Select Git revision
tetgenBR.cxx
Forked from
gmsh / gmsh
Source project has a limited visibility.
-
Christophe Geuzaine authoredChristophe Geuzaine authored
tetgenBR.cxx 603.83 KiB
// This file is part of Tetgen/BR, the Boundary Recovery code of TetGen
//
// Copyright 2015-2016 Weierstrass Institute for Applied Analysis and
// Stochastics
//
// This file is relicensed under the terms of LICENSE.txt for use in Gmsh thanks
// to a Software License Agreement between Weierstrass Institute for Applied
// Analysis and Stochastics and GMESH SPRL.
///////////////////////////////////////////////////////////////////////////////
// //
// TetGen //
// //
// A Quality Tetrahedral Mesh Generator and A 3D Delaunay Triangulator //
// //
// Version 1.5 //
// May 31, 2014 //
// //
// Copyright (C) 2002--2016 //
// //
// TetGen is freely available through the website: http://www.tetgen.org. //
// It may be copied, modified, and redistributed for non-commercial use. //
// Please consult the file LICENSE for the detailed copyright notices. //
// //
///////////////////////////////////////////////////////////////////////////////
// The following code of this file was automatically generated. Do not edit!
// TetGenBR -- The Boundary Recovery code of TetGen.
///////////////////////////////////////////////////////////////////////////////
// //
// parse_commandline() Read the command line, identify switches, and set //
// up options and file names. //
// //
// 'argc' and 'argv' are the same parameters passed to the function main() //
// of a C/C++ program. They together represent the command line user invoked //
// from an environment in which TetGen is running. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenbehavior::parse_commandline(int argc, char **argv)
{
int startindex;
int increment;
int meshnumber;
int i, j, k;
char workstring[1024];
// First determine the input style of the switches.
if (argc == 0) {
startindex = 0; // Switches are given without a dash.
argc = 1; // For running the following for-loop once.
commandline[0] = '\0';
} else {
startindex = 1;
strcpy(commandline, argv[0]);
strcat(commandline, " ");
}
for (i = startindex; i < argc; i++) {
// Remember the command line for output.
strcat(commandline, argv[i]);
strcat(commandline, " ");
if (startindex == 1) {
// Is this string a filename?
if (argv[i][0] != '-') {
strncpy(infilename, argv[i], 1024 - 1);
infilename[1024 - 1] = '\0';
continue;
} }
// Parse the individual switch from the string.
for (j = startindex; argv[i][j] != '\0'; j++) {
if (argv[i][j] == 'p') {
plc = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
facet_separate_ang_tol = (REAL) strtod(workstring, (char **) NULL);
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
(argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
facet_overlap_ang_tol = (REAL) strtod(workstring, (char **) NULL);
}
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
facet_small_ang_tol = (REAL) strtod(workstring, (char **) NULL);
}
}
} else if (argv[i][j] == 's') {
psc = 1;
} else if (argv[i][j] == 'Y') {
nobisect = 1;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
nobisect_nomerge = (argv[i][j + 1] - '0');
j++;
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
supsteiner_level = (argv[i][j + 1] - '0');
j++;
}
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
addsteiner_algo = (argv[i][j + 1] - '0');
j++;
}
} } else if (argv[i][j] == 'r') {
refine = 1;
} else if (argv[i][j] == 'q') {
quality = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
minratio = (REAL) strtod(workstring, (char **) NULL);
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
mindihedral = (REAL) strtod(workstring, (char **) NULL);
}
}
} else if (argv[i][j] == 'R') {
coarsen = 1;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
coarsen_param = (argv[i][j + 1] - '0');
j++;
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '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';
coarsen_percent = (REAL) strtod(workstring, (char **) NULL);
}
}
} else if (argv[i][j] == 'w') {
weighted = 1;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
weighted_param = (argv[i][j + 1] - '0');
j++;
}
} else if (argv[i][j] == 'b') {
// -b(brio_threshold/brio_ratio/hilbert_limit/hilbert_order)
brio_hilbert = 1;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
} workstring[k] = '\0';
brio_threshold = (int) strtol(workstring, (char **) &workstring, 0);
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
brio_ratio = (REAL) strtod(workstring, (char **) NULL);
}
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
hilbert_limit = (int) strtol(workstring, (char **) &workstring, 0);
}
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == '-')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
hilbert_order = (REAL) strtod(workstring, (char **) NULL);
}
}
if (brio_threshold == 0) { // -b0
brio_hilbert = 0; // Turn off BRIO-Hilbert sorting.
}
if (brio_ratio >= 1.0) { // -b/1
no_sort = 1;
brio_hilbert = 0; // Turn off BRIO-Hilbert sorting.
}
} else if (argv[i][j] == 'l') {
incrflip = 1;
} else if (argv[i][j] == 'L') {
flipinsert = 1;
} else if (argv[i][j] == 'm') {
metric = 1;
} else if (argv[i][j] == 'a') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
fixedvolume = 1;
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
(argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
j++; workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
maxvolume = (REAL) strtod(workstring, (char **) NULL);
} else {
varvolume = 1;
}
} else if (argv[i][j] == 'A') {
regionattrib = 1;
} else if (argv[i][j] == 'D') {
cdtrefine = 1;
if ((argv[i][j + 1] >= '1') && (argv[i][j + 1] <= '3')) {
reflevel = (argv[i][j + 1] - '1') + 1;
j++;
}
} else if (argv[i][j] == 'i') {
insertaddpoints = 1;
} else if (argv[i][j] == 'd') {
diagnose = 1;
} else if (argv[i][j] == 'c') {
convex = 1;
} else if (argv[i][j] == 'M') {
nomergefacet = 1;
nomergevertex = 1;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '1')) {
nomergefacet = (argv[i][j + 1] - '0');
j++;
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '1')) {
nomergevertex = (argv[i][j + 1] - '0');
j++;
}
}
} else if (argv[i][j] == 'X') {
if (argv[i][j + 1] == '1') {
nostaticfilter = 1;
j++;
} else {
noexact = 1;
}
} else if (argv[i][j] == 'z') {
if (argv[i][j + 1] == '1') { // -z1
reversetetori = 1;
j++;
} else {
zeroindex = 1; // -z
}
} else if (argv[i][j] == 'f') {
facesout++;
} else if (argv[i][j] == 'e') {
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] == 'k') {
vtkview = 1;
} else if (argv[i][j] == 'J') {
nojettison = 1;
} else if (argv[i][j] == 'B') {
nobound = 1;
} else if (argv[i][j] == 'N') {
nonodewritten = 1;
} else if (argv[i][j] == 'E') {
noelewritten = 1; } else if (argv[i][j] == 'F') {
nofacewritten = 1;
} else if (argv[i][j] == 'I') {
noiterationnum = 1;
} else if (argv[i][j] == 'S') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
(argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
steinerleft = (int) strtol(workstring, (char **) NULL, 0);
}
} else if (argv[i][j] == 'o') {
if (argv[i][j + 1] == '2') {
order = 2;
j++;
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
optmaxdihedral = (REAL) strtod(workstring, (char **) NULL);
}
}
} else if (argv[i][j] == 'O') {
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
optlevel = (argv[i][j + 1] - '0');
j++;
}
if ((argv[i][j + 1] == '/') || (argv[i][j + 1] == ',')) {
j++;
if ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '7')) {
optscheme = (argv[i][j + 1] - '0');
j++;
}
}
} else if (argv[i][j] == 'T') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
(argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
epsilon = (REAL) strtod(workstring, (char **) NULL);
}
} else if (argv[i][j] == 'C') {
docheck++;
} else if (argv[i][j] == 'Q') {
quiet = 1;
} else if (argv[i][j] == 'V') {
verbose++; } else if (argv[i][j] == 'x') {
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.')) {
k = 0;
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
(argv[i][j + 1] == '.') || (argv[i][j + 1] == 'e') ||
(argv[i][j + 1] == '-') || (argv[i][j + 1] == '+')) {
j++;
workstring[k] = argv[i][j];
k++;
}
workstring[k] = '\0';
tetrahedraperblock = (int) strtol(workstring, (char **) NULL, 0);
if (tetrahedraperblock > 8188) {
vertexperblock = tetrahedraperblock / 2;
shellfaceperblock = vertexperblock / 2;
} else {
tetrahedraperblock = 8188;
}
}
} else if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
(argv[i][j] == '?')) {
} else {
printf("Warning: Unknown switch -%c.\n", argv[i][j]);
}
}
}
if (startindex == 0) {
// Set a temporary filename for debugging output.
strcpy(infilename, "tetgen-tmpfile");
} else {
if (infilename[0] == '\0') {
}
// Recognize the object from file extension if it is available.
if (!strcmp(&infilename[strlen(infilename) - 5], ".node")) {
infilename[strlen(infilename) - 5] = '\0';
object = NODES;
} else if (!strcmp(&infilename[strlen(infilename) - 5], ".poly")) {
infilename[strlen(infilename) - 5] = '\0';
object = POLY;
plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 6], ".smesh")) {
infilename[strlen(infilename) - 6] = '\0';
object = POLY;
plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 4], ".off")) {
infilename[strlen(infilename) - 4] = '\0';
object = OFF;
plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 4], ".ply")) {
infilename[strlen(infilename) - 4] = '\0';
object = PLY;
plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 4], ".stl")) {
infilename[strlen(infilename) - 4] = '\0';
object = STL;
plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 5], ".mesh")) {
infilename[strlen(infilename) - 5] = '\0';
object = MEDIT;
if (!refine) plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 4], ".vtk")) {
infilename[strlen(infilename) - 4] = '\0';
object = VTK;
plc = 1;
} else if (!strcmp(&infilename[strlen(infilename) - 4], ".ele")) {
infilename[strlen(infilename) - 4] = '\0';
object = MESH;
refine = 1; }
}
if (nobisect && (!plc && !refine)) { // -Y
plc = 1; // Default -p option.
}
if (quality && (!plc && !refine)) { // -q
plc = 1; // Default -p option.
}
if (diagnose && !plc) { // -d
plc = 1;
}
if (refine && !quality) { // -r only
// Reconstruct a mesh, no mesh optimization.
optlevel = 0;
}
if (insertaddpoints && (optlevel == 0)) { // with -i option
optlevel = 2;
}
if (coarsen && (optlevel == 0)) { // with -R option
optlevel = 2;
}
// Detect improper combinations of switches.
if ((refine || plc) && weighted) {
printf("Error: Switches -w cannot use together with -p or -r.\n");
return false;
}
if (convex) { // -c
if (plc && !regionattrib) {
// -A (region attribute) is needed for marking exterior tets (-1).
regionattrib = 1;
}
}
// Note: -A must not used together with -r option.
// Be careful not to add an extra attribute to each element unless the
// input supports it (PLC in, but not refining a preexisting mesh).
if (refine || !plc) {
regionattrib = 0;
}
// Be careful not to allocate space for element area constraints that
// will never be assigned any value (other than the default -1.0).
if (!refine && !plc) {
varvolume = 0;
}
// If '-a' or '-aa' is in use, enable '-q' option too.
if (fixedvolume || varvolume) {
if (quality == 0) {
quality = 1;
if (!plc && !refine) {
plc = 1; // enable -p.
}
}
}
// No user-specified dihedral angle bound. Use default ones.
if (!quality) {
if (optmaxdihedral < 179.0) {
if (nobisect) { // with -Y option
optmaxdihedral = 179.0;
} else { // -p only
optmaxdihedral = 179.999;
}
}
if (optminsmtdihed < 179.999) {
optminsmtdihed = 179.999;
}
if (optminslidihed < 179.999) {
optminslidihed = 179.999; }
}
increment = 0;
strcpy(workstring, infilename);
j = 1;
while (workstring[j] != '\0') {
if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
increment = j + 1;
}
j++;
}
meshnumber = 0;
if (increment > 0) {
j = increment;
do {
if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
} else {
increment = 0;
}
j++;
} while (workstring[j] != '\0');
}
if (noiterationnum) {
strcpy(outfilename, infilename);
} else if (increment == 0) {
strcpy(outfilename, infilename);
strcat(outfilename, ".1");
} else {
workstring[increment] = '%';
workstring[increment + 1] = 'd';
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");
return true;
}
//// ////
//// ////
//// behavior_cxx /////////////////////////////////////////////////////////////
//// mempool_cxx //////////////////////////////////////////////////////////////
//// ////
//// ////
// Initialize fast lookup tables for mesh maniplulation primitives.
int tetgenmesh::bondtbl[12][12] = {{0,},};
int tetgenmesh::enexttbl[12] = {0,};
int tetgenmesh::eprevtbl[12] = {0,};
int tetgenmesh::enextesymtbl[12] = {0,};
int tetgenmesh::eprevesymtbl[12] = {0,};
int tetgenmesh::eorgoppotbl[12] = {0,};
int tetgenmesh::edestoppotbl[12] = {0,};
int tetgenmesh::fsymtbl[12][12] = {{0,},};
int tetgenmesh::facepivot1[12] = {0,};
int tetgenmesh::facepivot2[12][12] = {{0,},};
int tetgenmesh::tsbondtbl[12][6] = {{0,},};
int tetgenmesh::stbondtbl[12][6] = {{0,},};
int tetgenmesh::tspivottbl[12][6] = {{0,},};
int tetgenmesh::stpivottbl[12][6] = {{0,},};
// Table 'esymtbl' takes an directed edge (version) as input, returns the
// inversed edge (version) of it.
int tetgenmesh::esymtbl[12] = {9, 6, 11, 4, 3, 7, 1, 5, 10, 0, 8, 2};
// The following four tables give the 12 permutations of the set {0,1,2,3}.
// An offset 4 is added to each element for a direct access of the points
// in the tetrahedron data structure.
int tetgenmesh:: orgpivot[12] = {7, 7, 5, 5, 6, 4, 4, 6, 5, 6, 7, 4};
int tetgenmesh::destpivot[12] = {6, 4, 4, 6, 5, 6, 7, 4, 7, 7, 5, 5};
int tetgenmesh::apexpivot[12] = {5, 6, 7, 4, 7, 7, 5, 5, 6, 4, 4, 6};
int tetgenmesh::oppopivot[12] = {4, 5, 6, 7, 4, 5, 6, 7, 4, 5, 6, 7};
// The twelve versions correspond to six undirected edges. The following two
// tables map a version to an undirected edge and vice versa.
int tetgenmesh::ver2edge[12] = {0, 1, 2, 3, 3, 5, 1, 5, 4, 0, 4, 2};
int tetgenmesh::edge2ver[ 6] = {0, 1, 2, 3, 8, 5};
// Edge versions whose apex or opposite may be dummypoint.
int tetgenmesh::epivot[12] = {4, 5, 2, 11, 4, 5, 2, 11, 4, 5, 2, 11};
// Table 'snextpivot' takes an edge version as input, returns the next edge
// version in the same edge ring.
int tetgenmesh::snextpivot[6] = {2, 5, 4, 1, 0, 3};
// The following three tables give the 6 permutations of the set {0,1,2}.
// An offset 3 is added to each element for a direct access of the points
// in the triangle data structure.
int tetgenmesh::sorgpivot [6] = {3, 4, 4, 5, 5, 3};
int tetgenmesh::sdestpivot[6] = {4, 3, 5, 4, 3, 5};
int tetgenmesh::sapexpivot[6] = {5, 5, 3, 3, 4, 4};
///////////////////////////////////////////////////////////////////////////////
// //
// inittable() Initialize the look-up tables. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::inittables()
{
int soffset, toffset;
int i, j;
// i = t1.ver; j = t2.ver;
for (i = 0; i < 12; i++) {
for (j = 0; j < 12; j++) {
bondtbl[i][j] = (j & 3) + (((i & 12) + (j & 12)) % 12);
}
}
// i = t1.ver; j = t2.ver
for (i = 0; i < 12; i++) {
for (j = 0; j < 12; j++) {
fsymtbl[i][j] = (j + 12 - (i & 12)) % 12;
}
}
for (i = 0; i < 12; i++) {
facepivot1[i] = (esymtbl[i] & 3);
}
for (i = 0; i < 12; i++) {
for (j = 0; j < 12; j++) {
facepivot2[i][j] = fsymtbl[esymtbl[i]][j];
}
}
for (i = 0; i < 12; i++) {
enexttbl[i] = (i + 4) % 12;
eprevtbl[i] = (i + 8) % 12;
}
for (i = 0; i < 12; i++) {
enextesymtbl[i] = esymtbl[enexttbl[i]];
eprevesymtbl[i] = esymtbl[eprevtbl[i]];
}
for (i = 0; i < 12; i++) {
eorgoppotbl [i] = eprevtbl[esymtbl[enexttbl[i]]];
edestoppotbl[i] = enexttbl[esymtbl[eprevtbl[i]]];
}
// i = t.ver, j = s.shver
for (i = 0; i < 12; i++) {
for (j = 0; j < 6; j++) {
if ((j & 1) == 0) {
soffset = (6 - ((i & 12) >> 1)) % 6;
toffset = (12 - ((j & 6) << 1)) % 12;
} else {
soffset = (i & 12) >> 1;
toffset = (j & 6) << 1;
}
tsbondtbl[i][j] = (j & 1) + (((j & 6) + soffset) % 6);
stbondtbl[i][j] = (i & 3) + (((i & 12) + toffset) % 12);
}
}
// i = t.ver, j = s.shver
for (i = 0; i < 12; i++) {
for (j = 0; j < 6; j++) {
if ((j & 1) == 0) {
soffset = (i & 12) >> 1;
toffset = (j & 6) << 1;
} else {
soffset = (6 - ((i & 12) >> 1)) % 6;
toffset = (12 - ((j & 6) << 1)) % 12;
}
tspivottbl[i][j] = (j & 1) + (((j & 6) + soffset) % 6);
stpivottbl[i][j] = (i & 3) + (((i & 12) + toffset) % 12);
}
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// restart() Deallocate all objects in this pool. //
// //
// The pool returns to a fresh state, like after it was initialized, except //
// that no memory is freed to the operating system. Rather, the previously //
// allocated blocks are ready to be used. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::arraypool::restart()
{
objects = 0l;
}
///////////////////////////////////////////////////////////////////////////////// //
// poolinit() Initialize an arraypool for allocation of objects. //
// //
// Before the pool may be used, it must be initialized by this procedure. //
// After initialization, memory can be allocated and freed in this pool. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::arraypool::poolinit(int sizeofobject, int log2objperblk)
{
// Each object must be at least one byte long.
objectbytes = sizeofobject > 1 ? sizeofobject : 1;
log2objectsperblock = log2objperblk;
// Compute the number of objects in each block.
objectsperblock = ((int) 1) << log2objectsperblock;
objectsperblockmark = objectsperblock - 1;
// No memory has been allocated.
totalmemory = 0l;
// The top array has not been allocated yet.
toparray = (char **) NULL;
toparraylen = 0;
// Ready all indices to be allocated.
restart();
}
///////////////////////////////////////////////////////////////////////////////
// //
// arraypool() The constructor and destructor. //
// //
///////////////////////////////////////////////////////////////////////////////
tetgenmesh::arraypool::arraypool(int sizeofobject, int log2objperblk)
{
poolinit(sizeofobject, log2objperblk);
}
tetgenmesh::arraypool::~arraypool()
{
int i;
// Has anything been allocated at all?
if (toparray != (char **) NULL) {
// Walk through the top array.
for (i = 0; i < toparraylen; i++) {
// Check every pointer; NULLs may be scattered randomly.
if (toparray[i] != (char *) NULL) {
// Free an allocated block.
free((void *) toparray[i]);
}
}
// Free the top array.
free((void *) toparray);
}
// The top array is no longer allocated.
toparray = (char **) NULL;
toparraylen = 0;
objects = 0;
totalmemory = 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// getblock() Return (and perhaps create) the block containing the object //
// with a given index. //
// //
// This function takes care of allocating or resizing the top array if nece- //// ssary, and of allocating the block if it hasn't yet been allocated. //
// //
// Return a pointer to the beginning of the block (NOT the object). //
// //
///////////////////////////////////////////////////////////////////////////////
char* tetgenmesh::arraypool::getblock(int objectindex)
{
char **newarray;
char *block;
int newsize;
int topindex;
int i;
// Compute the index in the top array (upper bits).
topindex = objectindex >> log2objectsperblock;
// Does the top array need to be allocated or resized?
if (toparray == (char **) NULL) {
// Allocate the top array big enough to hold 'topindex', and NULL out
// its contents.
newsize = topindex + 128;
toparray = (char **) malloc((size_t) (newsize * sizeof(char *)));
toparraylen = newsize;
for (i = 0; i < newsize; i++) {
toparray[i] = (char *) NULL;
}
// Account for the memory.
totalmemory = newsize * (uintptr_t) sizeof(char *);
} else if (topindex >= toparraylen) {
// Resize the top array, making sure it holds 'topindex'.
newsize = 3 * toparraylen;
if (topindex >= newsize) {
newsize = topindex + 128;
}
// Allocate the new array, copy the contents, NULL out the rest, and
// free the old array.
newarray = (char **) malloc((size_t) (newsize * sizeof(char *)));
for (i = 0; i < toparraylen; i++) {
newarray[i] = toparray[i];
}
for (i = toparraylen; i < newsize; i++) {
newarray[i] = (char *) NULL;
}
free(toparray);
// Account for the memory.
totalmemory += (newsize - toparraylen) * sizeof(char *);
toparray = newarray;
toparraylen = newsize;
}
// Find the block, or learn that it hasn't been allocated yet.
block = toparray[topindex];
if (block == (char *) NULL) {
// Allocate a block at this index.
block = (char *) malloc((size_t) (objectsperblock * objectbytes));
toparray[topindex] = block;
// Account for the memory.
totalmemory += objectsperblock * objectbytes;
}
// Return a pointer to the block.
return block;
}
///////////////////////////////////////////////////////////////////////////////
// //
// lookup() Return the pointer to the object with a given index, or NULL //
// if the object's block doesn't exist yet. //
// //
///////////////////////////////////////////////////////////////////////////////
void* tetgenmesh::arraypool::lookup(int objectindex)
{
char *block;
int topindex;
// Has the top array been allocated yet?
if (toparray == (char **) NULL) {
return (void *) NULL;
}
// Compute the index in the top array (upper bits).
topindex = objectindex >> log2objectsperblock;
// Does the top index fit in the top array?
if (topindex >= toparraylen) {
return (void *) NULL;
}
// Find the block, or learn that it hasn't been allocated yet.
block = toparray[topindex];
if (block == (char *) NULL) {
return (void *) NULL;
}
// Compute a pointer to the object with the given index. Note that
// 'objectsperblock' is a power of two, so the & operation is a bit mask
// that preserves the lower bits.
return (void *)(block + (objectindex & (objectsperblock - 1)) * objectbytes);
}
///////////////////////////////////////////////////////////////////////////////
// //
// newindex() Allocate space for a fresh object from the pool. //
// //
// 'newptr' returns a pointer to the new object (it must not be a NULL). //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::arraypool::newindex(void **newptr)
{
// Allocate an object at index 'firstvirgin'.
int newindex = objects;
*newptr = (void *) (getblock(objects) +
(objects & (objectsperblock - 1)) * objectbytes);
objects++;
return newindex;
}
///////////////////////////////////////////////////////////////////////////////
// //
// memorypool() The constructors of memorypool. //
// //
///////////////////////////////////////////////////////////////////////////////
tetgenmesh::memorypool::memorypool()
{
firstblock = nowblock = (void **) NULL;
nextitem = (void *) NULL;
deaditemstack = (void *) NULL;
pathblock = (void **) NULL;
pathitem = (void *) NULL;
alignbytes = 0;
itembytes = itemwords = 0;
itemsperblock = 0;
items = maxitems = 0l;
unallocateditems = 0;
pathitemsleft = 0;
}
tetgenmesh::memorypool::memorypool(int bytecount, int itemcount, int wsize,
int alignment)
{
poolinit(bytecount, itemcount, wsize, alignment);
}
///////////////////////////////////////////////////////////////////////////////
// //
// ~memorypool() Free to the operating system all memory taken by a pool. //
// //
///////////////////////////////////////////////////////////////////////////////
tetgenmesh::memorypool::~memorypool()
{
while (firstblock != (void **) NULL) {
nowblock = (void **) *(firstblock);
free(firstblock);
firstblock = nowblock;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// poolinit() Initialize a pool of memory for allocation of items. //
// //
// A `pool' is created whose records have size at least `bytecount'. Items //
// will be allocated in `itemcount'-item blocks. Each item is assumed to be //
// a collection of words, and either pointers or floating-point values are //
// assumed to be the "primary" word type. (The "primary" word type is used //
// to determine alignment of items.) If `alignment' isn't zero, all items //
// will be `alignment'-byte aligned in memory. `alignment' must be either a //
// multiple or a factor of the primary word size; powers of two are safe. //
// `alignment' is normally used to create a few unused bits at the bottom of //
// each item's pointer, in which information may be stored. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::memorypool::poolinit(int bytecount,int itemcount,int wordsize,
int alignment)
{
// Find the proper alignment, which must be at least as large as:
// - The parameter `alignment'.
// - The primary word type, to avoid unaligned accesses.
// - sizeof(void *), so the stack of dead items can be maintained
// without unaligned accesses.
if (alignment > wordsize) {
alignbytes = alignment;
} else {
alignbytes = wordsize;
}
if ((int) sizeof(void *) > alignbytes) {
alignbytes = (int) sizeof(void *);
}
itemwords = ((bytecount + alignbytes - 1) / alignbytes)
* (alignbytes / wordsize);
itembytes = itemwords * wordsize;
itemsperblock = itemcount;
// Allocate a block of items. Space for `itemsperblock' items and one
// pointer (to point to the next block) are allocated, as well as space
// to ensure alignment of the items.
firstblock = (void **) malloc(itemsperblock * itembytes + sizeof(void *)
+ alignbytes);
if (firstblock == (void **) NULL) {
terminatetetgen(NULL, 1);
}
// Set the next block pointer to NULL.
*(firstblock) = (void *) NULL;
restart();}
///////////////////////////////////////////////////////////////////////////////
// //
// restart() Deallocate all items in this pool. //
// //
// The pool is returned to its starting state, except that no memory is //
// freed to the operating system. Rather, the previously allocated blocks //
// are ready to be reused. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::memorypool::restart()
{
uintptr_t alignptr;
items = 0;
maxitems = 0;
// Set the currently active block.
nowblock = firstblock;
// Find the first item in the pool. Increment by the size of (void *).
alignptr = (uintptr_t) (nowblock + 1);
// Align the item on an `alignbytes'-byte boundary.
nextitem = (void *)
(alignptr + (uintptr_t) alignbytes -
(alignptr % (uintptr_t) alignbytes));
// There are lots of unallocated items left in this block.
unallocateditems = itemsperblock;
// The stack of deallocated items is empty.
deaditemstack = (void *) NULL;
}
///////////////////////////////////////////////////////////////////////////////
// //
// alloc() Allocate space for an item. //
// //
///////////////////////////////////////////////////////////////////////////////
void* tetgenmesh::memorypool::alloc()
{
void *newitem;
void **newblock;
uintptr_t alignptr;
// First check the linked list of dead items. If the list is not
// empty, allocate an item from the list rather than a fresh one.
if (deaditemstack != (void *) NULL) {
newitem = deaditemstack; // Take first item in list.
deaditemstack = * (void **) deaditemstack;
} else {
// Check if there are any free items left in the current block.
if (unallocateditems == 0) {
// Check if another block must be allocated.
if (*nowblock == (void *) NULL) {
// Allocate a new block of items, pointed to by the previous block.
newblock = (void **) malloc(itemsperblock * itembytes + sizeof(void *)
+ alignbytes);
if (newblock == (void **) NULL) {
terminatetetgen(NULL, 1);
}
*nowblock = (void *) newblock;
// The next block pointer is NULL.
*newblock = (void *) NULL;
}
// Move to the new block.
nowblock = (void **) *nowblock;
// Find the first item in the block.
// Increment by the size of (void *).
alignptr = (uintptr_t) (nowblock + 1); // Align the item on an `alignbytes'-byte boundary.
nextitem = (void *)
(alignptr + (uintptr_t) alignbytes -
(alignptr % (uintptr_t) alignbytes));
// There are lots of unallocated items left in this block.
unallocateditems = itemsperblock;
}
// Allocate a new item.
newitem = nextitem;
// Advance `nextitem' pointer to next free item in block.
nextitem = (void *) ((uintptr_t) nextitem + itembytes);
unallocateditems--;
maxitems++;
}
items++;
return newitem;
}
///////////////////////////////////////////////////////////////////////////////
// //
// dealloc() Deallocate space for an item. //
// //
// The deallocated space is stored in a queue for later reuse. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::memorypool::dealloc(void *dyingitem)
{
// Push freshly killed item onto stack.
