry from the queue.
badfacedealloc(badtetrahedrons, remtet);
- }
- remtet = badfacetraverse(badtetrahedrons);
- }
- // Stop if the above loop was out by force.
- if (remtet != (badface *) NULL) break;
- }
-
- if (b->verbose) {
- if (striptetcount > 0l) {
- printf(" %ld tets are stripped off.\n", striptetcount);
- }
- if (fliptetcount > 0l) {
- printf(" %ld tets are flipped away.\n", fliptetcount);
- }
- }
-
- lastunrementry = (badface *) NULL;
- // Loop until pool 'badtetrahedrons' is empty.
- while (badtetrahedrons->items > 0) {
- badtetrahedrons->traversalinit();
- remtet = badfacetraverse(badtetrahedrons);
- while (remtet != (badface *) NULL) {
- // Make sure that the tet is still the same one when it was tested.
- // Subsequent transformations may have made it a different tet.
- if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
- dest(remtet->tt) == remtet->fdest &&
- apex(remtet->tt) == remtet->fapex &&
- oppo(remtet->tt) == remtet->foppo) {
- if (b->verbose > 1) {
- printf(" Repair tet (%d, %d, %d, %d).\n", pointmark(remtet->forg),
- pointmark(remtet->fdest), pointmark(remtet->fapex),
- pointmark(remtet->foppo));
- }
- if (!removetetbyrecon(remtet, false)) {
- // An unremoveable tet. Find if a segment which can be split.
- if (!removetetbysplit(remtet)) {
- // An unremoveable tet. Check if it forms a loop.
- if (lastunrementry != (badface *) NULL) {
- if (remtet == lastunrementry) break;
- } else {
- // Remember this tet as a breakpoint.
- lastunrementry = remtet;
+ remtet = badfacetraverse(badtetrahedrons);
+ }
+ for (i = 0; i < splittetlist->len(); i++) {
+ remtet = (badface *)(* splittetlist)[i];
+ // Make sure that the tet is still the same one when it was tested.
+ // Subsequent transformations may have made it a different tet.
+ if (!isdead(&remtet->tt) && org(remtet->tt) == remtet->forg &&
+ dest(remtet->tt) == remtet->fdest &&
+ apex(remtet->tt) == remtet->fapex &&
+ oppo(remtet->tt) == remtet->foppo) {
+ // The sliver may get smoothed due to a neighboring tet.
+ curdihed = facedihedral(remtet->forg, remtet->fdest, remtet->fapex,
+ remtet->foppo);
+ // The dihedral angle of a tet must less than PI, correct it.
+ if (curdihed > PI) curdihed = 2 * PI - curdihed;
+ // Is it a large angle?
+ if (curdihed > objdihed) {
+ remtet->key = cos(curdihed);
+ if (b->verbose > 1) {
+ printf(" Get sliver (%d, %d, %d, %d) %g (degree).\n",
+ pointmark(remtet->forg), pointmark(remtet->fdest),
+ pointmark(remtet->fapex), pointmark(remtet->foppo),
+ acos(remtet->key) / PI * 180.0);
+ }
+ if (!removeedge(remtet, optflag)) {
+ if (!smoothsliver(remtet, tetlist)) {
+ splitsliver(remtet, tetlist, ceillist);
+ }
}
- } else {
- // Clear the breakpoint.
- lastunrementry = (badface *) NULL;
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
}
- } else {
- // Clear the breakpoint.
- lastunrementry = (badface *) NULL;
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
}
- } else {
- // Remove the entry from the queue.
- badfacedealloc(badtetrahedrons, remtet);
}
- remtet = badfacetraverse(badtetrahedrons);
- }
- // Stop if the above loop was out by force.
- if (remtet != (badface *) NULL) break;
- }
-
- if (b->verbose) {
- if ((smoothcdtsegpt + smoothsegpt + smoothsubpt + smoothvolpt) > 0l) {
- printf(" %ld smooth points.\n",
- smoothcdtsegpt + smoothsegpt + smoothsubpt + smoothvolpt);
- }
- if (badtetrahedrons->items > 0l) {
- printf(" %ld remaining tets.\n", badtetrahedrons->items);
+ iter++;
+ } while ((badtetrahedrons->items > 0l) && (iter < b->optpasses));
+
+ if (b->verbose) {
+ printf(" %d passes.\n", iter);
+ if ((points->items - oldnum) > 0l) {
+ printf(" %ld points are inserted (%d on segment).\n",
+ points->items - oldnum, smoothsegverts);
+ }
+ if (optcount[1] > 0l) {
+ printf(" %ld faces are flipped.\n", optcount[1]);
+ }
+ if (optcount[3] + optcount[4] + optcount[5] + optcount[6] +
+ optcount[9] > 0l) {
+ printf(" %ld edges are flipped.\n", optcount[3] + optcount[4] +
+ optcount[5] + optcount[6] + optcount[9]);
+ }
+ // if (badtetrahedrons->items > 0l) {
+ // printf(" %ld edges remain.\n", badtetrahedrons->items);
+ // }
}
+ delete tetlist;
+ delete ceillist;
+ delete splittetlist;
}
delete badtetrahedrons;
@@ -28143,7 +30810,7 @@ void tetgenmesh::smoothmesh()
}
//
-// End of mesh smoothing routines
+// End of mesh optimization routines
//
//
@@ -28167,11 +30834,13 @@ void tetgenmesh::transfernodes()
REAL x, y, z;
int coordindex;
int attribindex;
+ int mtrindex;
int i, j;
// Read the points.
coordindex = 0;
attribindex = 0;
+ mtrindex = 0;
for (i = 0; i < in->numberofpoints; i++) {
makepoint(&pointloop);
// Read the point coordinates.
@@ -28182,6 +30851,10 @@ void tetgenmesh::transfernodes()
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++];
+ }
// Determine the smallest and largests x, y and z coordinates.
if (i == 0) {
xmin = xmax = x;
@@ -28197,7 +30870,6 @@ void tetgenmesh::transfernodes()
}
}
// 'longest' is the largest possible edge length formed by input vertices.
- // It is used as the measure to distinguish two identical points.
x = xmax - xmin;
y = ymax - ymin;
z = zmax - zmin;
@@ -28206,6 +30878,7 @@ void tetgenmesh::transfernodes()
printf("Error: The point set is trivial.\n");
terminatetetgen(1);
}
+ // Two identical points are distinguished by 'lengthlimit'.
lengthlimit = longest * b->epsilon * 1e+2;
}
@@ -28296,15 +30969,6 @@ void tetgenmesh::highorder()
int hitbdry, ptmark;
int i, j;
- // The 'edgeindex' (from 0 to 5) is list as follows:
- // 0 - (v0, v1), 1 - (v1, v2), 2 - (v2, v0)
- // 3 - (v3, v0), 4 - (v3, v1), 5 - (v3, v2)
- // Define an edgeindex map: (loc, ver)->edgeindex.
- int edgeindexmap[4][6] = {{0, 0, 1, 1, 2, 2},
- {3, 3, 4, 4, 0, 0},
- {4, 4, 5, 5, 1, 1},
- {5, 5, 3, 3, 2, 2}};
-
if (!b->quiet) {
printf("Adding vertices for second-order tetrahedra.\n");
}
@@ -28347,44 +31011,21 @@ void tetgenmesh::highorder()
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) {
// Operate on this edge.
- worktet = tetloop;
- worktet.loc = 0; worktet.ver = 0;
- // Get the correct edge in 'worktet'.
- switch(i) {
- case 0: // (v0, v1)
- break;
- case 1: // (v1, v2)
- enextself(worktet);
- break;
- case 2: // (v2, v0)
- enext2self(worktet);
- break;
- case 3: // (v3, v0)
- fnextself(worktet);
- enext2self(worktet);
- break;
- case 4: // (v3, v1)
- enextself(worktet);
- fnextself(worktet);
- enext2self(worktet);
- break;
- case 5: // (v3, v2)
- enext2self(worktet);
- fnextself(worktet);
- enext2self(worktet);
- }
+ worktet.loc = edge2locver[i][0];
+ worktet.ver = edge2locver[i][1];
// Create a new node on this edge.
torg = org(worktet);
tdest = dest(worktet);
// Create a new node in the middle of the edge.
newpoint = (point) points->alloc();
// Interpolate its attributes.
- // for (j = 0; j < 3 + in->numberofpointattributes; j++) {
- // newpoint[j] = 0.5 * (torg[j] + tdest[j]);
- // }
+ for (j = 0; j < 3 + in->numberofpointattributes; j++) {
+ newpoint[j] = 0.5 * (torg[j] + tdest[j]);
+ }
ptmark = (int) points->items - (in->firstnumber == 1 ? 0 : 1);
setpointmark(newpoint, ptmark);
// Add this node to its extra node list.
@@ -28399,7 +31040,7 @@ void tetgenmesh::highorder()
// Get the extra node list of 'spintet'.
adjextralist = (point *) spintet.tet[highorderindex];
// Find the index of its extra node list.
- j = edgeindexmap[spintet.loc][spintet.ver];
+ j = locver2edge[spintet.loc][spintet.ver];
// Only set 'newpoint' into 'adjextralist' if it is a NULL.
// Because two faces can belong to the same tetrahedron.
if (adjextralist[j] == (point) NULL) {
@@ -28457,8 +31098,7 @@ void tetgenmesh::outnodes(tetgenio* out)
}
}
- // nextras = in->numberofpointattributes;
- nextras = 0; // After version 1.4.0, don't output point attributes.
+ nextras = in->numberofpointattributes;
bmark = !b->nobound && in->pointmarkerlist;
// Avoid compile warnings.
@@ -28642,8 +31282,11 @@ void tetgenmesh::outmetrics(tetgenio* out)
{
FILE *outfile;
char outmtrfilename[FILENAMESIZE];
- point pointloop;
- int nextras, attribindex;
+ list *tetlist, *ptlist;
+ triface tetloop;
+ point ptloop, neipt;
+ REAL lave, len; // lmin, lmax,
+ int mtrindex;
int i;
if (out == (tetgenio *) NULL) {
@@ -28661,53 +31304,103 @@ void tetgenmesh::outmetrics(tetgenio* out)
// Avoid compile warnings.
outfile = (FILE *) NULL;
- attribindex = 0;
+ mtrindex = 0;
- nextras = 0;
- if (b->bgmesh) {
- nextras = bgm->in->numberofpointattributes;
- } else if (b->quality) {
- nextras = 1;
- }
if (out == (tetgenio *) NULL) {
outfile = fopen(outmtrfilename, "w");
if (outfile == (FILE *) NULL) {
printf("File I/O Error: Cannot create file %s.\n", outmtrfilename);
terminatetetgen(1);
}
- // Number of points, number of point attributes,
- fprintf(outfile, "%ld %d\n", points->items, nextras);
+ // Number of points, number of point metrices,
+ // fprintf(outfile, "%ld %d\n", points->items, sizeoftensor + 3);
+ fprintf(outfile, "%ld %d\n", points->items, 1);
} else {
- // Allocate space for 'pointattributelist' if necessary;
- if (nextras > 0) {
- out->pointattributelist = new REAL[points->items * nextras];
- if (out->pointattributelist == (REAL *) NULL) {
- printf("Error: Out of memory.\n");
- terminatetetgen(1);
- }
+ // Allocate space for 'pointmtrlist' if necessary;
+ // out->pointmtrlist = new REAL[points->items * (sizeoftensor + 3)];
+ out->pointmtrlist = new REAL[points->items];
+ if (out->pointmtrlist == (REAL *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
}
- out->numberofpointattributes = nextras;
- attribindex = 0;
+ out->numberofpointmtrs = 1; // (sizeoftensor + 3);
+ mtrindex = 0;
}
+ // Initialize the point2tet field of each point.
points->traversalinit();
- pointloop = pointtraverse();
- while (pointloop != (point) NULL) {
+ ptloop = pointtraverse();
+ while (ptloop != (point) NULL) {
+ setpoint2tet(ptloop, (tetrahedron) NULL);
+ ptloop = pointtraverse();
+ }
+ // Create the point-to-tet map.
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ for (i = 0; i < 4; i++) {
+ ptloop = (point) tetloop.tet[4 + i];
+ setpoint2tet(ptloop, encode(tetloop));
+ }
+ tetloop.tet = tetrahedrontraverse();
+ }
+
+ tetlist = new list(sizeof(triface), NULL, 256);
+ ptlist = new list(sizeof(point *), NULL, 256);
+
+ points->traversalinit();
+ ptloop = pointtraverse();
+ while (ptloop != (point) NULL) {
+ decode(point2tet(ptloop), tetloop);
+ if (!isdead(&tetloop)) {
+ // Form the star of p.
+ tetlist->append(&tetloop);
+ formstarpolyhedron(ptloop, tetlist, ptlist, true);
+ // lmin = longest;
+ // lmax = 0.0;
+ lave = 0.0;
+ for (i = 0; i < ptlist->len(); i++) {
+ neipt = * (point *)(* ptlist)[i];
+ len = distance(ptloop, neipt);
+ // lmin = lmin < len ? lmin : len;
+ // lmax = lmax > len ? lmax : len;
+ lave += len;
+ }
+ lave /= ptlist->len();
+ }
if (out == (tetgenio *) NULL) {
- for (i = 0; i < nextras; i++) {
- // Write an attribute.
- fprintf(outfile, "%-22.17e ", pointloop[3 + i]);
+ // for (i = 0; i < sizeoftensor; i++) {
+ // fprintf(outfile, "%-16.8e ", ptloop[pointmtrindex + i]);
+ // }
+ if (ptlist->len() > 0) {
+ // fprintf(outfile, "%-16.8e %-16.8e %-16.8e", lmin, lmax, lave);
+ fprintf(outfile, "%-16.8e ", lave);
+ } else {
+ fprintf(outfile, "0.0 "); // fprintf(outfile, "0.0 0.0 0.0");
}
fprintf(outfile, "\n");
} else {
- for (i = 0; i < nextras; i++) {
- // Output an attribute.
- out->pointattributelist[attribindex++] = pointloop[3 + i];
+ // for (i = 0; i < sizeoftensor; i++) {
+ // out->pointmtrlist[mtrindex++] = ptloop[pointmtrindex + i];
+ // }
+ if (ptlist->len() > 0) {
+ // out->pointmtrlist[mtrindex++] = lmin;
+ // out->pointmtrlist[mtrindex++] = lmax;
+ out->pointmtrlist[mtrindex++] = lave;
+ } else {
+ // out->pointmtrlist[mtrindex++] = 0.0;
+ // out->pointmtrlist[mtrindex++] = 0.0;
+ out->pointmtrlist[mtrindex++] = 0.0;
}
}
- pointloop = pointtraverse();
+ tetlist->clear();
+ ptlist->clear();
+ ptloop = pointtraverse();
}
+ delete tetlist;
+ delete ptlist;
+
if (out == (tetgenio *) NULL) {
fprintf(outfile, "# Generated by %s\n", b->commandline);
fclose(outfile);
@@ -28874,6 +31567,7 @@ void tetgenmesh::outfaces(tetgenio* out)
char facefilename[FILENAMESIZE];
int *elist;
int *emlist;
+ int neigh1, neigh2;
int index;
triface tface, tsymface;
face checkmark;
@@ -28927,6 +31621,14 @@ void tetgenmesh::outfaces(tetgenio* out)
terminatetetgen(1);
}
}
+ if (b->neighout > 1) {
+ // '-nn' switch.