*((void **) dyingitem) = deaditemstack;
deaditemstack = dyingitem;
items--;
}
///////////////////////////////////////////////////////////////////////////////
// //
// traversalinit() Prepare to traverse the entire list of items. //
// //
// This routine is used in conjunction with traverse(). //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::memorypool::traversalinit()
{
uintptr_t alignptr;
// Begin the traversal in the first block.
pathblock = firstblock;
// Find the first item in the block. Increment by the size of (void *).
alignptr = (uintptr_t) (pathblock + 1);
// Align with item on an `alignbytes'-byte boundary.
pathitem = (void *)
(alignptr + (uintptr_t) alignbytes -
(alignptr % (uintptr_t) alignbytes));
// Set the number of items left in the current block.
pathitemsleft = itemsperblock;
}
///////////////////////////////////////////////////////////////////////////////
// //
// traverse() Find the next item in the list. //
// //
// This routine is used in conjunction with traversalinit(). Be forewarned //
// that this routine successively returns all items in the list, including //
// deallocated ones on the deaditemqueue. It's up to you to figure out which //
// ones are actually dead. It can usually be done more space-efficiently by //
// a routine that knows something about the structure of the item. //
// //
///////////////////////////////////////////////////////////////////////////////
void* tetgenmesh::memorypool::traverse()
{
void *newitem;
uintptr_t alignptr;
// Stop upon exhausting the list of items.
if (pathitem == nextitem) {
return (void *) NULL;
}
// Check whether any untraversed items remain in the current block.
if (pathitemsleft == 0) {
// Find the next block.
pathblock = (void **) *pathblock;
// Find the first item in the block. Increment by the size of (void *).
alignptr = (uintptr_t) (pathblock + 1);
// Align with item on an `alignbytes'-byte boundary.
pathitem = (void *)
(alignptr + (uintptr_t) alignbytes -
(alignptr % (uintptr_t) alignbytes));
// Set the number of items left in the current block.
pathitemsleft = itemsperblock;
}
newitem = pathitem;
// Find the next item in the block.
pathitem = (void *) ((uintptr_t) pathitem + itembytes);
pathitemsleft--;
return newitem;
}
///////////////////////////////////////////////////////////////////////////////
// //
// makeindex2pointmap() Create a map from index to vertices. //
// //
// 'idx2verlist' returns the created map. Traverse all vertices, a pointer //
// to each vertex is set into the array. The pointer to the first vertex is //
// saved in 'idx2verlist[in->firstnumber]'. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::makeindex2pointmap(point*& idx2verlist)
{
point pointloop;
int idx;
if (b->verbose > 1) {
printf(" Constructing mapping from indices to points.\n");
}
idx2verlist = new point[points->items + 1];
points->traversalinit();
pointloop = pointtraverse();
idx = in->firstnumber;
while (pointloop != (point) NULL) {
idx2verlist[idx++] = pointloop;
pointloop = pointtraverse();
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// makesubfacemap() Create a map from vertex to subfaces incident at it. //
// //
// The map is returned in two arrays 'idx2faclist' and 'facperverlist'. All //
// subfaces incident at i-th vertex (i is counted from 0) are found in the //
// array facperverlist[j], where idx2faclist[i] <= j < idx2faclist[i + 1]. //
// Each entry in facperverlist[j] is a subface whose origin is the vertex. //
// //
// NOTE: These two arrays will be created inside this routine, don't forget //
// to free them after using. //// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::makepoint2submap(memorypool* pool, int*& idx2faclist,
face*& facperverlist)
{
face shloop;
int i, j, k;
if (b->verbose > 1) {
printf(" Making a map from points to subfaces.\n");
}
// Initialize 'idx2faclist'.
idx2faclist = new int[points->items + 1];
for (i = 0; i < points->items + 1; i++) idx2faclist[i] = 0;
// Loop all subfaces, counter the number of subfaces incident at a vertex.
pool->traversalinit();
shloop.sh = shellfacetraverse(pool);
while (shloop.sh != (shellface *) NULL) {
// Increment the number of incident subfaces for each vertex.
j = pointmark((point) shloop.sh[3]) - in->firstnumber;
idx2faclist[j]++;
j = pointmark((point) shloop.sh[4]) - in->firstnumber;
idx2faclist[j]++;
// Skip the third corner if it is a segment.
if (shloop.sh[5] != NULL) {
j = pointmark((point) shloop.sh[5]) - in->firstnumber;
idx2faclist[j]++;
}
shloop.sh = shellfacetraverse(pool);
}
// Calculate the total length of array 'facperverlist'.
j = idx2faclist[0];
idx2faclist[0] = 0; // Array starts from 0 element.
for (i = 0; i < points->items; i++) {
k = idx2faclist[i + 1];
idx2faclist[i + 1] = idx2faclist[i] + j;
j = k;
}
// The total length is in the last unit of idx2faclist.
facperverlist = new face[idx2faclist[i]];
// Loop all subfaces again, remember the subfaces at each vertex.
pool->traversalinit();
shloop.sh = shellfacetraverse(pool);
while (shloop.sh != (shellface *) NULL) {
j = pointmark((point) shloop.sh[3]) - in->firstnumber;
shloop.shver = 0; // save the origin.
facperverlist[idx2faclist[j]] = shloop;
idx2faclist[j]++;
// Is it a subface or a subsegment?
if (shloop.sh[5] != NULL) {
j = pointmark((point) shloop.sh[4]) - in->firstnumber;
shloop.shver = 2; // save the origin.
facperverlist[idx2faclist[j]] = shloop;
idx2faclist[j]++;
j = pointmark((point) shloop.sh[5]) - in->firstnumber;
shloop.shver = 4; // save the origin.
facperverlist[idx2faclist[j]] = shloop;
idx2faclist[j]++;
} else {
j = pointmark((point) shloop.sh[4]) - in->firstnumber;
shloop.shver = 1; // save the origin.
facperverlist[idx2faclist[j]] = shloop;
idx2faclist[j]++;
} shloop.sh = shellfacetraverse(pool);
}
// Contents in 'idx2faclist' are shifted, now shift them back.
for (i = points->items - 1; i >= 0; i--) {
idx2faclist[i + 1] = idx2faclist[i];
}
idx2faclist[0] = 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// tetrahedrondealloc() Deallocate space for a tet., marking it dead. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::tetrahedrondealloc(tetrahedron *dyingtetrahedron)
{
// Set tetrahedron's vertices to NULL. This makes it possible to detect
// dead tetrahedra when traversing the list of all tetrahedra.
dyingtetrahedron[4] = (tetrahedron) NULL;
// Dealloc the space to subfaces/subsegments.
if (dyingtetrahedron[8] != NULL) {
tet2segpool->dealloc((shellface *) dyingtetrahedron[8]);
}
if (dyingtetrahedron[9] != NULL) {
tet2subpool->dealloc((shellface *) dyingtetrahedron[9]);
}
tetrahedrons->dealloc((void *) dyingtetrahedron);
}
///////////////////////////////////////////////////////////////////////////////
// //
// tetrahedrontraverse() Traverse the tetrahedra, skipping dead ones. //
// //
///////////////////////////////////////////////////////////////////////////////
tetgenmesh::tetrahedron* tetgenmesh::tetrahedrontraverse()
{
tetrahedron *newtetrahedron;
do {
newtetrahedron = (tetrahedron *) tetrahedrons->traverse();
if (newtetrahedron == (tetrahedron *) NULL) {
return (tetrahedron *) NULL;
}
} while ((newtetrahedron[4] == (tetrahedron) NULL) ||
((point) newtetrahedron[7] == dummypoint));
return newtetrahedron;
}
tetgenmesh::tetrahedron* tetgenmesh::alltetrahedrontraverse()
{
tetrahedron *newtetrahedron;
do {
newtetrahedron = (tetrahedron *) tetrahedrons->traverse();
if (newtetrahedron == (tetrahedron *) NULL) {
return (tetrahedron *) NULL;
}
} while (newtetrahedron[4] == (tetrahedron) NULL); // Skip dead ones.
return newtetrahedron;
}
///////////////////////////////////////////////////////////////////////////////
// //
// shellfacedealloc() Deallocate space for a shellface, marking it dead. //
// Used both for dealloc a subface and subsegment. //// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::shellfacedealloc(memorypool *pool, shellface *dyingsh)
{
// Set shellface's vertices to NULL. This makes it possible to detect dead
// shellfaces when traversing the list of all shellfaces.
dyingsh[3] = (shellface) NULL;
pool->dealloc((void *) dyingsh);
}
///////////////////////////////////////////////////////////////////////////////
// //
// shellfacetraverse() Traverse the subfaces, skipping dead ones. Used //
// for both subfaces and subsegments pool traverse. //
// //
///////////////////////////////////////////////////////////////////////////////
tetgenmesh::shellface* tetgenmesh::shellfacetraverse(memorypool *pool)
{
shellface *newshellface;
do {
newshellface = (shellface *) pool->traverse();
if (newshellface == (shellface *) NULL) {
return (shellface *) NULL;
}
} while (newshellface[3] == (shellface) NULL); // Skip dead ones.
return newshellface;
}
///////////////////////////////////////////////////////////////////////////////
// //
// pointdealloc() Deallocate space for a point, marking it dead. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::pointdealloc(point dyingpoint)
{
// Mark the point as dead. This makes it possible to detect dead points
// when traversing the list of all points.
setpointtype(dyingpoint, DEADVERTEX);
points->dealloc((void *) dyingpoint);
}
///////////////////////////////////////////////////////////////////////////////
// //
// pointtraverse() Traverse the points, skipping dead ones. //
// //
///////////////////////////////////////////////////////////////////////////////
tetgenmesh::point tetgenmesh::pointtraverse()
{
point newpoint;
do {
newpoint = (point) points->traverse();
if (newpoint == (point) NULL) {
return (point) NULL;
}
} while (pointtype(newpoint) == DEADVERTEX); // Skip dead ones.
return newpoint;
}
///////////////////////////////////////////////////////////////////////////////
// //
// maketetrahedron() Create a new tetrahedron. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::maketetrahedron(triface *newtet)
{
newtet->tet = (tetrahedron *) tetrahedrons->alloc();
// Initialize the four adjoining tetrahedra to be "outer space".
newtet->tet[0] = NULL;
newtet->tet[1] = NULL;
newtet->tet[2] = NULL;
newtet->tet[3] = NULL;
// Four NULL vertices.
newtet->tet[4] = NULL;
newtet->tet[5] = NULL;
newtet->tet[6] = NULL;
newtet->tet[7] = NULL;
// No attached segments and subfaces yet.
newtet->tet[8] = NULL;
newtet->tet[9] = NULL;
// Initialize the marker (clear all flags).
setelemmarker(newtet->tet, 0);
for (int i = 0; i < numelemattrib; i++) {
setelemattribute(newtet->tet, i, 0.0);
}
if (b->varvolume) {
setvolumebound(newtet->tet, -1.0);
}
// Initialize the version to be Zero.
newtet->ver = 11;
}
///////////////////////////////////////////////////////////////////////////////
// //
// makeshellface() Create a new shellface with version zero. Used for //
// both subfaces and subsegments. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::makeshellface(memorypool *pool, face *newface)
{
newface->sh = (shellface *) pool->alloc();
// No adjointing subfaces.
newface->sh[0] = NULL;
newface->sh[1] = NULL;
newface->sh[2] = NULL;
// Three NULL vertices.
newface->sh[3] = NULL;
newface->sh[4] = NULL;
newface->sh[5] = NULL;
// No adjoining subsegments.
newface->sh[6] = NULL;
newface->sh[7] = NULL;
newface->sh[8] = NULL;
// No adjoining tetrahedra.
newface->sh[9] = NULL;
newface->sh[10] = NULL;
if (checkconstraints) {
// Initialize the maximum area bound.
setareabound(*newface, 0.0);
}
// Set the boundary marker to zero.
setshellmark(*newface, 0);
// Clear the infection and marktest bits.
((int *) (newface->sh))[shmarkindex + 1] = 0;
if (useinsertradius) {
setfacetindex(*newface, 0);
}
newface->shver = 0;}
///////////////////////////////////////////////////////////////////////////////
// //
// makepoint() Create a new point. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::makepoint(point* pnewpoint, enum verttype vtype)
{
int i;
*pnewpoint = (point) points->alloc();
// Initialize the point attributes.
for (i = 0; i < numpointattrib; i++) {
(*pnewpoint)[3 + i] = 0.0;
}
// Initialize the metric tensor.
for (i = 0; i < sizeoftensor; i++) {
(*pnewpoint)[pointmtrindex + i] = 0.0;
}
setpoint2tet(*pnewpoint, NULL);
setpoint2ppt(*pnewpoint, NULL);
if (b->plc || b->refine) {
// Initialize the point-to-simplex field.
setpoint2sh(*pnewpoint, NULL);
if (b->metric && (bgm != NULL)) {
setpoint2bgmtet(*pnewpoint, NULL);
}
}
// Initialize the point marker (starting from in->firstnumber).
setpointmark(*pnewpoint, (int) (points->items) - (!in->firstnumber));
// Clear all flags.
((int *) (*pnewpoint))[pointmarkindex + 1] = 0;
// Initialize (set) the point type.
setpointtype(*pnewpoint, vtype);
}
///////////////////////////////////////////////////////////////////////////////
// //
// initializepools() Calculate the sizes of the point, tetrahedron, and //
// subface. Initialize their memory pools. //
// //
// This routine also computes the indices 'pointmarkindex', 'point2simindex',//
// 'point2pbcptindex', 'elemattribindex', and 'volumeboundindex'. They are //
// used to find values within each point and tetrahedron, respectively. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::initializepools()
{
int pointsize = 0, elesize = 0, shsize = 0;
int i;
if (b->verbose) {
printf(" Initializing memorypools.\n");
printf(" tetrahedron per block: %d.\n", b->tetrahedraperblock);
}
inittables();
// There are three input point lists available, which are in, addin,
// and bgm->in. These point lists may have different number of
// attributes. Decide the maximum number.
numpointattrib = in->numberofpointattributes;
if (bgm != NULL) {
if (bgm->in->numberofpointattributes > numpointattrib) {
numpointattrib = bgm->in->numberofpointattributes;
} }
if (addin != NULL) {
if (addin->numberofpointattributes > numpointattrib) {
numpointattrib = addin->numberofpointattributes;
}
}
if (b->weighted || b->flipinsert) { // -w or -L.
// The internal number of point attribute needs to be at least 1
// (for storing point weights).
if (numpointattrib == 0) {
numpointattrib = 1;
}
}
// Default varconstraint = 0;
if (in->segmentconstraintlist || in->facetconstraintlist) {
checkconstraints = 1;
}
if (b->plc || b->refine) {
// Save the insertion radius for Steiner points if boundaries
// are allowed be split.
if (!b->nobisect || checkconstraints) {
useinsertradius = 1;
}
}
// The index within each point at which its metric tensor is found.
// Each vertex has three coordinates.
if (b->psc) {
// '-s' option (PSC), the u,v coordinates are provided.
pointmtrindex = 5 + numpointattrib;
// The index within each point at which its u, v coordinates are found.
// Comment: They are saved after the list of point attributes.
pointparamindex = pointmtrindex - 2;
} else {
pointmtrindex = 3 + numpointattrib;
}
// For '-m' option. A tensor field is provided (*.mtr or *.b.mtr file).
if (b->metric) {
// Decide the size (1, 3, or 6) of the metric tensor.
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 {
// For '-q' option. Make sure to have space for saving a scalar value.
sizeoftensor = b->quality ? 1 : 0;
}
if (useinsertradius) {
// Increase a space (REAL) for saving point insertion radius, it is
// saved directly after the metric.
sizeoftensor++;
}
pointinsradiusindex = pointmtrindex + sizeoftensor - 1;
// 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 = ((pointmtrindex + sizeoftensor) * sizeof(REAL)
+ sizeof(tetrahedron) - 1) / sizeof(tetrahedron);
if (b->plc || b->refine || b->voroout) {
// Increase the point size by three pointers, which are:
// - a pointer to a tet, read by point2tet();
// - a pointer to a parent point, read by point2ppt()).
// - a pointer to a subface or segment, read by point2sh(); if (b->metric && (bgm != (tetgenmesh *) NULL)) {
// Increase one pointer into the background mesh, point2bgmtet().
pointsize = (point2simindex + 4) * sizeof(tetrahedron);
} else {
pointsize = (point2simindex + 3) * sizeof(tetrahedron);
}
} else {
// Increase the point size by two pointer, which are:
// - a pointer to a tet, read by point2tet();
// - a pointer to a parent point, read by point2ppt()). -- Used by btree.
pointsize = (point2simindex + 2) * sizeof(tetrahedron);
}
// The index within each point at which the boundary marker is found,
// Ensure the point marker is aligned to a sizeof(int)-byte address.
pointmarkindex = (pointsize + sizeof(int) - 1) / sizeof(int);
// Now point size is the ints (indicated by pointmarkindex) plus:
// - an integer for boundary marker;
// - an integer for vertex type;
// - an integer for geometry tag (optional, -s option).
pointsize = (pointmarkindex + 2 + (b->psc ? 1 : 0)) * sizeof(tetrahedron);
// Initialize the pool of vertices.
points = new memorypool(pointsize, b->vertexperblock, sizeof(REAL), 0);
if (b->verbose) {
printf(" Size of a point: %d bytes.\n", points->itembytes);
}
// Initialize the infinite vertex.
dummypoint = (point) new char[pointsize];
// Initialize all fields of this point.
dummypoint[0] = 0.0;
dummypoint[1] = 0.0;
dummypoint[2] = 0.0;
for (i = 0; i < numpointattrib; i++) {
dummypoint[3 + i] = 0.0;
}
// Initialize the metric tensor.
for (i = 0; i < sizeoftensor; i++) {
dummypoint[pointmtrindex + i] = 0.0;
}
setpoint2tet(dummypoint, NULL);
setpoint2ppt(dummypoint, NULL);
if (b->plc || b->psc || b->refine) {
// Initialize the point-to-simplex field.
setpoint2sh(dummypoint, NULL);
if (b->metric && (bgm != NULL)) {
setpoint2bgmtet(dummypoint, NULL);
}
}
// Initialize the point marker (starting from in->firstnumber).
setpointmark(dummypoint, -1); // The unique marker for dummypoint.
// Clear all flags.
((int *) (dummypoint))[pointmarkindex + 1] = 0;
// Initialize (set) the point type.
setpointtype(dummypoint, UNUSEDVERTEX); // Does not matter.
// The number of bytes occupied by a tetrahedron is varying by the user-
// specified options. The contents of the first 12 pointers are listed
// in the following table:
// [0] |__ neighbor at f0 __|
// [1] |__ neighbor at f1 __|
// [2] |__ neighbor at f2 __|
// [3] |__ neighbor at f3 __|
// [4] |_____ vertex p0 ____|
// [5] |_____ vertex p1 ____|
// [6] |_____ vertex p2 ____|
// [7] |_____ vertex p3 ____|
// [8] |__ segments array __| (used by -p)
// [9] |__ subfaces array __| (used by -p) // [10] |_____ reserved _____|
// [11] |___ elem marker ____| (used as an integer)
elesize = 12 * sizeof(tetrahedron);
// The index to find the element markers. An integer containing varies
// flags and element counter.
if (!(sizeof(int) <= sizeof(tetrahedron)) ||
((sizeof(tetrahedron) % sizeof(int)))) {
terminatetetgen(this, 2);
}
elemmarkerindex = (elesize - sizeof(tetrahedron)) / sizeof(int);
// The actual number of element attributes. Note that if the
// `b->regionattrib' flag is set, an additional attribute will be added.
numelemattrib = in->numberoftetrahedronattributes + (b->regionattrib > 0);
// The index within each element at which its attributes are found, where
// the index is measured in REALs.
elemattribindex = (elesize + sizeof(REAL) - 1) / sizeof(REAL);
// The index within each element at which the maximum volume bound is
// found, where the index is measured in REALs.
volumeboundindex = elemattribindex + numelemattrib;
// If element attributes or an constraint are needed, increase the number
// of bytes occupied by an element.
if (b->varvolume) {
elesize = (volumeboundindex + 1) * sizeof(REAL);
} else if (numelemattrib > 0) {
elesize = volumeboundindex * sizeof(REAL);
}
// Having determined the memory size of an element, initialize the pool.
tetrahedrons = new memorypool(elesize, b->tetrahedraperblock, sizeof(void *),
16);
if (b->verbose) {
printf(" Size of a tetrahedron: %d (%d) bytes.\n", elesize,
tetrahedrons->itembytes);
}
if (b->plc || b->refine) { // if (b->useshelles) {
// The number of bytes occupied by a subface. The list of pointers
// stored in a subface are: three to other subfaces, three to corners,
// three to subsegments, two to tetrahedra.
shsize = 11 * sizeof(shellface);
// The index within each subface at which the maximum area bound is
// found, where the index is measured in REALs.
areaboundindex = (shsize + sizeof(REAL) - 1) / sizeof(REAL);
// If -q switch is in use, increase the number of bytes occupied by
// a subface for saving maximum area bound.
if (checkconstraints) {
shsize = (areaboundindex + 1) * sizeof(REAL);
} else {
shsize = areaboundindex * sizeof(REAL);
}
// The index within subface at which the facet marker is found. Ensure
// the marker is aligned to a sizeof(int)-byte address.
shmarkindex = (shsize + sizeof(int) - 1) / sizeof(int);
// Increase the number of bytes by two or three integers, one for facet
// marker, one for shellface type and flags, and optionally one
// for storing facet index (for mesh refinement).
shsize = (shmarkindex + 2 + useinsertradius) * sizeof(shellface);
// Initialize the pool of subfaces. Each subface record is eight-byte
// aligned so it has room to store an edge version (from 0 to 5) in
// the least three bits.
subfaces = new memorypool(shsize, b->shellfaceperblock, sizeof(void *), 8);
if (b->verbose) { printf(" Size of a shellface: %d (%d) bytes.\n", shsize,
subfaces->itembytes);
}
// Initialize the pool of subsegments. The subsegment's record is same
// with subface.
subsegs = new memorypool(shsize, b->shellfaceperblock, sizeof(void *), 8);
// Initialize the pool for tet-subseg connections.
tet2segpool = new memorypool(6 * sizeof(shellface), b->shellfaceperblock,
sizeof(void *), 0);
// Initialize the pool for tet-subface connections.
tet2subpool = new memorypool(4 * sizeof(shellface), b->shellfaceperblock,
sizeof(void *), 0);
// Initialize arraypools for segment & facet recovery.
subsegstack = new arraypool(sizeof(face), 10);
subfacstack = new arraypool(sizeof(face), 10);
subvertstack = new arraypool(sizeof(point), 8);
// Initialize arraypools for surface point insertion/deletion.
caveshlist = new arraypool(sizeof(face), 8);
caveshbdlist = new arraypool(sizeof(face), 8);
cavesegshlist = new arraypool(sizeof(face), 4);
cavetetshlist = new arraypool(sizeof(face), 8);
cavetetseglist = new arraypool(sizeof(face), 8);
caveencshlist = new arraypool(sizeof(face), 8);
caveencseglist = new arraypool(sizeof(face), 8);
}
// Initialize the pools for flips.
flippool = new memorypool(sizeof(badface), 1024, sizeof(void *), 0);
unflipqueue = new arraypool(sizeof(badface), 10);
// Initialize the arraypools for point insertion.
cavetetlist = new arraypool(sizeof(triface), 10);
cavebdrylist = new arraypool(sizeof(triface), 10);
caveoldtetlist = new arraypool(sizeof(triface), 10);
cavetetvertlist = new arraypool(sizeof(point), 10);
}
//// ////
//// ////
//// mempool_cxx //////////////////////////////////////////////////////////////
//// geom_cxx /////////////////////////////////////////////////////////////////
//// ////
//// ////
// PI is the ratio of a circle's circumference to its diameter.
REAL tetgenmesh::PI = 3.14159265358979323846264338327950288419716939937510582;
///////////////////////////////////////////////////////////////////////////////
// //
// insphere_s() Insphere test with symbolic perturbation. //
// //
// Given four points pa, pb, pc, and pd, test if the point pe lies inside or //
// outside the circumscribed sphere of the four points. //
// //
// Here we assume that the 3d orientation of the point sequence {pa, pb, pc, //
// pd} is positive (NOT zero), i.e., pd lies above the plane passing through //
// points pa, pb, and pc. Otherwise, the returned sign is flipped. //
// //
// Return a positive value (> 0) if pe lies inside, a negative value (< 0) //
// if pe lies outside the sphere, the returned value will not be zero. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::insphere_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe){
REAL sign;
sign = insphere(pa, pb, pc, pd, pe);
if (sign != 0.0) {
return sign;
}
// Symbolic perturbation.
point pt[5], swappt;
REAL oriA, oriB;
int swaps, count;
int n, i;
pt[0] = pa;
pt[1] = pb;
pt[2] = pc;
pt[3] = pd;
pt[4] = pe;
// Sort the five points such that their indices are in the increasing
// order. An optimized bubble sort algorithm is used, i.e., it has
// the worst case O(n^2) runtime, but it is usually much faster.
swaps = 0; // Record the total number of swaps.
n = 5;
do {
count = 0;
n = n - 1;
for (i = 0; i < n; i++) {
if (pointmark(pt[i]) > pointmark(pt[i+1])) {
swappt = pt[i]; pt[i] = pt[i+1]; pt[i+1] = swappt;
count++;
}
}
swaps += count;
} while (count > 0); // Continue if some points are swapped.
oriA = orient3d(pt[1], pt[2], pt[3], pt[4]);
if (oriA != 0.0) {
// Flip the sign if there are odd number of swaps.
if ((swaps % 2) != 0) oriA = -oriA;
return oriA;
}
oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]);
if (oriB == 0.0) {
terminatetetgen(this, 2);
}
// Flip the sign if there are odd number of swaps.
if ((swaps % 2) != 0) oriB = -oriB;
return oriB;
}
///////////////////////////////////////////////////////////////////////////////
// //
// orient4d_s() 4d orientation test with symbolic perturbation. //
// //
// Given four lifted points pa', pb', pc', and pd' in R^4,test if the lifted //
// point pe' in R^4 lies below or above the hyperplane passing through the //
// four points pa', pb', pc', and pd'. //
// //
// Here we assume that the 3d orientation of the point sequence {pa, pb, pc, //
// pd} is positive (NOT zero), i.e., pd lies above the plane passing through //
// the points pa, pb, and pc. Otherwise, the returned sign is flipped. //
// //
// Return a positive value (> 0) if pe' lies below, a negative value (< 0) //
// if pe' lies above the hyperplane, the returned value should not be zero. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::orient4d_s(REAL* pa, REAL* pb, REAL* pc, REAL* pd, REAL* pe,
REAL aheight, REAL bheight, REAL cheight,
REAL dheight, REAL eheight)
{
REAL sign;
sign = orient4d(pa, pb, pc, pd, pe,
aheight, bheight, cheight, dheight, eheight);
if (sign != 0.0) {
return sign;
}
// Symbolic perturbation.
point pt[5], swappt;
REAL oriA, oriB;
int swaps, count;
int n, i;
pt[0] = pa;
pt[1] = pb;
pt[2] = pc;
pt[3] = pd;
pt[4] = pe;
// Sort the five points such that their indices are in the increasing
// order. An optimized bubble sort algorithm is used, i.e., it has
// the worst case O(n^2) runtime, but it is usually much faster.
swaps = 0; // Record the total number of swaps.
n = 5;
do {
count = 0;
n = n - 1;
for (i = 0; i < n; i++) {
if (pointmark(pt[i]) > pointmark(pt[i+1])) {
swappt = pt[i]; pt[i] = pt[i+1]; pt[i+1] = swappt;
count++;
}
}
swaps += count;
} while (count > 0); // Continue if some points are swapped.
oriA = orient3d(pt[1], pt[2], pt[3], pt[4]);
if (oriA != 0.0) {
// Flip the sign if there are odd number of swaps.
if ((swaps % 2) != 0) oriA = -oriA;
return oriA;
}
oriB = -orient3d(pt[0], pt[2], pt[3], pt[4]);
if (oriB == 0.0) {
terminatetetgen(this, 2);
}
// Flip the sign if there are odd number of swaps.
if ((swaps % 2) != 0) oriB = -oriB;
return oriB;
}
///////////////////////////////////////////////////////////////////////////////
// //
// tri_edge_test() Triangle-edge intersection test. //
// //
// This routine takes a triangle T (with vertices A, B, C) and an edge E (P, //
// Q) in 3D, and tests if they intersect each other. //
// //
// If the point 'R' is not NULL, it lies strictly above the plane defined by //
// A, B, C. It is used in test when T and E are coplanar. //
// //
// If T and E intersect each other, they may intersect in different ways. If //
// 'level' > 0, their intersection type will be reported 'types' and 'pos'. //
// //// The return value indicates one of the following cases: //
// - 0, T and E are disjoint. //
// - 1, T and E intersect each other. //
// - 2, T and E are not coplanar. They intersect at a single point. //
// - 4, T and E are coplanar. They intersect at a single point or a line //
// segment (if types[1] != DISJOINT). //
// //
///////////////////////////////////////////////////////////////////////////////
#define SETVECTOR3(V, a0, a1, a2) (V)[0] = (a0); (V)[1] = (a1); (V)[2] = (a2)
#define SWAP2(a0, a1, tmp) (tmp) = (a0); (a0) = (a1); (a1) = (tmp)
int tetgenmesh::tri_edge_2d(point A, point B, point C, point P, point Q,
point R, int level, int *types, int *pos)
{
point U[3], V[3]; // The permuted vectors of points.
int pu[3], pv[3]; // The original positions of points.
REAL abovept[3];
REAL sA, sB, sC;
REAL s1, s2, s3, s4;
int z1;
if (R == NULL) {
// Calculate a lift point.
if (1) {
REAL n[3], len;
// Calculate a lift point, saved in dummypoint.
facenormal(A, B, C, n, 1, NULL);
len = sqrt(dot(n, n));
if (len != 0) {
n[0] /= len;
n[1] /= len;
n[2] /= len;
len = distance(A, B);
len += distance(B, C);
len += distance(C, A);
len /= 3.0;
R = abovept; //dummypoint;
R[0] = A[0] + len * n[0];
R[1] = A[1] + len * n[1];
R[2] = A[2] + len * n[2];
} else {
// The triangle [A,B,C] is (nearly) degenerate, i.e., it is (close)
// to a line. We need a line-line intersection test.
// !!! A non-save return value.!!!
return 0; // DISJOINT
}
}
}
// Test A's, B's, and C's orientations wrt plane PQR.
sA = orient3d(P, Q, R, A);
sB = orient3d(P, Q, R, B);
sC = orient3d(P, Q, R, C);
if (sA < 0) {
if (sB < 0) {
if (sC < 0) { // (---).
return 0;
} else {
if (sC > 0) { // (--+).
// All points are in the right positions.
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 0;
} else { // (--0). SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 1;
}
}
} else {
if (sB > 0) {
if (sC < 0) { // (-+-).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 0, 1, 2);
z1 = 0;
} else {
if (sC > 0) { // (-++).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 1, 0, 2);
z1 = 0;
} else { // (-+0).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 0, 1, 2);
z1 = 2;
}
}
} else {
if (sC < 0) { // (-0-).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 0, 1, 2);
z1 = 1;
} else {
if (sC > 0) { // (-0+).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 1, 0, 2);
z1 = 2;
} else { // (-00).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 1, 0, 2);
z1 = 3;
}
}
}
}
} else {
if (sA > 0) {
if (sB < 0) {
if (sC < 0) { // (+--).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 0, 1, 2);
z1 = 0;
} else {
if (sC > 0) { // (+-+).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 1, 0, 2);
z1 = 0; } else { // (+-0).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 1, 0, 2);
z1 = 2;
}
}
} else {
if (sB > 0) {
if (sC < 0) { // (++-).
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 0;
} else {
if (sC > 0) { // (+++).
return 0;
} else { // (++0).
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 1;
}
}
} else { // (+0#)
if (sC < 0) { // (+0-).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 0, 1, 2);
z1 = 2;
} else {
if (sC > 0) { // (+0+).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 1, 0, 2);
z1 = 1;
} else { // (+00).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 0, 1, 2);
z1 = 3;
}
}
}
}
} else {
if (sB < 0) {
if (sC < 0) { // (0--).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 0, 1, 2);
z1 = 1;
} else {
if (sC > 0) { // (0-+).
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 2;
} else { // (0-0).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 2, 0, 1); SETVECTOR3(pv, 1, 0, 2);
z1 = 3;
}
}
} else {
if (sB > 0) {
if (sC < 0) { // (0+-).
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 2;
} else {
if (sC > 0) { // (0++).
SETVECTOR3(U, B, C, A); // PT = ST x ST
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 1, 2, 0);
SETVECTOR3(pv, 1, 0, 2);
z1 = 1;
} else { // (0+0).
SETVECTOR3(U, C, A, B); // PT = ST
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 2, 0, 1);
SETVECTOR3(pv, 0, 1, 2);
z1 = 3;
}
}
} else { // (00#)
if (sC < 0) { // (00-).
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, Q, P, R); // PL = SL
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 3;
} else {
if (sC > 0) { // (00+).
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 3;
} else { // (000)
// Not possible unless ABC is degenerate.
// Avoiding compiler warnings.
SETVECTOR3(U, A, B, C); // I3
SETVECTOR3(V, P, Q, R); // I2
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 4;
}
}
}
}
}
}
s1 = orient3d(U[0], U[2], R, V[1]); // A, C, R, Q
s2 = orient3d(U[1], U[2], R, V[0]); // B, C, R, P
if (s1 > 0) {
return 0;
}
if (s2 < 0) {
return 0;
}
if (level == 0) {
return 1; // They are intersected.
}
if (z1 == 1) {
if (s1 == 0) { // (0###)
// C = Q.
types[0] = (int) SHAREVERT;
pos[0] = pu[2]; // C
pos[1] = pv[1]; // Q
types[1] = (int) DISJOINT;
} else {
if (s2 == 0) { // (#0##)
// C = P.
types[0] = (int) SHAREVERT;
pos[0] = pu[2]; // C
pos[1] = pv[0]; // P
types[1] = (int) DISJOINT;
} else { // (-+##)
// C in [P, Q].
types[0] = (int) ACROSSVERT;
pos[0] = pu[2]; // C
pos[1] = pv[0]; // [P, Q]
types[1] = (int) DISJOINT;
}
}
return 4;
}
s3 = orient3d(U[0], U[2], R, V[0]); // A, C, R, P
s4 = orient3d(U[1], U[2], R, V[1]); // B, C, R, Q
if (z1 == 0) { // (tritri-03)
if (s1 < 0) {
if (s3 > 0) {
if (s4 > 0) {
// [P, Q] overlaps [k, l] (-+++).
types[0] = (int) ACROSSEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[0]; // [P, Q]
types[1] = (int) TOUCHFACE;
pos[2] = 3; // [A, B, C]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// Q = l, [P, Q] contains [k, l] (-++0).
types[0] = (int) ACROSSEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[0]; // [P, Q]
types[1] = (int) TOUCHEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[1]; // Q
} else { // s4 < 0
// [P, Q] contains [k, l] (-++-).
types[0] = (int) ACROSSEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[0]; // [P, Q]
types[1] = (int) ACROSSEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[0]; // [P, Q]
}
}
} else {
if (s3 == 0) {
if (s4 > 0) {
// P = k, [P, Q] in [k, l] (-+0+).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[0]; // P
types[1] = (int) TOUCHFACE;
pos[2] = 3; // [A, B, C]
pos[3] = pv[1]; // Q
} else { if (s4 == 0) {
// [P, Q] = [k, l] (-+00).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[0]; // P
types[1] = (int) TOUCHEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[1]; // Q
} else {
// P = k, [P, Q] contains [k, l] (-+0-).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[0]; // P
types[1] = (int) ACROSSEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[0]; // [P, Q]
}
}
} else { // s3 < 0
if (s2 > 0) {
if (s4 > 0) {
// [P, Q] in [k, l] (-+-+).
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[0]; // P
types[1] = (int) TOUCHFACE;
pos[2] = 3; // [A, B, C]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// Q = l, [P, Q] in [k, l] (-+-0).
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[0]; // P
types[1] = (int) TOUCHEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[1]; // Q
} else { // s4 < 0
// [P, Q] overlaps [k, l] (-+--).
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[0]; // P
types[1] = (int) ACROSSEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[0]; // [P, Q]
}
}
} else { // s2 == 0
// P = l (#0##).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[1]; // [B, C]
pos[1] = pv[0]; // P
types[1] = (int) DISJOINT;
}
}
}
} else { // s1 == 0
// Q = k (0####)
types[0] = (int) TOUCHEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[1]; // Q
types[1] = (int) DISJOINT;
}
} else if (z1 == 2) { // (tritri-23)
if (s1 < 0) {
if (s3 > 0) {
if (s4 > 0) {
// [P, Q] overlaps [A, l] (-+++).
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A pos[1] = pv[0]; // [P, Q]
types[1] = (int) TOUCHFACE;
pos[2] = 3; // [A, B, C]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// Q = l, [P, Q] contains [A, l] (-++0).
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // [P, Q]
types[1] = (int) TOUCHEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[1]; // Q
} else { // s4 < 0
// [P, Q] contains [A, l] (-++-).
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // [P, Q]
types[1] = (int) ACROSSEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[0]; // [P, Q]
}
}
} else {
if (s3 == 0) {
if (s4 > 0) {
// P = A, [P, Q] in [A, l] (-+0+).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // P
types[1] = (int) TOUCHFACE;
pos[2] = 3; // [A, B, C]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// [P, Q] = [A, l] (-+00).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // P
types[1] = (int) TOUCHEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[1]; // Q
} else { // s4 < 0
// Q = l, [P, Q] in [A, l] (-+0-).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // P
types[1] = (int) ACROSSEDGE;
pos[2] = pu[1]; // [B, C]
pos[3] = pv[0]; // [P, Q]
}
}
} else { // s3 < 0
if (s2 > 0) {
if (s4 > 0) {
// [P, Q] in [A, l] (-+-+).
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[0]; // P
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[1]; // Q
} else {
if (s4 == 0) {
// Q = l, [P, Q] in [A, l] (-+-0).
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[0]; // P
types[0] = (int) TOUCHEDGE;
pos[0] = pu[1]; // [B, C] pos[1] = pv[1]; // Q
} else { // s4 < 0
// [P, Q] overlaps [A, l] (-+--).
types[0] = (int) TOUCHFACE;
pos[0] = 3; // [A, B, C]
pos[1] = pv[0]; // P
types[0] = (int) ACROSSEDGE;
pos[0] = pu[1]; // [B, C]
pos[1] = pv[0]; // [P, Q]
}
}
} else { // s2 == 0
// P = l (#0##).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[1]; // [B, C]
pos[1] = pv[0]; // P
types[1] = (int) DISJOINT;
}
}
}
} else { // s1 == 0
// Q = A (0###).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[1]; // Q
types[1] = (int) DISJOINT;
}
} else if (z1 == 3) { // (tritri-33)
if (s1 < 0) {
if (s3 > 0) {
if (s4 > 0) {
// [P, Q] overlaps [A, B] (-+++).
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // [P, Q]
types[1] = (int) TOUCHEDGE;
pos[2] = pu[0]; // [A, B]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// Q = B, [P, Q] contains [A, B] (-++0).
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // [P, Q]
types[1] = (int) SHAREVERT;
pos[2] = pu[1]; // B
pos[3] = pv[1]; // Q
} else { // s4 < 0
// [P, Q] contains [A, B] (-++-).
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // [P, Q]
types[1] = (int) ACROSSVERT;
pos[2] = pu[1]; // B
pos[3] = pv[0]; // [P, Q]
}
}
} else {
if (s3 == 0) {
if (s4 > 0) {
// P = A, [P, Q] in [A, B] (-+0+).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // P
types[1] = (int) TOUCHEDGE;
pos[2] = pu[0]; // [A, B]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// [P, Q] = [A, B] (-+00). types[0] = (int) SHAREEDGE;
pos[0] = pu[0]; // [A, B]
pos[1] = pv[0]; // [P, Q]
types[1] = (int) DISJOINT;
} else { // s4 < 0
// P= A, [P, Q] in [A, B] (-+0-).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[0]; // P
types[1] = (int) ACROSSVERT;
pos[2] = pu[1]; // B
pos[3] = pv[0]; // [P, Q]
}
}
} else { // s3 < 0
if (s2 > 0) {
if (s4 > 0) {
// [P, Q] in [A, B] (-+-+).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[0]; // [A, B]
pos[1] = pv[0]; // P
types[1] = (int) TOUCHEDGE;
pos[2] = pu[0]; // [A, B]
pos[3] = pv[1]; // Q
} else {
if (s4 == 0) {
// Q = B, [P, Q] in [A, B] (-+-0).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[0]; // [A, B]
pos[1] = pv[0]; // P
types[1] = (int) SHAREVERT;
pos[2] = pu[1]; // B
pos[3] = pv[1]; // Q
} else { // s4 < 0
// [P, Q] overlaps [A, B] (-+--).
types[0] = (int) TOUCHEDGE;
pos[0] = pu[0]; // [A, B]
pos[1] = pv[0]; // P
types[1] = (int) ACROSSVERT;
pos[2] = pu[1]; // B
pos[3] = pv[0]; // [P, Q]
}
}
} else { // s2 == 0
// P = B (#0##).
types[0] = (int) SHAREVERT;
pos[0] = pu[1]; // B
pos[1] = pv[0]; // P
types[1] = (int) DISJOINT;
}
}
}
} else { // s1 == 0
// Q = A (0###).
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[1]; // Q
types[1] = (int) DISJOINT;
}
}
return 4;
}
int tetgenmesh::tri_edge_tail(point A,point B,point C,point P,point Q,point R,
REAL sP,REAL sQ,int level,int *types,int *pos)
{
point U[3], V[3]; //, Ptmp;
int pu[3], pv[3]; //, itmp;
REAL s1, s2, s3; int z1;
if (sP < 0) {
if (sQ < 0) { // (--) disjoint
return 0;
} else {
if (sQ > 0) { // (-+)
SETVECTOR3(U, A, B, C);
SETVECTOR3(V, P, Q, R);
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 0;
} else { // (-0)
SETVECTOR3(U, A, B, C);
SETVECTOR3(V, P, Q, R);
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 1;
}
}
} else {
if (sP > 0) { // (+-)
if (sQ < 0) {
SETVECTOR3(U, A, B, C);
SETVECTOR3(V, Q, P, R); // P and Q are flipped.
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 0;
} else {
if (sQ > 0) { // (++) disjoint
return 0;
} else { // (+0)
SETVECTOR3(U, B, A, C); // A and B are flipped.
SETVECTOR3(V, P, Q, R);
SETVECTOR3(pu, 1, 0, 2);
SETVECTOR3(pv, 0, 1, 2);
z1 = 1;
}
}
} else { // sP == 0
if (sQ < 0) { // (0-)
SETVECTOR3(U, A, B, C);
SETVECTOR3(V, Q, P, R); // P and Q are flipped.
SETVECTOR3(pu, 0, 1, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 1;
} else {
if (sQ > 0) { // (0+)
SETVECTOR3(U, B, A, C); // A and B are flipped.
SETVECTOR3(V, Q, P, R); // P and Q are flipped.
SETVECTOR3(pu, 1, 0, 2);
SETVECTOR3(pv, 1, 0, 2);
z1 = 1;
} else { // (00)
// A, B, C, P, and Q are coplanar.
z1 = 2;
}
}
}
}
if (z1 == 2) {
// The triangle and the edge are coplanar.
return tri_edge_2d(A, B, C, P, Q, R, level, types, pos);
}
s1 = orient3d(U[0], U[1], V[0], V[1]);
if (s1 < 0) {
return 0; }
s2 = orient3d(U[1], U[2], V[0], V[1]);
if (s2 < 0) {
return 0;
}
s3 = orient3d(U[2], U[0], V[0], V[1]);
if (s3 < 0) {
return 0;
}
if (level == 0) {
return 1; // The are intersected.
}
types[1] = (int) DISJOINT; // No second intersection point.
if (z1 == 0) {
if (s1 > 0) {
if (s2 > 0) {
if (s3 > 0) { // (+++)
// [P, Q] passes interior of [A, B, C].
types[0] = (int) ACROSSFACE;
pos[0] = 3; // interior of [A, B, C]
pos[1] = 0; // [P, Q]
} else { // s3 == 0 (++0)
// [P, Q] intersects [C, A].
types[0] = (int) ACROSSEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = 0; // [P, Q]
}
} else { // s2 == 0
if (s3 > 0) { // (+0+)
// [P, Q] intersects [B, C].
types[0] = (int) ACROSSEDGE;
pos[0] = pu[1]; // [B, C]
pos[1] = 0; // [P, Q]
} else { // s3 == 0 (+00)
// [P, Q] passes C.
types[0] = (int) ACROSSVERT;
pos[0] = pu[2]; // C
pos[1] = 0; // [P, Q]
}
}
} else { // s1 == 0
if (s2 > 0) {
if (s3 > 0) { // (0++)
// [P, Q] intersects [A, B].
types[0] = (int) ACROSSEDGE;
pos[0] = pu[0]; // [A, B]
pos[1] = 0; // [P, Q]
} else { // s3 == 0 (0+0)
// [P, Q] passes A.
types[0] = (int) ACROSSVERT;
pos[0] = pu[0]; // A
pos[1] = 0; // [P, Q]
}
} else { // s2 == 0
if (s3 > 0) { // (00+)
// [P, Q] passes B.
types[0] = (int) ACROSSVERT;
pos[0] = pu[1]; // B
pos[1] = 0; // [P, Q]
}
}
}
} else { // z1 == 1
if (s1 > 0) {
if (s2 > 0) { if (s3 > 0) { // (+++)
// Q lies in [A, B, C].
types[0] = (int) TOUCHFACE;
pos[0] = 0; // [A, B, C]
pos[1] = pv[1]; // Q
} else { // s3 == 0 (++0)
// Q lies on [C, A].
types[0] = (int) TOUCHEDGE;
pos[0] = pu[2]; // [C, A]
pos[1] = pv[1]; // Q
}
} else { // s2 == 0
if (s3 > 0) { // (+0+)
// Q lies on [B, C].
types[0] = (int) TOUCHEDGE;
pos[0] = pu[1]; // [B, C]
pos[1] = pv[1]; // Q
} else { // s3 == 0 (+00)
// Q = C.
types[0] = (int) SHAREVERT;
pos[0] = pu[2]; // C
pos[1] = pv[1]; // Q
}
}
} else { // s1 == 0
if (s2 > 0) {
if (s3 > 0) { // (0++)
// Q lies on [A, B].
types[0] = (int) TOUCHEDGE;
pos[0] = pu[0]; // [A, B]
pos[1] = pv[1]; // Q
} else { // s3 == 0 (0+0)
// Q = A.
types[0] = (int) SHAREVERT;
pos[0] = pu[0]; // A
pos[1] = pv[1]; // Q
}
} else { // s2 == 0
if (s3 > 0) { // (00+)
// Q = B.
types[0] = (int) SHAREVERT;
pos[0] = pu[1]; // B
pos[1] = pv[1]; // Q
}
}
}
}
// T and E intersect in a single point.
return 2;
}
int tetgenmesh::tri_edge_test(point A, point B, point C, point P, point Q,
point R, int level, int *types, int *pos)
{
REAL sP, sQ;
// Test the locations of P and Q with respect to ABC.
sP = orient3d(A, B, C, P);
sQ = orient3d(A, B, C, Q);
return tri_edge_tail(A, B, C, P, Q, R, sP, sQ, level, types, pos);
}
///////////////////////////////////////////////////////////////////////////////
// //
// tri_tri_inter() Test whether two triangle (abc) and (opq) are //
// intersecting or not. //
// //
// Return 0 if they are disjoint. Otherwise, return 1. 'type' returns one of //// the four cases: SHAREVERTEX, SHAREEDGE, SHAREFACE, and INTERSECT. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::tri_edge_inter_tail(REAL* A, REAL* B, REAL* C, REAL* P,
REAL* Q, REAL s_p, REAL s_q)
{
int types[2], pos[4];
int ni; // =0, 2, 4
ni = tri_edge_tail(A, B, C, P, Q, NULL, s_p, s_q, 1, types, pos);
if (ni > 0) {
if (ni == 2) {
// Get the intersection type.
if (types[0] == (int) SHAREVERT) {
return (int) SHAREVERT;
} else {
return (int) INTERSECT;
}
} else if (ni == 4) {
// There may be two intersections.
if (types[0] == (int) SHAREVERT) {
if (types[1] == (int) DISJOINT) {
return (int) SHAREVERT;
} else {
return (int) INTERSECT;
}
} else {
if (types[0] == (int) SHAREEDGE) {
return (int) SHAREEDGE;
} else {
return (int) INTERSECT;
}
}
}
}
return (int) DISJOINT;
}
int tetgenmesh::tri_tri_inter(REAL* A,REAL* B,REAL* C,REAL* O,REAL* P,REAL* Q)
{
REAL s_o, s_p, s_q;
REAL s_a, s_b, s_c;
s_o = orient3d(A, B, C, O);
s_p = orient3d(A, B, C, P);
s_q = orient3d(A, B, C, Q);
if ((s_o * s_p > 0.0) && (s_o * s_q > 0.0)) {
// o, p, q are all in the same halfspace of ABC.
return 0; // DISJOINT;
}
s_a = orient3d(O, P, Q, A);
s_b = orient3d(O, P, Q, B);
s_c = orient3d(O, P, Q, C);
if ((s_a * s_b > 0.0) && (s_a * s_c > 0.0)) {
// a, b, c are all in the same halfspace of OPQ.
return 0; // DISJOINT;
}
int abcop, abcpq, abcqo;
int shareedge = 0;
abcop = tri_edge_inter_tail(A, B, C, O, P, s_o, s_p);
if (abcop == (int) INTERSECT) {
return (int) INTERSECT;
} else if (abcop == (int) SHAREEDGE) {
shareedge++; }
abcpq = tri_edge_inter_tail(A, B, C, P, Q, s_p, s_q);
if (abcpq == (int) INTERSECT) {
return (int) INTERSECT;
} else if (abcpq == (int) SHAREEDGE) {
shareedge++;
}
abcqo = tri_edge_inter_tail(A, B, C, Q, O, s_q, s_o);
if (abcqo == (int) INTERSECT) {
return (int) INTERSECT;
} else if (abcqo == (int) SHAREEDGE) {
shareedge++;
}
if (shareedge == 3) {
// opq are coincident with abc.
return (int) SHAREFACE;
}
// Continue to detect whether opq and abc are intersecting or not.
int opqab, opqbc, opqca;
opqab = tri_edge_inter_tail(O, P, Q, A, B, s_a, s_b);
if (opqab == (int) INTERSECT) {
return (int) INTERSECT;
}
opqbc = tri_edge_inter_tail(O, P, Q, B, C, s_b, s_c);
if (opqbc == (int) INTERSECT) {
return (int) INTERSECT;
}
opqca = tri_edge_inter_tail(O, P, Q, C, A, s_c, s_a);
if (opqca == (int) INTERSECT) {
return (int) INTERSECT;
}
// At this point, two triangles are not intersecting and not coincident.
// They may be share an edge, or share a vertex, or disjoint.
if (abcop == (int) SHAREEDGE) {
// op is coincident with an edge of abc.
return (int) SHAREEDGE;
}
if (abcpq == (int) SHAREEDGE) {
// pq is coincident with an edge of abc.
return (int) SHAREEDGE;
}
if (abcqo == (int) SHAREEDGE) {
// qo is coincident with an edge of abc.
return (int) SHAREEDGE;
}
// They may share a vertex or disjoint.
if (abcop == (int) SHAREVERT) {
return (int) SHAREVERT;
}
if (abcpq == (int) SHAREVERT) {
// q is the coincident vertex.
return (int) SHAREVERT;
}
// They are disjoint.
return (int) DISJOINT;
}
///////////////////////////////////////////////////////////////////////////////
// //
// lu_decmp() Compute the LU decomposition of a matrix. //
// //
// Compute the LU decomposition of a (non-singular) square matrix A using //
// partial pivoting and implicit row exchanges. The result is: //
// A = P * L * U, //
// where P is a permutation matrix, L is unit lower triangular, and U is //// upper triangular. The factored form of A is used in combination with //
// 'lu_solve()' to solve linear equations: Ax = b, or invert a matrix. //
// //
// The inputs are a square matrix 'lu[N..n+N-1][N..n+N-1]', it's size is 'n'.//
// On output, 'lu' is replaced by the LU decomposition of a rowwise permuta- //
// tion of itself, 'ps[N..n+N-1]' is an output vector that records the row //
// permutation effected by the partial pivoting, effectively, 'ps' array //
// tells the user what the permutation matrix P is; 'd' is output as +1/-1 //
// depending on whether the number of row interchanges was even or odd, //
// respectively. //
// //
// Return true if the LU decomposition is successfully computed, otherwise, //
// return false in case that A is a singular matrix. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::lu_decmp(REAL lu[4][4], int n, int* ps, REAL* d, int N)
{
REAL scales[4];
REAL pivot, biggest, mult, tempf;
int pivotindex = 0;
int i, j, k;
*d = 1.0; // No row interchanges yet.
for (i = N; i < n + N; i++) { // For each row.
// Find the largest element in each row for row equilibration
biggest = 0.0;
for (j = N; j < n + N; j++)
if (biggest < (tempf = fabs(lu[i][j])))
biggest = tempf;
if (biggest != 0.0)
scales[i] = 1.0 / biggest;
else {
scales[i] = 0.0;
return false; // Zero row: singular matrix.
}
ps[i] = i; // Initialize pivot sequence.
}
for (k = N; k < n + N - 1; k++) { // For each column.
// Find the largest element in each column to pivot around.
biggest = 0.0;
for (i = k; i < n + N; i++) {
if (biggest < (tempf = fabs(lu[ps[i]][k]) * scales[ps[i]])) {
biggest = tempf;
pivotindex = i;
}
}
if (biggest == 0.0) {
return false; // Zero column: singular matrix.
}
if (pivotindex != k) { // Update pivot sequence.
j = ps[k];
ps[k] = ps[pivotindex];
ps[pivotindex] = j;
*d = -(*d); // ...and change the parity of d.
}
// Pivot, eliminating an extra variable each time
pivot = lu[ps[k]][k];
for (i = k + 1; i < n + N; i++) {
lu[ps[i]][k] = mult = lu[ps[i]][k] / pivot;
if (mult != 0.0) {
for (j = k + 1; j < n + N; j++)
lu[ps[i]][j] -= mult * lu[ps[k]][j];
}
}
}
// (lu[ps[n + N - 1]][n + N - 1] == 0.0) ==> A is singular.
return lu[ps[n + N - 1]][n + N - 1] != 0.0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// lu_solve() Solves the linear equation: Ax = b, after the matrix A //
// has been decomposed into the lower and upper triangular //
// matrices L and U, where A = LU. //
// //
// 'lu[N..n+N-1][N..n+N-1]' is input, not as the matrix 'A' but rather as //
// its LU decomposition, computed by the routine 'lu_decmp'; 'ps[N..n+N-1]' //
// is input as the permutation vector returned by 'lu_decmp'; 'b[N..n+N-1]' //
// is input as the right-hand side vector, and returns with the solution //
// vector. 'lu', 'n', and 'ps' are not modified by this routine and can be //
// left in place for successive calls with different right-hand sides 'b'. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N)
{
int i, j;
REAL X[4], dot;
for (i = N; i < n + N; i++) X[i] = 0.0;
// Vector reduction using U triangular matrix.
for (i = N; i < n + N; i++) {
dot = 0.0;
for (j = N; j < i + N; j++)
dot += lu[ps[i]][j] * X[j];
X[i] = b[ps[i]] - dot;
}
// Back substitution, in L triangular matrix.
for (i = n + N - 1; i >= N; i--) {
dot = 0.0;
for (j = i + 1; j < n + N; j++)
dot += lu[ps[i]][j] * X[j];
X[i] = (X[i] - dot) / lu[ps[i]][i];
}
for (i = N; i < n + N; i++) b[i] = X[i];
}
///////////////////////////////////////////////////////////////////////////////
// //
// incircle3d() 3D in-circle test. //
// //
// Return a negative value if pd is inside the circumcircle of the triangle //
// pa, pb, and pc. //
// //
// IMPORTANT: It assumes that [a,b] is the common edge, i.e., the two input //
// triangles are [a,b,c] and [b,a,d]. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::incircle3d(point pa, point pb, point pc, point pd)
{
REAL area2[2], n1[3], n2[3], c[3];
REAL sign, r, d;
// Calculate the areas of the two triangles [a, b, c] and [b, a, d].
facenormal(pa, pb, pc, n1, 1, NULL);
area2[0] = dot(n1, n1);
facenormal(pb, pa, pd, n2, 1, NULL);
area2[1] = dot(n2, n2);
if (area2[0] > area2[1]) {
// Choose [a, b, c] as the base triangle. circumsphere(pa, pb, pc, NULL, c, &r);
d = distance(c, pd);
} else {
// Choose [b, a, d] as the base triangle.
if (area2[1] > 0) {
circumsphere(pb, pa, pd, NULL, c, &r);
d = distance(c, pc);
} else {
// The four points are collinear. This case only happens on the boundary.
return 0; // Return "not inside".
}
}
sign = d - r;
if (fabs(sign) / r < b->epsilon) {
sign = 0;
}
return sign;
}
///////////////////////////////////////////////////////////////////////////////
// //
// facenormal() Calculate the normal of the face. //
// //
// The normal of the face abc can be calculated by the cross product of 2 of //
// its 3 edge vectors. A better choice of two edge vectors will reduce the //
// numerical error during the calculation. Burdakov proved that the optimal //
// basis problem is equivalent to the minimum spanning tree problem with the //
// edge length be the functional, see Burdakov, "A greedy algorithm for the //
// optimal basis problem", BIT 37:3 (1997), 591-599. If 'pivot' > 0, the two //
// short edges in abc are chosen for the calculation. //
// //
// If 'lav' is not NULL and if 'pivot' is set, the average edge length of //
// the edges of the face [a,b,c] is returned. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::facenormal(point pa, point pb, point pc, REAL *n, int pivot,
REAL* lav)
{
REAL v1[3], v2[3], v3[3], *pv1, *pv2;
REAL L1, L2, L3;
v1[0] = pb[0] - pa[0]; // edge vector v1: a->b
v1[1] = pb[1] - pa[1];
v1[2] = pb[2] - pa[2];
v2[0] = pa[0] - pc[0]; // edge vector v2: c->a
v2[1] = pa[1] - pc[1];
v2[2] = pa[2] - pc[2];
// Default, normal is calculated by: v1 x (-v2) (see Fig. fnormal).
if (pivot > 0) {
// Choose edge vectors by Burdakov's algorithm.
v3[0] = pc[0] - pb[0]; // edge vector v3: b->c
v3[1] = pc[1] - pb[1];
v3[2] = pc[2] - pb[2];
L1 = dot(v1, v1);
L2 = dot(v2, v2);
L3 = dot(v3, v3);
// Sort the three edge lengths.
if (L1 < L2) {
if (L2 < L3) {
pv1 = v1; pv2 = v2; // n = v1 x (-v2).
} else {
pv1 = v3; pv2 = v1; // n = v3 x (-v1).
}
} else {
if (L1 < L3) {
pv1 = v1; pv2 = v2; // n = v1 x (-v2). } else {
pv1 = v2; pv2 = v3; // n = v2 x (-v3).
}
}
if (lav) {
// return the average edge length.
*lav = (sqrt(L1) + sqrt(L2) + sqrt(L3)) / 3.0;
}
} else {
pv1 = v1; pv2 = v2; // n = v1 x (-v2).