+ out->adjtetlist = new int[subfaces->items * 2];
+ if (out->adjtetlist == (int *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
+ }
out->numberoftrifaces = faces;
elist = out->trifacelist;
emlist = out->trifacemarkerlist;
@@ -28973,6 +31675,15 @@ void tetgenmesh::outfaces(tetgenio* out)
marker = tsymface.tet != dummytet ? 1 : 0;
}
}
+ if (b->neighout > 1) {
+ // '-nn' switch. Output adjacent tets indices.
+ neigh1 = * (int *)(tface.tet + elemmarkerindex);
+ if (tsymface.tet != dummytet) {
+ neigh2 = * (int *)(tsymface.tet + elemmarkerindex);
+ } else {
+ neigh2 = -1;
+ }
+ }
if (out == (tetgenio *) NULL) {
// Face number, indices of three vertices.
fprintf(outfile, "%5d %4d %4d %4d", facenumber,
@@ -28982,6 +31693,9 @@ void tetgenmesh::outfaces(tetgenio* out)
// Output a boundary marker.
fprintf(outfile, " %d", marker);
}
+ if (b->neighout > 1) {
+ fprintf(outfile, " %5d %5d", neigh1, neigh2);
+ }
fprintf(outfile, "\n");
} else {
// Output indices of three vertices.
@@ -28991,6 +31705,10 @@ void tetgenmesh::outfaces(tetgenio* out)
if (bmark) {
emlist[facenumber - in->firstnumber] = marker;
}
+ if (b->neighout > 1) {
+ out->adjtetlist[(facenumber - in->firstnumber) * 2] = neigh1;
+ out->adjtetlist[(facenumber - in->firstnumber) * 2 + 1] = neigh2;
+ }
}
facenumber++;
}
@@ -29125,7 +31843,7 @@ void tetgenmesh::outsubfaces(tetgenio* out)
char facefilename[FILENAMESIZE];
int *elist;
int *emlist;
- int index;
+ int index, index1, index2;
triface abuttingtet;
face faceloop;
point torg, tdest, tapex;
@@ -29151,7 +31869,8 @@ void tetgenmesh::outsubfaces(tetgenio* out)
outfile = (FILE *) NULL;
elist = (int *) NULL;
emlist = (int *) NULL;
- index = marker = 0;
+ index = index1 = index2 = 0;
+ faceid = marker = 0;
neigh1 = neigh2 = 0;
bmark = !b->nobound && in->facetmarkerlist;
@@ -29190,7 +31909,6 @@ void tetgenmesh::outsubfaces(tetgenio* out)
out->numberoftrifaces = subfaces->items;
elist = out->trifacelist;
emlist = out->trifacemarkerlist;
- index = 0;
}
// Determine the first index (0 or 1).
@@ -29258,15 +31976,163 @@ void tetgenmesh::outsubfaces(tetgenio* out)
elist[index++] = pointmark(tdest) - shift;
elist[index++] = pointmark(tapex) - shift;
if (bmark) {
- emlist[facenumber - in->firstnumber] = marker;
+ emlist[index1++] = marker;
+ }
+ if (b->neighout > 1) {
+ out->adjtetlist[index2++] = neigh1;
+ out->adjtetlist[index2++] = neigh2;
+ }
+ }
+ facenumber++;
+ faceloop.sh = shellfacetraverse(subfaces);
+ }
+
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "# Generated by %s\n", b->commandline);
+ fclose(outfile);
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// outedges() Output all edges to a .edge file or a structure. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::outedges(tetgenio* out)
+{
+ FILE *outfile;
+ char edgefilename[FILENAMESIZE];
+ int *elist, *emlist;
+ int index, index1;
+ triface tetloop, worktet, spintet;
+ face checksh;
+ point torg, tdest;
+ long faces, edges;
+ int firstindex, shift;
+ int edgenumber, faceid, marker;
+ int hitbdry, i;
+
+ if (out == (tetgenio *) NULL) {
+ strcpy(edgefilename, b->outfilename);
+ strcat(edgefilename, ".edge");
+ }
+
+ if (!b->quiet) {
+ if (out == (tetgenio *) NULL) {
+ printf("Writing %s.\n", edgefilename);
+ } else {
+ printf("Writing edges.\n");
+ }
+ }
+
+ // Avoid compile warnings.
+ outfile = (FILE *) NULL;
+ elist = (int *) NULL;
+ emlist = (int *) NULL;
+ index = index1 = 0;
+ faceid = marker = 0;
+
+ // Using the Euler formula (V-E+F-T=1) to get the total number of edges.
+ faces = (4l * tetrahedrons->items + hullsize) / 2l;
+ edges = points->items + faces - tetrahedrons->items - 1l;
+
+ if (out == (tetgenio *) NULL) {
+ outfile = fopen(edgefilename, "w");
+ if (outfile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot create file %s.\n", edgefilename);
+ terminatetetgen(1);
+ }
+ // Write the number of edges, boundary markers (0 or 1).
+ fprintf(outfile, "%ld %d\n", edges, !b->nobound);
+ } else {
+ // Allocate memory for 'edgelist'.
+ out->edgelist = new int[edges * 2];
+ if (out->edgelist == (int *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
+ if (!b->nobound) {
+ out->edgemarkerlist = new int[edges];
+ }
+ out->numberofedges = edges;
+ elist = out->edgelist;
+ emlist = out->edgemarkerlist;
+ }
+
+ // Determine the first index (0 or 1).
+ firstindex = b->zeroindex ? 0 : in->firstnumber;
+ shift = 0; // Default no shiftment.
+ if ((in->firstnumber == 1) && (firstindex == 0)) {
+ shift = 1; // Shift (reduce) the output indices by 1.
+ }
+
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ edgenumber = firstindex; // in->firstnumber;
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ // Count the number of Voronoi faces. Look at the six edges of each
+ // tetrahedron. Count the edge only if the tetrahedron's pointer is
+ // smaller than those of all other tetrahedra that share the edge.
+ worktet.tet = tetloop.tet;
+ for (i = 0; i < 6; i++) {
+ worktet.loc = edge2locver[i][0];
+ worktet.ver = edge2locver[i][1];
+ adjustedgering(worktet, CW);
+ spintet = worktet;
+ hitbdry = 0;
+ while (hitbdry < 2) {
+ if (fnextself(spintet)) {
+ if (apex(spintet) == apex(worktet)) break;
+ if (spintet.tet < worktet.tet) break;
+ } else {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(worktet, spintet);
+ fnextself(spintet); // In the same tet.
+ }
+ }
}
- if (b->neighout > 1) {
- out->adjtetlist[(facenumber - in->firstnumber) * 2] = neigh1;
- out->adjtetlist[(facenumber - in->firstnumber) * 2 + 1] = neigh2;
+ // Count this edge if no adjacent tets are smaller than this tet.
+ if (spintet.tet >= worktet.tet) {
+ torg = org(worktet);
+ tdest = dest(worktet);
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "%5d %4d %4d", edgenumber,
+ pointmark(torg) - shift, pointmark(tdest) - shift);
+ } else {
+ // Output three vertices of this face;
+ elist[index++] = pointmark(torg) - shift;
+ elist[index++] = pointmark(tdest) - shift;
+ }
+ if (!b->nobound) {
+ if (hitbdry > 0) {
+ // It is a boundary edge. Get the boundary marker of the facet
+ // containing this edge. Note there may have more than one
+ // facet, choose one arbitrarily.
+ if ((b->plc || b->refine) && in->facetmarkerlist) {
+ tspivot(spintet, checksh);
+ faceid = shellmark(checksh) - 1;
+ marker = in->facetmarkerlist[faceid];
+ } else {
+ marker = 1; // Indicate it's a boundary edge.
+ }
+ } else {
+ marker = 0;
+ }
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " %d", marker);
+ } else {
+ emlist[index1++] = marker;
+ }
+ }
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "\n");
+ }
+ edgenumber++;
}
}
- facenumber++;
- faceloop.sh = shellfacetraverse(subfaces);
+ tetloop.tet = tetrahedrontraverse();
}
if (out == (tetgenio *) NULL) {
@@ -29301,7 +32167,7 @@ void tetgenmesh::outsubsegments(tetgenio* out)
if (out == (tetgenio *) NULL) {
printf("Writing %s.\n", edgefilename);
} else {
- printf("Writing faces.\n");
+ printf("Writing edges.\n");
}
}
@@ -29327,7 +32193,6 @@ void tetgenmesh::outsubsegments(tetgenio* out)
}
out->numberofedges = subsegs->items;
elist = out->edgelist;
- index = 0;
}
// Determine the first index (0 or 1).
@@ -29351,102 +32216,545 @@ void tetgenmesh::outsubsegments(tetgenio* out)
elist[index++] = pointmark(torg) - shift;
elist[index++] = pointmark(tdest) - shift;
}
- edgenumber++;
- edgeloop.sh = shellfacetraverse(subsegs);
+ edgenumber++;
+ edgeloop.sh = shellfacetraverse(subsegs);
+ }
+
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "# Generated by %s\n", b->commandline);
+ fclose(outfile);
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// outneighbors() Output tet neighbors to a .neigh file or a structure. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::outneighbors(tetgenio* out)
+{
+ FILE *outfile;
+ char neighborfilename[FILENAMESIZE];
+ int *nlist;
+ int index;
+ triface tetloop, tetsym;
+ int neighbor1, neighbor2, neighbor3, neighbor4;
+ int firstindex;
+ int elementnumber;
+
+ if (out == (tetgenio *) NULL) {
+ strcpy(neighborfilename, b->outfilename);
+ strcat(neighborfilename, ".neigh");
+ }
+
+ if (!b->quiet) {
+ if (out == (tetgenio *) NULL) {
+ printf("Writing %s.\n", neighborfilename);
+ } else {
+ printf("Writing neighbors.\n");
+ }
+ }
+
+ // Avoid compile warnings.
+ outfile = (FILE *) NULL;
+ nlist = (int *) NULL;
+ index = 0;
+
+ if (out == (tetgenio *) NULL) {
+ outfile = fopen(neighborfilename, "w");
+ if (outfile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot create file %s.\n", neighborfilename);
+ terminatetetgen(1);
+ }
+ // Number of tetrahedra, four faces per tetrahedron.
+ fprintf(outfile, "%ld %d\n", tetrahedrons->items, 4);
+ } else {
+ // Allocate memory for 'neighborlist'.
+ out->neighborlist = new int[tetrahedrons->items * 4];
+ if (out->neighborlist == (int *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
+ nlist = out->neighborlist;
+ }
+
+ // Determine the first index (0 or 1).
+ firstindex = b->zeroindex ? 0 : in->firstnumber;
+
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ elementnumber = firstindex; // in->firstnumber;
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ tetloop.loc = 2;
+ sym(tetloop, tetsym);
+ neighbor1 = * (int *) (tetsym.tet + elemmarkerindex);
+ tetloop.loc = 3;
+ sym(tetloop, tetsym);
+ neighbor2 = * (int *) (tetsym.tet + elemmarkerindex);
+ tetloop.loc = 1;
+ sym(tetloop, tetsym);
+ neighbor3 = * (int *) (tetsym.tet + elemmarkerindex);
+ tetloop.loc = 0;
+ sym(tetloop, tetsym);
+ neighbor4 = * (int *) (tetsym.tet + elemmarkerindex);
+ if (out == (tetgenio *) NULL) {
+ // Tetrahedra number, neighboring tetrahedron numbers.
+ fprintf(outfile, "%4d %4d %4d %4d %4d\n", elementnumber,
+ neighbor1, neighbor2, neighbor3, neighbor4);
+ } else {
+ nlist[index++] = neighbor1;
+ nlist[index++] = neighbor2;
+ nlist[index++] = neighbor3;
+ nlist[index++] = neighbor4;
+ }
+ tetloop.tet = tetrahedrontraverse();
+ elementnumber++;
+ }
+
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "# Generated by %s\n", b->commandline);
+ fclose(outfile);
+ }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// outvoronoi() Output the Voronoi diagram to .v.node, .v.edge, v.face, //
+// and .v.cell. //
+// //
+// The Voronoi diagram is the geometric dual of the Delaunay triangulation. //
+// The Voronoi vertices are the circumcenters of Delaunay tetrahedra. Each //
+// Voronoi edge connects two Voronoi vertices at two sides of a common Dela- //
+// unay face. At a face of convex hull, it becomes a ray (goto the infinity).//
+// A Voronoi face is the convex hull of all Voronoi vertices around a common //
+// Delaunay edge. It is a closed polygon for any interal Delaunay edge. At a //
+// ridge, it is unbounded. Each Voronoi cell is the convex hull of all Vor- //
+// onoi vertices around a common Delaunay vertex. It is a polytope for any //
+// internal Delaunay vertex. It is an unbounded polyhedron for a Delaunay //
+// vertex belonging to the convex hull. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+void tetgenmesh::outvoronoi(tetgenio* out)
+{
+ FILE *outfile;
+ char outfilename[FILENAMESIZE];
+ tetgenio::voroedge *vedge;
+ tetgenio::vorofacet *vfacet;
+ list *tetlist, *ptlist;
+ triface tetloop, worktet, spintet;
+ point pt[4], ptloop, neipt;
+ REAL ccent[3], infvec[3], vec1[3], vec2[3], L;
+ long faces, edges;
+ int *tetfaceindexarray, *tetedgeindexarray;
+ int arraysize, *vertarray;
+ int vpointcount, vedgecount, vfacecount, tcount;
+ int index, shift;
+ int end1, end2;
+ int hitbdry, i, j, k;
+
+ // Output Voronoi vertices to .v.node file.
+ if (out == (tetgenio *) NULL) {
+ strcpy(outfilename, b->outfilename);
+ strcat(outfilename, ".v.node");
+ }
+
+ if (!b->quiet) {
+ if (out == (tetgenio *) NULL) {
+ printf("Writing %s.\n", outfilename);
+ } else {
+ printf("Writing Voronoi vertices.\n");
+ }
+ }
+
+ // Determine the first index (0 or 1).
+ shift = (b->zeroindex ? 0 : in->firstnumber);
+ // The number of Delaunay faces (= the number of Voronoi edges).
+ faces = (4l * tetrahedrons->items + hullsize) / 2l;
+ // The number of Delaunay edges (= the number of Voronoi faces).
+ edges = points->items + faces - tetrahedrons->items - 1;
+ outfile = (FILE *) NULL; // Avoid compile warnings.
+
+ if (out == (tetgenio *) NULL) {
+ outfile = fopen(outfilename, "w");
+ if (outfile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot create file %s.\n", outfilename);
+ terminatetetgen(1);
+ }
+ // Number of voronoi points, 3 dim, no attributes, no marker.
+ fprintf(outfile, "%ld 3 0 0\n", tetrahedrons->items);
+ } else {
+ // Allocate space for 'vpointlist'.
+ out->numberofvpoints = (int) tetrahedrons->items;
+ out->vpointlist = new REAL[out->numberofvpoints * 3];
+ if (out->vpointlist == (REAL *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
+ }
+
+ // Loop the tetrahedronlist once, do the following:
+ // (1) Output Voronoi vertices (the circumcenter of the tetrahedron).