}
// Calculate the face normal.
cross(pv1, pv2, n);
// Inverse the direction;
n[0] = -n[0];
n[1] = -n[1];
n[2] = -n[2];
}
///////////////////////////////////////////////////////////////////////////////
// //
// shortdistance() Returns the shortest distance from point p to a line //
// defined by two points e1 and e2. //
// //
// First compute the projection length l_p of the vector v1 = p - e1 along //
// the vector v2 = e2 - e1. Then Pythagoras' Theorem is used to compute the //
// shortest distance. //
// //
// This routine allows that p is collinear with the line. In this case, the //
// return value is zero. The two points e1 and e2 should not be identical. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::shortdistance(REAL* p, REAL* e1, REAL* e2)
{
REAL v1[3], v2[3];
REAL len, l_p;
v1[0] = e2[0] - e1[0];
v1[1] = e2[1] - e1[1];
v1[2] = e2[2] - e1[2];
v2[0] = p[0] - e1[0];
v2[1] = p[1] - e1[1];
v2[2] = p[2] - e1[2];
len = sqrt(dot(v1, v1));
v1[0] /= len;
v1[1] /= len;
v1[2] /= len;
l_p = dot(v1, v2);
return sqrt(dot(v2, v2) - l_p * l_p);
}
///////////////////////////////////////////////////////////////////////////////
// //
// triarea() Return the area of a triangle. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::triarea(REAL* pa, REAL* pb, REAL* pc)
{
REAL A[4][4];
// 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)
return 0.5 * sqrt(dot(A[2], A[2])); // The area of [a,b,c].
}
REAL tetgenmesh::orient3dfast(REAL *pa, REAL *pb, REAL *pc, REAL *pd)
{
REAL adx, bdx, cdx;
REAL ady, bdy, cdy;
REAL adz, bdz, cdz;
adx = pa[0] - pd[0];
bdx = pb[0] - pd[0];
cdx = pc[0] - pd[0];
ady = pa[1] - pd[1];
bdy = pb[1] - pd[1];
cdy = pc[1] - pd[1];
adz = pa[2] - pd[2];
bdz = pb[2] - pd[2];
cdz = pc[2] - pd[2];
return adx * (bdy * cdz - bdz * cdy)
+ bdx * (cdy * adz - cdz * ady)
+ cdx * (ady * bdz - adz * bdy);
}
///////////////////////////////////////////////////////////////////////////////
// //
// interiorangle() Return the interior angle (0 - 2 * PI) between vectors //
// o->p1 and o->p2. //
// //
// 'n' is the normal of the plane containing face (o, p1, p2). The interior //
// angle is the total angle rotating from o->p1 around n to o->p2. Exchange //
// the position of p1 and p2 will get the complement angle of the other one. //
// i.e., interiorangle(o, p1, p2) = 2 * PI - interiorangle(o, p2, p1). Set //
// 'n' be NULL if you only want the interior angle between 0 - PI. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::interiorangle(REAL* o, REAL* p1, REAL* p2, REAL* n)
{
REAL v1[3], v2[3], np[3];
REAL theta, costheta, lenlen;
REAL ori, len1, len2;
// Get the interior angle (0 - PI) between o->p1, and o->p2.
v1[0] = p1[0] - o[0];
v1[1] = p1[1] - o[1];
v1[2] = p1[2] - o[2];
v2[0] = p2[0] - o[0];
v2[1] = p2[1] - o[1];
v2[2] = p2[2] - o[2];
len1 = sqrt(dot(v1, v1));
len2 = sqrt(dot(v2, v2));
lenlen = len1 * len2;
costheta = dot(v1, v2) / lenlen;
if (costheta > 1.0) {
costheta = 1.0; // Roundoff.
} else if (costheta < -1.0) {
costheta = -1.0; // Roundoff.
}
theta = acos(costheta);
if (n != NULL) {
// Get a point above the face (o, p1, p2);
np[0] = o[0] + n[0]; np[1] = o[1] + n[1];
np[2] = o[2] + n[2];
// Adjust theta (0 - 2 * PI).
ori = orient3d(p1, o, np, p2);
if (ori > 0.0) {
theta = 2 * PI - theta;
}
}
return theta;
}
///////////////////////////////////////////////////////////////////////////////
// //
// projpt2edge() Return the projection point from a point to an edge. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::projpt2edge(REAL* p, REAL* e1, REAL* e2, REAL* prj)
{
REAL v1[3], v2[3];
REAL len, l_p;
v1[0] = e2[0] - e1[0];
v1[1] = e2[1] - e1[1];
v1[2] = e2[2] - e1[2];
v2[0] = p[0] - e1[0];
v2[1] = p[1] - e1[1];
v2[2] = p[2] - e1[2];
len = sqrt(dot(v1, v1));
v1[0] /= len;
v1[1] /= len;
v1[2] /= len;
l_p = dot(v1, v2);
prj[0] = e1[0] + l_p * v1[0];
prj[1] = e1[1] + l_p * v1[1];
prj[2] = e1[2] + l_p * v1[2];
}
///////////////////////////////////////////////////////////////////////////////
// //
// projpt2face() Return the projection point from a point to a face. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::projpt2face(REAL* p, REAL* f1, REAL* f2, REAL* f3, REAL* prj)
{
REAL fnormal[3], v1[3];
REAL len, dist;
// Get the unit face normal.
facenormal(f1, f2, f3, fnormal, 1, NULL);
len = sqrt(fnormal[0]*fnormal[0] + fnormal[1]*fnormal[1] +
fnormal[2]*fnormal[2]);
fnormal[0] /= len;
fnormal[1] /= len;
fnormal[2] /= len;
// Get the vector v1 = |p - f1|.
v1[0] = p[0] - f1[0];
v1[1] = p[1] - f1[1];
v1[2] = p[2] - f1[2];
// Get the project distance.
dist = dot(fnormal, v1);
// Get the project point.
prj[0] = p[0] - dist * fnormal[0];
prj[1] = p[1] - dist * fnormal[1];
prj[2] = p[2] - dist * fnormal[2];}
///////////////////////////////////////////////////////////////////////////////
// //
// tetalldihedral() Get all (six) dihedral angles of a tet. //
// //
// If 'cosdd' is not NULL, it returns the cosines of the 6 dihedral angles, //
// the edge indices are given in the global array 'edge2ver'. If 'cosmaxd' //
// (or 'cosmind') is not NULL, it returns the cosine of the maximal (or //
// minimal) dihedral angle. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::tetalldihedral(point pa, point pb, point pc, point pd,
REAL* cosdd, REAL* cosmaxd, REAL* cosmind)
{
REAL N[4][3], vol, cosd, len;
int f1 = 0, f2 = 0, i, j;
vol = 0; // Check if the tet is valid or not.
// Get four normals of faces of the tet.
tetallnormal(pa, pb, pc, pd, N, &vol);
if (vol > 0) {
// Normalize the normals.
for (i = 0; i < 4; i++) {
len = sqrt(dot(N[i], N[i]));
if (len != 0.0) {
for (j = 0; j < 3; j++) N[i][j] /= len;
} else {
// There are degeneracies, such as duplicated vertices.
vol = 0; //assert(0);
}
}
}
if (vol <= 0) { // if (vol == 0.0) {
// A degenerated tet or an inverted tet.
facenormal(pc, pb, pd, N[0], 1, NULL);
facenormal(pa, pc, pd, N[1], 1, NULL);
facenormal(pb, pa, pd, N[2], 1, NULL);
facenormal(pa, pb, pc, N[3], 1, NULL);
// Normalize the normals.
for (i = 0; i < 4; i++) {
len = sqrt(dot(N[i], N[i]));
if (len != 0.0) {
for (j = 0; j < 3; j++) N[i][j] /= len;
} else {
// There are degeneracies, such as duplicated vertices.
break; // Not a valid normal.
}
}
if (i < 4) {
// Do not calculate dihedral angles.
// Set all angles be 0 degree. There will be no quality optimization for
// this tet! Use volume optimization to correct it.
if (cosdd != NULL) {
for (i = 0; i < 6; i++) {
cosdd[i] = -1.0; // 180 degree.
}
}
// This tet has zero volume.
if (cosmaxd != NULL) {
*cosmaxd = -1.0; // 180 degree.
}
if (cosmind != NULL) {
*cosmind = -1.0; // 180 degree.
}
return false; }
}
// Calculate the cosine of the dihedral angles of the edges.
for (i = 0; i < 6; i++) {
switch (i) {
case 0: f1 = 0; f2 = 1; break; // [c,d].
case 1: f1 = 1; f2 = 2; break; // [a,d].
case 2: f1 = 2; f2 = 3; break; // [a,b].
case 3: f1 = 0; f2 = 3; break; // [b,c].
case 4: f1 = 2; f2 = 0; break; // [b,d].
case 5: f1 = 1; f2 = 3; break; // [a,c].
}
cosd = -dot(N[f1], N[f2]);
if (cosd < -1.0) cosd = -1.0; // Rounding.
if (cosd > 1.0) cosd = 1.0; // Rounding.
if (cosdd) cosdd[i] = cosd;
if (cosmaxd || cosmind) {
if (i == 0) {
if (cosmaxd) *cosmaxd = cosd;
if (cosmind) *cosmind = cosd;
} else {
if (cosmaxd) *cosmaxd = cosd < *cosmaxd ? cosd : *cosmaxd;
if (cosmind) *cosmind = cosd > *cosmind ? cosd : *cosmind;
}
}
}
return true;
}
///////////////////////////////////////////////////////////////////////////////
// //
// tetallnormal() Get the in-normals of the four faces of a given tet. //
// //
// Let tet be abcd. N[4][3] returns the four normals, which are: N[0] cbd, //
// N[1] acd, N[2] bad, N[3] abc (exactly corresponding to the face indices //
// of the mesh data structure). These normals are unnormalized. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::tetallnormal(point pa, point pb, point pc, point pd,
REAL N[4][3], REAL* volume)
{
REAL A[4][4], rhs[4], D;
int indx[4];
int i, j;
// get the entries of A[3][3].
for (i = 0; i < 3; i++) A[0][i] = pa[i] - pd[i]; // d->a vec
for (i = 0; i < 3; i++) A[1][i] = pb[i] - pd[i]; // d->b vec
for (i = 0; i < 3; i++) A[2][i] = pc[i] - pd[i]; // d->c vec
// Compute the inverse of matrix A, to get 3 normals of the 4 faces.
if (lu_decmp(A, 3, indx, &D, 0)) { // Decompose the matrix just once.
if (volume != NULL) {
// Get the volume of the tet.
*volume = fabs((A[indx[0]][0] * A[indx[1]][1] * A[indx[2]][2])) / 6.0;
}
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];
} else {
// The tet is degenerated.
if (volume != NULL) { *volume = 0;
}
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// tetaspectratio() Calculate the aspect ratio of the tetrahedron. //
// //
// The aspect ratio of a tet is L/h, where L is the longest edge length, and //
// h is the shortest height of the tet. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::tetaspectratio(point pa, point pb, point pc, point pd)
{
REAL V[6][3], edgelength[6], longlen;
REAL vda[3], vdb[3], vdc[3];
REAL N[4][3], A[4][4], rhs[4], D;
REAL H[4], volume, minheightinv;
int indx[4];
int i, j;
// Set the edge vectors: V[0], ..., V[5]
for (i = 0; i < 3; i++) V[0][i] = pa[i] - pd[i];
for (i = 0; i < 3; i++) V[1][i] = pb[i] - pd[i];
for (i = 0; i < 3; i++) V[2][i] = pc[i] - pd[i];
for (i = 0; i < 3; i++) V[3][i] = pb[i] - pa[i];
for (i = 0; i < 3; i++) V[4][i] = pc[i] - pb[i];
for (i = 0; i < 3; i++) V[5][i] = pa[i] - pc[i];
// Get the squares of the edge lengths.
for (i = 0; i < 6; i++) edgelength[i] = dot(V[i], V[i]);
// Calculate the longest and shortest edge length.
longlen = edgelength[0];
for (i = 1; i < 6; i++) {
longlen = edgelength[i] > longlen ? edgelength[i] : longlen;
}
// 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.
// 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 < 4; i++) {
if (H[i] > minheightinv) minheightinv = H[i];
}
return sqrt(longlen) * minheightinv;
}
///////////////////////////////////////////////////////////////////////////////
// //
// circumsphere() Calculate the smallest circumsphere (center and radius) //
// of the given three or four points. //
// //
// The circumsphere of four points (a tetrahedron) is unique if they are not //
// degenerate. If 'pd = NULL', the smallest circumsphere of three points is //
// the diametral sphere of the triangle if they are not degenerate. //
// //
// Return TRUE if the input points are not degenerate and the circumcenter //
// and circumradius are returned in 'cent' and 'radius' respectively if they //
// are not NULLs. Otherwise, return FALSE, the four points are co-planar. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::circumsphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd,
REAL* cent, REAL* radius)
{
REAL A[4][4], rhs[4], D;
int indx[4];
// 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];
A[1][0] = pc[0] - pa[0];
A[1][1] = pc[1] - pa[1];
A[1][2] = pc[2] - pa[2];
if (pd != NULL) {
A[2][0] = pd[0] - pa[0];
A[2][1] = pd[1] - pa[1];
A[2][2] = pd[2] - pa[2];
} else {
cross(A[0], A[1], A[2]);
}
// 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]);
if (pd != NULL) {
rhs[2] = 0.5 * dot(A[2], A[2]);
} else {
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)) {
if (radius != (REAL *) NULL) *radius = 0.0;
return false;
}
lu_solve(A, 3, indx, rhs, 0);
if (cent != (REAL *) NULL) {
cent[0] = pa[0] + rhs[0];
cent[1] = pa[1] + rhs[1];
cent[2] = pa[2] + rhs[2];
}
if (radius != (REAL *) NULL) {
*radius = sqrt(rhs[0] * rhs[0] + rhs[1] * rhs[1] + rhs[2] * rhs[2]);
}
return true;}
///////////////////////////////////////////////////////////////////////////////
// //
// orthosphere() Calulcate the orthosphere of four weighted points. //
// //
// A weighted point (p, P^2) can be interpreted as a sphere centered at the //
// point 'p' with a radius 'P'. The 'height' of 'p' is pheight = p[0]^2 + //
// p[1]^2 + p[2]^2 - P^2. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::orthosphere(REAL* pa, REAL* pb, REAL* pc, REAL* pd,
REAL aheight, REAL bheight, REAL cheight,
REAL dheight, REAL* orthocent, REAL* radius)
{
REAL A[4][4], rhs[4], D;
int indx[4];
// Set the coefficient matrix A (4 x 4).
A[0][0] = 1.0; A[0][1] = pa[0]; A[0][2] = pa[1]; A[0][3] = pa[2];
A[1][0] = 1.0; A[1][1] = pb[0]; A[1][2] = pb[1]; A[1][3] = pb[2];
A[2][0] = 1.0; A[2][1] = pc[0]; A[2][2] = pc[1]; A[2][3] = pc[2];
A[3][0] = 1.0; A[3][1] = pd[0]; A[3][2] = pd[1]; A[3][3] = pd[2];
// Set the right hand side vector (4 x 1).
rhs[0] = 0.5 * aheight;
rhs[1] = 0.5 * bheight;
rhs[2] = 0.5 * cheight;
rhs[3] = 0.5 * dheight;
// Solve the 4 by 4 equations use LU decomposition with partial pivoting
// and backward and forward substitute..
if (!lu_decmp(A, 4, indx, &D, 0)) {
if (radius != (REAL *) NULL) *radius = 0.0;
return false;
}
lu_solve(A, 4, indx, rhs, 0);
if (orthocent != (REAL *) NULL) {
orthocent[0] = rhs[1];
orthocent[1] = rhs[2];
orthocent[2] = rhs[3];
}
if (radius != (REAL *) NULL) {
// rhs[0] = - rheight / 2;
// rheight = - 2 * rhs[0];
// = r[0]^2 + r[1]^2 + r[2]^2 - radius^2
// radius^2 = r[0]^2 + r[1]^2 + r[2]^2 -rheight
// = r[0]^2 + r[1]^2 + r[2]^2 + 2 * rhs[0]
*radius = sqrt(rhs[1] * rhs[1] + rhs[2] * rhs[2] + rhs[3] * rhs[3]
+ 2.0 * rhs[0]);
}
return true;
}
///////////////////////////////////////////////////////////////////////////////
// //
// planelineint() Calculate the intersection of a line and a plane. //
// //
// The equation of a plane (points P are on the plane with normal N and P3 //
// on the plane) can be written as: N dot (P - P3) = 0. The equation of the //
// line (points P on the line passing through P1 and P2) can be written as: //
// P = P1 + u (P2 - P1). The intersection of these two occurs when: //
// N dot (P1 + u (P2 - P1)) = N dot P3. //
// Solving for u gives: //
// N dot (P3 - P1) //
// u = ------------------. //
// N dot (P2 - P1) //
// If the denominator is 0 then N (the normal to the plane) is perpendicular //// to the line. Thus the line is either parallel to the plane and there are //
// no solutions or the line is on the plane in which case there are an infi- //
// nite number of solutions. //
// //
// The plane is given by three points pa, pb, and pc, e1 and e2 defines the //
// line. If u is non-zero, The intersection point (if exists) returns in ip. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::planelineint(REAL* pa, REAL* pb, REAL* pc, REAL* e1, REAL* e2,
REAL* ip, REAL* u)
{
REAL n[3], det, det1;
// Calculate N.
facenormal(pa, pb, pc, n, 1, NULL);
// Calculate N dot (e2 - e1).
det = n[0] * (e2[0] - e1[0]) + n[1] * (e2[1] - e1[1])
+ n[2] * (e2[2] - e1[2]);
if (det != 0.0) {
// Calculate N dot (pa - e1)
det1 = n[0] * (pa[0] - e1[0]) + n[1] * (pa[1] - e1[1])
+ n[2] * (pa[2] - e1[2]);
*u = det1 / det;
ip[0] = e1[0] + *u * (e2[0] - e1[0]);
ip[1] = e1[1] + *u * (e2[1] - e1[1]);
ip[2] = e1[2] + *u * (e2[2] - e1[2]);
} else {
*u = 0.0;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// linelineint() Calculate the intersection(s) of two line segments. //
// //
// Calculate the line segment [P, Q] that is the shortest route between two //
// lines from A to B and C to D. Calculate also the values of tp and tq //
// where: P = A + tp (B - A), and Q = C + tq (D - C). //
// //
// Return 1 if the line segment exists. Otherwise, return 0. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::linelineint(REAL* A, REAL* B, REAL* C, REAL* D, REAL* P,
REAL* Q, REAL* tp, REAL* tq)
{
REAL vab[3], vcd[3], vca[3];
REAL vab_vab, vcd_vcd, vab_vcd;
REAL vca_vab, vca_vcd;
REAL det, eps;
int i;
for (i = 0; i < 3; i++) {
vab[i] = B[i] - A[i];
vcd[i] = D[i] - C[i];
vca[i] = A[i] - C[i];
}
vab_vab = dot(vab, vab);
vcd_vcd = dot(vcd, vcd);
vab_vcd = dot(vab, vcd);
det = vab_vab * vcd_vcd - vab_vcd * vab_vcd;
// Round the result.
eps = det / (fabs(vab_vab * vcd_vcd) + fabs(vab_vcd * vab_vcd));
if (eps < b->epsilon) {
return 0;
}
vca_vab = dot(vca, vab);
vca_vcd = dot(vca, vcd);
*tp = (vcd_vcd * (- vca_vab) + vab_vcd * vca_vcd) / det;
*tq = (vab_vcd * (- vca_vab) + vab_vab * vca_vcd) / det;
for (i = 0; i < 3; i++) P[i] = A[i] + (*tp) * vab[i];
for (i = 0; i < 3; i++) Q[i] = C[i] + (*tq) * vcd[i];
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// tetprismvol() Calculate the volume of a tetrahedral prism in 4D. //
// //
// A tetrahedral prism is a convex uniform polychoron (four dimensional poly-//
// tope). It has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular //
// prisms. It has 14 faces: 8 triangular and 6 square. It has 16 edges and 8 //
// vertices. (Wikipedia). //
// //
// Let 'p0', ..., 'p3' be four affinely independent points in R^3. They form //
// the lower tetrahedral facet of the prism. The top tetrahedral facet is //
// formed by four vertices, 'p4', ..., 'p7' in R^4, which is obtained by //
// lifting each vertex of the lower facet into R^4 by a weight (height). A //
// canonical choice of the weights is the square of Euclidean norm of of the //
// points (vectors). //
// //
// //
// The return value is (4!) 24 times of the volume of the tetrahedral prism. //
// //
///////////////////////////////////////////////////////////////////////////////
REAL tetgenmesh::tetprismvol(REAL* p0, REAL* p1, REAL* p2, REAL* p3)
{
REAL *p4, *p5, *p6, *p7;
REAL w4, w5, w6, w7;
REAL vol[4];
p4 = p0;
p5 = p1;
p6 = p2;
p7 = p3;
// TO DO: these weights can be pre-calculated!
w4 = dot(p0, p0);
w5 = dot(p1, p1);
w6 = dot(p2, p2);
w7 = dot(p3, p3);
// Calculate the volume of the tet-prism.
vol[0] = orient4d(p5, p6, p4, p3, p7, w5, w6, w4, 0, w7);
vol[1] = orient4d(p3, p6, p2, p0, p1, 0, w6, 0, 0, 0);
vol[2] = orient4d(p4, p6, p3, p0, p1, w4, w6, 0, 0, 0);
vol[3] = orient4d(p6, p5, p4, p3, p1, w6, w5, w4, 0, 0);
return fabs(vol[0]) + fabs(vol[1]) + fabs(vol[2]) + fabs(vol[3]);
}
///////////////////////////////////////////////////////////////////////////////
// //
// calculateabovepoint() Calculate a point above a facet in 'dummypoint'. //
// //
///////////////////////////////////////////////////////////////////////////////
bool tetgenmesh::calculateabovepoint(arraypool *facpoints, point *ppa,
point *ppb, point *ppc)
{
point *ppt, pa, pb, pc;
REAL v1[3], v2[3], n[3]; REAL lab, len, A, area;
REAL x, y, z;
int i;
ppt = (point *) fastlookup(facpoints, 0);
pa = *ppt; // a is the first point.
pb = pc = NULL; // Avoid compiler warnings.
// Get a point b s.t. the length of [a, b] is maximal.
lab = 0;
for (i = 1; i < facpoints->objects; i++) {
ppt = (point *) fastlookup(facpoints, i);
x = (*ppt)[0] - pa[0];
y = (*ppt)[1] - pa[1];
z = (*ppt)[2] - pa[2];
len = x * x + y * y + z * z;
if (len > lab) {
lab = len;
pb = *ppt;
}
}
lab = sqrt(lab);
if (lab == 0) {
if (!b->quiet) {
printf("Warning: All points of a facet are coincident with %d.\n",
pointmark(pa));
}
return false;
}
// Get a point c s.t. the area of [a, b, c] is maximal.
v1[0] = pb[0] - pa[0];
v1[1] = pb[1] - pa[1];
v1[2] = pb[2] - pa[2];
A = 0;
for (i = 1; i < facpoints->objects; i++) {
ppt = (point *) fastlookup(facpoints, i);
v2[0] = (*ppt)[0] - pa[0];
v2[1] = (*ppt)[1] - pa[1];
v2[2] = (*ppt)[2] - pa[2];
cross(v1, v2, n);
area = dot(n, n);
if (area > A) {
A = area;
pc = *ppt;
}
}
if (A == 0) {
// All points are collinear. No above point.
if (!b->quiet) {
printf("Warning: All points of a facet are collinaer with [%d, %d].\n",
pointmark(pa), pointmark(pb));
}
return false;
}
// Calculate an above point of this facet.
facenormal(pa, pb, pc, n, 1, NULL);
len = sqrt(dot(n, n));
n[0] /= len;
n[1] /= len;
n[2] /= len;
lab /= 2.0; // Half the maximal length.
dummypoint[0] = pa[0] + lab * n[0];
dummypoint[1] = pa[1] + lab * n[1];
dummypoint[2] = pa[2] + lab * n[2];
if (ppa != NULL) {
// Return the three points.
*ppa = pa; *ppb = pb;
*ppc = pc;
}
return true;
}
///////////////////////////////////////////////////////////////////////////////
// //
// Calculate an above point. It lies above the plane containing the subface //
// [a,b,c], and save it in dummypoint. Moreover, the vector pa->dummypoint //
// is the normal of the plane. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::calculateabovepoint4(point pa, point pb, point pc, point pd)
{
REAL n1[3], n2[3], *norm;
REAL len, len1, len2;
// Select a base.
facenormal(pa, pb, pc, n1, 1, NULL);
len1 = sqrt(dot(n1, n1));
facenormal(pa, pb, pd, n2, 1, NULL);
len2 = sqrt(dot(n2, n2));
if (len1 > len2) {
norm = n1;
len = len1;
} else {
norm = n2;
len = len2;
}
norm[0] /= len;
norm[1] /= len;
norm[2] /= len;
len = distance(pa, pb);
dummypoint[0] = pa[0] + len * norm[0];
dummypoint[1] = pa[1] + len * norm[1];
dummypoint[2] = pa[2] + len * norm[2];
}
///////////////////////////////////////////////////////////////////////////////
// //
// report_overlapping_facets() Report two overlapping facets. //
// //
// Two subfaces, f1 [a, b, c] and f2 [a, b, d], share the same edge [a, b]. //
// 'dihedang' is the dihedral angle between these two facets. It must less //
// than the variable 'b->facet_overlap_angle_tol'. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::report_overlapping_facets(face *f1, face *f2, REAL dihedang)
{
point pa, pb, pc, pd;
pa = sorg(*f1);
pb = sdest(*f1);
pc = sapex(*f1);
pd = sapex(*f2);
if (pc != pd) {
printf("Found two %s self-intersecting facets.\n",
dihedang > 0 ? "nearly" : "exactly");
printf(" 1st: [%d, %d, %d] #%d\n",
pointmark(pa), pointmark(pb), pointmark(pc), shellmark(*f1));
printf(" 2nd: [%d, %d, %d] #%d\n",
pointmark(pa), pointmark(pb), pointmark(pd), shellmark(*f2));
if (dihedang > 0) {
printf("The dihedral angle between them is %g degree.\n",
dihedang / PI * 180.0); printf("Hint: You may use -p/# to decrease the dihedral angle");
printf(" tolerance %g (degree).\n", b->facet_overlap_ang_tol);
}
} else {
if (shellmark(*f1) != shellmark(*f2)) {
// Two identical faces from two different facet.
printf("Found two overlapping facets.\n");
} else {
printf("Found two duplicated facets.\n");
}
printf(" 1st: [%d, %d, %d] #%d\n",
pointmark(pa), pointmark(pb), pointmark(pc), shellmark(*f1));
printf(" 2nd: [%d, %d, %d] #%d\n",
pointmark(pa), pointmark(pb), pointmark(pd), shellmark(*f2));
}
// Return the information
sevent.e_type = 6;
sevent.f_marker1 = shellmark(*f1);
sevent.f_vertices1[0] = pointmark(pa);
sevent.f_vertices1[1] = pointmark(pb);
sevent.f_vertices1[2] = pointmark(pc);
sevent.f_marker2 = shellmark(*f2);
sevent.f_vertices2[0] = pointmark(pa);
sevent.f_vertices2[1] = pointmark(pb);
sevent.f_vertices2[2] = pointmark(pd);
terminatetetgen(this, 3);
}
///////////////////////////////////////////////////////////////////////////////
// //
// report_selfint_edge() Report a self-intersection at an edge. //
// //
// The edge 'e1'->'e2' and the tetrahedron 'itet' intersect. 'dir' indicates //
// that the edge intersects the tet at its origin vertex (ACROSSVERTEX), or //
// its current face (ACROSSFACE), or its current edge (ACROSSEDGE). //
// If 'iedge' is not NULL, it is either a segment or a subface that contains //
// the edge 'e1'->'e2'. It is used to report the geometry entity. //
// //
// Since it is a self-intersection, the vertex, edge or face of 'itet' that //
// is intersecting with this edge must be an input vertex, a segment, or a //
// subface, respectively. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::report_selfint_edge(point e1, point e2, face *iedge,
triface* itet, enum interresult dir)
{
point forg = NULL, fdest = NULL, fapex = NULL;
int etype = 0, geomtag = 0, facemark = 0;
if (iedge != NULL) {
if (iedge->sh[5] != NULL) {
etype = 2; // A subface
forg = e1;
fdest = e2;
fapex = sapex(*iedge);
facemark = shellmark(*iedge);
} else {
etype = 1; // A segment
forg = farsorg(*iedge);
fdest = farsdest(*iedge);
// Get a facet containing this segment.
face parentsh;
spivot(*iedge, parentsh);
if (parentsh.sh != NULL) {
facemark = shellmark(parentsh);
}
} geomtag = shellmark(*iedge);
}
if (dir == SHAREEDGE) {
// Two edges (segments) are coincide.
face colseg;
tsspivot1(*itet, colseg);
if (etype == 1) {
if (colseg.sh != iedge->sh) {
face parentsh;
spivot(colseg, parentsh);
printf("PLC Error: Two segments are overlapping.\n");
printf(" Segment 1: [%d, %d] #%d (%d)\n", pointmark(sorg(colseg)),
pointmark(sdest(colseg)), shellmark(colseg),
parentsh.sh ? shellmark(parentsh) : 0);
printf(" Segment 2: [%d, %d] #%d (%d)\n", pointmark(forg),
pointmark(fdest), geomtag, facemark);
sevent.e_type = 4;
sevent.f_marker1 = (parentsh.sh ? shellmark(parentsh) : 0);
sevent.s_marker1 = shellmark(colseg);
sevent.f_vertices1[0] = pointmark( sorg(colseg));
sevent.f_vertices1[1] = pointmark(sdest(colseg));
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = facemark;
sevent.s_marker2 = geomtag;
sevent.f_vertices2[0] = pointmark(forg);
sevent.f_vertices2[1] = pointmark(fdest);
sevent.f_vertices2[2] = 0;
} else {
// Two identical segments. Why report it?
terminatetetgen(this, 2);
}
} else if (etype == 2) {
printf("PLC Error: A segment lies in a facet.\n");
printf(" Segment: [%d, %d] #%d\n", pointmark(sorg(colseg)),
pointmark(sdest(colseg)), shellmark(colseg));
printf(" Facet: [%d,%d,%d] #%d\n", pointmark(forg),
pointmark(fdest), pointmark(fapex), geomtag);
sevent.e_type = 5;
sevent.f_marker1 = 0;
sevent.s_marker1 = shellmark(colseg);
sevent.f_vertices1[0] = pointmark( sorg(colseg));
sevent.f_vertices1[1] = pointmark(sdest(colseg));
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(forg);
sevent.f_vertices2[1] = pointmark(fdest);
sevent.f_vertices2[2] = pointmark(fapex);
}
} else if (dir == SHAREFACE) {
// Two triangles (subfaces) are coincide.
face colface;
tspivot(*itet, colface);
if (etype == 2) {
if (colface.sh != iedge->sh) {
printf("PLC Error: Two facets are overlapping.\n");
printf(" Facet 1: [%d,%d,%d] #%d\n", pointmark(forg),
pointmark(fdest), pointmark(fapex), geomtag);
printf(" Facet 2: [%d,%d,%d] #%d\n", pointmark(sorg(colface)),
pointmark(sdest(colface)), pointmark(sapex(colface)),
shellmark(colface));
sevent.e_type = 6;
sevent.f_marker1 = geomtag;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = pointmark(fapex);
sevent.f_marker2 = shellmark(colface);
sevent.s_marker2 = 0; sevent.f_vertices2[0] = pointmark(sorg(colface));
sevent.f_vertices2[1] = pointmark(sdest(colface));
sevent.f_vertices2[2] = pointmark(sapex(colface));
} else {
// Two identical subfaces. Why report it?
terminatetetgen(this, 2);
}
} else {
terminatetetgen(this, 2);
}
} else if (dir == ACROSSVERT) {
point pp = dest(*itet);
if ((pointtype(pp) == RIDGEVERTEX) || (pointtype(pp) == FACETVERTEX)
|| (pointtype(pp) == VOLVERTEX)) {
if (etype == 1) {
printf("PLC Error: A vertex lies in a segment.\n");
printf(" Vertex: [%d] (%g,%g,%g).\n",pointmark(pp),pp[0],pp[1],pp[2]);
printf(" Segment: [%d, %d] #%d (%d)\n", pointmark(forg),
pointmark(fdest), geomtag, facemark);
sevent.e_type = 7;
sevent.f_marker1 = 0;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(pp);
sevent.f_vertices1[1] = 0;
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = facemark;
sevent.s_marker2 = geomtag;
sevent.f_vertices2[0] = pointmark(forg);
sevent.f_vertices2[1] = pointmark(fdest);
sevent.f_vertices2[2] = 0;
sevent.int_point[0] = pp[0];
sevent.int_point[1] = pp[1];
sevent.int_point[2] = pp[2];
} else if (etype == 2) {
printf("PLC Error: A vertex lies in a facet.\n");
printf(" Vertex: [%d] (%g,%g,%g).\n",pointmark(pp),pp[0],pp[1],pp[2]);
printf(" Facet: [%d,%d,%d] #%d\n", pointmark(forg), pointmark(fdest),
pointmark(fapex), geomtag);
sevent.e_type = 8;
sevent.f_marker1 = 0;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(pp);
sevent.f_vertices1[1] = 0;
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(forg);
sevent.f_vertices2[1] = pointmark(fdest);
sevent.f_vertices2[2] = pointmark(fapex);
sevent.int_point[0] = pp[0];
sevent.int_point[1] = pp[1];
sevent.int_point[2] = pp[2];
}
} else if (pointtype(pp) == FREESEGVERTEX) {
face parentseg, parentsh;
sdecode(point2sh(pp), parentseg);
spivot(parentseg, parentsh);
if (parentseg.sh != NULL) {
point p1 = farsorg(parentseg);
point p2 = farsdest(parentseg);
if (etype == 1) {
printf("PLC Error: Two segments intersect at point (%g,%g,%g).\n",
pp[0], pp[1], pp[2]);
printf(" Segment 1: [%d, %d], #%d (%d)\n", pointmark(forg),
pointmark(fdest), geomtag, facemark);
printf(" Segment 2: [%d, %d], #%d (%d)\n", pointmark(p1),
pointmark(p2), shellmark(parentseg),
parentsh.sh ? shellmark(parentsh) : 0);
sevent.e_type = 1;
sevent.f_marker1 = facemark; sevent.s_marker1 = geomtag;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = (parentsh.sh ? shellmark(parentsh) : 0);
sevent.s_marker2 = shellmark(parentseg);
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = 0;
sevent.int_point[0] = pp[0];
sevent.int_point[1] = pp[1];
sevent.int_point[2] = pp[2];
} else if (etype == 2) {
printf("PLC Error: A segment and a facet intersect at point");
printf(" (%g,%g,%g).\n", pp[0], pp[1], pp[2]);
printf(" Segment: [%d, %d], #%d (%d)\n", pointmark(p1),
pointmark(p2), shellmark(parentseg),
parentsh.sh ? shellmark(parentsh) : 0);
printf(" Facet: [%d,%d,%d] #%d\n", pointmark(forg),
pointmark(fdest), pointmark(fapex), geomtag);
sevent.e_type = 2;
sevent.f_marker1 = (parentsh.sh ? shellmark(parentsh) : 0);
sevent.s_marker1 = shellmark(parentseg);
sevent.f_vertices1[0] = pointmark(p1);
sevent.f_vertices1[1] = pointmark(p2);
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(forg);
sevent.f_vertices2[1] = pointmark(fdest);
sevent.f_vertices2[2] = pointmark(fapex);
sevent.int_point[0] = pp[0];
sevent.int_point[1] = pp[1];
sevent.int_point[2] = pp[2];
}
} else {
terminatetetgen(this, 2); // Report a bug.
}
} else if (pointtype(pp) == FREEFACETVERTEX) {
face parentsh;
sdecode(point2sh(pp), parentsh);
if (parentsh.sh != NULL) {
point p1 = sorg(parentsh);
point p2 = sdest(parentsh);
point p3 = sapex(parentsh);
if (etype == 1) {
printf("PLC Error: A segment and a facet intersect at point");
printf(" (%g,%g,%g).\n", pp[0], pp[1], pp[2]);
printf(" Segment : [%d, %d], #%d (%d)\n", pointmark(forg),
pointmark(fdest), geomtag, facemark);
printf(" Facet : [%d, %d, %d] #%d.\n", pointmark(p1),
pointmark(p2), pointmark(p3), shellmark(parentsh));
sevent.e_type = 2;
sevent.f_marker1 = facemark;
sevent.s_marker1 = geomtag;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = shellmark(parentsh);
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = pp[0];
sevent.int_point[1] = pp[1];
sevent.int_point[2] = pp[2];
} else if (etype == 2) {
printf("PLC Error: Two facets intersect at point (%g,%g,%g).\n",
pp[0], pp[1], pp[2]);
printf(" Facet 1: [%d, %d, %d] #%d.\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag);
printf(" Facet 2: [%d, %d, %d] #%d.\n", pointmark(p1),
pointmark(p2), pointmark(p3), shellmark(parentsh));
sevent.e_type = 3;
sevent.f_marker1 = geomtag;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = pointmark(fapex);
sevent.f_marker2 = shellmark(parentsh);
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = pp[0];
sevent.int_point[1] = pp[1];
sevent.int_point[2] = pp[2];
}
} else {
terminatetetgen(this, 2); // Report a bug.
}
} else if (pointtype(pp) == FREEVOLVERTEX) {
// This is not a PLC error.
// We should shift the vertex.
// not down yet.
terminatetetgen(this, 2); // Report a bug.
} else {
terminatetetgen(this, 2); // Report a bug.
}
terminatetetgen(this, 3);
} else if (dir == ACROSSEDGE) {
if (issubseg(*itet)) {
face checkseg;
tsspivot1(*itet, checkseg);
face parentsh;
spivot(checkseg, parentsh);
// Calulcate the intersecting point.
point p1 = sorg(checkseg);
point p2 = sdest(checkseg);
REAL P[3], Q[3], tp = 0, tq = 0;
linelineint(e1, e2, p1, p2, P, Q, &tp, &tq);
if (etype == 1) {
printf("PLC Error: Two segments intersect at point (%g,%g,%g).\n",
P[0], P[1], P[2]);
printf(" Segment 1: [%d, %d] #%d (%d)\n", pointmark(forg),
pointmark(fdest), geomtag, facemark);
printf(" Segment 2: [%d, %d] #%d (%d)\n", pointmark(p1),
pointmark(p2), shellmark(checkseg),
parentsh.sh ? shellmark(parentsh) : 0);
sevent.e_type = 1;
sevent.f_marker1 = facemark;
sevent.s_marker1 = geomtag;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = (parentsh.sh ? shellmark(parentsh) : 0);
sevent.s_marker2 = shellmark(checkseg);
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = 0;
sevent.int_point[0] = P[0];
sevent.int_point[1] = P[1];
sevent.int_point[2] = P[2];
} else if (etype == 2) {
printf("PLC Error: A segment and a facet intersect at point");
printf(" (%g,%g,%g).\n", P[0], P[1], P[2]);
printf(" Segment: [%d, %d] #%d (%d)\n", pointmark(p1),
pointmark(p2), shellmark(checkseg),
parentsh.sh ? shellmark(parentsh) : 0);
printf(" Facet: [%d, %d, %d] #%d.\n", pointmark(forg), pointmark(fdest), pointmark(fapex), geomtag);
sevent.e_type = 2;
sevent.f_marker1 = (parentsh.sh ? shellmark(parentsh) : 0);
sevent.s_marker1 = shellmark(checkseg);
sevent.f_vertices1[0] = pointmark(p1);
sevent.f_vertices1[1] = pointmark(p2);
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(forg);
sevent.f_vertices2[1] = pointmark(fdest);
sevent.f_vertices2[2] = pointmark(fapex);
sevent.int_point[0] = P[0];
sevent.int_point[1] = P[1];
sevent.int_point[2] = P[2];
}
terminatetetgen(this, 3);
}
} else if (dir == ACROSSFACE) {
if (issubface(*itet)) {
face checksh;
tspivot(*itet, checksh);
point p1 = sorg(checksh);
point p2 = sdest(checksh);
point p3 = sapex(checksh);
REAL ip[3], u = 0;
planelineint(p1, p2, p3, e1, e2, ip, &u);
if (etype == 1) {
printf("PLC Error: A segment and a facet intersect at point");
printf(" (%g,%g,%g).\n", ip[0], ip[1], ip[2]);
printf(" Segment: [%d, %d] #%d (%d)\n", pointmark(forg),
pointmark(fdest), geomtag, facemark);
printf(" Facet: [%d, %d, %d] #%d.\n", pointmark(p1),
pointmark(p2), pointmark(p3), shellmark(checksh));
sevent.e_type = 2;
sevent.f_marker1 = facemark;
sevent.s_marker1 = geomtag;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = shellmark(checksh);
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = ip[0];
sevent.int_point[1] = ip[1];
sevent.int_point[2] = ip[2];
} else if (etype == 2) {
printf("PLC Error: Two facets intersect at point (%g,%g,%g).\n",
ip[0], ip[1], ip[2]);
printf(" Facet 1: [%d, %d, %d] #%d.\n", pointmark(forg),
pointmark(fdest), pointmark(fapex), geomtag);
printf(" Facet 2: [%d, %d, %d] #%d.\n", pointmark(p1),
pointmark(p2), pointmark(p3), shellmark(checksh));
sevent.e_type = 3;
sevent.f_marker1 = geomtag;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(forg);
sevent.f_vertices1[1] = pointmark(fdest);
sevent.f_vertices1[2] = pointmark(fapex);
sevent.f_marker2 = shellmark(checksh);
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = ip[0];
sevent.int_point[1] = ip[1];
sevent.int_point[2] = ip[2];
} terminatetetgen(this, 3);
}
} else {
// An unknown 'dir'.
terminatetetgen(this, 2);
}
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// report_selfint_face() Report a self-intersection at a facet. //
// //
// The triangle with vertices 'p1', 'p2', and 'p3' intersects with the edge //
// of the tetrahedra 'iedge'. The intersection type is reported by 'intflag',//
// 'types', and 'poss'. //
// //
// This routine ASSUMES (1) the triangle (p1,p2,p3) must belong to a facet, //
// 'sface' is a subface of the same facet; and (2) 'iedge' must be either a //
// segment or an edge of another facet. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::report_selfint_face(point p1, point p2, point p3, face* sface,
triface* iedge, int intflag, int* types, int* poss)
{
face iface;
point e1 = NULL, e2 = NULL, e3 = NULL;
int etype = 0, geomtag = 0, facemark = 0;
geomtag = shellmark(*sface);
if (issubface(*iedge)) {
tspivot(*iedge, iface);
e1 = sorg(iface);
e2 = sdest(iface);
e3 = sapex(iface);
etype = 2;
facemark = geomtag;
} else if (issubseg(*iedge)) {
tsspivot1(*iedge, iface);
e1 = farsorg(iface);
e2 = farsdest(iface);
etype = 1;
face parentsh;
spivot(iface, parentsh);
facemark = shellmark(parentsh);
} else {
terminatetetgen(this, 2);
}
if (intflag == 2) {
// The triangle and the edge intersect only at one point.
REAL ip[3], u = 0;
planelineint(p1, p2, p3, e1, e2, ip, &u);
if ((types[0] == (int) ACROSSFACE) ||
(types[0] == (int) ACROSSEDGE)) {
// The triangle and the edge intersect in their interiors.
if (etype == 1) {
printf("PLC Error: A segment and a facet intersect at point");
printf(" (%g,%g,%g).\n", ip[0], ip[1], ip[2]);
printf(" Segment: [%d,%d] #%d (%d)\n", pointmark(e1), pointmark(e2),
shellmark(iface), facemark);
printf(" Facet: [%d,%d,%d] #%d\n", pointmark(p1),
pointmark(p2), pointmark(p3), geomtag);
sevent.e_type = 2;
sevent.f_marker1 = facemark;
sevent.s_marker1 = shellmark(iface);
sevent.f_vertices1[0] = pointmark(e1);
sevent.f_vertices1[1] = pointmark(e2); sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = ip[0];
sevent.int_point[1] = ip[1];
sevent.int_point[2] = ip[2];
} else {
printf("PLC Error: Two facets intersect at point");
printf(" (%g,%g,%g).\n", ip[0], ip[1], ip[2]);
printf(" Facet 1: [%d,%d,%d] #%d\n", pointmark(e1), pointmark(e2),
pointmark(sorg(iface)), shellmark(iface));
printf(" Facet 2: [%d,%d,%d] #%d\n", pointmark(p1),
pointmark(p2), pointmark(p3), geomtag);
sevent.e_type = 3;
sevent.f_marker1 = shellmark(iface);
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(e1);
sevent.f_vertices1[1] = pointmark(e2);
sevent.f_vertices1[2] = pointmark(sorg(iface));
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = ip[0];
sevent.int_point[1] = ip[1];
sevent.int_point[2] = ip[2];
}
} else if (types[0] == (int) ACROSSVERT) {
// A vertex of the triangle and the edge intersect.
point crosspt = NULL;
if (poss[0] == 0) {
crosspt = p1;
} else if (poss[0] == 1) {
crosspt = p2;
} else if (poss[0] == 2) {
crosspt = p3;
} else {
terminatetetgen(this, 2);
}
if (!issteinerpoint(crosspt)) {
if (etype == 1) {
printf("PLC Error: A vertex and a segment intersect at (%g,%g,%g)\n",
crosspt[0], crosspt[1], crosspt[2]);
printf(" Vertex: #%d\n", pointmark(crosspt));
printf(" Segment: [%d,%d] #%d (%d)\n", pointmark(e1), pointmark(e2),
shellmark(iface), facemark);
sevent.e_type = 7;
sevent.f_marker1 = 0;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(crosspt);
sevent.f_vertices1[1] = 0;
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = facemark;
sevent.s_marker2 = shellmark(iface);
sevent.f_vertices2[0] = pointmark(e1);
sevent.f_vertices2[1] = pointmark(e2);
sevent.f_vertices2[2] = 0;
sevent.int_point[0] = crosspt[0];
sevent.int_point[1] = crosspt[1];
sevent.int_point[2] = crosspt[2];
} else {
printf("PLC Error: A vertex and a facet intersect at (%g,%g,%g)\n",
crosspt[0], crosspt[1], crosspt[2]);
printf(" Vertex: #%d\n", pointmark(crosspt));
printf(" Facet: [%d,%d,%d] #%d\n", pointmark(p1),
pointmark(p2), pointmark(p3), geomtag); sevent.e_type = 8;
sevent.f_marker1 = 0;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(crosspt);
sevent.f_vertices1[1] = 0;
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = crosspt[0];
sevent.int_point[1] = crosspt[1];
sevent.int_point[2] = crosspt[2];
}
} else {
// It is a Steiner point. To be processed.
terminatetetgen(this, 2);
}
} else if ((types[0] == (int) TOUCHFACE) ||
(types[0] == (int) TOUCHEDGE)) {
// The triangle and a vertex of the edge intersect.
point touchpt = NULL;
if (poss[1] == 0) {
touchpt = org(*iedge);
} else if (poss[1] == 1) {
touchpt = dest(*iedge);
} else {
terminatetetgen(this, 2);
}
if (!issteinerpoint(touchpt)) {
printf("PLC Error: A vertex and a facet intersect at (%g,%g,%g)\n",
touchpt[0], touchpt[1], touchpt[2]);
printf(" Vertex: #%d\n", pointmark(touchpt));
printf(" Facet: [%d,%d,%d] #%d\n", pointmark(p1),
pointmark(p2), pointmark(p3), geomtag);
sevent.e_type = 8;
sevent.f_marker1 = 0;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(touchpt);
sevent.f_vertices1[1] = 0;
sevent.f_vertices1[2] = 0;
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
sevent.int_point[0] = touchpt[0];
sevent.int_point[1] = touchpt[1];
sevent.int_point[2] = touchpt[2];
} else {
// It is a Steiner point. To be processed.
terminatetetgen(this, 2);
}
} else if (types[0] == (int) SHAREVERT) {
terminatetetgen(this, 2);
} else {
terminatetetgen(this, 2);
}
} else if (intflag == 4) {
if (types[0] == (int) SHAREFACE) {
printf("PLC Error: Two facets are overlapping.\n");
printf(" Facet 1: [%d,%d,%d] #%d\n", pointmark(e1),
pointmark(e2), pointmark(e3), facemark);
printf(" Facet 2: [%d,%d,%d] #%d\n", pointmark(p1),
pointmark(p2), pointmark(p3), geomtag);
sevent.e_type = 6;
sevent.f_marker1 = facemark;
sevent.s_marker1 = 0;
sevent.f_vertices1[0] = pointmark(e1); sevent.f_vertices1[1] = pointmark(e2);
sevent.f_vertices1[2] = pointmark(e3);
sevent.f_marker2 = geomtag;
sevent.s_marker2 = 0;
sevent.f_vertices2[0] = pointmark(p1);
sevent.f_vertices2[1] = pointmark(p2);
sevent.f_vertices2[2] = pointmark(p3);
} else {
terminatetetgen(this, 2);
}
} else {
terminatetetgen(this, 2);
}
terminatetetgen(this, 3);
return 0;
}
//// ////
//// ////
//// geom_cxx /////////////////////////////////////////////////////////////////
//// flip_cxx /////////////////////////////////////////////////////////////////
//// ////
//// ////
///////////////////////////////////////////////////////////////////////////////
// //
// flip23() Perform a 2-to-3 flip (face-to-edge flip). //
// //
// 'fliptets' is an array of three tets (handles), where the [0] and [1] are //
// [a,b,c,d] and [b,a,c,e]. The three new tets: [e,d,a,b], [e,d,b,c], and //
// [e,d,c,a] are returned in [0], [1], and [2] of 'fliptets'. As a result, //
// The face [a,b,c] is removed, and the edge [d,e] is created. //
// //
// If 'hullflag' > 0, hull tets may be involved in this flip, i.e., one of //
// the five vertices may be 'dummypoint'. There are two canonical cases: //
// (1) d is 'dummypoint', then all three new tets are hull tets. If e is //
// 'dummypoint', we reconfigure e to d, i.e., turn it up-side down. //
// (2) c is 'dummypoint', then two new tets: [e,d,b,c] and [e,d,c,a], are //
// hull tets. If a or b is 'dummypoint', we reconfigure it to c, i.e., //
// rotate the three input tets counterclockwisely (right-hand rule) //
// until a or b is in c's position. //
// //
// If 'fc->enqflag' is set, convex hull faces will be queued for flipping. //
// In particular, if 'fc->enqflag' is 1, it is called by incrementalflip() //
// after the insertion of a new point. It is assumed that 'd' is the new //
// point. IN this case, only link faces of 'd' are queued. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flip23(triface* fliptets, int hullflag, flipconstraints *fc)
{
triface topcastets[3], botcastets[3];
triface newface, casface;
point pa, pb, pc, pd, pe;
REAL attrib, volume;
int dummyflag = 0; // range = {-1, 0, 1, 2}.
int i;
if (hullflag > 0) {
// Check if e is dummypoint.
if (oppo(fliptets[1]) == dummypoint) {
// Swap the two old tets.
newface = fliptets[0];
fliptets[0] = fliptets[1];
fliptets[1] = newface;
dummyflag = -1; // d is dummypoint.
} else {
// Check if either a or b is dummypoint. if (org(fliptets[0]) == dummypoint) {
dummyflag = 1; // a is dummypoint.
enextself(fliptets[0]);
eprevself(fliptets[1]);
} else if (dest(fliptets[0]) == dummypoint) {
dummyflag = 2; // b is dummypoint.
eprevself(fliptets[0]);
enextself(fliptets[1]);
} else {
dummyflag = 0; // either c or d may be dummypoint.
}
}
}
pa = org(fliptets[0]);
pb = dest(fliptets[0]);
pc = apex(fliptets[0]);
pd = oppo(fliptets[0]);
pe = oppo(fliptets[1]);
flip23count++;
// Get the outer boundary faces.
for (i = 0; i < 3; i++) {
fnext(fliptets[0], topcastets[i]);
enextself(fliptets[0]);
}
for (i = 0; i < 3; i++) {
fnext(fliptets[1], botcastets[i]);
eprevself(fliptets[1]);
}
// Re-use fliptets[0] and fliptets[1].
fliptets[0].ver = 11;
fliptets[1].ver = 11;
setelemmarker(fliptets[0].tet, 0); // Clear all flags.
setelemmarker(fliptets[1].tet, 0);
// NOTE: the element attributes and volume constraint remain unchanged.
if (checksubsegflag) {
// Dealloc the space to subsegments.
if (fliptets[0].tet[8] != NULL) {
tet2segpool->dealloc((shellface *) fliptets[0].tet[8]);
fliptets[0].tet[8] = NULL;
}
if (fliptets[1].tet[8] != NULL) {
tet2segpool->dealloc((shellface *) fliptets[1].tet[8]);
fliptets[1].tet[8] = NULL;
}
}
if (checksubfaceflag) {
// Dealloc the space to subfaces.
if (fliptets[0].tet[9] != NULL) {
tet2subpool->dealloc((shellface *) fliptets[0].tet[9]);
fliptets[0].tet[9] = NULL;
}
if (fliptets[1].tet[9] != NULL) {
tet2subpool->dealloc((shellface *) fliptets[1].tet[9]);
fliptets[1].tet[9] = NULL;
}
}
// Create a new tet.
maketetrahedron(&(fliptets[2]));
// The new tet have the same attributes from the old tet.
for (i = 0; i < numelemattrib; i++) {
attrib = elemattribute(fliptets[0].tet, i);
setelemattribute(fliptets[2].tet, i, attrib);
}
if (b->varvolume) {
volume = volumebound(fliptets[0].tet);
setvolumebound(fliptets[2].tet, volume); }
if (hullflag > 0) {
// Check if d is dummytet.
if (pd != dummypoint) {
setvertices(fliptets[0], pe, pd, pa, pb); // [e,d,a,b] *
setvertices(fliptets[1], pe, pd, pb, pc); // [e,d,b,c] *
// Check if c is dummypoint.
if (pc != dummypoint) {
setvertices(fliptets[2], pe, pd, pc, pa); // [e,d,c,a] *
} else {
setvertices(fliptets[2], pd, pe, pa, pc); // [d,e,a,c]
esymself(fliptets[2]); // [e,d,c,a] *
}
// The hullsize does not change.
} else {
// d is dummypoint.
setvertices(fliptets[0], pa, pb, pe, pd); // [a,b,e,d]
setvertices(fliptets[1], pb, pc, pe, pd); // [b,c,e,d]
setvertices(fliptets[2], pc, pa, pe, pd); // [c,a,e,d]
// Adjust the faces to [e,d,a,b], [e,d,b,c], [e,d,c,a] *
for (i = 0; i < 3; i++) {
eprevesymself(fliptets[i]);
enextself(fliptets[i]);
}
// We deleted one hull tet, and created three hull tets.
hullsize += 2;
}
} else {
setvertices(fliptets[0], pe, pd, pa, pb); // [e,d,a,b] *
setvertices(fliptets[1], pe, pd, pb, pc); // [e,d,b,c] *
setvertices(fliptets[2], pe, pd, pc, pa); // [e,d,c,a] *
}
if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol
REAL volneg[2], volpos[3], vol_diff;
if (pd != dummypoint) {
if (pc != dummypoint) {
volpos[0] = tetprismvol(pe, pd, pa, pb);
volpos[1] = tetprismvol(pe, pd, pb, pc);
volpos[2] = tetprismvol(pe, pd, pc, pa);
volneg[0] = tetprismvol(pa, pb, pc, pd);
volneg[1] = tetprismvol(pb, pa, pc, pe);
} else { // pc == dummypoint
volpos[0] = tetprismvol(pe, pd, pa, pb);
volpos[1] = 0.;
volpos[2] = 0.;
volneg[0] = 0.;
volneg[1] = 0.;
}
} else { // pd == dummypoint.
volpos[0] = 0.;
volpos[1] = 0.;
volpos[2] = 0.;
volneg[0] = 0.;
volneg[1] = tetprismvol(pb, pa, pc, pe);
}
vol_diff = volpos[0] + volpos[1] + volpos[2] - volneg[0] - volneg[1];
fc->tetprism_vol_sum += vol_diff; // Update the total sum.
}
// Bond three new tets together.
for (i = 0; i < 3; i++) {
esym(fliptets[i], newface);
bond(newface, fliptets[(i + 1) % 3]);
}
// Bond to top outer boundary faces (at [a,b,c,d]).
for (i = 0; i < 3; i++) {
eorgoppo(fliptets[i], newface); // At edges [b,a], [c,b], [a,c].
bond(newface, topcastets[i]); }
// Bond bottom outer boundary faces (at [b,a,c,e]).
for (i = 0; i < 3; i++) {
edestoppo(fliptets[i], newface); // At edges [a,b], [b,c], [c,a].
bond(newface, botcastets[i]);
}
if (checksubsegflag) {
// Bond subsegments if there are.