+ // (2) Make a map from points-to-tetrahedra (for Voronoi cells).
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ vpointcount = 0;
+ index = 0;
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ // Calculate the circumcenter.
+ for (i = 0; i < 4; i++) {
+ pt[i] = (point) tetloop.tet[4 + i];
+ setpoint2tet(pt[i], encode(tetloop));
+ }
+ 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]);
+ } else {
+ out->vpointlist[index++] = ccent[0];
+ out->vpointlist[index++] = ccent[1];
+ out->vpointlist[index++] = ccent[2];
+ }
+ // Remember the index of this element.
+ * (int *) (tetloop.tet + elemmarkerindex) = vpointcount;
+ vpointcount++;
+ tetloop.tet = tetrahedrontraverse();
+ }
+ // Set the outside element marker.
+ * (int *) (dummytet + elemmarkerindex) = -1;
+
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "# Generated by %s\n", b->commandline);
+ fclose(outfile);
+ }
+
+ // Output Voronoi edges to .v.edge file.
+ if (out == (tetgenio *) NULL) {
+ strcpy(outfilename, b->outfilename);
+ strcat(outfilename, ".v.edge");
+ }
+
+ if (!b->quiet) {
+ if (out == (tetgenio *) NULL) {
+ printf("Writing %s.\n", outfilename);
+ } else {
+ printf("Writing Voronoi edges.\n");
+ }
+ }
+
+ if (out == (tetgenio *) NULL) {
+ outfile = fopen(outfilename, "w");
+ if (outfile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot create file %s.\n", outfilename);
+ terminatetetgen(1);
+ }
+ // Number of Voronoi edges, no marker.
+ fprintf(outfile, "%ld 0\n", faces);
+ } else {
+ // Allocate space for 'vpointlist'.
+ out->numberofedges = (int) faces;
+ out->vedgelist = new tetgenio::voroedge[out->numberofvedges];
+ }
+
+ // Loop the tetrahedronlist once, output the Voronoi edges. The index of
+ // each Voronoi edge corresponding to the index of the Delaunay face.
+ // The four faces' indices of each tetrahedron are saved in the list
+ // 'tetfaceindexarray', in the entry of i, where i (0-based) is the
+ // index of this tetrahedron (= vpointcount).
+ tetfaceindexarray = new int[tetrahedrons->items * 4];
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ vedgecount = 0;
+ index = 0;
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ // Count the number of Voronoi edges. Look at the four faces of each
+ // tetrahedron. Count the face if the tetrahedron's pointer is
+ // smaller than its neighbor's or the neighbor is outside.
+ end1 = * (int *) (tetloop.tet + elemmarkerindex);
+ for (i = 0; i < 4; i++) {
+ decode(tetloop.tet[i], worktet);
+ if ((worktet.tet == dummytet) || (tetloop.tet < worktet.tet)) {
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "%4d %4d", vedgecount + shift, end1 + shift);
+ } else {
+ vedge = &(out->vedgelist[index++]);
+ vedge->v1 = end1 + shift;
+ }
+ end2 = * (int *) (worktet.tet + elemmarkerindex);
+ // Note that end2 may be -1 (worktet.tet is outside).
+ if (end2 == -1) {
+ // Calculate the out normal of this hull face.
+ worktet.tet = tetloop.tet;
+ worktet.loc = i;
+ worktet.ver = 1; // The CW edge ring.
+ pt[0] = org(worktet);
+ pt[1] = dest(worktet);
+ pt[2] = apex(worktet);
+ for (j = 0; j < 3; j++) vec1[j] = pt[1][j] - pt[0][j];
+ for (j = 0; j < 3; j++) vec2[j] = pt[2][j] - pt[0][j];
+ cross(vec1, vec2, infvec);
+ // Normalize it.
+ L = sqrt(infvec[0] * infvec[0] + infvec[1] * infvec[1]
+ + infvec[2] * infvec[2]);
+ if (L > 0) for (j = 0; j < 3; j++) infvec[j] /= L;
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " -1");
+ fprintf(outfile, " %g %g %g\n", infvec[0], infvec[1], infvec[2]);
+ } else {
+ vedge->v2 = -1;
+ vedge->vnormal[0] = infvec[0];
+ vedge->vnormal[1] = infvec[1];
+ vedge->vnormal[2] = infvec[2];
+ }
+ } else {
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " %4d\n", end2 + shift);
+ } else {
+ vedge->v2 = end2 + shift;
+ vedge->vnormal[0] = 0.0;
+ vedge->vnormal[1] = 0.0;
+ vedge->vnormal[2] = 0.0;
+ }
+ }
+ // Save the face index in this tet and its neighbor if exists.
+ tetfaceindexarray[end1 * 4 + i] = vedgecount;
+ if (end2 != -1) {
+ tetfaceindexarray[end2 * 4 + worktet.loc] = vedgecount;
+ }
+ vedgecount++;
+ }
+ }
+ tetloop.tet = tetrahedrontraverse();
+ }
+
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "# Generated by %s\n", b->commandline);
+ fclose(outfile);
+ }
+
+ // Output Voronoi faces to .v.face file.
+ if (out == (tetgenio *) NULL) {
+ strcpy(outfilename, b->outfilename);
+ strcat(outfilename, ".v.face");
+ }
+
+ if (!b->quiet) {
+ if (out == (tetgenio *) NULL) {
+ printf("Writing %s.\n", outfilename);
+ } else {
+ printf("Writing Voronoi faces.\n");
+ }
+ }
+
+ if (out == (tetgenio *) NULL) {
+ outfile = fopen(outfilename, "w");
+ if (outfile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot create file %s.\n", outfilename);
+ terminatetetgen(1);
+ }
+ // Number of Voronoi faces.
+ fprintf(outfile, "%ld 0\n", edges);
+ } else {
+ out->numberofvfacets = edges;
+ out->vfacetlist = new tetgenio::vorofacet[out->numberofvfacets];
+ if (out->vfacetlist == (tetgenio::vorofacet *) NULL) {
+ printf("Error: Out of memory.\n");
+ terminatetetgen(1);
+ }
+ }
+
+ // Loop the tetrahedronlist once, Output Voronoi facets. The index of each
+ // Voronoi facet corresponding to the index of the Delaunay edge. The
+ // six edges' indices of each tetrahedron are saved in the list 'tetedge-
+ // indexarray', in the entry of i, where i (0-based) is the index of
+ // this tetrahedron (= vpointcount).
+ tetedgeindexarray = new int[tetrahedrons->items * 6];
+ tetrahedrons->traversalinit();
+ tetloop.tet = tetrahedrontraverse();
+ vfacecount = 0;
+ while (tetloop.tet != (tetrahedron *) NULL) {
+ // Count the number of Voronoi faces. Look at the six edges of each
+ // tetrahedron. Count the edge only if the tetrahedron's pointer is
+ // smaller than those of all other tetrahedra that share the edge.
+ worktet = tetloop;
+ for (i = 0; i < 6; i++) {
+ worktet.loc = edge2locver[i][0];
+ worktet.ver = edge2locver[i][1];
+ // Now count the number of tets surrounding this edge.
+ tcount = 1;
+ adjustedgering(worktet, CW);
+ spintet = worktet;
+ hitbdry = 0;
+ while (hitbdry < 2) {
+ if (fnextself(spintet)) {
+ if (apex(spintet) == apex(worktet)) break;
+ if (spintet.tet < worktet.tet) break;
+ tcount++;
+ } else {
+ hitbdry++;
+ if (hitbdry < 2) {
+ esym(worktet, spintet);
+ fnextself(spintet); // In the same tet.
+ }
+ }
+ }
+ // Count this edge if no adjacent tets are smaller than this tet.
+ if (spintet.tet >= worktet.tet) {
+ // Get the two endpoints of this edge.
+ pt[0] = org(worktet);
+ pt[1] = dest(worktet);
+ end1 = pointmark(pt[0]) - in->firstnumber;
+ end2 = pointmark(pt[1]) - in->firstnumber;
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "%4d %4d %4d %-2d ", vfacecount + shift,
+ end1 + shift, end2 + shift, tcount + (hitbdry > 0));
+ } else {
+ vfacet = &(out->vfacetlist[vfacecount]);
+ vfacet->c1 = end1 + shift;
+ vfacet->c2 = end2 + shift;
+ vfacet->elist = new int[tcount + (hitbdry > 0) + 1];
+ vfacet->elist[0] = tcount + (hitbdry > 0);
+ index = 1;
+ }
+ // If hitbdry > 0, then spintet is a hull face.
+ if (hitbdry > 0) {
+ // The edge list starts with a ray.
+ vpointcount = * (int *) (spintet.tet + elemmarkerindex);
+ vedgecount = tetfaceindexarray[vpointcount * 4 + spintet.loc];
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " %d", vedgecount + shift);
+ } else {
+ vfacet->elist[index++] = vedgecount + shift;
+ }
+ // Save this facet number in tet.
+ tetedgeindexarray[vpointcount * 6 +
+ locver2edge[spintet.loc][spintet.ver]] = vfacecount;
+ esymself(spintet);
+ fnextself(spintet); // In the same tet.
+ }
+ // Output internal Voronoi edges.
+ for (j = 0; j < tcount; j++) {
+ vpointcount = * (int *) (spintet.tet + elemmarkerindex);
+ vedgecount = tetfaceindexarray[vpointcount * 4 + spintet.loc];
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " %d", vedgecount + shift);
+ } else {
+ vfacet->elist[index++] = vedgecount + shift;
+ }
+ // Save this facet number in tet.
+ tetedgeindexarray[vpointcount * 6 +
+ locver2edge[spintet.loc][spintet.ver]] = vfacecount;
+ fnextself(spintet);
+ }
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "\n");
+ }
+ vfacecount++;
+ }
+ } // if (i = 0; i < 6; i++)
+ tetloop.tet = tetrahedrontraverse();
}
if (out == (tetgenio *) NULL) {
fprintf(outfile, "# Generated by %s\n", b->commandline);
fclose(outfile);
}
-}
-
-///////////////////////////////////////////////////////////////////////////////
-// //
-// outneighbors() Output tet neighbors to a .neigh file or a structure. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::outneighbors(tetgenio* out)
-{
- FILE *outfile;
- char neighborfilename[FILENAMESIZE];
- int *nlist;
- int index;
- triface tetloop, tetsym;
- int neighbor1, neighbor2, neighbor3, neighbor4;
- int firstindex;
- int elementnumber;
+ // Output Voronoi cells to .v.cell file.
if (out == (tetgenio *) NULL) {
- strcpy(neighborfilename, b->outfilename);
- strcat(neighborfilename, ".neigh");
+ strcpy(outfilename, b->outfilename);
+ strcat(outfilename, ".v.cell");
}
-
+
if (!b->quiet) {
if (out == (tetgenio *) NULL) {
- printf("Writing %s.\n", neighborfilename);
+ printf("Writing %s.\n", outfilename);
} else {
- printf("Writing neighbors.\n");
+ printf("Writing Voronoi cells.\n");
}
}
- // Avoid compile warnings.
- outfile = (FILE *) NULL;
- nlist = (int *) NULL;
- index = 0;
-
if (out == (tetgenio *) NULL) {
- outfile = fopen(neighborfilename, "w");
+ outfile = fopen(outfilename, "w");
if (outfile == (FILE *) NULL) {
- printf("File I/O Error: Cannot create file %s.\n", neighborfilename);
+ printf("File I/O Error: Cannot create file %s.\n", outfilename);
terminatetetgen(1);
}
- // Number of tetrahedra, four faces per tetrahedron.
- fprintf(outfile, "%ld %d\n", tetrahedrons->items, 4);
+ // Number of Voronoi cells.
+ fprintf(outfile, "%ld\n", points->items);
} else {
- // Allocate memory for 'neighborlist'.
- out->neighborlist = new int[tetrahedrons->items * 4];
- if (out->neighborlist == (int *) NULL) {
+ out->numberofvcells = points->items;
+ out->vcelllist = new int*[out->numberofvcells];
+ if (out->vcelllist == (int **) NULL) {
printf("Error: Out of memory.\n");
terminatetetgen(1);
}
- nlist = out->neighborlist;
- index = 0;
}
- // Determine the first index (0 or 1).
- firstindex = b->zeroindex ? 0 : in->firstnumber;
-
- tetrahedrons->traversalinit();
- tetloop.tet = tetrahedrontraverse();
- elementnumber = firstindex; // in->firstnumber;
- while (tetloop.tet != (tetrahedron *) NULL) {
- tetloop.loc = 2;
- sym(tetloop, tetsym);
- neighbor1 = * (int *) (tetsym.tet + elemmarkerindex);
- tetloop.loc = 3;
- sym(tetloop, tetsym);
- neighbor2 = * (int *) (tetsym.tet + elemmarkerindex);
- tetloop.loc = 1;
- sym(tetloop, tetsym);
- neighbor3 = * (int *) (tetsym.tet + elemmarkerindex);
- tetloop.loc = 0;
- sym(tetloop, tetsym);
- neighbor4 = * (int *) (tetsym.tet + elemmarkerindex);
- if (out == (tetgenio *) NULL) {
- // Tetrahedra number, neighboring tetrahedron numbers.
- fprintf(outfile, "%4d %4d %4d %4d %4d\n", elementnumber,
- neighbor1, neighbor2, neighbor3, neighbor4);
- } else {
- nlist[index++] = neighbor1;
- nlist[index++] = neighbor2;
- nlist[index++] = neighbor3;
- nlist[index++] = neighbor4;
+ // Loop through point list, for each point, output a Voronoi cell.
+ tetlist = new list(sizeof(triface), NULL, 256);
+ ptlist = new list(sizeof(point *), NULL, 256);
+ points->traversalinit();
+ ptloop = pointtraverse();
+ vpointcount = 0;
+ while (ptloop != (point) NULL) {
+ decode(point2tet(ptloop), tetloop);
+ // assert(!isdead(&tetloop));
+ if (!isdead(&tetloop)) {
+ // Form the star of p.
+ tetlist->append(&tetloop);
+ formstarpolyhedron(ptloop, tetlist, ptlist, true);
+ tcount = ptlist->len();
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "%4d %-2d ", vpointcount + shift, tcount);
+ } else {
+ arraysize = tcount;
+ vertarray = out->vcelllist[vpointcount];
+ vertarray = new int[arraysize + 1];
+ vertarray[0] = arraysize;
+ index = 1;
+ }
+ // List Voronoi facets bounding this cell.
+ for (i = 0; i < ptlist->len(); i++) {
+ neipt = * (point *)(* ptlist)[i];
+ // Find a tet in tetlist having edge (ptloop, neipt) -- Very Slow.
+ for (j = 0; j < tetlist->len(); j++) {
+ tetloop = * (triface *)(* tetlist)[j];
+ for (k = 0; k < 6; k++) {
+ tetloop.loc = edge2locver[k][0];
+ tetloop.ver = edge2locver[k][1];
+ if (org(tetloop) == ptloop) {
+ if (dest(tetloop) == neipt) break;
+ } else if (org(tetloop) == neipt) {
+ if (dest(tetloop) == ptloop) break;
+ }
+ }
+ if (k < 6) break; // Found this edge.