// Each new tet has 5 edges to be checked (except the edge [e,d]).
face checkseg;
// The middle three: [a,b], [b,c], [c,a].
for (i = 0; i < 3; i++) {
if (issubseg(topcastets[i])) {
tsspivot1(topcastets[i], checkseg);
eorgoppo(fliptets[i], newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
}
// The top three: [d,a], [d,b], [d,c]. Two tets per edge.
for (i = 0; i < 3; i++) {
eprev(topcastets[i], casface);
if (issubseg(casface)) {
tsspivot1(casface, checkseg);
enext(fliptets[i], newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
esym(fliptets[(i + 2) % 3], newface);
eprevself(newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
}
// The bot three: [a,e], [b,e], [c,e]. Two tets per edge.
for (i = 0; i < 3; i++) {
enext(botcastets[i], casface);
if (issubseg(casface)) {
tsspivot1(casface, checkseg);
eprev(fliptets[i], newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
esym(fliptets[(i + 2) % 3], newface);
enextself(newface);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
}
} // if (checksubsegflag)
if (checksubfaceflag) {
// Bond 6 subfaces if there are.
face checksh;
for (i = 0; i < 3; i++) {
if (issubface(topcastets[i])) {
tspivot(topcastets[i], checksh);
eorgoppo(fliptets[i], newface);
sesymself(checksh);
tsbond(newface, checksh);
if (fc->chkencflag & 2) {
enqueuesubface(badsubfacs, &checksh); }
}
}
for (i = 0; i < 3; i++) {
if (issubface(botcastets[i])) {
tspivot(botcastets[i], checksh);
edestoppo(fliptets[i], newface);
sesymself(checksh);
tsbond(newface, checksh);
if (fc->chkencflag & 2) {
enqueuesubface(badsubfacs, &checksh);
}
}
}
} // if (checksubfaceflag)
if (fc->chkencflag & 4) {
// Put three new tets into check list.
for (i = 0; i < 3; i++) {
enqueuetetrahedron(&(fliptets[i]));
}
}
// Update the point-to-tet map.
setpoint2tet(pa, (tetrahedron) fliptets[0].tet);
setpoint2tet(pb, (tetrahedron) fliptets[0].tet);
setpoint2tet(pc, (tetrahedron) fliptets[1].tet);
setpoint2tet(pd, (tetrahedron) fliptets[0].tet);
setpoint2tet(pe, (tetrahedron) fliptets[0].tet);
if (hullflag > 0) {
if (dummyflag != 0) {
// Restore the original position of the points (for flipnm()).
if (dummyflag == -1) {
// Reverse the edge.
for (i = 0; i < 3; i++) {
esymself(fliptets[i]);
}
// Swap the last two new tets.
newface = fliptets[1];
fliptets[1] = fliptets[2];
fliptets[2] = newface;
} else {
// either a or b were swapped.
if (dummyflag == 1) {
// a is dummypoint.
newface = fliptets[0];
fliptets[0] = fliptets[2];
fliptets[2] = fliptets[1];
fliptets[1] = newface;
} else { // dummyflag == 2
// b is dummypoint.
newface = fliptets[0];
fliptets[0] = fliptets[1];
fliptets[1] = fliptets[2];
fliptets[2] = newface;
}
}
}
}
if (fc->enqflag > 0) {
// Queue faces which may be locally non-Delaunay.
for (i = 0; i < 3; i++) {
eprevesym(fliptets[i], newface);
flippush(flipstack, &newface);
}
if (fc->enqflag > 1) {
for (i = 0; i < 3; i++) {
enextesym(fliptets[i], newface); flippush(flipstack, &newface);
}
}
}
recenttet = fliptets[0];
}
///////////////////////////////////////////////////////////////////////////////
// //
// flip32() Perform a 3-to-2 flip (edge-to-face flip). //
// //
// 'fliptets' is an array of three tets (handles), which are [e,d,a,b], //
// [e,d,b,c], and [e,d,c,a]. The two new tets: [a,b,c,d] and [b,a,c,e] are //
// returned in [0] and [1] of 'fliptets'. As a result, the edge [e,d] is //
// replaced by the face [a,b,c]. //
// //
// If 'hullflag' > 0, hull tets may be involved in this flip, i.e., one of //
// the five vertices may be 'dummypoint'. There are two canonical cases: //
// (1) d is 'dummypoint', then [a,b,c,d] is hull tet. If e is 'dummypoint',//
// we reconfigure e to d, i.e., turnover it. //
// (2) c is 'dummypoint' then both [a,b,c,d] and [b,a,c,e] are hull tets. //
// If a or b is 'dummypoint', we reconfigure it to c, i.e., rotate the //
// three old tets counterclockwisely (right-hand rule) until a or b //
// is in c's position. //
// //
// If 'fc->enqflag' is set, convex hull faces will be queued for flipping. //
// In particular, if 'fc->enqflag' is 1, it is called by incrementalflip() //
// after the insertion of a new point. It is assumed that 'a' is the new //
// point. In this case, only link faces of 'a' are queued. //
// //
// If 'checksubfaceflag' is on (global variable), and assume [e,d] is not a //
// segment. There may be two (interior) subfaces sharing at [e,d], which are //
// [e,d,p] and [e,d,q], where the pair (p,q) may be either (a,b), or (b,c), //
// or (c,a) In such case, a 2-to-2 flip is performed on these two subfaces //
// and two new subfaces [p,q,e] and [p,q,d] are created. They are inserted //
// back into the tetrahedralization. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flip32(triface* fliptets, int hullflag, flipconstraints *fc)
{
triface topcastets[3], botcastets[3];
triface newface, casface;
face flipshs[3];
face checkseg;
point pa, pb, pc, pd, pe;
REAL attrib, volume;
int dummyflag = 0; // Rangle = {-1, 0, 1, 2}
int spivot = -1, scount = 0; // for flip22()
int t1ver;
int i, j;
if (hullflag > 0) {
// Check if e is 'dummypoint'.
if (org(fliptets[0]) == dummypoint) {
// Reverse the edge.
for (i = 0; i < 3; i++) {
esymself(fliptets[i]);
}
// Swap the last two tets.
newface = fliptets[1];
fliptets[1] = fliptets[2];
fliptets[2] = newface;
dummyflag = -1; // e is dummypoint.
} else {
// Check if a or b is the 'dummypoint'.
if (apex(fliptets[0]) == dummypoint) {
dummyflag = 1; // a is dummypoint.
newface = fliptets[0]; fliptets[0] = fliptets[1];
fliptets[1] = fliptets[2];
fliptets[2] = newface;
} else if (apex(fliptets[1]) == dummypoint) {
dummyflag = 2; // b is dummypoint.
newface = fliptets[0];
fliptets[0] = fliptets[2];
fliptets[2] = fliptets[1];
fliptets[1] = newface;
} else {
dummyflag = 0; // either c or d may be dummypoint.
}
}
}
pa = apex(fliptets[0]);
pb = apex(fliptets[1]);
pc = apex(fliptets[2]);
pd = dest(fliptets[0]);
pe = org(fliptets[0]);
flip32count++;
// Get the outer boundary faces.
for (i = 0; i < 3; i++) {
eorgoppo(fliptets[i], casface);
fsym(casface, topcastets[i]);
}
for (i = 0; i < 3; i++) {
edestoppo(fliptets[i], casface);
fsym(casface, botcastets[i]);
}
if (checksubfaceflag) {
// Check if there are interior subfaces at the edge [e,d].
for (i = 0; i < 3; i++) {
tspivot(fliptets[i], flipshs[i]);
if (flipshs[i].sh != NULL) {
// Found an interior subface.
stdissolve(flipshs[i]); // Disconnect the sub-tet bond.
scount++;
} else {
spivot = i;
}
}
}
// Re-use fliptets[0] and fliptets[1].
fliptets[0].ver = 11;
fliptets[1].ver = 11;
setelemmarker(fliptets[0].tet, 0); // Clear all flags.
setelemmarker(fliptets[1].tet, 0);
if (checksubsegflag) {
// Dealloc the space to subsegments.
if (fliptets[0].tet[8] != NULL) {
tet2segpool->dealloc((shellface *) fliptets[0].tet[8]);
fliptets[0].tet[8] = NULL;
}
if (fliptets[1].tet[8] != NULL) {
tet2segpool->dealloc((shellface *) fliptets[1].tet[8]);
fliptets[1].tet[8] = NULL;
}
}
if (checksubfaceflag) {
// Dealloc the space to subfaces.
if (fliptets[0].tet[9] != NULL) {
tet2subpool->dealloc((shellface *) fliptets[0].tet[9]);
fliptets[0].tet[9] = NULL;
}
if (fliptets[1].tet[9] != NULL) { tet2subpool->dealloc((shellface *) fliptets[1].tet[9]);
fliptets[1].tet[9] = NULL;
}
}
if (checksubfaceflag) {
if (scount > 0) {
// The element attributes and volume constraint must be set correctly.
// There are two subfaces involved in this flip. The three tets are
// separated into two different regions, one may be exterior. The
// first region has two tets, and the second region has only one.
// The two created tets must be in the same region as the first region.
// The element attributes and volume constraint must be set correctly.
//assert(spivot != -1);
// The tet fliptets[spivot] is in the first region.
for (j = 0; j < 2; j++) {
for (i = 0; i < numelemattrib; i++) {
attrib = elemattribute(fliptets[spivot].tet, i);
setelemattribute(fliptets[j].tet, i, attrib);
}
if (b->varvolume) {
volume = volumebound(fliptets[spivot].tet);
setvolumebound(fliptets[j].tet, volume);
}
}
}
}
// Delete an old tet.
tetrahedrondealloc(fliptets[2].tet);
if (hullflag > 0) {
// Check if c is dummypointc.
if (pc != dummypoint) {
// Check if d is dummypoint.
if (pd != dummypoint) {
// No hull tet is involved.
} else {
// We deleted three hull tets, and created one hull tet.
hullsize -= 2;
}
setvertices(fliptets[0], pa, pb, pc, pd);
setvertices(fliptets[1], pb, pa, pc, pe);
} else {
// c is dummypoint. The two new tets are hull tets.
setvertices(fliptets[0], pb, pa, pd, pc);
setvertices(fliptets[1], pa, pb, pe, pc);
// Adjust badc -> abcd.
esymself(fliptets[0]);
// Adjust abec -> bace.
esymself(fliptets[1]);
// The hullsize does not change.
}
} else {
setvertices(fliptets[0], pa, pb, pc, pd);
setvertices(fliptets[1], pb, pa, pc, pe);
}
if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol
REAL volneg[3], volpos[2], vol_diff;
if (pc != dummypoint) {
if (pd != dummypoint) {
volneg[0] = tetprismvol(pe, pd, pa, pb);
volneg[1] = tetprismvol(pe, pd, pb, pc);
volneg[2] = tetprismvol(pe, pd, pc, pa);
volpos[0] = tetprismvol(pa, pb, pc, pd);
volpos[1] = tetprismvol(pb, pa, pc, pe);
} else { // pd == dummypoint
volneg[0] = 0.;
volneg[1] = 0.;
volneg[2] = 0.;
volpos[0] = 0.; volpos[1] = tetprismvol(pb, pa, pc, pe);
}
} else { // pc == dummypoint.
volneg[0] = tetprismvol(pe, pd, pa, pb);
volneg[1] = 0.;
volneg[2] = 0.;
volpos[0] = 0.;
volpos[1] = 0.;
}
vol_diff = volpos[0] + volpos[1] - volneg[0] - volneg[1] - volneg[2];
fc->tetprism_vol_sum += vol_diff; // Update the total sum.
}
// Bond abcd <==> bace.
bond(fliptets[0], fliptets[1]);
// Bond new faces to top outer boundary faces (at abcd).
for (i = 0; i < 3; i++) {
esym(fliptets[0], newface);
bond(newface, topcastets[i]);
enextself(fliptets[0]);
}
// Bond new faces to bottom outer boundary faces (at bace).
for (i = 0; i < 3; i++) {
esym(fliptets[1], newface);
bond(newface, botcastets[i]);
eprevself(fliptets[1]);
}
if (checksubsegflag) {
// Bond 9 segments to new (flipped) tets.
for (i = 0; i < 3; i++) { // edges a->b, b->c, c->a.
if (issubseg(topcastets[i])) {
tsspivot1(topcastets[i], checkseg);
tssbond1(fliptets[0], checkseg);
sstbond1(checkseg, fliptets[0]);
tssbond1(fliptets[1], checkseg);
sstbond1(checkseg, fliptets[1]);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
eprevself(fliptets[1]);
}
// The three top edges.
for (i = 0; i < 3; i++) { // edges b->d, c->d, a->d.
esym(fliptets[0], newface);
eprevself(newface);
enext(topcastets[i], casface);
if (issubseg(casface)) {
tsspivot1(casface, checkseg);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
}
// The three bot edges.
for (i = 0; i < 3; i++) { // edges b<-e, c<-e, a<-e.
esym(fliptets[1], newface);
enextself(newface);
eprev(botcastets[i], casface);
if (issubseg(casface)) {
tsspivot1(casface, checkseg);
tssbond1(newface, checkseg);
sstbond1(checkseg, newface);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg); }
}
eprevself(fliptets[1]);
}
} // if (checksubsegflag)
if (checksubfaceflag) {
face checksh;
// Bond the top three casing subfaces.
for (i = 0; i < 3; i++) { // At edges [b,a], [c,b], [a,c]
if (issubface(topcastets[i])) {
tspivot(topcastets[i], checksh);
esym(fliptets[0], newface);
sesymself(checksh);
tsbond(newface, checksh);
if (fc->chkencflag & 2) {
enqueuesubface(badsubfacs, &checksh);
}
}
enextself(fliptets[0]);
}
// Bond the bottom three casing subfaces.
for (i = 0; i < 3; i++) { // At edges [a,b], [b,c], [c,a]
if (issubface(botcastets[i])) {
tspivot(botcastets[i], checksh);
esym(fliptets[1], newface);
sesymself(checksh);
tsbond(newface, checksh);
if (fc->chkencflag & 2) {
enqueuesubface(badsubfacs, &checksh);
}
}
eprevself(fliptets[1]);
}
if (scount > 0) {
face flipfaces[2];
// Perform a 2-to-2 flip in subfaces.
flipfaces[0] = flipshs[(spivot + 1) % 3];
flipfaces[1] = flipshs[(spivot + 2) % 3];
sesymself(flipfaces[1]);
flip22(flipfaces, 0, fc->chkencflag);
// Connect the flipped subfaces to flipped tets.
// First go to the corresponding flipping edge.
// Re-use top- and botcastets[0].
topcastets[0] = fliptets[0];
botcastets[0] = fliptets[1];
for (i = 0; i < ((spivot + 1) % 3); i++) {
enextself(topcastets[0]);
eprevself(botcastets[0]);
}
// Connect the top subface to the top tets.
esymself(topcastets[0]);
sesymself(flipfaces[0]);
// Check if there already exists a subface.
tspivot(topcastets[0], checksh);
if (checksh.sh == NULL) {
tsbond(topcastets[0], flipfaces[0]);
fsymself(topcastets[0]);
sesymself(flipfaces[0]);
tsbond(topcastets[0], flipfaces[0]);
} else {
// An invalid 2-to-2 flip. Report a bug.
terminatetetgen(this, 2);
}
// Connect the bot subface to the bottom tets.
esymself(botcastets[0]);
sesymself(flipfaces[1]);
// Check if there already exists a subface.
tspivot(botcastets[0], checksh); if (checksh.sh == NULL) {
tsbond(botcastets[0], flipfaces[1]);
fsymself(botcastets[0]);
sesymself(flipfaces[1]);
tsbond(botcastets[0], flipfaces[1]);
} else {
// An invalid 2-to-2 flip. Report a bug.
terminatetetgen(this, 2);
}
} // if (scount > 0)
} // if (checksubfaceflag)
if (fc->chkencflag & 4) {
// Put two new tets into check list.
for (i = 0; i < 2; i++) {
enqueuetetrahedron(&(fliptets[i]));
}
}
setpoint2tet(pa, (tetrahedron) fliptets[0].tet);
setpoint2tet(pb, (tetrahedron) fliptets[0].tet);
setpoint2tet(pc, (tetrahedron) fliptets[0].tet);
setpoint2tet(pd, (tetrahedron) fliptets[0].tet);
setpoint2tet(pe, (tetrahedron) fliptets[1].tet);
if (hullflag > 0) {
if (dummyflag != 0) {
// Restore the original position of the points (for flipnm()).
if (dummyflag == -1) {
// e were dummypoint. Swap the two new tets.
newface = fliptets[0];
fliptets[0] = fliptets[1];
fliptets[1] = newface;
} else {
// a or b was dummypoint.
if (dummyflag == 1) {
eprevself(fliptets[0]);
enextself(fliptets[1]);
} else { // dummyflag == 2
enextself(fliptets[0]);
eprevself(fliptets[1]);
}
}
}
}
if (fc->enqflag > 0) {
// Queue faces which may be locally non-Delaunay.
// pa = org(fliptets[0]); // 'a' may be a new vertex.
enextesym(fliptets[0], newface);
flippush(flipstack, &newface);
eprevesym(fliptets[1], newface);
flippush(flipstack, &newface);
if (fc->enqflag > 1) {
//pb = dest(fliptets[0]);
eprevesym(fliptets[0], newface);
flippush(flipstack, &newface);
enextesym(fliptets[1], newface);
flippush(flipstack, &newface);
//pc = apex(fliptets[0]);
esym(fliptets[0], newface);
flippush(flipstack, &newface);
esym(fliptets[1], newface);
flippush(flipstack, &newface);
}
}
recenttet = fliptets[0];
}
///////////////////////////////////////////////////////////////////////////////
// //
// flip41() Perform a 4-to-1 flip (Remove a vertex). //
// //
// 'fliptets' is an array of four tetrahedra in the star of the removing //
// vertex 'p'. Let the four vertices in the star of p be a, b, c, and d. The //
// four tets in 'fliptets' are: [p,d,a,b], [p,d,b,c], [p,d,c,a], and [a,b,c, //
// p]. On return, 'fliptets[0]' is the new tet [a,b,c,d]. //
// //
// If 'hullflag' is set (> 0), one of the five vertices may be 'dummypoint'. //
// The 'hullsize' may be changed. Note that p may be dummypoint. In this //
// case, four hull tets are replaced by one real tet. //
// //
// If 'checksubface' flag is set (>0), it is possible that there are three //
// interior subfaces connecting at p. If so, a 3-to-1 flip is performed to //
// to remove p from the surface triangulation. //
// //
// If it is called by the routine incrementalflip(), we assume that d is the //
// newly inserted vertex. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flip41(triface* fliptets, int hullflag, flipconstraints *fc)
{
triface topcastets[3], botcastet;
triface newface, neightet;
face flipshs[4];
point pa, pb, pc, pd, pp;
int dummyflag = 0; // in {0, 1, 2, 3, 4}
int spivot = -1, scount = 0;
int t1ver;
int i;
pa = org(fliptets[3]);
pb = dest(fliptets[3]);
pc = apex(fliptets[3]);
pd = dest(fliptets[0]);
pp = org(fliptets[0]); // The removing vertex.
flip41count++;
// Get the outer boundary faces.
for (i = 0; i < 3; i++) {
enext(fliptets[i], topcastets[i]);
fnextself(topcastets[i]); // [d,a,b,#], [d,b,c,#], [d,c,a,#]
enextself(topcastets[i]); // [a,b,d,#], [b,c,d,#], [c,a,d,#]
}
fsym(fliptets[3], botcastet); // [b,a,c,#]
if (checksubfaceflag) {
// Check if there are three subfaces at 'p'.
// Re-use 'newface'.
for (i = 0; i < 3; i++) {
fnext(fliptets[3], newface); // [a,b,p,d],[b,c,p,d],[c,a,p,d].
tspivot(newface, flipshs[i]);
if (flipshs[i].sh != NULL) {
spivot = i; // Remember this subface.
scount++;
}
enextself(fliptets[3]);
}
if (scount > 0) {
// There are three subfaces connecting at p.
if (scount < 3) {
// The new subface is one of {[a,b,d], [b,c,d], [c,a,d]}.
// Go to the tet containing the three subfaces.
fsym(topcastets[spivot], neightet);
// Get the three subfaces connecting at p.
for (i = 0; i < 3; i++) {
esym(neightet, newface); tspivot(newface, flipshs[i]);
eprevself(neightet);
}
} else {
spivot = 3; // The new subface is [a,b,c].
}
}
} // if (checksubfaceflag)
// Re-use fliptets[0] for [a,b,c,d].
fliptets[0].ver = 11;
setelemmarker(fliptets[0].tet, 0); // Clean all flags.
// NOTE: the element attributes and volume constraint remain unchanged.
if (checksubsegflag) {
// Dealloc the space to subsegments.
if (fliptets[0].tet[8] != NULL) {
tet2segpool->dealloc((shellface *) fliptets[0].tet[8]);
fliptets[0].tet[8] = NULL;
}
}
if (checksubfaceflag) {
// Dealloc the space to subfaces.
if (fliptets[0].tet[9] != NULL) {
tet2subpool->dealloc((shellface *) fliptets[0].tet[9]);
fliptets[0].tet[9] = NULL;
}
}
// Delete the other three tets.
for (i = 1; i < 4; i++) {
tetrahedrondealloc(fliptets[i].tet);
}
if (pp != dummypoint) {
// Mark the point pp as unused.
setpointtype(pp, UNUSEDVERTEX);
unuverts++;
}
// Create the new tet [a,b,c,d].
if (hullflag > 0) {
// One of the five vertices may be 'dummypoint'.
if (pa == dummypoint) {
// pa is dummypoint.
setvertices(fliptets[0], pc, pb, pd, pa);
esymself(fliptets[0]); // [b,c,a,d]
eprevself(fliptets[0]); // [a,b,c,d]
dummyflag = 1;
} else if (pb == dummypoint) {
setvertices(fliptets[0], pa, pc, pd, pb);
esymself(fliptets[0]); // [c,a,b,d]
enextself(fliptets[0]); // [a,b,c,d]
dummyflag = 2;
} else if (pc == dummypoint) {
setvertices(fliptets[0], pb, pa, pd, pc);
esymself(fliptets[0]); // [a,b,c,d]
dummyflag = 3;
} else if (pd == dummypoint) {
setvertices(fliptets[0], pa, pb, pc, pd);
dummyflag = 4;
} else {
setvertices(fliptets[0], pa, pb, pc, pd);
if (pp == dummypoint) {
dummyflag = -1;
} else {
dummyflag = 0;
}
}
if (dummyflag > 0) {
// We deleted 3 hull tets, and create 1 hull tet. hullsize -= 2;
} else if (dummyflag < 0) {
// We deleted 4 hull tets.
hullsize -= 4;
// meshedges does not change.
}
} else {
setvertices(fliptets[0], pa, pb, pc, pd);
}
if (fc->remove_ndelaunay_edge) { // calc_tetprism_vol
REAL volneg[4], volpos[1], vol_diff;
if (dummyflag > 0) {
if (pa == dummypoint) {
volneg[0] = 0.;
volneg[1] = tetprismvol(pp, pd, pb, pc);
volneg[2] = 0.;
volneg[3] = 0.;
} else if (pb == dummypoint) {
volneg[0] = 0.;
volneg[1] = 0.;
volneg[2] = tetprismvol(pp, pd, pc, pa);
volneg[3] = 0.;
} else if (pc == dummypoint) {
volneg[0] = tetprismvol(pp, pd, pa, pb);
volneg[1] = 0.;
volneg[2] = 0.;
volneg[3] = 0.;
} else { // pd == dummypoint
volneg[0] = 0.;
volneg[1] = 0.;
volneg[2] = 0.;
volneg[3] = tetprismvol(pa, pb, pc, pp);
}
volpos[0] = 0.;
} else if (dummyflag < 0) {
volneg[0] = 0.;
volneg[1] = 0.;
volneg[2] = 0.;
volneg[3] = 0.;
volpos[0] = tetprismvol(pa, pb, pc, pd);
} else {
volneg[0] = tetprismvol(pp, pd, pa, pb);
volneg[1] = tetprismvol(pp, pd, pb, pc);
volneg[2] = tetprismvol(pp, pd, pc, pa);
volneg[3] = tetprismvol(pa, pb, pc, pp);
volpos[0] = tetprismvol(pa, pb, pc, pd);
}
vol_diff = volpos[0] - volneg[0] - volneg[1] - volneg[2] - volneg[3];
fc->tetprism_vol_sum += vol_diff; // Update the total sum.
}
// Bond the new tet to adjacent tets.
for (i = 0; i < 3; i++) {
esym(fliptets[0], newface); // At faces [b,a,d], [c,b,d], [a,c,d].
bond(newface, topcastets[i]);
enextself(fliptets[0]);
}
bond(fliptets[0], botcastet);
if (checksubsegflag) {
face checkseg;
// Bond 6 segments (at edges of [a,b,c,d]) if there there are.
for (i = 0; i < 3; i++) {
eprev(topcastets[i], newface); // At edges [d,a],[d,b],[d,c].
if (issubseg(newface)) {
tsspivot1(newface, checkseg);
esym(fliptets[0], newface);
enextself(newface); // At edges [a,d], [b,d], [c,d].
tssbond1(newface, checkseg); sstbond1(checkseg, newface);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
}
for (i = 0; i < 3; i++) {
if (issubseg(topcastets[i])) {
tsspivot1(topcastets[i], checkseg); // At edges [a,b],[b,c],[c,a].
tssbond1(fliptets[0], checkseg);
sstbond1(checkseg, fliptets[0]);
if (fc->chkencflag & 1) {
enqueuesubface(badsubsegs, &checkseg);
}
}
enextself(fliptets[0]);
}
}
if (checksubfaceflag) {
face checksh;
// Bond 4 subfaces (at faces of [a,b,c,d]) if there are.
for (i = 0; i < 3; i++) {
if (issubface(topcastets[i])) {
tspivot(topcastets[i], checksh); // At faces [a,b,d],[b,c,d],[c,a,d]
esym(fliptets[0], newface); // At faces [b,a,d],[c,b,d],[a,c,d]
sesymself(checksh);
tsbond(newface, checksh);
if (fc->chkencflag & 2) {
enqueuesubface(badsubfacs, &checksh);
}
}
enextself(fliptets[0]);
}
if (issubface(botcastet)) {
tspivot(botcastet, checksh); // At face [b,a,c]
sesymself(checksh);
tsbond(fliptets[0], checksh);
if (fc->chkencflag & 2) {
enqueuesubface(badsubfacs, &checksh);
}
}
if (spivot >= 0) {
// Perform a 3-to-1 flip in surface triangulation.
// Depending on the value of 'spivot', the three subfaces are:
// - 0: [a,b,p], [b,d,p], [d,a,p]
// - 1: [b,c,p], [c,d,p], [d,b,p]
// - 2: [c,a,p], [a,d,p], [d,c,p]
// - 3: [a,b,p], [b,c,p], [c,a,p]
// Adjust the three subfaces such that their origins are p, i.e.,
// - 3: [p,a,b], [p,b,c], [p,c,a]. (Required by the flip31()).
for (i = 0; i < 3; i++) {
senext2self(flipshs[i]);
}
flip31(flipshs, 0);
// Delete the three old subfaces.
for (i = 0; i < 3; i++) {
shellfacedealloc(subfaces, flipshs[i].sh);
}
if (spivot < 3) {
// // Bond the new subface to the new tet [a,b,c,d].
tsbond(topcastets[spivot], flipshs[3]);
fsym(topcastets[spivot], newface);
sesym(flipshs[3], checksh);
tsbond(newface, checksh);
} else {
// Bound the new subface [a,b,c] to the new tet [a,b,c,d].
tsbond(fliptets[0], flipshs[3]); fsym(fliptets[0], newface);
sesym(flipshs[3], checksh);
tsbond(newface, checksh);
}
} // if (spivot > 0)
} // if (checksubfaceflag)
if (fc->chkencflag & 4) {
enqueuetetrahedron(&(fliptets[0]));
}
// Update the point-to-tet map.
setpoint2tet(pa, (tetrahedron) fliptets[0].tet);
setpoint2tet(pb, (tetrahedron) fliptets[0].tet);
setpoint2tet(pc, (tetrahedron) fliptets[0].tet);
setpoint2tet(pd, (tetrahedron) fliptets[0].tet);
if (fc->enqflag > 0) {
// Queue faces which may be locally non-Delaunay.
flippush(flipstack, &(fliptets[0])); // [a,b,c] (opposite to new point).
if (fc->enqflag > 1) {
for (i = 0; i < 3; i++) {
esym(fliptets[0], newface);
flippush(flipstack, &newface);
enextself(fliptets[0]);
}
}
}
recenttet = fliptets[0];
}
///////////////////////////////////////////////////////////////////////////////
// //
// flipnm() Flip an edge through a sequence of elementary flips. //
// //
// 'abtets' is an array of 'n' tets in the star of edge [a,b].These tets are //
// ordered in a counterclockwise cycle with respect to the vector a->b, i.e.,//
// use the right-hand rule. //
// //
// 'level' (>= 0) indicates the current link level. If 'level > 0', we are //
// flipping a link edge of an edge [a',b'], and 'abedgepivot' indicates //
// which link edge, i.e., [c',b'] or [a',c'], is [a,b] These two parameters //
// allow us to determine the new tets after a 3-to-2 flip, i.e., tets that //
// do not inside the reduced star of edge [a',b']. //
// //
// If the flag 'fc->unflip' is set, this routine un-does the flips performed //
// in flipnm([a,b]) so that the mesh is returned to its original state //
// before doing the flipnm([a,b]) operation. //
// //
// The return value is an integer nn, where nn <= n. If nn is 2, then the //
// edge is flipped. The first and the second tets in 'abtets' are new tets. //
// Otherwise, nn > 2, the edge is not flipped, and nn is the number of tets //
// in the current star of [a,b]. //
// //
// ASSUMPTIONS: //
// - Neither a nor b is 'dummypoint'. //
// - [a,b] must not be a segment. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::flipnm(triface* abtets, int n, int level, int abedgepivot,
flipconstraints* fc)
{
triface fliptets[3], spintet, flipedge;
triface *tmpabtets, *parytet;
point pa, pb, pc, pd, pe, pf;
REAL ori;
int hullflag, hulledgeflag;
int reducflag, rejflag; int reflexlinkedgecount;
int edgepivot;
int n1, nn;
int t1ver;
int i, j;
pa = org(abtets[0]);
pb = dest(abtets[0]);
if (n > 3) {
// Try to reduce the size of the Star(ab) by flipping a face in it.
reflexlinkedgecount = 0;
for (i = 0; i < n; i++) {
// Let the face of 'abtets[i]' be [a,b,c].
if (checksubfaceflag) {
if (issubface(abtets[i])) {
continue; // Skip a subface.
}
}
// Do not flip this face if it is involved in two Stars.
if ((elemcounter(abtets[i]) > 1) ||
(elemcounter(abtets[(i - 1 + n) % n]) > 1)) {
continue;
}
pc = apex(abtets[i]);
pd = apex(abtets[(i + 1) % n]);
pe = apex(abtets[(i - 1 + n) % n]);
if ((pd == dummypoint) || (pe == dummypoint)) {
continue; // [a,b,c] is a hull face.
}
// Decide whether [a,b,c] is flippable or not.
reducflag = 0;
hullflag = (pc == dummypoint); // pc may be dummypoint.
hulledgeflag = 0;
if (hullflag == 0) {
ori = orient3d(pb, pc, pd, pe); // Is [b,c] locally convex?
if (ori > 0) {
ori = orient3d(pc, pa, pd, pe); // Is [c,a] locally convex?
if (ori > 0) {
// Test if [a,b] is locally convex OR flat.
ori = orient3d(pa, pb, pd, pe);
if (ori > 0) {
// Found a 2-to-3 flip: [a,b,c] => [e,d]
reducflag = 1;
} else if (ori == 0) {
// [a,b] is flat.
if (n == 4) {
// The "flat" tet can be removed immediately by a 3-to-2 flip.
reducflag = 1;
// Check if [e,d] is a hull edge.
pf = apex(abtets[(i + 2) % n]);
hulledgeflag = (pf == dummypoint);
}
}
}
}
if (!reducflag) {
reflexlinkedgecount++;
}
} else {
// 'c' is dummypoint.
if (n == 4) {
// Let the vertex opposite to 'c' is 'f'.