+ }
+ assert(j < tetlist->len());
+ // k is the right edge number.
+ end1 = * (int *) (tetloop.tet + elemmarkerindex);
+ vfacecount = tetedgeindexarray[end1 * 6 + k];
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, " %d", vfacecount + shift);
+ } else {
+ vertarray[index++] = vfacecount + shift;
+ }
+ } // for (i = 0; i < ptlist->len(); i++) {
+ if (out == (tetgenio *) NULL) {
+ fprintf(outfile, "\n");
+ }
+ vpointcount++;
}
- tetloop.tet = tetrahedrontraverse();
- elementnumber++;
+ tetlist->clear();
+ ptlist->clear();
+ ptloop = pointtraverse();
}
+ delete tetlist;
+ delete ptlist;
+ delete [] tetfaceindexarray;
+ delete [] tetedgeindexarray;
if (out == (tetgenio *) NULL) {
fprintf(outfile, "# Generated by %s\n", b->commandline);
@@ -29779,7 +33087,7 @@ void tetgenmesh::outmesh2medit(char* mfilename)
tetrahedron* tetptr;
triface tface, tsymface;
face segloop, checkmark;
- point pointloop, p1, p2, p3, p4;
+ point ptloop, p1, p2, p3, p4;
long faces;
int pointnumber;
int i;
@@ -29813,20 +33121,19 @@ void tetgenmesh::outmesh2medit(char* mfilename)
fprintf(outfile, "%ld\n", points->items);
points->traversalinit();
- pointloop = pointtraverse();
+ ptloop = pointtraverse();
pointnumber = 1; // Medit need start number form 1.
- while (pointloop != (point) NULL) {
+ while (ptloop != (point) NULL) {
// Point coordinates.
- fprintf(outfile, "%.17g %.17g %.17g",
- pointloop[0], pointloop[1], pointloop[2]);
+ fprintf(outfile, "%.17g %.17g %.17g", ptloop[0], ptloop[1], ptloop[2]);
if (in->numberofpointattributes > 0) {
// Write an attribute, ignore others if more than one.
- fprintf(outfile, " %.17g\n", pointloop[3]);
+ fprintf(outfile, " %.17g\n", ptloop[3]);
} else {
fprintf(outfile, " 0\n");
}
- setpointmark(pointloop, pointnumber);
- pointloop = pointtraverse();
+ setpointmark(ptloop, pointnumber);
+ ptloop = pointtraverse();
pointnumber++;
}
@@ -29927,7 +33234,7 @@ void tetgenmesh::outmesh2gid(char* gfilename)
tetrahedron* tetptr;
triface tface, tsymface;
face sface;
- point pointloop, p1, p2, p3, p4;
+ point ptloop, p1, p2, p3, p4;
int pointnumber;
int elementnumber;
@@ -29953,19 +33260,19 @@ void tetgenmesh::outmesh2gid(char* gfilename)
fprintf(outfile, "coordinates\n");
points->traversalinit();
- pointloop = pointtraverse();
+ ptloop = pointtraverse();
pointnumber = 1; // Gid need start number form 1.
- while (pointloop != (point) NULL) {
+ while (ptloop != (point) NULL) {
// Point coordinates.
fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber,
- pointloop[0], pointloop[1], pointloop[2]);
+ ptloop[0], ptloop[1], ptloop[2]);
if (in->numberofpointattributes > 0) {
// Write an attribute, ignore others if more than one.
- fprintf(outfile, " %.17g", pointloop[3]);
+ fprintf(outfile, " %.17g", ptloop[3]);
}
fprintf(outfile, "\n");
- setpointmark(pointloop, pointnumber);
- pointloop = pointtraverse();
+ setpointmark(ptloop, pointnumber);
+ ptloop = pointtraverse();
pointnumber++;
}
@@ -30015,19 +33322,19 @@ void tetgenmesh::outmesh2gid(char* gfilename)
fprintf(outfile, "coordinates\n");
points->traversalinit();
- pointloop = pointtraverse();
+ ptloop = pointtraverse();
pointnumber = 1; // Gid need start number form 1.
- while (pointloop != (point) NULL) {
+ while (ptloop != (point) NULL) {
// Point coordinates.
fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber,
- pointloop[0], pointloop[1], pointloop[2]);
+ ptloop[0], ptloop[1], ptloop[2]);
if (in->numberofpointattributes > 0) {
// Write an attribute, ignore others if more than one.
- fprintf(outfile, " %.17g", pointloop[3]);
+ fprintf(outfile, " %.17g", ptloop[3]);
}
fprintf(outfile, "\n");
- setpointmark(pointloop, pointnumber);
- pointloop = pointtraverse();
+ setpointmark(ptloop, pointnumber);
+ ptloop = pointtraverse();
pointnumber++;
}
@@ -30081,7 +33388,7 @@ void tetgenmesh::outmesh2off(char* ofilename)
FILE *outfile;
char offfilename[FILENAMESIZE];
triface tface, tsymface;
- point pointloop, p1, p2, p3;
+ point ptloop, p1, p2, p3;
long faces;
int shift;
@@ -30111,11 +33418,10 @@ void tetgenmesh::outmesh2off(char* ofilename)
// Write the points.
points->traversalinit();
- pointloop = pointtraverse();
- while (pointloop != (point) NULL) {
- fprintf(outfile, " %.17g %.17g %.17g\n", pointloop[0], pointloop[1],
- pointloop[2]);
- pointloop = pointtraverse();
+ ptloop = pointtraverse();
+ while (ptloop != (point) NULL) {
+ fprintf(outfile, " %.17g %.17g %.17g\n",ptloop[0], ptloop[1], ptloop[2]);
+ ptloop = pointtraverse();
}
// OFF always use zero as the first index.
@@ -30527,10 +33833,10 @@ void tetgenmesh::checkdelaunay(REAL eps, queue* flipqueue)
case T32: printf("\"T32\""); break;
case T22: printf("\"T22\""); break;
case T44: printf("\"T44\""); break;
- case UNFLIPABLE: printf("\"UNFLIPABLE\""); break;
+ case N32: printf("\"N32\""); break;
+ case N40: printf("\"N40\""); break;
case FORBIDDENFACE:printf("\"FORBIDDENFACE\""); break;
case FORBIDDENEDGE:printf("\"FORBIDDENEDGE\""); break;
- case NONCONVEX:printf("\"NONCONVEX\""); break;
}
printf("\n");
}
@@ -30552,69 +33858,6 @@ void tetgenmesh::checkdelaunay(REAL eps, queue* flipqueue)
}
}
-///////////////////////////////////////////////////////////////////////////////
-// //
-// checkdegeneracy() Check if the point set contains degeneracies. //
-// //
-// 'eps' is a relative error tolerance for testing approximatly degeneracies.//
-// Set it to zero if only exact test is desired. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
-void tetgenmesh::checkdegeneracy(REAL eps)
-{
- triface tetraloop;
- triface oppotet;
- point tetorg, tetdest, tetapex, tetoppo;
- point oppooppo;
- REAL sign;
- int horrors;
-
- if (!b->quiet) {
- printf(" Checking degeneracies in the point set...\n");
- }
- horrors = 0;
- // Run through the list of triangles, checking each one.
- tetrahedrons->traversalinit();
- tetraloop.tet = tetrahedrontraverse();
- while (tetraloop.tet != (tetrahedron *) NULL) {
- // Check all four faces of the tetrahedron.
- for (tetraloop.loc = 0; tetraloop.loc < 4; tetraloop.loc++) {
- tetorg = org(tetraloop);
- tetdest = dest(tetraloop);
- tetapex = apex(tetraloop);
- tetoppo = oppo(tetraloop);
- sym(tetraloop, oppotet);
- oppooppo = oppo(oppotet);
- // Only do test if there is an adjoining tetrahedron whose pointer is
- // larger (to ensure that each pair isn't tested twice).
- if ((oppotet.tet != dummytet) && (tetoppo != (point) NULL) &&
- (oppooppo != (point) NULL) && (tetraloop.tet < oppotet.tet)) {
- sign = insphere(tetdest, tetorg, tetapex, tetoppo, oppooppo);
- if ((sign != 0.0) && (eps > 0.0)) {
- if (iscospheric(tetdest, tetorg, tetapex, tetoppo, oppooppo, sign,
- eps)) sign = 0.0;
- }
- if (sign == 0.0) {
- printf(" !! Degenerate set (%d, %d, %d, %d, %d).\n",
- pointmark(tetorg), pointmark(tetdest), pointmark(tetapex),
- pointmark(tetoppo), pointmark(oppooppo));
- horrors++;
- }
- }
- }
- tetraloop.tet = tetrahedrontraverse();
- }
-
- if (horrors == 0) {
- if (!b->quiet) {
- printf(" The point set is non-degenerate.\n");
- }
- } else {
- printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
- }
-}
-
///////////////////////////////////////////////////////////////////////////////
// //
// checkconforming() Ensure that the mesh is conforming Delaunay. //
@@ -30673,9 +33916,14 @@ void tetgenmesh::checkconforming()
// //
///////////////////////////////////////////////////////////////////////////////
+#ifdef SELF_CHECK
+
void tetgenmesh::algorithmicstatistics()
{
+ /*
printf("Algorithmic statistics:\n\n");
+ printf(" Point location millisecond: %g\n", (REAL) tloctime * 1e+3);
+ printf(" Flip millisecond: %g\n", (REAL) tfliptime * 1e+3);
if (b->plc || b->refine) {
printf(" Number of facet above points calculations: %ld\n", abovecount);
}
@@ -30684,12 +33932,11 @@ void tetgenmesh::algorithmicstatistics()
r3count);
}
if (b->quality) {
- printf(" Bowyer-Watson counts (seg, sub, vol)\n");
- printf(" Insert vertices: %ld, %ld, %ld\n",
+ printf(" Bowyer-Watson insertions: seg %ld, sub %ld, vol %ld.\n",
bowatsegcount, bowatsubcount, bowatvolcount);
- printf(" Update cavities: %ld, %ld, %ld\n",
+ printf(" Bowyer-Watson corrections: seg %ld, sub %ld, vol %ld\n",
updsegcount, updsubcount, updvolcount);
- printf(" Failed cavities: %ld, %ld, %ld\n",
+ printf(" Bowyer-Watson failures: seg %ld, sub %ld, vol %ld\n",
failsegcount, failsubcount, failvolcount);
printf(" Number of repair flips: %ld.\n", repairflipcount);
printf(" Number of circumcenters outside Bowat-cav.: %ld.\n",
@@ -30698,25 +33945,21 @@ void tetgenmesh::algorithmicstatistics()
printf(" Segment split rules: R2 %ld, R3 %ld\n", r2count, r3count);
printf(" Number of CDT enforcement points: %ld.\n", cdtenforcesegpts);
}
- printf(" Reject vertices counts:\n");
- printf(" Rejected seg splits: %ld.\n", rejsegpts);
- printf(" Rejected sub splits: %ld.\n", rejsubpts);
- printf(" Rejected tet splits: %ld.\n", rejtetpts);
- if (b->smooth) {
- printf(" Mesh smooth counts:\n");
- printf(" %4ld cdt enforcement points.\n", smoothcdtsegpt);
- printf(" %4ld segment points.\n", smoothsegpt);
- printf(" %4ld facet points.\n", smoothsubpt);
- printf(" %4ld volume points.\n", smoothvolpt);
- printf(" %4ld failed cdt enforcement points.\n", unsmoothcdtsegpt);
- printf(" %4ld unimproved segment points.\n", unsmoothsegpt);
- printf(" %4ld unimproved facet points.\n", unsmoothsubpt);
- printf(" %4ld unimproved volume points.\n", unsmoothvolpt);
+ printf(" Number of Rejections: seg %ld, sub %ld, tet %ld.\n", rejsegpts,
+ rejsubpts, rejtetpts);
+ if (b->optlevel) {
+ printf(
+ " Optimization flips: f32 %ld, f44 %ld, f56 %ld, f68 %ld, fnm %ld.\n",
+ optcount[3], optcount[4], optcount[5], optcount[6], optcount[9]);
+ printf(" Optimization segment deletions: %ld.\n", optcount[1]);
}
}
printf("\n");
+ */
}
+#endif // #ifdef SELF_CHECK
+
///////////////////////////////////////////////////////////////////////////////
// //
// qualitystatistics() Print statistics about the quality of the mesh. //
@@ -30725,25 +33968,28 @@ void tetgenmesh::algorithmicstatistics()
void tetgenmesh::qualitystatistics()
{
- triface tetloop;
+ triface tetloop, neightet;
point p[4];
char sbuf[128];
REAL radiusratiotable[12];
REAL aspectratiotable[12];
REAL A[4][4], rhs[4], D;
REAL V[6][3], N[4][3], H[4]; // edge-vectors, face-normals, face-heights.
- REAL edgelength[6], alldihed[6];
+ REAL edgelength[6], alldihed[6], faceangle[3];
REAL shortest, longest;
REAL smallestvolume, biggestvolume;
REAL smallestdiangle, biggestdiangle;
+ REAL smallestfaangle, biggestfaangle;
REAL tetvol, minaltitude;
REAL cirradius, minheightinv; // insradius;
REAL shortlen, longlen;
REAL tetaspect, tetradius;
REAL smalldiangle, bigdiangle;
+ REAL smallfaangle, bigfaangle;
int radiustable[12];
int aspecttable[16];
int dihedangletable[18];
+ int faceangletable[18];
int indx[4];
int radiusindex;
int aspectindex;
@@ -30773,6 +34019,7 @@ void tetgenmesh::qualitystatistics()
for (i = 0; i < 12; i++) radiustable[i] = 0;
for (i = 0; i < 12; i++) aspecttable[i] = 0;
for (i = 0; i < 18; i++) dihedangletable[i] = 0;
+ for (i = 0; i < 18; i++) faceangletable[i] = 0;
minaltitude = xmax - xmin + ymax - ymin + zmax - zmin;
minaltitude = minaltitude * minaltitude;
@@ -30780,8 +34027,8 @@ void tetgenmesh::qualitystatistics()
longest = 0.0;
smallestvolume = minaltitude;
biggestvolume = 0.0;
- smallestdiangle = 180.0;
- biggestdiangle = 0.0;
+ smallestdiangle = smallestfaangle = 180.0;
+ biggestdiangle = biggestfaangle = 0.0;
// Loop all elements, calculate quality parameters for each element.
tetrahedrons->traversalinit();
@@ -30925,6 +34172,45 @@ void tetgenmesh::qualitystatistics()
}
dihedangletable[tendegree]++;
+ // Calulate the largest and smallest face angles.
+ tetloop.ver = 0;
+ for (tetloop.loc = 0; tetloop.loc < 4; tetloop.loc++) {
+ sym(tetloop, neightet);
+ // Only do the calulation once for a face.
+ if ((neightet.tet == dummytet) || (tetloop.tet < neightet.tet)) {
+ p[0] = org(tetloop);
+ p[1] = dest(tetloop);
+ p[2] = apex(tetloop);
+ faceangle[0] = interiorangle(p[0], p[1], p[2], NULL);
+ faceangle[1] = interiorangle(p[1], p[2], p[0], NULL);
+ faceangle[2] = PI - (faceangle[0] + faceangle[1]);
+ // Translate angles into degrees.
+ for (i = 0; i < 3; i++) {
+ faceangle[i] = (faceangle[i] * 180.0) / PI;
+ }
+ // Calculate the largest and smallest face angles.
+ for (i = 0; i < 3; i++) {
+ if (i == 0) {
+ smallfaangle = bigfaangle = faceangle[i];
+ } else {
+ smallfaangle = faceangle[i] < smallfaangle ?
+ faceangle[i] : smallfaangle;
+ bigfaangle = faceangle[i] > bigfaangle ? faceangle[i] : bigfaangle;
+ }
+ if (faceangle[i] < smallestfaangle) {
+ smallestfaangle = faceangle[i];
+ }
+ if (faceangle[i] > biggestfaangle) {
+ biggestfaangle = faceangle[i];
+ }
+ }
+ tendegree = (int) (smallfaangle / 10.);
+ faceangletable[tendegree]++;
+ tendegree = (int) (bigfaangle / 10.);
+ faceangletable[tendegree]++;
+ }
+ }
+
// Calculate aspect ratio and radius-edge ratio for this element.
tetradius = cirradius / sqrt(shortlen);
// tetaspect = sqrt(longlen) / (2.0 * insradius);
@@ -30951,6 +34237,12 @@ void tetgenmesh::qualitystatistics()
smallestvolume, biggestvolume);
printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
shortest, longest);
+ sprintf(sbuf, "%.17g", biggestfaangle);
+ if (strlen(sbuf) > 8) {
+ sbuf[8] = '\0';
+ }
+ printf(" Smallest facangle: %14.5g | Largest facangle: %s\n",
+ smallestfaangle, sbuf);
sprintf(sbuf, "%.17g", biggestdiangle);
if (strlen(sbuf) > 8) {
sbuf[8] = '\0';
@@ -30958,6 +34250,7 @@ void tetgenmesh::qualitystatistics()
printf(" Smallest dihedral: %14.5g | Largest dihedral: %s\n\n",
smallestdiangle, sbuf);
+ /*
printf(" Radius-edge ratio histogram:\n");
printf(" < %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
radiusratiotable[0], radiustable[0], radiusratiotable[5],
@@ -30974,6 +34267,7 @@ void tetgenmesh::qualitystatistics()
printf(" (A tetrahedron's radius-edge ratio is its radius of ");
printf("circumsphere divided\n");
printf(" by its shortest edge length)\n\n");
+ */
printf(" Aspect ratio histogram:\n");
printf(" < %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
@@ -30992,6 +34286,18 @@ void tetgenmesh::qualitystatistics()
printf(" divided by its\n");
printf(" smallest side height)\n\n");
+ printf(" Face angle histogram:\n");
+ for (i = 0; i < 9; i++) {
+ printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
+ i * 10, i * 10 + 10, faceangletable[i],
+ i * 10 + 90, i * 10 + 100, faceangletable[i + 9]);
+ }
+ if (minfaceang != PI) {
+ printf(" Minimum input face angle is %g (degree).\n",
+ minfaceang / PI * 180.0);
+ }
+ printf("\n");
+
printf(" Dihedral angle histogram:\n");
// Print the three two rows:
printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
@@ -31009,7 +34315,10 @@ void tetgenmesh::qualitystatistics()
60, 70, dihedangletable[7], 170, 175, dihedangletable[16]);
printf(" %3d - %2d degrees: %8d | %3d - %3d degrees: %8d\n",
70, 80, dihedangletable[8], 175, 180, dihedangletable[17]);
-
+ if (minfacetdihed != PI) {
+ printf(" Minimum input facet dihedral angle is %g (degree).\n",
+ minfacetdihed / PI * 180.0);
+ }
printf("\n");
}
@@ -31028,6 +34337,7 @@ void tetgenmesh::statistics()
}
if (b->plc) {
printf(" Input facets: %d\n", in->numberoffacets);
+ printf(" Input segments: %ld\n", insegments);
printf(" Input holes: %d\n", in->numberofholes);
printf(" Input regions: %d\n", in->numberofregions);
}
@@ -31035,20 +34345,35 @@ void tetgenmesh::statistics()
printf("\n Mesh points: %ld\n", points->items);
printf(" Mesh tetrahedra: %ld\n", tetrahedrons->items);
if (b->plc || b->refine) {
- printf(" Mesh faces: %ld\n", (4l * tetrahedrons->items + hullsize) / 2l);
+ printf(" Mesh triangles: %ld\n", (4l*tetrahedrons->items+hullsize)/2l);
}
if (b->plc || b->refine) {
printf(" Mesh subfaces: %ld\n", subfaces->items);
printf(" Mesh subsegments: %ld\n\n", subsegs->items);
} else {
- printf(" Convex hull faces: %ld\n\n", hullsize);
+ printf(" Convex hull triangles: %ld\n\n", hullsize);
}
if (b->verbose > 0) {
+ qualitystatistics();
+ unsigned long totalmeshbytes;
+ printf("Memory allocation statistics:\n\n");
+ printf(" Maximum number of vertices: %ld\n", points->maxitems);
+ totalmeshbytes = points->maxitems * points->itembytes;
+ printf(" Maximum number of tetrahedra: %ld\n", tetrahedrons->maxitems);
+ totalmeshbytes += tetrahedrons->maxitems * tetrahedrons->itembytes;
+ if (subfaces != (memorypool *) NULL) {
+ printf(" Maximum number of subfaces: %ld\n", subfaces->maxitems);
+ totalmeshbytes += subfaces->maxitems * subfaces->itembytes;
+ }
+ if (subsegs != (memorypool *) NULL) {
+ printf(" Maximum number of segments: %ld\n", subsegs->maxitems);
+ totalmeshbytes += subsegs->maxitems * subsegs->itembytes;
+ }
+ printf(" Approximate heap memory used by the mesh (K bytes): %g\n\n",
+ (double) totalmeshbytes / 1024.0);
#ifdef SELF_CHECK
- // algorithmicstatistics();
+ algorithmicstatistics();
#endif
- qualitystatistics();
- printf("\n");
}
}
@@ -31144,7 +34469,7 @@ tetgenmesh::tetgenmesh()
longest = 0.0;
hullsize = 0l;
insegments = 0l;
- pointlfsindex = 0;
+ pointmtrindex = 0;
pointmarkindex = 0;
point2simindex = 0;
point2pbcptindex = 0;
@@ -31154,6 +34479,7 @@ tetgenmesh::tetgenmesh()
shmarkindex = 0;
areaboundindex = 0;
checksubfaces = 0;
+ checksubsegs = 0;
checkpbcs = 0;
varconstraint = 0;
nonconvex = 0;
@@ -31164,10 +34490,11 @@ tetgenmesh::tetgenmesh()
collapverts = 0;
unsupverts = 0;
jettisoninverts = 0;
- symbolic = 0;
+ symbolic = 1;
samples = 0l;
- randomseed = 0l;
+ randomseed = 1l;
macheps = 0.0;
+ minfaceang = minfacetdihed = PI;
maxcavfaces = maxcavverts = 0;
expcavcount = 0;
abovecount = 0l;
@@ -31176,10 +34503,11 @@ tetgenmesh::tetgenmesh()
repairflipcount = 0l;
outbowatcircumcount = 0l;
failvolcount = failsubcount = failsegcount = 0l;
- r1count = r2count = r3count = r4count = 0l;
+ r1count = r2count = r3count = 0l;
cdtenforcesegpts = 0l;
rejsegpts = rejsubpts = rejtetpts = 0l;
flip23s = flip32s = flip22s = flip44s = 0l;
+ tloctime = tfliptime = 0.0;
}
//
@@ -31214,31 +34542,29 @@ tetgenmesh::tetgenmesh()
// //
///////////////////////////////////////////////////////////////////////////////
-#include <time.h> // Defined type clock_t, constant CLOCKS_PER_SEC.
-
void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
- tetgenio *bgmesh)
+ tetgenio *addin, tetgenio *bgmin)
{
tetgenmesh m;
- clock_t tv0, tv1, tv2, tv3, tv4, tv5, tv6, tv7, tv8, tv9, tv10, tv11;
+ // Variables for timing the performance of TetGen (defined in time.h).
+ clock_t tv[14];
- tv0 = clock();
+ tv[0] = clock();
m.b = b;
m.in = in;
m.macheps = exactinit();
m.steinerleft = b->steiner;
- if (b->bgmesh) {
- // '-m' switch
+ if (b->metric) {
m.bgm = new tetgenmesh();
m.bgm->b = b;
- m.bgm->in = bgmesh;
+ m.bgm->in = bgmin;
m.bgm->macheps = exactinit();
}
m.initializepools();
m.transfernodes();
- tv1 = clock();
+ tv[1] = clock();
if (b->refine) {
m.reconstructmesh();
@@ -31246,103 +34572,149 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.delaunizevertices();
}
- tv2 = clock();
+ tv[2] = clock();
+
if (!b->quiet) {
if (b->refine) {
- printf("Mesh reconstruction seconds: %g\n",
- (tv2 - tv1) / (REAL) CLOCKS_PER_SEC);
+ printf("Mesh reconstruction seconds:");
+ } else {
+ printf("Delaunay seconds:");
+ }
+ printf(" %g\n", (tv[2] - tv[1]) / (REAL) CLOCKS_PER_SEC);
+ }
+
+ if (b->metric) {
+ if (bgmin != (tetgenio *) NULL) {
+ m.bgm->initializepools();
+ m.bgm->transfernodes();
+ m.bgm->reconstructmesh();
} else {
- printf("Delaunay seconds: %g\n", (tv2 - tv1) / (REAL) CLOCKS_PER_SEC);
+ m.bgm->in = in;
+ m.bgm->initializepools();
+ m.duplicatebgmesh();
+ }
+ }
+
+ tv[3] = clock();
+
+ if (!b->quiet) {
+ if (b->metric) {
+ printf("Background mesh reconstruct seconds: %g\n",
+ (tv[3] - tv[2]) / (REAL) CLOCKS_PER_SEC);
}
}
if (b->useshelles && !b->refine) {
- m.insegments = m.meshsurface();
+ m.meshsurface();
if (b->diagnose != 1) {
- m.incrperturbvertices(b->epsilon); // '-p' switch.
+ m.markacutevertices(89.0);
+ m.incrperturbvertices(b->epsilon);
m.delaunizesegments();
+ if (m.checkpbcs) {
+ long oldnum;
+ do {
+ oldnum = m.points->items;
+ m.incrperturbvertices(b->epsilon);
+ if (m.points->items > oldnum) {
+ oldnum = m.points->items;
+ m.delaunizesegments();
+ }
+ } while (oldnum < m.points->items);
+ }
m.constrainedfacets();
} else {
- m.detectinterfaces(); // '-d' switch.
+ m.detectinterfaces();
}
}
- tv3 = clock();
+ tv[4] = clock();
+
if (!b->quiet) {
if (b->useshelles && !b->refine) {
if (b->diagnose != 1) {
- printf("Segment and facet seconds: %g\n",
- (tv3 - tv2) / (REAL) CLOCKS_PER_SEC);
+ printf("Segment and facet ");
} else {
- printf("Intersection seconds: %g\n",
- (tv3 - tv2) / (REAL) CLOCKS_PER_SEC);
+ printf("Intersection ");
}
- }
+ printf("seconds: %g\n", (tv[4] - tv[3]) / (REAL) CLOCKS_PER_SEC);
+ }
}
if (b->plc && !(b->diagnose == 1)) {
m.carveholes();
}
- tv4 = clock();
+ tv[5] = clock();
+
if (!b->quiet) {
if (b->plc && !(b->diagnose == 1)) {
- printf("Hole seconds: %g\n", (tv4 - tv3) / (REAL) CLOCKS_PER_SEC);
+ printf("Hole seconds: %g\n", (tv[5] - tv[4]) / (REAL) CLOCKS_PER_SEC);
}
}
if ((b->plc || b->refine) && !(b->diagnose == 1)) {
- m.repairmesh();
+ m.optimizemesh(false);
}
- tv5 = clock();
+ tv[6] = clock();
+
if (!b->quiet) {
if ((b->plc || b->refine) && !(b->diagnose == 1)) {
- printf("Repair seconds: %g\n", (tv5 - tv4) / (REAL) CLOCKS_PER_SEC);
+ printf("Repair seconds: %g\n", (tv[6] - tv[5]) / (REAL) CLOCKS_PER_SEC);
}
}
if ((b->plc && b->nobisect) && !(b->diagnose == 1)) {
- m.removesteiners();
+ m.removesteiners(false);
}
- tv6 = clock();
+ tv[7] = clock();
+
if (!b->quiet) {
if ((b->plc && b->nobisect) && !(b->diagnose == 1)) {
printf("Steiner removal seconds: %g\n",
- (tv6 - tv5) / (REAL) CLOCKS_PER_SEC);
+ (tv[7] - tv[6]) / (REAL) CLOCKS_PER_SEC);
}
}
- if (b->insertaddpoints) {
- if (in->numberofaddpoints == 0) {
- in->load_addnodes(b->infilename);
- }
- if (in->numberofaddpoints > 0) {
- m.insertaddpoints();
+ if (b->insertaddpoints && (addin != (tetgenio *) NULL)) {
+ if (addin->numberofpoints > 0) {
+ m.insertconstrainedpoints(addin);
}
}
- tv7 = clock();
+ tv[8] = clock();
+
if (!b->quiet) {
- if ((b->plc || b->refine) && (in->numberofaddpoints > 0)) {
- printf("Add points seconds: %g\n", (tv7 - tv6) / (REAL) CLOCKS_PER_SEC);
+ if ((b->plc || b->refine) && (b->insertaddpoints)) {
+ printf("Constrained points seconds: %g\n",
+ (tv[8] - tv[7]) / (REAL) CLOCKS_PER_SEC);
}
}
- if (b->bgmesh) {
- // '-b' switch
- m.bgm->initializepools();
- m.bgm->transfernodes();
- m.bgm->reconstructmesh();
+ if (b->metric) {
m.interpolatesizemap();
}
- tv8 = clock();
+ tv[9] = clock();
+
+ if (!b->quiet) {
+ if (b->metric) {
+ printf("Size interpolating seconds: %g\n",
+ (tv[9] - tv[8]) / (REAL) CLOCKS_PER_SEC);
+ }
+ }
+
+ if (b->coarse) {
+ m.removesteiners(true);
+ }
+
+ tv[10] = clock();
+
if (!b->quiet) {
- if (b->bgmesh) {
- printf("Background mesh reconstruct seconds: %g\n",
- (tv8 - tv7) / (REAL) CLOCKS_PER_SEC);
+ if (b->coarse) {
+ printf("Mesh coarsening seconds: %g\n",
+ (tv[10] - tv[9]) / (REAL) CLOCKS_PER_SEC);
}
}
@@ -31350,21 +34722,25 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.enforcequality();
}
- tv9 = clock();
+ tv[11] = clock();
+
if (!b->quiet) {
if (b->quality) {
- printf("Quality seconds: %g\n", (tv9 - tv8) / (REAL) CLOCKS_PER_SEC);
+ printf("Quality seconds: %g\n",
+ (tv[11] - tv[10]) / (REAL) CLOCKS_PER_SEC);
}
}
- if (b->quality && b->smooth) {
- m.smoothmesh();
+ if (b->quality && (b->optlevel > 0)) {
+ m.optimizemesh(true);
}
- tv10 = clock();
+ tv[12] = clock();
+
if (!b->quiet) {
- if (b->quality && b->smooth) {
- printf("Smooth seconds: %g\n", (tv10 - tv9) / (REAL) CLOCKS_PER_SEC);
+ if (b->quality && (b->optlevel > 0)) {
+ printf("Optimize seconds: %g\n",
+ (tv[12] - tv[11]) / (REAL) CLOCKS_PER_SEC);
}
}
@@ -31393,13 +34769,12 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
} else {
if (b->diagnose == 1) {
if (m.subfaces->items > 0l) {
- // Only output when there are intersecting faces.