// A 4-to-4 flip is possible if the two tets [d,e,f,a] and [e,d,f,b]
// are valid tets. // Note: When the mesh is not convex, it is possible that [a,b] is
// locally non-convex (at hull faces [a,b,e] and [b,a,d]).
// In this case, an edge flip [a,b] to [e,d] is still possible.
pf = apex(abtets[(i + 2) % n]);
ori = orient3d(pd, pe, pf, pa);
if (ori < 0) {
ori = orient3d(pe, pd, pf, pb);
if (ori < 0) {
// Found a 4-to-4 flip: [a,b] => [e,d]
reducflag = 1;
ori = 0; // Signal as a 4-to-4 flip (like a co-planar case).
hulledgeflag = 1; // [e,d] is a hull edge.
}
}
}
} // if (hullflag)
if (reducflag) {
if (nonconvex && hulledgeflag) {
// We will create a hull edge [e,d]. Make sure it does not exist.
if (getedge(pe, pd, &spintet)) {
// The 2-to-3 flip is not a topological valid flip.
reducflag = 0;
}
}
}
if (reducflag) {
// [a,b,c] could be removed by a 2-to-3 flip.
rejflag = 0;
if (fc->checkflipeligibility) {
// Check if the flip can be performed.
rejflag = checkflipeligibility(1, pa, pb, pc, pd, pe, level,
abedgepivot, fc);
}
if (!rejflag) {
// Do flip: [a,b,c] => [e,d].
fliptets[0] = abtets[i];
fsym(fliptets[0], fliptets[1]); // abtets[i-1].
flip23(fliptets, hullflag, fc);
// Shrink the array 'abtets', maintain the original order.
// Two tets 'abtets[i-1] ([a,b,e,c])' and 'abtets[i] ([a,b,c,d])'
// are flipped, i.e., they do not in Star(ab) anymore.
// 'fliptets[0]' ([e,d,a,b]) is in Star(ab), it is saved in
// 'abtets[i-1]' (adjust it to be [a,b,e,d]), see below:
//
// before after
// [0] |___________| [0] |___________|
// ... |___________| ... |___________|
// [i-1] |_[a,b,e,c]_| [i-1] |_[a,b,e,d]_|
// [i] |_[a,b,c,d]_| --> [i] |_[a,b,d,#]_|
// [i+1] |_[a,b,d,#]_| [i+1] |_[a,b,#,*]_|
// ... |___________| ... |___________|
// [n-2] |___________| [n-2] |___________|
// [n-1] |___________| [n-1] |_[i]_2-t-3_|
//
edestoppoself(fliptets[0]); // [a,b,e,d]
// Increase the counter of this new tet (it is in Star(ab)).
increaseelemcounter(fliptets[0]);
abtets[(i - 1 + n) % n] = fliptets[0];
for (j = i; j < n - 1; j++) {
abtets[j] = abtets[j + 1]; // Upshift
}
// The last entry 'abtets[n-1]' is empty. It is used in two ways:
// (i) it remembers the vertex 'c' (in 'abtets[n-1].tet'), and
// (ii) it remembers the position [i] where this flip took place.
// These information let us to either undo this flip or recover
// the original edge link (for collecting new created tets).
abtets[n - 1].tet = (tetrahedron *) pc; abtets[n - 1].ver = 0; // Clear it.
// 'abtets[n - 1].ver' is in range [0,11] -- only uses 4 bits.
// Use the 5th bit in 'abtets[n - 1].ver' to signal a 2-to-3 flip.
abtets[n - 1].ver |= (1 << 4);
// The poisition [i] of this flip is saved above the 7th bit.
abtets[n - 1].ver |= (i << 6);
if (fc->collectnewtets) {
// Push the two new tets [e,d,b,c] and [e,d,c,a] into a stack.
// Re-use the global array 'cavetetlist'.
for (j = 1; j < 3; j++) {
cavetetlist->newindex((void **) &parytet);
*parytet = fliptets[j]; // fliptets[1], fliptets[2].
}
}
// Star(ab) is reduced. Try to flip the edge [a,b].
nn = flipnm(abtets, n - 1, level, abedgepivot, fc);
if (nn == 2) {
// The edge has been flipped.
return nn;
} else { // if (nn > 2)
// The edge is not flipped.
if (fc->unflip || (ori == 0)) {
// Undo the previous 2-to-3 flip, i.e., do a 3-to-2 flip to
// transform [e,d] => [a,b,c].
// 'ori == 0' means that the previous flip created a degenerated
// tet. It must be removed.
// Remember that 'abtets[i-1]' is [a,b,e,d]. We can use it to
// find another two tets [e,d,b,c] and [e,d,c,a].
fliptets[0] = abtets[(i-1 + (n-1)) % (n-1)]; // [a,b,e,d]
edestoppoself(fliptets[0]); // [e,d,a,b]
fnext(fliptets[0], fliptets[1]); // [1] is [e,d,b,c]
fnext(fliptets[1], fliptets[2]); // [2] is [e,d,c,a]
// Restore the two original tets in Star(ab).
flip32(fliptets, hullflag, fc);
// Marktest the two restored tets in Star(ab).
for (j = 0; j < 2; j++) {
increaseelemcounter(fliptets[j]);
}
// Expand the array 'abtets', maintain the original order.
for (j = n - 2; j>= i; j--) {
abtets[j + 1] = abtets[j]; // Downshift
}
// Insert the two new tets 'fliptets[0]' [a,b,c,d] and
// 'fliptets[1]' [b,a,c,e] into the (i-1)-th and i-th entries,
// respectively.
esym(fliptets[1], abtets[(i - 1 + n) % n]); // [a,b,e,c]
abtets[i] = fliptets[0]; // [a,b,c,d]
nn++;
if (fc->collectnewtets) {
// Pop two (flipped) tets from the stack.
cavetetlist->objects -= 2;
}
} // if (unflip || (ori == 0))
} // if (nn > 2)
if (!fc->unflip) {
// The flips are not reversed. The current Star(ab) can not be
// further reduced. Return its current size (# of tets).
return nn;
}
// unflip is set.
// Continue the search for flips.
}
} // if (reducflag)
} // i
// The Star(ab) is not reduced. if (reflexlinkedgecount > 0) {
// There are reflex edges in the Link(ab).
if (((b->fliplinklevel < 0) && (level < autofliplinklevel)) ||
((b->fliplinklevel >= 0) && (level < b->fliplinklevel))) {
// Try to reduce the Star(ab) by flipping a reflex edge in Link(ab).
for (i = 0; i < n; i++) {
// Do not flip this face [a,b,c] if there are two Stars involved.
if ((elemcounter(abtets[i]) > 1) ||
(elemcounter(abtets[(i - 1 + n) % n]) > 1)) {
continue;
}
pc = apex(abtets[i]);
if (pc == dummypoint) {
continue; // [a,b] is a hull edge.
}
pd = apex(abtets[(i + 1) % n]);
pe = apex(abtets[(i - 1 + n) % n]);
if ((pd == dummypoint) || (pe == dummypoint)) {
continue; // [a,b,c] is a hull face.
}
edgepivot = 0; // No edge is selected yet.
// Test if [b,c] is locally convex or flat.
ori = orient3d(pb, pc, pd, pe);
if (ori <= 0) {
// Select the edge [c,b].
enext(abtets[i], flipedge); // [b,c,a,d]
edgepivot = 1;
}
if (!edgepivot) {
// Test if [c,a] is locally convex or flat.
ori = orient3d(pc, pa, pd, pe);
if (ori <= 0) {
// Select the edge [a,c].
eprev(abtets[i], flipedge); // [c,a,b,d].
edgepivot = 2;
}
}
if (!edgepivot) continue;
// An edge is selected.
if (checksubsegflag) {
// Do not flip it if it is a segment.
if (issubseg(flipedge)) {
if (fc->collectencsegflag) {
face checkseg, *paryseg;
tsspivot1(flipedge, checkseg);
if (!sinfected(checkseg)) {
// Queue this segment in list.
sinfect(checkseg);
caveencseglist->newindex((void **) &paryseg);
*paryseg = checkseg;
}
}
continue;
}
}
// Try to flip the selected edge ([c,b] or [a,c]).
esymself(flipedge);
// Count the number of tets at the edge.
n1 = 0;
j = 0; // Sum of the star counters.
spintet = flipedge;
while (1) {
n1++;
j += (elemcounter(spintet)); fnextself(spintet);
if (spintet.tet == flipedge.tet) break;
}
if (n1 < 3) {
// This is only possible when the mesh contains inverted
// elements. Reprot a bug.
terminatetetgen(this, 2);
}
if (j > 2) {
// The Star(flipedge) overlaps other Stars.
continue; // Do not flip this edge.
}
if ((b->flipstarsize > 0) && (n1 > b->flipstarsize)) {
// The star size exceeds the given limit.
continue; // Do not flip it.
}
// Allocate spaces for Star(flipedge).
tmpabtets = new triface[n1];
// Form the Star(flipedge).
j = 0;
spintet = flipedge;
while (1) {
tmpabtets[j] = spintet;
// Increase the star counter of this tet.
increaseelemcounter(tmpabtets[j]);
j++;
fnextself(spintet);
if (spintet.tet == flipedge.tet) break;
}
// Try to flip the selected edge away.
nn = flipnm(tmpabtets, n1, level + 1, edgepivot, fc);
if (nn == 2) {
// The edge is flipped. Star(ab) is reduced.
// Shrink the array 'abtets', maintain the original order.
if (edgepivot == 1) {
// 'tmpabtets[0]' is [d,a,e,b] => contains [a,b].
spintet = tmpabtets[0]; // [d,a,e,b]
enextself(spintet);
esymself(spintet);
enextself(spintet); // [a,b,e,d]
} else {
// 'tmpabtets[1]' is [b,d,e,a] => contains [a,b].
spintet = tmpabtets[1]; // [b,d,e,a]
eprevself(spintet);
esymself(spintet);
eprevself(spintet); // [a,b,e,d]
} // edgepivot == 2
increaseelemcounter(spintet); // It is in Star(ab).
// Put the new tet at [i-1]-th entry.
abtets[(i - 1 + n) % n] = spintet;
for (j = i; j < n - 1; j++) {
abtets[j] = abtets[j + 1]; // Upshift
}
// Remember the flips in the last entry of the array 'abtets'.
// They can be used to recover the flipped edge.
abtets[n - 1].tet = (tetrahedron *) tmpabtets; // The star(fedge).
abtets[n - 1].ver = 0; // Clear it.
// Use the 1st and 2nd bit to save 'edgepivot' (1 or 2).
abtets[n - 1].ver |= edgepivot;
// Use the 6th bit to signal this n1-to-m1 flip.
abtets[n - 1].ver |= (1 << 5);
// The poisition [i] of this flip is saved from 7th to 19th bit.
abtets[n - 1].ver |= (i << 6);
// The size of the star 'n1' is saved from 20th bit.
abtets[n - 1].ver |= (n1 << 19);
// Remember the flipped link vertex 'c'. It can be used to recover
// the original edge link of [a,b], and to collect new tets.
tmpabtets[0].tet = (tetrahedron *) pc;
tmpabtets[0].ver = (1 << 5); // Flag it as a vertex handle.
// Continue to flip the edge [a,b].
nn = flipnm(abtets, n - 1, level, abedgepivot, fc);
if (nn == 2) {
// The edge has been flipped.
return nn;
} else { // if (nn > 2) {
// The edge is not flipped.
if (fc->unflip) {
// Recover the flipped edge ([c,b] or [a,c]).
// The sequence of flips are saved in 'tmpabtets'.
// abtets[(i-1) % (n-1)] is [a,b,e,d], i.e., the tet created by
// the flipping of edge [c,b] or [a,c].It must still exist in
// Star(ab). It is the start tet to recover the flipped edge.
if (edgepivot == 1) {
// The flip edge is [c,b].
tmpabtets[0] = abtets[((i-1)+(n-1))%(n-1)]; // [a,b,e,d]
eprevself(tmpabtets[0]);
esymself(tmpabtets[0]);
eprevself(tmpabtets[0]); // [d,a,e,b]
fsym(tmpabtets[0], tmpabtets[1]); // [a,d,e,c]
} else {
// The flip edge is [a,c].
tmpabtets[1] = abtets[((i-1)+(n-1))%(n-1)]; // [a,b,e,d]
enextself(tmpabtets[1]);
esymself(tmpabtets[1]);
enextself(tmpabtets[1]); // [b,d,e,a]
fsym(tmpabtets[1], tmpabtets[0]); // [d,b,e,c]
} // if (edgepivot == 2)
// Recover the flipped edge ([c,b] or [a,c]).
flipnm_post(tmpabtets, n1, 2, edgepivot, fc);
// Insert the two recovered tets into Star(ab).
for (j = n - 2; j >= i; j--) {
abtets[j + 1] = abtets[j]; // Downshift
}
if (edgepivot == 1) {
// tmpabtets[0] is [c,b,d,a] ==> contains [a,b]
// tmpabtets[1] is [c,b,a,e] ==> contains [a,b]
// tmpabtets[2] is [c,b,e,d]
fliptets[0] = tmpabtets[1];
enextself(fliptets[0]);
esymself(fliptets[0]); // [a,b,e,c]
fliptets[1] = tmpabtets[0];
esymself(fliptets[1]);
eprevself(fliptets[1]); // [a,b,c,d]
} else {
// tmpabtets[0] is [a,c,d,b] ==> contains [a,b]
// tmpabtets[1] is [a,c,b,e] ==> contains [a,b]
// tmpabtets[2] is [a,c,e,d]
fliptets[0] = tmpabtets[1];
eprevself(fliptets[0]);
esymself(fliptets[0]); // [a,b,e,c]
fliptets[1] = tmpabtets[0];
esymself(fliptets[1]);
enextself(fliptets[1]); // [a,b,c,d]
} // edgepivot == 2
for (j = 0; j < 2; j++) {
increaseelemcounter(fliptets[j]);
}
// Insert the two recovered tets into Star(ab).
abtets[(i - 1 + n) % n] = fliptets[0];
abtets[i] = fliptets[1];
nn++; // Release the allocated spaces.
delete [] tmpabtets;
} // if (unflip)
} // if (nn > 2)
if (!fc->unflip) {
// The flips are not reversed. The current Star(ab) can not be
// further reduced. Return its size (# of tets).
return nn;
}
// unflip is set.
// Continue the search for flips.
} else {
// The selected edge is not flipped.
if (!fc->unflip) {
// Release the memory used in this attempted flip.
flipnm_post(tmpabtets, n1, nn, edgepivot, fc);
}
// Decrease the star counters of tets in Star(flipedge).
for (j = 0; j < nn; j++) {
decreaseelemcounter(tmpabtets[j]);
}
// Release the allocated spaces.
delete [] tmpabtets;
}
} // i
} // if (level...)
} // if (reflexlinkedgecount > 0)
} else {
// Check if a 3-to-2 flip is possible.
// Let the three apexes be c, d,and e. Hull tets may be involved. If so,
// we rearrange them such that the vertex e is dummypoint.
hullflag = 0;
if (apex(abtets[0]) == dummypoint) {
pc = apex(abtets[1]);
pd = apex(abtets[2]);
pe = apex(abtets[0]);
hullflag = 1;
} else if (apex(abtets[1]) == dummypoint) {
pc = apex(abtets[2]);
pd = apex(abtets[0]);
pe = apex(abtets[1]);
hullflag = 2;
} else {
pc = apex(abtets[0]);
pd = apex(abtets[1]);
pe = apex(abtets[2]);
hullflag = (pe == dummypoint) ? 3 : 0;
}
reducflag = 0;
rejflag = 0;
if (hullflag == 0) {
// Make sure that no inverted tet will be created, i.e. the new tets
// [d,c,e,a] and [c,d,e,b] must be valid tets.
ori = orient3d(pd, pc, pe, pa);
if (ori < 0) {
ori = orient3d(pc, pd, pe, pb);
if (ori < 0) {
reducflag = 1;
}
}
} else {
// [a,b] is a hull edge.
// Note: This can happen when it is in the middle of a 4-to-4 flip.
// Note: [a,b] may even be a non-convex hull edge.
if (!nonconvex) { // The mesh is convex, only do flip if it is a coplanar hull edge.
ori = orient3d(pa, pb, pc, pd);
if (ori == 0) {
reducflag = 1;
}
} else { // nonconvex
reducflag = 1;
}
if (reducflag == 1) {
// [a,b], [a,b,c] and [a,b,d] are on the convex hull.
// Make sure that no inverted tet will be created.
point searchpt = NULL, chkpt;
REAL bigvol = 0.0, ori1, ori2;
// Search an interior vertex which is an apex of edge [c,d].
// In principle, it can be arbitrary interior vertex. To avoid
// numerical issue, we choose the vertex which belongs to a tet
// 't' at edge [c,d] and 't' has the biggest volume.
fliptets[0] = abtets[hullflag % 3]; // [a,b,c,d].
eorgoppoself(fliptets[0]); // [d,c,b,a]
spintet = fliptets[0];
while (1) {
fnextself(spintet);
chkpt = oppo(spintet);
if (chkpt == pb) break;
if ((chkpt != dummypoint) && (apex(spintet) != dummypoint)) {
ori = -orient3d(pd, pc, apex(spintet), chkpt);
if (ori > bigvol) {
bigvol = ori;
searchpt = chkpt;
}
}
}
if (searchpt != NULL) {
// Now valid the configuration.
ori1 = orient3d(pd, pc, searchpt, pa);
ori2 = orient3d(pd, pc, searchpt, pb);
if (ori1 * ori2 >= 0.0) {
reducflag = 0; // Not valid.
} else {
ori1 = orient3d(pa, pb, searchpt, pc);
ori2 = orient3d(pa, pb, searchpt, pd);
if (ori1 * ori2 >= 0.0) {
reducflag = 0; // Not valid.
}
}
} else {
// No valid searchpt is found.
reducflag = 0; // Do not flip it.
}
} // if (reducflag == 1)
} // if (hullflag == 1)
if (reducflag) {
// A 3-to-2 flip is possible.
if (checksubfaceflag) {
// This edge (must not be a segment) can be flipped ONLY IF it belongs
// to either 0 or 2 subfaces. In the latter case, a 2-to-2 flip in
// the surface mesh will be automatically performed within the
// 3-to-2 flip.
nn = 0;
edgepivot = -1; // Re-use it.
for (j = 0; j < 3; j++) {
if (issubface(abtets[j])) {
nn++; // Found a subface.
} else {
edgepivot = j;
}
}
if (nn == 1) {
// Found only 1 subface containing this edge. This can happen in // the boundary recovery phase. The neighbor subface is not yet
// recovered. This edge should not be flipped at this moment.
rejflag = 1;
} else if (nn == 2) {
// Found two subfaces. A 2-to-2 flip is possible. Validate it.
// Below we check if the two faces [p,q,a] and [p,q,b] are subfaces.
eorgoppo(abtets[(edgepivot + 1) % 3], spintet); // [q,p,b,a]
if (issubface(spintet)) {
rejflag = 1; // Conflict to a 2-to-2 flip.
} else {
esymself(spintet);
if (issubface(spintet)) {
rejflag = 1; // Conflict to a 2-to-2 flip.
}
}
} else if (nn == 3) {
// Report a bug.
terminatetetgen(this, 2);
}
}
if (!rejflag && fc->checkflipeligibility) {
// Here we must exchange 'a' and 'b'. Since in the check... function,
// we assume the following point sequence, 'a,b,c,d,e', where
// the face [a,b,c] will be flipped and the edge [e,d] will be
// created. The two new tets are [a,b,c,d] and [b,a,c,e].
rejflag = checkflipeligibility(2, pc, pd, pe, pb, pa, level,
abedgepivot, fc);
}
if (!rejflag) {
// Do flip: [a,b] => [c,d,e]
flip32(abtets, hullflag, fc);
if (fc->remove_ndelaunay_edge) {
if (level == 0) {
// It is the desired removing edge. Check if we have improved
// the objective function.
if ((fc->tetprism_vol_sum >= 0.0) ||
(fabs(fc->tetprism_vol_sum) < fc->bak_tetprism_vol)) {
// No improvement! flip back: [c,d,e] => [a,b].
flip23(abtets, hullflag, fc);
// Increase the element counter -- They are in cavity.
for (j = 0; j < 3; j++) {
increaseelemcounter(abtets[j]);
}
return 3;
}
} // if (level == 0)
}
if (fc->collectnewtets) {
// Collect new tets.
if (level == 0) {
// Push the two new tets into stack.
for (j = 0; j < 2; j++) {
cavetetlist->newindex((void **) &parytet);
*parytet = abtets[j];
}
} else {
// Only one of the new tets is collected. The other one is inside
// the reduced edge star. 'abedgepivot' is either '1' or '2'.
cavetetlist->newindex((void **) &parytet);
if (abedgepivot == 1) { // [c,b]
*parytet = abtets[1];
} else {
*parytet = abtets[0];
}
}
} // if (fc->collectnewtets)
return 2;
}
} // if (reducflag)
} // if (n == 3)
// The current (reduced) Star size.
return n;
}
///////////////////////////////////////////////////////////////////////////////
// //
// flipnm_post() Post process a n-to-m flip. //
// //
// IMPORTANT: This routine only works when there is no other flip operation //
// is done after flipnm([a,b]) which attempts to remove an edge [a,b]. //
// //
// 'abtets' is an array of 'n' (>= 3) tets which are in the original star of //
// [a,b] before flipnm([a,b]). 'nn' (< n) is the value returned by flipnm. //
// If 'nn == 2', the edge [a,b] has been flipped. 'abtets[0]' and 'abtets[1]'//
// are [c,d,e,b] and [d,c,e,a], i.e., a 2-to-3 flip can recover the edge [a, //
// b] and its initial Star([a,b]). If 'nn >= 3' edge [a,b] still exists in //
// current mesh and 'nn' is the current number of tets in Star([a,b]). //
// //
// Each 'abtets[i]', where nn <= i < n, saves either a 2-to-3 flip or a //
// flipnm([p1,p2]) operation ([p1,p2] != [a,b]) which created the tet //
// 'abtets[t-1]', where '0 <= t <= i'. These information can be used to //
// undo the flips performed in flipnm([a,b]) or to collect new tets created //
// by the flipnm([a,b]) operation. //
// //
// Default, this routine only walks through the flips and frees the spaces //
// allocated during the flipnm([a,b]) operation. //
// //
// If the flag 'fc->unflip' is set, this routine un-does the flips performed //
// in flipnm([a,b]) so that the mesh is returned to its original state //
// before doing the flipnm([a,b]) operation. //
// //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::flipnm_post(triface* abtets, int n, int nn, int abedgepivot,
flipconstraints* fc)
{
triface fliptets[3], flipface;
triface *tmpabtets;
int fliptype;
int edgepivot;
int t, n1;
int i, j;
if (nn == 2) {
// The edge [a,b] has been flipped.
// 'abtets[0]' is [c,d,e,b] or [#,#,#,b].
// 'abtets[1]' is [d,c,e,a] or [#,#,#,a].
if (fc->unflip) {
// Do a 2-to-3 flip to recover the edge [a,b]. There may be hull tets.
flip23(abtets, 1, fc);
if (fc->collectnewtets) {
// Pop up new (flipped) tets from the stack.
if (abedgepivot == 0) {
// Two new tets were collected.
cavetetlist->objects -= 2;
} else {
// Only one of the two new tets was collected.
cavetetlist->objects -= 1;
}
}
}
// The initial size of Star(ab) is 3.
nn++;
}
// Walk through the performed flips.
for (i = nn; i < n; i++) { // At the beginning of each step 'i', the size of the Star([a,b]) is 'i'.
// At the end of this step, the size of the Star([a,b]) is 'i+1'.
// The sizes of the Link([a,b]) are the same.
fliptype = ((abtets[i].ver >> 4) & 3); // 0, 1, or 2.
if (fliptype == 1) {
// It was a 2-to-3 flip: [a,b,c]->[e,d].
t = (abtets[i].ver >> 6);
if (fc->unflip) {
if (b->verbose > 2) {
printf(" Recover a 2-to-3 flip at f[%d].\n", t);
}
// 'abtets[(t-1)%i]' is the tet [a,b,e,d] in current Star(ab), i.e.,
// it is created by a 2-to-3 flip [a,b,c] => [e,d].
fliptets[0] = abtets[((t - 1) + i) % i]; // [a,b,e,d]
eprevself(fliptets[0]);
esymself(fliptets[0]);
enextself(fliptets[0]); // [e,d,a,b]
fnext(fliptets[0], fliptets[1]); // [e,d,b,c]
fnext(fliptets[1], fliptets[2]); // [e,d,c,a]
// Do a 3-to-2 flip: [e,d] => [a,b,c].
// NOTE: hull tets may be invloved.
flip32(fliptets, 1, fc);
// Expand the array 'abtets', maintain the original order.
// The new array length is (i+1).
for (j = i - 1; j >= t; j--) {
abtets[j + 1] = abtets[j]; // Downshift
}
// The tet abtets[(t-1)%i] is deleted. Insert the two new tets
// 'fliptets[0]' [a,b,c,d] and 'fliptets[1]' [b,a,c,e] into
// the (t-1)-th and t-th entries, respectively.
esym(fliptets[1], abtets[((t-1) + (i+1)) % (i+1)]); // [a,b,e,c]
abtets[t] = fliptets[0]; // [a,b,c,d]
if (fc->collectnewtets) {
// Pop up two (flipped) tets from the stack.
cavetetlist->objects -= 2;
}
}
} else if (fliptype == 2) {
tmpabtets = (triface *) (abtets[i].tet);
n1 = ((abtets[i].ver >> 19) & 8191); // \sum_{i=0^12}{2^i} = 8191
edgepivot = (abtets[i].ver & 3);
t = ((abtets[i].ver >> 6) & 8191);
if (fc->unflip) {
if (b->verbose > 2) {
printf(" Recover a %d-to-m flip at e[%d] of f[%d].\n", n1,
edgepivot, t);
}
// Recover the flipped edge ([c,b] or [a,c]).
// abtets[(t - 1 + i) % i] is [a,b,e,d], i.e., the tet created by
// the flipping of edge [c,b] or [a,c]. It must still exist in
// Star(ab). Use it to recover the flipped edge.
if (edgepivot == 1) {
// The flip edge is [c,b].
tmpabtets[0] = abtets[(t - 1 + i) % i]; // [a,b,e,d]
eprevself(tmpabtets[0]);
esymself(tmpabtets[0]);
eprevself(tmpabtets[0]); // [d,a,e,b]
fsym(tmpabtets[0], tmpabtets[1]); // [a,d,e,c]
} else {
// The flip edge is [a,c].
tmpabtets[1] = abtets[(t - 1 + i) % i]; // [a,b,e,d]
enextself(tmpabtets[1]);
esymself(tmpabtets[1]);
enextself(tmpabtets[1]); // [b,d,e,a]
fsym(tmpabtets[1], tmpabtets[0]); // [d,b,e,c]
} // if (edgepivot == 2)
// Do a n1-to-m1 flip to recover the flipped edge ([c,b] or [a,c]).
flipnm_post(tmpabtets, n1, 2, edgepivot, fc);
// Insert the two recovered tets into the original Star(ab).
for (j = i - 1; j >= t; j--) {
abtets[j + 1] = abtets[j]; // Downshift
}
if (edgepivot == 1) {
// tmpabtets[0] is [c,b,d,a] ==> contains [a,b]
// tmpabtets[1] is [c,b,a,e] ==> contains [a,b]
// tmpabtets[2] is [c,b,e,d]
fliptets[0] = tmpabtets[1];
enextself(fliptets[0]);
esymself(fliptets[0]); // [a,b,e,c]
fliptets[1] = tmpabtets[0];
esymself(fliptets[1]);
eprevself(fliptets[1]); // [a,b,c,d]
} else {
// tmpabtets[0] is [a,c,d,b] ==> contains [a,b]
// tmpabtets[1] is [a,c,b,e] ==> contains [a,b]
// tmpabtets[2] is [a,c,e,d]
fliptets[0] = tmpabtets[1];
eprevself(fliptets[0]);
esymself(fliptets[0]); // [a,b,e,c]
fliptets[1] = tmpabtets[0];
esymself(fliptets[1]);
enextself(fliptets[1]); // [a,b,c,d]
} // edgepivot == 2
// Insert the two recovered tets into Star(ab).
abtets[((t-1) + (i+1)) % (i+1)] = fliptets[0];
abtets[t] = fliptets[1];
}
else {
// Only free the spaces.
flipnm_post(tmpabtets, n1, 2, edgepivot, fc);
} // if (!unflip)
if (b->verbose > 2) {
printf(" Release %d spaces at f[%d].\n", n1, i);
}
delete [] tmpabtets;
}
} // i
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// insertpoint() Insert a point into current tetrahedralization. //
// //
// The Bowyer-Watson (B-W) algorithm is used to add a new point p into the //
// tetrahedralization T. It first finds a "cavity", denoted as C, in T, C //
// consists of tetrahedra in T that "conflict" with p. If T is a Delaunay //
// tetrahedralization, then all boundary faces (triangles) of C are visible //
// by p, i.e.,C is star-shaped. We can insert p into T by first deleting all //
// tetrahedra in C, then creating new tetrahedra formed by boundary faces of //
// C and p. If T is not a DT, then C may be not star-shaped. It must be //
// modified so that it becomes star-shaped. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::insertpoint(point insertpt, triface *searchtet, face *splitsh,
face *splitseg, insertvertexflags *ivf)
{
arraypool *swaplist;
triface *cavetet, spintet, neightet, neineitet, *parytet;
triface oldtet, newtet, newneitet;
face checksh, neighsh, *parysh;
face checkseg, *paryseg;
point *pts, pa, pb, pc, *parypt;
enum locateresult loc = OUTSIDE;
REAL sign, ori;
REAL attrib, volume; bool enqflag;
int t1ver;
int i, j, k, s;
if (b->verbose > 2) {
printf(" Insert point %d\n", pointmark(insertpt));
}
// Locate the point.
if (searchtet->tet != NULL) {
loc = (enum locateresult) ivf->iloc;
}
if (loc == OUTSIDE) {
if (searchtet->tet == NULL) {
if (!b->weighted) {
randomsample(insertpt, searchtet);
} else {
// Weighted DT. There may exist dangling vertex.