- m.outnodes(out);
+ m.outnodes(out); // Only output when self-intersecting faces exist.
}
} else {
m.outnodes(out);
- if (b->metric) {
- m.outmetrics(out);
+ if (b->quality || b->metric) {
+ // m.outmetrics(out);
}
}
}
@@ -31423,24 +34798,20 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
} else {
if (b->facesout) {
if (m.tetrahedrons->items > 0l) {
- // Output all faces.
- m.outfaces(out);
+ m.outfaces(out); // Output all faces.
}
} else {
if (b->diagnose == 1) {
if (m.subfaces->items > 0l) {
- // Only output when there are intersecting faces.
- m.outsubfaces(out);
+ m.outsubfaces(out); // Only output self-intersecting faces.
}
} else if (b->plc || b->refine) {
if (m.subfaces->items > 0l) {
- // Output boundary faces.
- m.outsubfaces(out);
+ m.outsubfaces(out); // Output boundary faces.
}
} else {
if (m.tetrahedrons->items > 0l) {
- // Output convex hull faces.
- m.outhullfaces(out);
+ m.outhullfaces(out); // Output convex hull faces.
}
}
}
@@ -31450,9 +34821,11 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.outpbcnodes(out);
}
- if (b->edgesout && b->plc) {
- if (m.subsegs->items > 0l) {
- m.outsubsegments(out);
+ if (b->edgesout) {
+ if (b->edgesout > 1) {
+ m.outedges(out); // -ee, output all mesh edges.
+ } else {
+ m.outsubsegments(out); // -e, only output subsegments.
}
}
@@ -31479,11 +34852,17 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.outneighbors(out);
}
- tv11 = clock();
+ if (b->voroout) {
+ m.outvoronoi(out);
+ }
+
+ tv[13] = clock();
+
if (!b->quiet) {
- printf("\nOutput seconds: %g\n", (tv11 - tv10) / (REAL) CLOCKS_PER_SEC);
+ printf("\nOutput seconds: %g\n",
+ (tv[13] - tv[12]) / (REAL) CLOCKS_PER_SEC);
printf("Total running seconds: %g\n",
- (tv11 - tv0) / (REAL) CLOCKS_PER_SEC);
+ (tv[13] - tv[0]) / (REAL) CLOCKS_PER_SEC);
}
if (b->docheck) {
@@ -31505,7 +34884,7 @@ void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
m.statistics();
}
- if (bgmesh) {
+ if (b->metric) {
delete m.bgm;
}
}
@@ -31529,7 +34908,7 @@ int main(int argc, char *argv[])
///////////////////////////////////////////////////////////////////////////////
void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
- tetgenio *bgmesh)
+ tetgenio *addin, tetgenio *bgmin)
#endif // not TETLIBRARY
@@ -31538,7 +34917,7 @@ void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
#ifndef TETLIBRARY
- tetgenio in, bgmesh;
+ tetgenio in, addin, bgmin;
if (!b.parse_commandline(argc, argv)) {
terminatetetgen(1);
@@ -31552,16 +34931,21 @@ void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
terminatetetgen(1);
}
}
- if (b.bgmesh) {
- if (!bgmesh.load_tetmesh(b.bgmeshfilename)) {
- bgmesh.numberoftetrahedra = 0l;
+ if (b.insertaddpoints) {
+ if (!addin.load_node(b.addinfilename)) {
+ addin.numberofpoints = 0l;
+ }
+ }
+ if (b.metric) {
+ if (!bgmin.load_tetmesh(b.bgmeshfilename)) {
+ bgmin.numberoftetrahedra = 0l;
}
}
- if (bgmesh.numberoftetrahedra > 0l) {
- tetrahedralize(&b, &in, NULL, &bgmesh);
+ if (bgmin.numberoftetrahedra > 0l) {
+ tetrahedralize(&b, &in, NULL, &addin, &bgmin);
} else {
- tetrahedralize(&b, &in, NULL, NULL);
+ tetrahedralize(&b, &in, NULL, &addin, NULL);
}
return 0;
@@ -31571,7 +34955,7 @@ void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
if (!b.parse_commandline(switches)) {
terminatetetgen(1);
}
- tetrahedralize(&b, in, out, bgmesh);
+ tetrahedralize(&b, in, out, addin, bgmin);
#endif // not TETLIBRARY
}
diff --git a/contrib/Tetgen/tetgen.h b/contrib/Tetgen/tetgen.h
index 55b8f3a604..74106f9260 100644
--- a/contrib/Tetgen/tetgen.h
+++ b/contrib/Tetgen/tetgen.h
@@ -5,16 +5,22 @@
// A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator //
// //
// Version 1.4 //
-// January 14, 2006 //
+// April 16, 2007 //
// //
-// Copyright 2002, 2004, 2005, 2006 //
+// Copyright (C) 2002--2007 //
// Hang Si //
-// Rathausstr. 9, 10178 Berlin, Germany //
+// Research Group Numerical Mathematics and Scientific Computing //
+// Weierstrass Institute for Applied Analysis and Stochastics //
+// Mohrenstr. 39, 10117 Berlin, Germany //
// si@wias-berlin.de //
// //
-// You can obtain TetGen via internet: http://tetgen.berlios.de. It may be //
-// freely copied, modified, and redistributed under the copyright notices //
-// given in the file LICENSE. //
+// TetGen is freely available through the website: http://tetgen.berlios.de. //
+// It may be copied, modified, and redistributed for non-commercial use. //
+// Please consult the file LICENSE for the detailed copyright notices. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+///////////////////////////////////////////////////////////////////////////////
// //
// TetGen computes Delaunay tetrahedralizations, constrained Delaunay tetra- //
// hedralizations, and quality Delaunay tetrahedral meshes. The latter are //
@@ -28,26 +34,25 @@
// //
// The efficient Delaunay tetrahedralization algorithm is: H. Edelsbrunner //
// and N. R. Shah, "Incremental Topological Flipping Works for Regular //
-// Triangulations". Algorithmica 15: 223-241, 1996. //
+// Triangulations". Algorithmica 15: 223--241, 1996. //
// //
// The constrained Delaunay tetrahedralization algorithm is described in: //
// H. Si and K. Gaertner, "Meshing Piecewise Linear Complexes by Constr- //
// ained Delaunay Tetrahedralizations". In Proceeding of the 14th Inter- //
// national Meshing Roundtable. September 2005. //
// //
-// The Delaunay refinement algorithm is from: Hang Si, "On Refinement of //
-// Constrained Delaunay Tetrahedralizations". In Proceeding of the 15th //
-// International Meshing Roundtable. September 2006. //
+// The mesh refinement algorithm is from: Hang Si, "Adaptive Tetrahedral //
+// Mesh Generation by Constrained Delaunay Refinement". WIAS Preprint No. //
+// 1176, Berlin 2006. //
// //
// The mesh data structure of TetGen is a combination of two types of mesh //
// data structures. The tetrahedron-based mesh data structure introduced //
// by Shewchuk is eligible for tetrahedralization algorithms. The triangle //
// -edge data structure developed by Muecke is adopted for representing //
-// boundary elements: subfaces and subsegments. Both data structures have //
-// a set of fast mesh manipulation primitives. //
+// boundary elements: subfaces and subsegments. //
// //
// J. R. Shewchuk, "Delaunay Refinement Mesh Generation". PhD thesis, //
-// Carnegie Mellon University, 1997. //
+// Carnegie Mellon University, Pittsburgh, PA, 1997. //
// //
// E. P. Muecke, "Shapes and Implementations in Three-Dimensional //
// Geometry". PhD thesis, Univ. of Illinois, Urbana, Illinois, 1993. //
@@ -74,6 +79,15 @@
// //
///////////////////////////////////////////////////////////////////////////////
+// Here are the most general used head files for C/C++ programs.
+
+#include <stdio.h> // Standard IO: FILE, NULL, EOF, printf(), ...
+#include <stdlib.h> // Standard lib: abort(), system(), getenv(), ...
+#include <string.h> // String lib: strcpy(), strcat(), strcmp(), ...
+#include <math.h> // Math lib: sin(), sqrt(), pow(), ...
+#include <time.h> // Defined type clock_t, constant CLOCKS_PER_SEC.
+#include <assert.h>
+
///////////////////////////////////////////////////////////////////////////////
// //
// TetGen Library Overview //
@@ -128,40 +142,30 @@
#define REAL double
#endif // not defined SINGLE
-// Here are the most general used head files for C/C++ programs.
-
-#include <stdio.h> // Standard IO: FILE, NULL, EOF, printf(), ...
-#include <stdlib.h> // Standard lib: abort(), system(), getenv(), ...
-#include <string.h> // String lib: strcpy(), strcat(), strcmp(), ...
-#include <math.h> // Math lib: sin(), sqrt(), pow(), ...
-#include <assert.h>
-
///////////////////////////////////////////////////////////////////////////////
// //
-// The tetgenio data type //
+// tetgenio Passing data into and out of the library of TetGen. //
// //
-// Used to pass data into and out of the library of TetGen. //
+// The tetgenio data structure is actually a collection of arrays of points, //
+// facets, tetrahedra, and so forth. The library will read and write these //
+// arrays according to the options specified in tetgenbehavior structure. //
// //
// If you want to program with the library of TetGen, it's necessary for you //
-// to understand the tetgenio data type, while the other two data types can //
-// be hidden through calling the global function "tetrahedralize()". As you //
-// will see, that tetgenio is just a collection of arrays to storing points //
-// (by coodinates), tetrahedra (by indexes), faces, boundary markers, and so //
-// forth. Each array corresponds to a list of data in the file formats of //
-// TetGen. It is necessary to understand TetGen's input/output file formats //
-// (see user's manual) before using tetgenio objects. //
-// //
-// Once an object of tetgenio is declared (or created), all arrays of it are //
-// automatically initialized to NULLs (by routine initialize()). Before they //
-// can be used, one has to first allocate enough memory for them, i.e., use //
-// either 'malloc()' or 'new' operator. On deletion of the object, one needs //
-// to free the memory occupied by these arrays. Routine deinitialize() will //
-// be automatically called. It will deallocate the memory for an array if it //
-// is not a NULL. However, it assumes that the memory is allocated by 'new' //
-// (C++ operator). If you use malloc(), you should free() them and set the //
-// pointers to NULLs before reaching deinitialize(). //
-// //
-// In all cases, the first item in any array is stored starting at index [0].//
+// to understand this data type,while the other two structures can be hidden //
+// through calling the global function "tetrahedralize()". Each array corre- //
+// sponds to a list of data in the file formats of TetGen. It is necessary //
+// to understand TetGen's input/output file formats (see user's manual). //
+// //
+// Once an object of tetgenio is declared, no array is created. One has to //
+// allocate enough memory for them, e.g., use the "new" operator in C++. On //
+// deletion of the object, the memory occupied by these arrays needs to be //
+// freed. Routine deinitialize() will be automatically called. It will de- //
+// allocate the memory for an array if it is not a NULL. However, it assumes //
+// that the memory is allocated by the C++ "new" operator. If you use malloc //
+// (), you should free() them and set the pointers to NULLs before reaching //
+// deinitialize(). //
+// //
+// In all cases, the first item in an array is stored starting at index [0]. //
// However, that item is item number `firstnumber' which may be '0' or '1'. //
// Be sure to set the 'firstnumber' be '1' if your indices pointing into the //
// pointlist is starting from '1'. Default, it is initialized be '0'. //
@@ -218,6 +222,30 @@ class tetgenio {
f->numberofholes = 0;
}
+ // A 'voroedge' is an edge of the Voronoi diagram. It corresponds to a
+ // Delaunay face. Each voroedge is either a line segment connecting
+ // two Voronoi vertices or a ray starting from a Voronoi vertex to an
+ // "infinite vertex". 'v1' and 'v2' are two indices pointing to the
+ // list of Voronoi vertices. 'v1' must be non-negative, while 'v2' may
+ // be -1 if it is a ray, in this case, the unit normal of this ray is
+ // given in 'vnormal'.
+ typedef struct {
+ int v1, v2;
+ REAL vnormal[3];
+ } voroedge;
+
+ // A 'vorofacet' is an facet of the Voronoi diagram. It corresponds to a
+ // Delaunay edge. Each Voronoi facet is a convex polygon formed by a
+ // list of Voronoi edges, it may not be closed. 'c1' and 'c2' are two
+ // indices pointing into the list of Voronoi cells, i.e., the two cells
+ // share this facet. 'elist' is an array of indices pointing into the
+ // list of Voronoi edges, 'elist[0]' saves the number of Voronoi edges
+ // (including rays) of this facet.
+ typedef struct {
+ int c1, c2;
+ 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
@@ -236,27 +264,27 @@ class tetgenio {
// Items are numbered starting from 'firstnumber' (0 or 1), default is 0.
int firstnumber;
-
// Dimension of the mesh (2 or 3), default is 3.
int mesh_dim;
+ // Does the lines in .node file contain index or not, default is TRUE.
+ bool useindex;
- // `pointlist': An array of point coordinates. The first point's x
+ // 'pointlist': An array of point coordinates. The first point's x
// coordinate is at index [0] and its y coordinate at index [1], its
// z coordinate is at index [2], followed by the coordinates of the
// remaining points. Each point occupies three REALs.
- // `pointattributelist': An array of point attributes. Each point's
- // attributes occupy `numberofpointattributes' REALs.
- // 'addpointlist': An array of additional point coordinates.
- // 'addpointattributelist': An array of attributes for addition points.
+ // 'pointattributelist': An array of point attributes. Each point's
+ // 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 int per point.
REAL *pointlist;
REAL *pointattributelist;
- REAL *addpointlist;
- REAL *addpointattributelist;
+ REAL *pointmtrlist;
int *pointmarkerlist;
int numberofpoints;
int numberofpointattributes;
- int numberofaddpoints;
+ int numberofpointmtrs;
// `elementlist': An array of element (triangle or tetrahedron) corners.
// The first element's first corner is at index [0], followed by its
@@ -314,13 +342,6 @@ class tetgenio {
REAL *segmentconstraintlist;
int numberofsegmentconstraints;
- // `nodeconstraintlist': An array of segment length constraints. Two
- // REALs per constraint. The first one is the index (pointing into
- // 'pointlist') of the node, the second is its edge length bound.
- // Note the 'nodeconstraintlist' is used only for the 'q' switch.
- REAL *nodeconstraintlist;
- int numberofnodeconstraints;
-
// 'pbcgrouplist': An array of periodic boundary condition groups.
pbcgroup *pbcgrouplist;
int numberofpbcgroups;
@@ -331,7 +352,7 @@ class tetgenio {
// `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 '-n'
+ // indicates outside (no adj. tet). This list is output when '-nn'
// switch is used.
// `trifacemarkerlist': An array of face markers; one int per face.
int *trifacelist;
@@ -347,6 +368,21 @@ class tetgenio {
int *edgemarkerlist;
int numberofedges;
+ // 'vpointlist': An array of Voronoi vertex coordinates (like pointlist).
+ // 'vedgelist': An array of Voronoi edges. Each entry is a 'voroedge'.
+ // 'vfacetlist': An array of Voronoi facets. Each entry is a 'vorofacet'.
+ // 'vcelllist': An array of Voronoi cells. Each entry is an array of
+ // indices pointing into 'vfacetlist'. The 0th entry is used to store
+ // the length of this array.
+ REAL *vpointlist;
+ voroedge *vedgelist;
+ vorofacet *vfacetlist;
+ int **vcelllist;
+ int numberofvpoints;
+ int numberofvedges;
+ int numberofvfacets;
+ int numberofvcells;
+
public:
// Initialize routine.
@@ -356,7 +392,6 @@ class tetgenio {
// Input & output routines.
bool load_node_call(FILE* infile, int markers, char* nodefilename);
bool load_node(char* filename);
- bool load_addnodes(char* filename);
bool load_pbc(char* filename);
bool load_var(char* filename);
bool load_mtr(char* filename);
@@ -367,6 +402,7 @@ class tetgenio {
bool load_medit(char* filename);
bool load_plc(char* filename, int object);
bool load_tetmesh(char* filename);
+ bool load_voronoi(char* filename);
void save_nodes(char* filename);
void save_elements(char* filename);
void save_faces(char* filename);
@@ -387,9 +423,7 @@ class tetgenio {
///////////////////////////////////////////////////////////////////////////////
// //
-// The tetgenbehavior data type //
-// //
-// Used to parse command line switches and file names. //
+// tetgenbehavior Parsing command line switches and file names. //
// //
// It includes a list of variables corresponding to the commandline switches //
// for control the behavior of TetGen. These varibales are all initialized //
@@ -425,28 +459,29 @@ class tetgenbehavior {
enum objecttype {NONE, NODES, POLY, OFF, PLY, STL, MEDIT, MESH};
- // Variables of command line switches. Each variable is corresponding
- // to a specific switch and will be properly initialized. Read the
- // user's manul to find out the meaning of these switches.
+ // Variables of command line switches. Each variable corresponds to a
+ // switch and will be initialized. The meanings of these switches
+ // are explained in the user's manul.
int plc; // '-p' switch, 0.
- int refine; // '-r' switch, 0.
int quality; // '-q' switch, 0.
- int smooth; // '-s' switch, 0.
+ int refine; // '-r' switch, 0.
+ int coarse; // '-R' switch, 0.
int metric; // '-m' switch, 0.
- int bgmesh; // '-b' switch, 0.
int varvolume; // '-a' switch without number, 0.
int fixedvolume; // '-a' switch with number, 0.
int insertaddpoints; // '-i' switch, 0.
int regionattrib; // '-A' switch, 0.
- int offcenter; // '-R' switch, 0.
int conformdel; // '-D' switch, 0.
int diagnose; // '-d' switch, 0.
int zeroindex; // '-z' switch, 0.
+ int optlevel; // number specified after '-s' switch, 3.
+ int optpasses; // number specified after '-ss' switch, 5.
int order; // element order, specified after '-o' switch, 1.
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 gidview; // '-G' switch, 0.
int geomview; // '-O' switch, 0.
@@ -455,26 +490,27 @@ class tetgenbehavior {
int noelewritten; // '-E' switch, 0.
int nofacewritten; // '-F' switch, 0.
int noiterationnum; // '-I' switch, 0.
- int nomerge; // count of how often '-M' switch is selected, 0.
+ int nomerge; // '-M',switch, 0.
int nobisect; // count of how often '-Y' switch is selected, 0.
- int noflip; // do not perform flips. '-Y' switch. 0.
+ int noflip; // do not perform flips. '-X' switch. 0.
int nojettison; // do not jettison redundants nodes. '-J' switch. 0.
int steiner; // number after '-S' switch. 0.
int fliprepair; // '-X' switch, 1.
+ int offcenter; // '-R' switch, 0.
int docheck; // '-C' switch, 0.
int quiet; // '-Q' switch, 0.
int verbose; // count of how often '-V' switch is selected, 0.
- int tol; // count of how often '-T' switch is selected, 0.
- int useshelles; // '-p', '-r', '-q', '-d', or '-c' switch, 0.
+ int useshelles; // '-p', '-r', '-q', '-d', or '-R' switch, 0.
REAL minratio; // number after '-q' switch, 2.0.
REAL goodratio; // number calculated from 'minratio', 0.0.
REAL minangle; // minimum angle bound, 20.0.
REAL goodangle; // cosine squared of minangle, 0.0.
REAL maxvolume; // number after '-a' switch, -1.0.
- REAL maxdihedral; // number after '-s' switch, 175.0.
- REAL alpha1; // number after '-R' switch, sqrt(2).
- REAL alpha2; // number after '-RR' switch, 1/sqrt(2).
- REAL alpha3; // number after '-RRR' switch, 0.6.
+ REAL mindihedral; // number after '-qq' switch, 5.0.
+ REAL maxdihedral; // number after '-qqq' switch, 165.0.
+ REAL alpha1; // number after '-m' switch, sqrt(2).
+ REAL alpha2; // number after '-mm' switch, 1.0.
+ REAL alpha3; // number after '-mmm' switch, 0.6.
REAL epsilon; // number after '-T' switch, 1.0e-8.
REAL epsilon2; // number after '-TT' switch, 1.0e-5.
enum objecttype object; // determined by -p, or -r switch. NONE.
@@ -483,6 +519,7 @@ class tetgenbehavior {
char commandline[1024];
char infilename[1024];
char outfilename[1024];
+ char addinfilename[1024];
char bgmeshfilename[1024];
tetgenbehavior();
@@ -505,9 +542,8 @@ class tetgenbehavior {
// //
// 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 the composition of geometric algorithms. TetGen uses //
-// two 3D geometric predicates, which are the orientation test and the in- //
-// sphere test (e.g. the locally Deklaunay test). //
+// 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 //
@@ -590,20 +626,15 @@ class tetgenmesh {
// read from input (.node file or tetgenio structure) or an isolated
// vertex (outside the mesh). It is the default type for a newpoint.
enum verttype {UNUSEDVERTEX, DUPLICATEDVERTEX, NACUTEVERTEX, ACUTEVERTEX,
- FREESEGVERTEX, FACETVERTEX, FREESUBVERTEX, VOLVERTEX,
- FREEVOLVERTEX, DEADVERTEX = -32768};
+ FREESEGVERTEX, FREESUBVERTEX, FREEVOLVERTEX, DEADVERTEX = -32768};
- // Labels that signify the type of a subface/subsegment. A subface is
- // SKINNY if it has two edges which are subsegments and form a small
- // angle (e.g., 10 degree); a subsegment is a SHARP if it is between
- // two facets which form an acute dihedral angle.
- enum shestype {NSHARPNSKINNY, SHARP, SKINNY};
+ // Labels that signify the type of a subface/subsegment.
+ enum shestype {NSHARP, SHARP};
// Labels that signify the type of flips can be applied on a face.
// A flipable face has the one of the types T23, T32, T22, and T44.
- // Types UNFLIPABLE, NONCONVEX are unflipable.
- enum fliptype {T23, T32, T22, T44, UNFLIPABLE, FORBIDDENFACE,
- FORBIDDENEDGE, NONCONVEX};
+ // Types N32, N40 are unflipable.
+ enum fliptype {T23, T32, T22, T44, N32, N40, FORBIDDENFACE, FORBIDDENEDGE};
// Labels that signify the result of triangle-triangle intersection test.
// Two triangles are DISJOINT, or adjoint at a vertex SHAREVERTEX, or
@@ -767,7 +798,7 @@ class tetgenmesh {
// The point data structure. It is actually an array of REALs:
// - x, y and z coordinates;
// - a list of user-defined point attributes (optional);
- // - a REAL of local feature sizes (optional -p switch);
+ // - a list of REALs of a user-defined metric tensor (optional);
// - a pointer to a simplex (tet, tri, edge, or vertex);
// - a pointer to a parent (or duplicate) point;
// - a pointer to a tet in background mesh (optional);
@@ -913,61 +944,6 @@ class tetgenmesh {
REAL transmat[2][4][4];
};
-///////////////////////////////////////////////////////////////////////////////
-// //
-// The Metric tensor data structure //
-// //
-// A metric is a function that specifies the "distance" between two points //
-// in a metric space E. Recall if d(p, q) is a metric of E, then we have: //
-// (1) d(p, q) = d(q, p). (d is symmetric) //
-// (2) d(p, q) = 0 if and only if p = q. //
-// (3) d(p, x) + d(x, q) >= d(p, q). (d satisfies triangle inequality) //
-// //
-// In d dimensions, the metric tensor of a point p is a (dxd) symmetric //
-// positive definie (non-degenerate) matrix M(p). Very roughly, it tells how //
-// to compute the distance of p and other points in the metric space of p. //
-// d_M(p, q) = \sqrt{(p - q)' M (p -q)}. //
-// If for any point p, a metric tensor M(p) is given, the field of tensors //
-// thus defines a Riemannian space. For example, if M(q) is a metric tensor //
-// defined on q. Then the distance d(p, q) can be calculated by: //
-// d(p, q) = \int_{0}{1} \sqrt((p - q)' M(t) (p - q)) dt. //
-// where M(t) is the interpolation of metric tensors between p and q, M(0) = //
-// M(p) and M(1) = M(q). //
-// //
-// A metric tensor in three dimension, for example, is a matrix: //
-// | a b c | //
-// M = | b d e | //
-// | c e f | //
-// such that a > 0, d > 0, f > 0, det(M) = adf + 2bce -ccd - eea - bbf > 0. //
-// //
-// It is defined as an array mat[6] = {a, b, c, d, e, f}. Operation on //
-// tensors are defined as well. //
-// //
-///////////////////////////////////////////////////////////////////////////////
-
- class metric {
-
- public:
-
- REAL mat[6];
-
- // Initialization.
- void init() {for (int i = 0; i < 6; i++) mat[i] = 0.0;}
- void set(REAL a, REAL b, REAL c, REAL d, REAL e, REAL f) {
- mat[0] = a; mat[1] = b; mat[2] = c;
- mat[3] = d; mat[4] = e;
- mat[5] = f;
- }
- void set(REAL a, REAL d, REAL f) {
- mat[0] = a; mat[1] = 0.0; mat[2] = 0.0;
- mat[3] = d; mat[4] = 0.0;
- mat[5] = f;
- }
-
- // Constructors.
- metric() {init();}
- };
-
///////////////////////////////////////////////////////////////////////////////
// //
// The list, link and queue data structures //
@@ -998,12 +974,8 @@ class tetgenmesh {
// take two pointers of the corresponding date type, perform the
// comparation, and return -1, 0 or 1 indicating the default linear
// order of them.
-
- // Compare two 'integers'.
static int compare_2_ints(const void* x, const void* y);
- // Compare two 'longs'.
static int compare_2_longs(const void* x, const void* y);
- // Compare two 'unsigned longs'.
static int compare_2_unsignedlongs(const void* x, const void* y);
// The function used to determine the size of primitive data types and
@@ -1196,7 +1168,7 @@ class tetgenmesh {
bool locate(int pos);
void *add(void* newitem);
void *insert(int pos, void* insitem);
- void *del(void* delitem);
+ void *deletenode(void** delnode);
void *del(int pos);
void *getitem();
void *getnitem(int pos);
@@ -1207,7 +1179,7 @@ class tetgenmesh {
// //
// Queue data structure. //
// //
-// A 'queue' is a basically a link. Following is an image of a queue. //
+// A 'queue' is basically a link. Following is an image of a queue. //
// ___________ ___________ ___________ //
// Pop() <-- |_ _|<--|_ _|<--|_ _| <-- Push() //
// |_ Data0 _| |_ Data1 _| |_ Data2 _| //
@@ -1221,12 +1193,27 @@ class tetgenmesh {
public:
queue(int bytes, int count = 256) : link(bytes, NULL, count) {}
- queue(char* str, int count = 256) : link(str, count) {}
-
- int empty() { return linkitems == 0; }
- void *push(void* newitem) { return link::add(newitem); }
- void *bot() { return link::getnitem(1); }
- void *pop() { return link::del(1); }
+ bool empty() { return linkitems == 0; }
+ void *push(void* newitem) {return link::add(newitem);}
+ void *pop() {return link::deletenode((void **) *head);}
+ // Stack is implemented as a single link list.
+ void *stackpush() {
+ void **newnode = (void **) alloc();
+ // if (newitem != (void *) NULL) {
+ // memcpy((void *)(newnode + 2), newitem, linkitembytes);
+ // }
+ void **nextnode = (void **) *head;
+ *head = (void *) newnode;
+ *newnode = (void *) nextnode;
+ linkitems++;
+ return (void *)(newnode + 2);
+ }
+ void *stackpop() {
+ void **deadnode = (void **) *head;
+ *head = *deadnode;
+ linkitems--;
+ return (void *)(deadnode + 2);
+ }
};
///////////////////////////////////////////////////////////////////////////////
@@ -1287,7 +1274,9 @@ class tetgenmesh {
// enqueue an item. The queues are ordered from 63 (highest priority)
// to 0 (lowest priority).
badface *subquefront[3], **subquetail[3];
- badface *tetquefront[64], **tetquetail[64];
+ badface *tetquefront[64], *tetquetail[64];
+ int nextnonemptyq[64];
+ int firstnonemptyq, recentq;
// Pointer to a recently visited tetrahedron. Improves point location
// if proximate points are inserted sequentially.
@@ -1299,7 +1288,8 @@ class tetgenmesh {
long hullsize; // Number of faces of convex hull.
long insegments; // Number of input segments.
int steinerleft; // Number of Steiner points not yet used.
- int pointlfsindex; // Index to find the local feature size of a point.
+ int sizeoftensor; // Number of REALs per metric tensor.
+ int pointmtrindex; // Index to find the metric tensor 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.
@@ -1310,6 +1300,7 @@ class tetgenmesh {
int shmarkindex; // Index to find boundary marker of a subface.
int areaboundindex; // Index to find area bound of a subface.
int checksubfaces; // Are there subfaces in the mesh yet?
+ int checksubsegs; // Are there subsegs in the mesh yet?
int checkpbcs; // Are there periodic boundary conditions?
int varconstraint; // Are there variant (node, seg, facet) constraints?
int nonconvex; // Is current mesh non-convex?
@@ -1319,12 +1310,15 @@ class tetgenmesh {
int suprelverts; // The number of suppressed relocated vertices.
int collapverts; // The number of collapsed relocated vertices.
int unsupverts; // The number of unsuppressed vertices.
+ int smoothsegverts; // The number of smoothed vertices.
+ int smoothvolverts; // The number of smoothed vertices.
int jettisoninverts; // The number of jettisoned input vertices.
int symbolic; // Use symbolic insphere test.
long samples; // Number of random samples for point location.
unsigned long randomseed; // Current random number seed.
REAL macheps; // The machine epsilon.
REAL cosmaxdihed, cosmindihed; // The cosine values of max/min dihedral.
+ REAL minfaceang, minfacetdihed; // The minimum input (dihedral) angles.
int maxcavfaces, maxcavverts; // The size of the largest cavity.
int expcavcount; // The times of expanding cavitys.
long abovecount; // Number of abovepoints calculation.
@@ -1333,13 +1327,12 @@ class tetgenmesh {
long failvolcount, failsubcount, failsegcount; // Bow-Wat fails.
long repairflipcount; // Number of flips for repairing segments.
long outbowatcircumcount; // Number of circumcenters outside Bowat-cav.
- long r1count, r2count, r3count, r4count; // Number of rules performed.
+ long r1count, r2count, r3count; // Numbers of edge splitting rules.
long cdtenforcesegpts; // Number of CDT enforcement points.
long rejsegpts, rejsubpts, rejtetpts; // Number of rejected points.
- long striptetcount, fliptetcount, unimprovecount; // Mesh smooth counts.
- long smoothcdtsegpt, smoothsegpt, smoothsubpt, smoothvolpt;
- long unsmoothcdtsegpt, unsmoothsegpt, unsmoothsubpt, unsmoothvolpt;
+ long optcount[10]; // Numbers of various optimizing operations.
long flip23s, flip32s, flip22s, flip44s; // Number of flips performed.
+ REAL tloctime, tfliptime; // Time (microseconds) of point location.
///////////////////////////////////////////////////////////////////////////////
// //
@@ -1383,6 +1376,10 @@ class tetgenmesh {
// new 'ver'. Note: Only valid for 'ver' equals one of {0, 2, 4}.
static int locver2nextf[4][6][2];
+ // The edge number (from 0 to 5) of a tet is defined as follows:
+ static int locver2edge[4][6];
+ static int edge2locver[6][2];
+
// For enumerating three edges of a triangle.
static int plus1mod3[3];
static int minus1mod3[3];
@@ -1476,7 +1473,7 @@ class tetgenmesh {
inline void tspivot(triface& t, face& s);
inline void stpivot(face& s, triface& t);
inline void tsbond(triface& t, face& s);
- inline void tsdissolve(triface& t);
+ inline void tsdissolve(triface& t);
inline void stdissolve(face& s);
// Primitives for interacting subfaces and subsegs.
@@ -1484,6 +1481,10 @@ class tetgenmesh {
inline void ssbond(face& s, face& edge);
inline void ssdissolve(face& s);
+ inline void tsspivot1(triface& t, face& seg);
+ inline void tssbond1(triface& t, face& seg);
+ inline void tssdissolve1(triface& t);
+
// Primitives for points.
inline int pointmark(point pt);
inline void setpointmark(point pt, int value);
@@ -1509,7 +1510,6 @@ class tetgenmesh {
inline bool isfacehaspoint(face* t, point testpoint);
inline bool isfacehasedge(face* s, point tend1, point tend2);
inline bool issymexist(triface* t);
- bool getnextface(triface*, triface*);
void getnextsface(face*, face*);
void tsspivot(triface*, face*);
void sstpivot(face*, triface*);
@@ -1544,16 +1544,14 @@ class tetgenmesh {
enum interresult edge_vert_col_inter(REAL*, REAL*, REAL*);
enum interresult edge_edge_cop_inter(REAL*, REAL*, REAL*, REAL*, REAL*);
enum interresult tri_vert_cop_inter(REAL*, REAL*, REAL*, REAL*, REAL*);
- enum interresult tri_edge_cop_inter(REAL*, REAL*, REAL*, REAL*, REAL*,
- REAL*);
+ enum interresult tri_edge_cop_inter(REAL*, REAL*, REAL*,REAL*,REAL*,REAL*);
enum interresult tri_edge_inter_tail(REAL*, REAL*, REAL*, REAL*, REAL*,
- REAL, REAL);
+ REAL, REAL);
enum interresult tri_edge_inter(REAL*, REAL*, REAL*, REAL*, REAL*);
enum interresult tri_tri_inter(REAL*, REAL*, REAL*, REAL*, REAL*, REAL*);
// Geometric predicates
- REAL insphere_sos(REAL*, REAL*, REAL*, REAL*, REAL*, int, int, int, int,
- int);
+ REAL insphere_sos(REAL*, REAL*, REAL*, REAL*, REAL*, int, int,int,int,int);
bool iscollinear(REAL*, REAL*, REAL*, REAL eps);
bool iscoplanar(REAL*, REAL*, REAL*, REAL*, REAL vol6, REAL eps);
bool iscospheric(REAL*, REAL*, REAL*, REAL*, REAL*, REAL vol24, REAL eps);
@@ -1576,6 +1574,7 @@ class tetgenmesh {
REAL facedihedral(REAL* pa, REAL* pb, REAL* pc1, REAL* pc2);
void tetalldihedral(point, point, point, point, REAL*, REAL*, REAL*);
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);
void inscribedsphere(REAL*, REAL*, REAL*, REAL*, REAL* cent, REAL* radius);
void rotatepoint(REAL* p, REAL rotangle, REAL* p1, REAL* p2);
@@ -1611,6 +1610,7 @@ class tetgenmesh {
enum locateresult preciselocate(point searchpt, triface* searchtet, long);
enum locateresult locate(point searchpt, triface* searchtet);
enum locateresult adjustlocate(point, triface*, enum locateresult, REAL);
+ enum locateresult hullwalk(point searchpt, triface* hulltet);
enum locateresult locatesub(point searchpt, face* searchsh, int, REAL);
enum locateresult adjustlocatesub(point, face*, enum locateresult, REAL);
enum locateresult locateseg(point searchpt, face* searchseg);
@@ -1635,8 +1635,15 @@ class tetgenmesh {
void flip22(triface* flipface, queue* flipqueue);
void flip22sub(face* flipedge, queue* flipqueue);
long flip(queue* flipqueue, badface **plastflip);
+ long lawson(list *misseglist, queue* flipqueue);
void undoflip(badface *lastflip);
long flipsub(queue* flipqueue);
+ bool removetetbypeeloff(triface *striptet);
+ bool removefacebyflip23(REAL *key, triface*, triface*, queue*);
+ bool removeedgebyflip22(REAL *key, int, triface*, queue*);
+ bool removeedgebyflip32(REAL *key, triface*, triface*, queue*);
+ bool removeedgebytranNM(REAL*,int,triface*,triface*,point,point,queue*);
+ bool removeedgebycombNM(REAL*,int,triface*,int*,triface*,triface*,queue*);
void splittetrahedron(point newpoint, triface* splittet, queue* flipqueue);
void unsplittetrahedron(triface* splittet);
@@ -1652,6 +1659,8 @@ class tetgenmesh {
bool approx, queue* flipqueue);
void undosite(enum insertsiteresult insresult, triface* splittet,
point torg, point tdest, point tapex, point toppo);
+ void closeopenface(triface* openface, queue* flipque);
+ void inserthullsite(point inspoint, triface* horiz, queue* flipque);
void formbowatcavitysub(point, face*, list*, list*);
void formbowatcavityquad(point, list*, list*);
@@ -1674,8 +1683,6 @@ class tetgenmesh {
// Delaunay tetrahedralization routines.
void formstarpolyhedron(point pt, list* tetlist, list* verlist, bool);
bool unifypoint(point testpt, triface*, enum locateresult, REAL);
- void closeopenface(triface* openface, queue* flipque);
- void inserthullsite(point inspoint, triface* horiz, queue* flipque);
void incrflipdelaunay(triface*, point*, long, bool, bool, REAL, queue*);
long delaunizevertices();
@@ -1698,7 +1705,7 @@ class tetgenmesh {
int holes, REAL* holelist, memorypool* viri, queue*);
void retrievenewsubs(list* newshlist, bool removeseg);
void unifysegments();
- void mergefacets(queue* flipqueue);
+ void mergefacets(queue* flipqueue);
long meshsurface();
// Detect intersecting facets of PLC.
@@ -1732,6 +1739,8 @@ class tetgenmesh {
point scoutrefpoint(triface* searchtet, point tend);
point getsegmentorigin(face* splitseg);
point getsplitpoint(face* splitseg, point refpoint);
+ bool insertsegment(face *insseg, list *misseglist);
+ void tallmissegs(list *misseglist);
void delaunizesegments();
// Facets recovery routines.
@@ -1791,46 +1800,43 @@ class tetgenmesh {
void restorepolyhedron(list* oldtetlist);
bool suppressfacetpoint(face* supsh, list* frontlist, list* misfrontlist,
list* ptlist, list* conlist, memorypool* viri,
- queue* flipque);
+ queue* flipque, bool noreloc, bool optflag);
bool suppresssegpoint(face* supseg, list* spinshlist, list* newsegshlist,
list* frontlist, list* misfrontlist, list* ptlist,
- list* conlist, memorypool* viri, queue* flipque);
- bool suppressvolpoint(point suppt, list* frontlist, list* misfrontlist,
- list* ptlist, queue* flipque);
- bool collapseedgepoint(point colpt, list* oldtetlist, list* newtetlist,
- list* ptlist);
- void removesteiners();
-
- // Mesh reconstruction rotuines.
+ list* conlist, memorypool* viri, queue* flipque,
+ bool noreloc, bool optflag);
+ bool suppressvolpoint(triface* suptet, list* frontlist, list* misfrontlist,
+ list* ptlist, queue* flipque, bool optflag);
+ bool smoothpoint(point smthpt, point, point, list *starlist, bool, REAL*);
+ void removesteiners(bool coarseflag);
+
+ // Mesh reconstruction routines.
long reconstructmesh();
- bool intettest(point testpt, triface* testtet, REAL eps);
- void insertaddpoints();
-
+ // Constrained points insertion routines.
+ void insertconstrainedpoints(tetgenio *addio);
// Background mesh operations.
- bool interpolatepointsize(point pt, triface* bgmtet, long *scount);
- void searchpointrecursive(triface *curtet, long *scount);
+ bool p1interpolatebgm(point pt, triface* bgmtet, long *scount);
void interpolatesizemap();
+ void duplicatebgmesh();
// Delaunay refinement routines.
- void calclocalfeaturesizes();
- void marksharpsubsegs(REAL dihedbound);
- void markskinnysubfaces(REAL anglebound);
- void enqueuebadtet(triface* tt, REAL key, REAL* cent);
+ void marksharpsegments(REAL sharpangle);
+ void decidefeaturepointsizes();
void enqueueencsub(face* ss, point encpt, int quenumber, REAL* cent);
- badface* dequeuebadtet();
badface* dequeueencsub(int* quenumber);
+ void enqueuebadtet(triface* tt, REAL key, REAL* cent);
+ badface* topbadtetra();
+ void dequeuebadtet();
bool checkseg4encroach(face* testseg, point testpt, point*, bool enqflag);
bool checksub4encroach(face* testsub, point testpt, bool enqflag);
- bool checkseg4badqual(face* testseg, bool enqflag);
- bool checksub4badqual(face* testsub, bool enqflag);
bool checktet4badqual(triface* testtet, bool enqflag);
bool acceptsegpt(point segpt, point refpt, face* splitseg);
bool acceptfacpt(point facpt, list* subceillist, list* verlist);
bool acceptvolpt(point volpt, list* ceillist, list* verlist);
void getsplitpoint(point e1, point e2, point refpt, point newpt);
void shepardinterpolate(point newpt, list* verlist);
- void setnewpointsize(point newpt, list* verlist);
- void splitencseg(point, face*, list*, list*, list*, queue*, bool, bool);
+ void setnewpointsize(point newpt, point e1, point e2);
+ void splitencseg(point, face*, list*, list*, list*,queue*,bool,bool,bool);
bool tallencsegs(point testpt, int n, list** ceillists);
bool tallencsubs(point testpt, int n, list** ceillists);
void tallbadtetrahedrons();
@@ -1839,16 +1845,15 @@ class tetgenmesh {
void repairbadtets();
void enforcequality();
- // Mesh Smoothing routines.
+ // Mesh optimization routines.
+ void dumpbadtets();
bool checktet4ill(triface* testtet, bool enqflag);
- bool checktet4sliver(triface* testtet, bool chkill, bool enqflag);
- void removetetbystripoff(triface *striptet);
- void removetetbyflip32(triface *fliptet, bool enq, bool chkill);
- bool removetetbyrecon(badface* remtet, bool chkill);
- bool removetetbysplit(badface* remtet);
- void tallslivers(bool chkill);
- void repairmesh();
- void smoothmesh();
+ bool checktet4opt(triface* testtet, bool enqflag);
+ bool removeedge(badface* remedge, bool optflag);
+ bool smoothsliver(badface* remedge, list *starlist);
+ bool splitsliver(badface* remedge, list *tetlist, list *ceillist);
+ void tallslivers(bool optflag);
+ void optimizemesh(bool optflag);
// I/O routines
void transfernodes();
@@ -1860,8 +1865,10 @@ class tetgenmesh {
void outfaces(tetgenio* out);
void outhullfaces(tetgenio* out);
void outsubfaces(tetgenio* out);
+ void outedges(tetgenio* out);
void outsubsegments(tetgenio* out);
void outneighbors(tetgenio* out);
+ void outvoronoi(tetgenio* out);
void outpbcnodes(tetgenio* out);
void outsmesh(char* smfilename);
void outmesh2medit(char* mfilename);
@@ -1873,7 +1880,6 @@ class tetgenmesh {
void checkmesh();
void checkshells();
void checkdelaunay(REAL eps, queue* flipqueue);
- void checkdegeneracy(REAL eps);
void checkconforming();
void algorithmicstatistics();
void qualitystatistics();
@@ -1893,23 +1899,18 @@ class tetgenmesh {
// Delaunay tetrahedralizations, constrained Delaunay //
// tetrahedralizations, quality tetrahedral meshes. //
// //
-// Two functions (interfaces) are available. The difference is only the way //
-// of passing switches. One directly accepts an object of 'tetgenbehavior', //
-// while the other accepts a string which is the same as one can used in the //
-// command line. The latter may be more convenient for users who don't want //
-// to kown the 'tetgenbehavir' structure. //
-// //
// 'in' is an object of 'tetgenio' which contains a PLC you want to tetrahed-//
// ralize or a previously generated tetrahedral mesh you want to refine. It //
// must not be a NULL. 'out' is another object of 'tetgenio' for storing the //
// generated tetrahedral mesh. It can be a NULL. If so, the output will be //
-// saved to file(s). //
+// saved to file(s). If 'bgmin' != NULL, it contains a background mesh which //
+// defines a mesh size distruction function. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetrahedralize(tetgenbehavior *b, tetgenio *in, tetgenio *out,
- tetgenio *bgmesh = NULL);
+ tetgenio *addin = NULL, tetgenio *bgmin = NULL);
void tetrahedralize(char *switches, tetgenio *in, tetgenio *out,
- tetgenio *bgmesh = NULL);
+ tetgenio *addin = NULL, tetgenio *bgmin = NULL);
#endif // #ifndef tetgenH
--
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