*searchtet = recenttet;
}
}
// Locate the point.
loc = locate(insertpt, searchtet);
}
ivf->iloc = (int) loc; // The return value.
if (b->weighted) {
if (loc != OUTSIDE) {
// Check if this vertex is regular.
pts = (point *) searchtet->tet;
sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt,
pts[4][3], pts[5][3], pts[6][3], pts[7][3],
insertpt[3]);
if (sign > 0) {
// This new vertex lies above the lower hull. Do not insert it.
ivf->iloc = (int) NONREGULAR;
return 0;
}
}
}
// Create the initial cavity C(p) which contains all tetrahedra that
// intersect p. It may include 1, 2, or n tetrahedra.
// If p lies on a segment or subface, also create the initial sub-cavity
// sC(p) which contains all subfaces (and segment) which intersect p.
if (loc == OUTSIDE) {
flip14count++;
// The current hull will be enlarged.
// Add four adjacent boundary tets into list.
for (i = 0; i < 4; i++) {
decode(searchtet->tet[i], neightet);
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
}
infect(*searchtet);
caveoldtetlist->newindex((void **) &parytet);
*parytet = *searchtet;
} else if (loc == INTETRAHEDRON) {
flip14count++;
// Add four adjacent boundary tets into list.
for (i = 0; i < 4; i++) {
decode(searchtet->tet[i], neightet);
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
} infect(*searchtet);
caveoldtetlist->newindex((void **) &parytet);
*parytet = *searchtet;
} else if (loc == ONFACE) {
flip26count++;
// Add six adjacent boundary tets into list.
j = (searchtet->ver & 3); // The current face number.
for (i = 1; i < 4; i++) {
decode(searchtet->tet[(j + i) % 4], neightet);
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
}
decode(searchtet->tet[j], spintet);
j = (spintet.ver & 3); // The current face number.
for (i = 1; i < 4; i++) {
decode(spintet.tet[(j + i) % 4], neightet);
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
}
infect(spintet);
caveoldtetlist->newindex((void **) &parytet);
*parytet = spintet;
infect(*searchtet);
caveoldtetlist->newindex((void **) &parytet);
*parytet = *searchtet;
if (ivf->splitbdflag) {
if ((splitsh != NULL) && (splitsh->sh != NULL)) {
// Create the initial sub-cavity sC(p).
smarktest(*splitsh);
caveshlist->newindex((void **) &parysh);
*parysh = *splitsh;
}
} // if (splitbdflag)
} else if (loc == ONEDGE) {
flipn2ncount++;
// Add all adjacent boundary tets into list.
spintet = *searchtet;
while (1) {
eorgoppo(spintet, neightet);
decode(neightet.tet[neightet.ver & 3], neightet);
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
edestoppo(spintet, neightet);
decode(neightet.tet[neightet.ver & 3], neightet);
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
infect(spintet);
caveoldtetlist->newindex((void **) &parytet);
*parytet = spintet;
fnextself(spintet);
if (spintet.tet == searchtet->tet) break;
} // while (1)
if (ivf->splitbdflag) {
// Create the initial sub-cavity sC(p).
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
smarktest(*splitseg);
splitseg->shver = 0;
spivot(*splitseg, *splitsh);
}
if (splitsh != NULL) {
if (splitsh->sh != NULL) {
// Collect all subfaces share at this edge.
pa = sorg(*splitsh);
neighsh = *splitsh; while (1) {
// Adjust the origin of its edge to be 'pa'.
if (sorg(neighsh) != pa) {
sesymself(neighsh);
}
// Add this face into list (in B-W cavity).
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
*parysh = neighsh;
// Add this face into face-at-splitedge list.
cavesegshlist->newindex((void **) &parysh);
*parysh = neighsh;
// Go to the next face at the edge.
spivotself(neighsh);
// Stop if all faces at the edge have been visited.
if (neighsh.sh == splitsh->sh) break;
if (neighsh.sh == NULL) break;
} // while (1)
} // if (not a dangling segment)
}
} // if (splitbdflag)
} else if (loc == INSTAR) {
// We assume that all tets in the star are given in 'caveoldtetlist',
// and they are all infected.
// Collect the boundary faces of the star.
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
// Check its 4 neighbor tets.
for (j = 0; j < 4; j++) {
decode(cavetet->tet[j], neightet);
if (!infected(neightet)) {
// It's a boundary face.
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
}
}
}
} else if (loc == ONVERTEX) {
// The point already exist. Do nothing and return.
return 0;
}
if (ivf->bowywat) {
// Update the cavity C(p) using the Bowyer-Watson algorithm.
swaplist = cavetetlist;
cavetetlist = cavebdrylist;
cavebdrylist = swaplist;
for (i = 0; i < cavetetlist->objects; i++) {
// 'cavetet' is an adjacent tet at outside of the cavity.
cavetet = (triface *) fastlookup(cavetetlist, i);
// The tet may be tested and included in the (enlarged) cavity.
if (!infected(*cavetet)) {
// Check for two possible cases for this tet:
// (1) It is a cavity tet, or
// (2) it is a cavity boundary face.
enqflag = false;
if (!marktested(*cavetet)) {
// Do Delaunay (in-sphere) test.
pts = (point *) cavetet->tet;
if (pts[7] != dummypoint) {
// A volume tet. Operate on it.
if (b->weighted) {
sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], insertpt,
pts[4][3], pts[5][3], pts[6][3], pts[7][3],
insertpt[3]);
} else {
sign = insphere_s(pts[4], pts[5], pts[6], pts[7], insertpt);
} enqflag = (sign < 0.0);
} else {
if (!nonconvex) {
// Test if this hull face is visible by the new point.
ori = orient3d(pts[4], pts[5], pts[6], insertpt);
if (ori < 0) {
// A visible hull face.
// Include it in the cavity. The convex hull will be enlarged.
enqflag = true;
} else if (ori == 0.0) {
// A coplanar hull face. We need to test if this hull face is
// Delaunay or not. We test if the adjacent tet (not faked)
// of this hull face is Delaunay or not.
decode(cavetet->tet[3], neineitet);
if (!infected(neineitet)) {
if (!marktested(neineitet)) {
// Do Delaunay test on this tet.
pts = (point *) neineitet.tet;
if (b->weighted) {
sign = orient4d_s(pts[4],pts[5],pts[6],pts[7], insertpt,
pts[4][3], pts[5][3], pts[6][3],
pts[7][3], insertpt[3]);
} else {
sign = insphere_s(pts[4],pts[5],pts[6],pts[7], insertpt);
}
enqflag = (sign < 0.0);
}
} else {
// The adjacent tet is non-Delaunay. The hull face is non-
// Delaunay as well. Include it in the cavity.
enqflag = true;
} // if (!infected(neineitet))
} // if (ori == 0.0)
} else {
// A hull face (must be a subface).
// We FIRST include it in the initial cavity if the adjacent tet
// (not faked) of this hull face is not Delaunay wrt p.
// Whether it belongs to the final cavity will be determined
// during the validation process. 'validflag'.
decode(cavetet->tet[3], neineitet);
if (!infected(neineitet)) {
if (!marktested(neineitet)) {
// Do Delaunay test on this tet.
pts = (point *) neineitet.tet;
if (b->weighted) {
sign = orient4d_s(pts[4],pts[5],pts[6],pts[7], insertpt,
pts[4][3], pts[5][3], pts[6][3],
pts[7][3], insertpt[3]);
} else {
sign = insphere_s(pts[4],pts[5],pts[6],pts[7], insertpt);
}
enqflag = (sign < 0.0);
}
} else {
// The adjacent tet is non-Delaunay. The hull face is non-
// Delaunay as well. Include it in the cavity.
enqflag = true;
} // if (infected(neineitet))
} // if (nonconvex)
} // if (pts[7] != dummypoint)
marktest(*cavetet); // Only test it once.
} // if (!marktested(*cavetet))
if (enqflag) {
// Found a tet in the cavity. Put other three faces in check list.
k = (cavetet->ver & 3); // The current face number
for (j = 1; j < 4; j++) {
decode(cavetet->tet[(j + k) % 4], neightet);
cavetetlist->newindex((void **) &parytet);
*parytet = neightet; }
infect(*cavetet);
caveoldtetlist->newindex((void **) &parytet);
*parytet = *cavetet;
} else {
// Found a boundary face of the cavity.
cavetet->ver = epivot[cavetet->ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = *cavetet;
}
} // if (!infected(*cavetet))
} // i
cavetetlist->restart(); // Clear the working list.
} // if (ivf->bowywat)
if (checksubsegflag) {
// Collect all segments of C(p).
shellface *ssptr;
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
if ((ssptr = (shellface*) cavetet->tet[8]) != NULL) {
for (j = 0; j < 6; j++) {
if (ssptr[j]) {
sdecode(ssptr[j], checkseg);
if (!sinfected(checkseg)) {
sinfect(checkseg);
cavetetseglist->newindex((void **) &paryseg);
*paryseg = checkseg;
}
}
} // j
}
} // i
// Uninfect collected segments.
for (i = 0; i < cavetetseglist->objects; i++) {
paryseg = (face *) fastlookup(cavetetseglist, i);
suninfect(*paryseg);
}
} // if (checksubsegflag)
if (checksubfaceflag) {
// Collect all subfaces of C(p).
shellface *sptr;
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
if ((sptr = (shellface*) cavetet->tet[9]) != NULL) {
for (j = 0; j < 4; j++) {
if (sptr[j]) {
sdecode(sptr[j], checksh);
if (!sinfected(checksh)) {
sinfect(checksh);
cavetetshlist->newindex((void **) &parysh);
*parysh = checksh;
}
}
} // j
}
} // i
// Uninfect collected subfaces.
for (i = 0; i < cavetetshlist->objects; i++) {
parysh = (face *) fastlookup(cavetetshlist, i);
suninfect(*parysh);
}
} // if (checksubfaceflag)
if ((ivf->iloc == (int) OUTSIDE) && ivf->refineflag) {
// The vertex lies outside of the domain. And it does not encroach // upon any boundary segment or subface. Do not insert it.
insertpoint_abort(splitseg, ivf);
return 0;
}
if (ivf->splitbdflag) {
// The new point locates in surface mesh. Update the sC(p).
// We have already 'smarktested' the subfaces which directly intersect
// with p in 'caveshlist'. From them, we 'smarktest' their neighboring
// subfaces which are included in C(p). Do not across a segment.
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
checksh = *parysh;
for (j = 0; j < 3; j++) {
if (!isshsubseg(checksh)) {
spivot(checksh, neighsh);
if (!smarktested(neighsh)) {
stpivot(neighsh, neightet);
if (infected(neightet)) {
fsymself(neightet);
if (infected(neightet)) {
// This subface is inside C(p).
// Check if its diametrical circumsphere encloses 'p'.
// The purpose of this check is to avoid forming invalid
// subcavity in surface mesh.
sign = incircle3d(sorg(neighsh), sdest(neighsh),
sapex(neighsh), insertpt);
if (sign < 0) {
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
*parysh = neighsh;
}
}
}
}
}
senextself(checksh);
} // j
} // i
} // if (ivf->splitbdflag)
if (ivf->validflag) {
// Validate C(p) and update it if it is not star-shaped.
int cutcount = 0;
if (ivf->respectbdflag) {
// The initial cavity may include subfaces which are not on the facets
// being splitting. Find them and make them as boundary of C(p).
// Comment: We have already 'smarktested' the subfaces in sC(p). They
// are completely inside C(p).
for (i = 0; i < cavetetshlist->objects; i++) {
parysh = (face *) fastlookup(cavetetshlist, i);
stpivot(*parysh, neightet);
if (infected(neightet)) {
fsymself(neightet);
if (infected(neightet)) {
// Found a subface inside C(p).
if (!smarktested(*parysh)) {
// It is possible that this face is a boundary subface.
// Check if it is a hull face.
//assert(apex(neightet) != dummypoint);
if (oppo(neightet) != dummypoint) {
fsymself(neightet);
}
if (oppo(neightet) != dummypoint) {
ori = orient3d(org(neightet), dest(neightet), apex(neightet),
insertpt);
if (ori < 0) {
// A visible face, get its neighbor face.
fsymself(neightet); ori = -ori; // It must be invisible by p.
}
} else {
// A hull tet. It needs to be cut.
ori = 1;
}
// Cut this tet if it is either invisible by or coplanar with p.
if (ori >= 0) {
uninfect(neightet);
unmarktest(neightet);
cutcount++;
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
// Add three new faces to find new boundaries.
for (j = 0; j < 3; j++) {
esym(neightet, neineitet);
neineitet.ver = epivot[neineitet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neineitet;
enextself(neightet);
}
} // if (ori >= 0)
}
}
}
} // i
// The initial cavity may include segments in its interior. We need to
// Update the cavity so that these segments are on the boundary of
// the cavity.
for (i = 0; i < cavetetseglist->objects; i++) {
paryseg = (face *) fastlookup(cavetetseglist, i);
// Check this segment if it is not a splitting segment.
if (!smarktested(*paryseg)) {
sstpivot1(*paryseg, neightet);
spintet = neightet;
while (1) {
if (!infected(spintet)) break;
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
if (infected(spintet)) {
// Find an adjacent tet at this segment such that both faces
// at this segment are not visible by p.
pa = org(neightet);
pb = dest(neightet);
spintet = neightet;
j = 0;
while (1) {
// Check if this face is visible by p.
pc = apex(spintet);
if (pc != dummypoint) {
ori = orient3d(pa, pb, pc, insertpt);
if (ori >= 0) {
// Not visible. Check another face in this tet.
esym(spintet, neineitet);
pc = apex(neineitet);
if (pc != dummypoint) {
ori = orient3d(pb, pa, pc, insertpt);
if (ori >= 0) {
// Not visible. Found this face.
j = 1; // Flag that it is found.
break;
}
}
}
}
fnextself(spintet);
if (spintet.tet == neightet.tet) break; }
if (j == 0) {
// Not found such a face.
terminatetetgen(this, 2);
}
neightet = spintet;
if (b->verbose > 3) {
printf(" Cut tet (%d, %d, %d, %d)\n",
pointmark(org(neightet)), pointmark(dest(neightet)),
pointmark(apex(neightet)), pointmark(oppo(neightet)));
}
uninfect(neightet);
unmarktest(neightet);
cutcount++;
neightet.ver = epivot[neightet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neightet;
// Add three new faces to find new boundaries.
for (j = 0; j < 3; j++) {
esym(neightet, neineitet);
neineitet.ver = epivot[neineitet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neineitet;
enextself(neightet);
}
}
}
} // i
} // if (ivf->respectbdflag)
// Update the cavity by removing invisible faces until it is star-shaped.
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
// 'cavetet' is an exterior tet adjacent to the cavity.
// Check if its neighbor is inside C(p).
fsym(*cavetet, neightet);
if (infected(neightet)) {
if (apex(*cavetet) != dummypoint) {
// It is a cavity boundary face. Check its visibility.
if (oppo(neightet) != dummypoint) {
// Check if this face is visible by the new point.
if (issubface(neightet)) {
// We should only create a new tet that has a reasonable volume.
// Re-use 'volume' and 'attrib'.
pa = org(*cavetet);
pb = dest(*cavetet);
pc = apex(*cavetet);
volume = orient3dfast(pa, pb, pc, insertpt);
attrib = distance(pa, pb) * distance(pb, pc) * distance(pc, pa);
if ((fabs(volume) / attrib) < b->epsilon) {
ori = 0.0;
} else {
ori = orient3d(pa, pb, pc, insertpt);
}
} else {
ori = orient3d(org(*cavetet), dest(*cavetet), apex(*cavetet),
insertpt);
}
enqflag = (ori > 0);
// Comment: if ori == 0 (coplanar case), we also cut the tet.
} else {
// It is a hull face. And its adjacent tet (at inside of the
// domain) has been cut from the cavity. Cut it as well.
//assert(nonconvex);
enqflag = false;
}
} else {
enqflag = true; // A hull edge.
}
if (enqflag) { // This face is valid, save it.
cavetetlist->newindex((void **) &parytet);
*parytet = *cavetet;
} else {
uninfect(neightet);
unmarktest(neightet);
cutcount++;
// Add three new faces to find new boundaries.
for (j = 0; j < 3; j++) {
esym(neightet, neineitet);
neineitet.ver = epivot[neineitet.ver];
cavebdrylist->newindex((void **) &parytet);
*parytet = neineitet;
enextself(neightet);
}
// 'cavetet' is not on the cavity boundary anymore.
unmarktest(*cavetet);
}
} else {
// 'cavetet' is not on the cavity boundary anymore.
unmarktest(*cavetet);
}
} // i
if (cutcount > 0) {
// The cavity has been updated.
// Update the cavity boundary faces.
cavebdrylist->restart();
for (i = 0; i < cavetetlist->objects; i++) {
cavetet = (triface *) fastlookup(cavetetlist, i);
// 'cavetet' was an exterior tet adjacent to the cavity.
fsym(*cavetet, neightet);
if (infected(neightet)) {
// It is a cavity boundary face.
cavebdrylist->newindex((void **) &parytet);
*parytet = *cavetet;
} else {
// Not a cavity boundary face.
unmarktest(*cavetet);
}
}
// Update the list of old tets.
cavetetlist->restart();
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
if (infected(*cavetet)) {
cavetetlist->newindex((void **) &parytet);
*parytet = *cavetet;
}
}
// Swap 'cavetetlist' and 'caveoldtetlist'.
swaplist = caveoldtetlist;
caveoldtetlist = cavetetlist;
cavetetlist = swaplist;
// The cavity should contain at least one tet.
if (caveoldtetlist->objects == 0l) {
insertpoint_abort(splitseg, ivf);
ivf->iloc = (int) BADELEMENT;
return 0;
}
if (ivf->splitbdflag) {
int cutshcount = 0;
// Update the sub-cavity sC(p).
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
if (smarktested(*parysh)) {
enqflag = false; stpivot(*parysh, neightet);
if (infected(neightet)) {
fsymself(neightet);
if (infected(neightet)) {
enqflag = true;
}
}
if (!enqflag) {
sunmarktest(*parysh);
// Use the last entry of this array to fill this entry.
j = caveshlist->objects - 1;
checksh = * (face *) fastlookup(caveshlist, j);
*parysh = checksh;
cutshcount++;
caveshlist->objects--; // The list is shrinked.
i--;
}
}
}
if (cutshcount > 0) {
i = 0; // Count the number of invalid subfaces/segments.
// Valid the updated sub-cavity sC(p).
if (loc == ONFACE) {
if ((splitsh != NULL) && (splitsh->sh != NULL)) {
// The to-be split subface should be in sC(p).
if (!smarktested(*splitsh)) i++;
}
} else if (loc == ONEDGE) {
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
// The to-be split segment should be in sC(p).
if (!smarktested(*splitseg)) i++;
}
if ((splitsh != NULL) && (splitsh->sh != NULL)) {
// All subfaces at this edge should be in sC(p).
pa = sorg(*splitsh);
neighsh = *splitsh;
while (1) {
// Adjust the origin of its edge to be 'pa'.
if (sorg(neighsh) != pa) {
sesymself(neighsh);
}
// Add this face into list (in B-W cavity).
if (!smarktested(neighsh)) i++;
// Go to the next face at the edge.
spivotself(neighsh);
// Stop if all faces at the edge have been visited.
if (neighsh.sh == splitsh->sh) break;
if (neighsh.sh == NULL) break;
} // while (1)
}
}
if (i > 0) {
// The updated sC(p) is invalid. Do not insert this vertex.
insertpoint_abort(splitseg, ivf);
ivf->iloc = (int) BADELEMENT;
return 0;
}
} // if (cutshcount > 0)
} // if (ivf->splitbdflag)
} // if (cutcount > 0)
} // if (ivf->validflag)
if (ivf->refineflag) {
// The new point is inserted by Delaunay refinement, i.e., it is the
// circumcenter of a tetrahedron, or a subface, or a segment.
// Do not insert this point if the tetrahedron, or subface, or segment
// is not inside the final cavity. if (((ivf->refineflag == 1) && !infected(ivf->refinetet)) ||
((ivf->refineflag == 2) && !smarktested(ivf->refinesh))) {
insertpoint_abort(splitseg, ivf);
ivf->iloc = (int) BADELEMENT;
return 0;
}
} // if (ivf->refineflag)
if (b->plc && (loc != INSTAR)) {
// Reject the new point if it lies too close to an existing point (b->plc),
// or it lies inside a protecting ball of near vertex (ivf->rejflag & 4).
// Collect the list of vertices of the initial cavity.
if (loc == OUTSIDE) {
pts = (point *) &(searchtet->tet[4]);
for (i = 0; i < 3; i++) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = pts[i];
}
} else if (loc == INTETRAHEDRON) {
pts = (point *) &(searchtet->tet[4]);
for (i = 0; i < 4; i++) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = pts[i];
}
} else if (loc == ONFACE) {
pts = (point *) &(searchtet->tet[4]);
for (i = 0; i < 3; i++) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = pts[i];
}
if (pts[3] != dummypoint) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = pts[3];
}
fsym(*searchtet, spintet);
if (oppo(spintet) != dummypoint) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = oppo(spintet);
}
} else if (loc == ONEDGE) {
spintet = *searchtet;
cavetetvertlist->newindex((void **) &parypt);
*parypt = org(spintet);
cavetetvertlist->newindex((void **) &parypt);
*parypt = dest(spintet);
while (1) {
if (apex(spintet) != dummypoint) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = apex(spintet);
}
fnextself(spintet);
if (spintet.tet == searchtet->tet) break;
}
}
int rejptflag = (ivf->rejflag & 4);
REAL rd;
pts = NULL;
for (i = 0; i < cavetetvertlist->objects; i++) {
parypt = (point *) fastlookup(cavetetvertlist, i);
rd = distance(*parypt, insertpt);
// Is the point very close to an existing point?
if (rd < minedgelength) {
pts = parypt;
loc = NEARVERTEX;
break;
}
if (rejptflag) {
// Is the point encroaches upon an existing point? if (rd < (0.5 * (*parypt)[pointmtrindex])) {
pts = parypt;
loc = ENCVERTEX;
break;
}
}
}
cavetetvertlist->restart(); // Clear the work list.
if (pts != NULL) {
// The point is either too close to an existing vertex (NEARVERTEX)
// or encroaches upon (inside the protecting ball) of that vertex.
if (loc == NEARVERTEX) {
if (!issteinerpoint(insertpt) && b->nomergevertex) { // -M0/1 option.
// 'insertpt' is an input vertex.
// In this case, we still insert this vertex. Issue a warning.
if (!b->quiet) {
printf("Warning: Two points, %d and %d, are very close.\n",
pointmark(insertpt), pointmark(*pts));
printf(" Creating a very short edge (len = %g) (< %g).\n",
rd, minedgelength);
printf(" You may try a smaller tolerance (-T) (current is %g)\n",
b->epsilon);
printf(" to avoid this warning.\n");
}
} else {
point2tetorg(*pts, *searchtet);
insertpoint_abort(splitseg, ivf);
ivf->iloc = (int) loc;
return 0;
}
} else { // loc == ENCVERTEX
// The point lies inside the protection ball.
point2tetorg(*pts, *searchtet);
insertpoint_abort(splitseg, ivf);
ivf->iloc = (int) loc;
return 0;
}
}
} // if (b->plc && (loc != INSTAR))
if (b->weighted || ivf->cdtflag || ivf->smlenflag
) {
// There may be other vertices inside C(p). We need to find them.
// Collect all vertices of C(p).
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
//assert(infected(*cavetet));
pts = (point *) &(cavetet->tet[4]);
for (j = 0; j < 4; j++) {
if (pts[j] != dummypoint) {
if (!pinfected(pts[j])) {
pinfect(pts[j]);
cavetetvertlist->newindex((void **) &parypt);
*parypt = pts[j];
}
}
} // j
} // i
// Uninfect all collected (cavity) vertices.
for (i = 0; i < cavetetvertlist->objects; i++) {
parypt = (point *) fastlookup(cavetetvertlist, i);
puninfect(*parypt);
}
if (ivf->smlenflag) {
REAL len;
// Get the length of the shortest edge connecting to 'newpt'.
parypt = (point *) fastlookup(cavetetvertlist, 0);
ivf->smlen = distance(*parypt, insertpt);
ivf->parentpt = *parypt; for (i = 1; i < cavetetvertlist->objects; i++) {
parypt = (point *) fastlookup(cavetetvertlist, i);
len = distance(*parypt, insertpt);
if (len < ivf->smlen) {
ivf->smlen = len;
ivf->parentpt = *parypt;
}
}
}
}
if (ivf->cdtflag) {
// Unmark tets.
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
unmarktest(*cavetet);
}
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
unmarktest(*cavetet);
}
// Clean up arrays which are not needed.
cavetetlist->restart();
if (checksubsegflag) {
cavetetseglist->restart();
}
if (checksubfaceflag) {
cavetetshlist->restart();
}
return 1;
}
// Before re-mesh C(p). Process the segments and subfaces which are on the
// boundary of C(p). Make sure that each such segment or subface is
// connecting to a tet outside C(p). So we can re-connect them to the
// new tets inside the C(p) later.
if (checksubsegflag) {
for (i = 0; i < cavetetseglist->objects; i++) {
paryseg = (face *) fastlookup(cavetetseglist, i);
// Operate on it if it is not the splitting segment, i.e., in sC(p).
if (!smarktested(*paryseg)) {
// Check if the segment is inside the cavity.
// 'j' counts the num of adjacent tets of this seg.
// 'k' counts the num of adjacent tets which are 'sinfected'.
j = k = 0;
sstpivot1(*paryseg, neightet);
spintet = neightet;
while (1) {
j++;
if (!infected(spintet)) {
neineitet = spintet; // An outer tet. Remember it.
} else {
k++; // An in tet.
}
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
// assert(j > 0);
if (k == 0) {
// The segment is not connect to C(p) anymore. Remove it by
// Replacing it by the last entry of this list.
s = cavetetseglist->objects - 1;
checkseg = * (face *) fastlookup(cavetetseglist, s);
*paryseg = checkseg;
cavetetseglist->objects--;
i--;
} else if (k < j) {
// The segment is on the boundary of C(p). sstbond1(*paryseg, neineitet);
} else { // k == j
// The segment is inside C(p).
if (!ivf->splitbdflag) {
checkseg = *paryseg;
sinfect(checkseg); // Flag it as an interior segment.
caveencseglist->newindex((void **) &paryseg);
*paryseg = checkseg;
} else {
//assert(0); // Not possible.
terminatetetgen(this, 2);
}
}
} else {
// assert(smarktested(*paryseg));
// Flag it as an interior segment. Do not queue it, since it will
// be deleted after the segment splitting.
sinfect(*paryseg);
}
} // i
} // if (checksubsegflag)
if (checksubfaceflag) {
for (i = 0; i < cavetetshlist->objects; i++) {
parysh = (face *) fastlookup(cavetetshlist, i);
// Operate on it if it is not inside the sub-cavity sC(p).
if (!smarktested(*parysh)) {
// Check if this subface is inside the cavity.
k = 0;
for (j = 0; j < 2; j++) {
stpivot(*parysh, neightet);
if (!infected(neightet)) {
checksh = *parysh; // Remember this side.
} else {
k++;
}
sesymself(*parysh);
}
if (k == 0) {
// The subface is not connected to C(p). Remove it.
s = cavetetshlist->objects - 1;
checksh = * (face *) fastlookup(cavetetshlist, s);
*parysh = checksh;
cavetetshlist->objects--;
i--;
} else if (k == 1) {
// This side is the outer boundary of C(p).
*parysh = checksh;
} else { // k == 2
if (!ivf->splitbdflag) {
checksh = *parysh;
sinfect(checksh); // Flag it.
caveencshlist->newindex((void **) &parysh);
*parysh = checksh;
} else {
//assert(0); // Not possible.
terminatetetgen(this, 2);
}
}
} else {
// assert(smarktested(*parysh));
// Flag it as an interior subface. Do not queue it. It will be
// deleted after the facet point insertion.
sinfect(*parysh);
}
} // i
} // if (checksubfaceflag)
// Create new tetrahedra to fill the cavity.
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
neightet = *cavetet;
unmarktest(neightet); // Unmark it.
// Get the oldtet (inside the cavity).
fsym(neightet, oldtet);
if (apex(neightet) != dummypoint) {
// Create a new tet in the cavity.
maketetrahedron(&newtet);
setorg(newtet, dest(neightet));
setdest(newtet, org(neightet));
setapex(newtet, apex(neightet));
setoppo(newtet, insertpt);
} else {
// Create a new hull tet.
hullsize++;
maketetrahedron(&newtet);
setorg(newtet, org(neightet));
setdest(newtet, dest(neightet));
setapex(newtet, insertpt);
setoppo(newtet, dummypoint); // It must opposite to face 3.
// Adjust back to the cavity bounday face.
esymself(newtet);
}
// The new tet inherits attribtes from the old tet.
for (j = 0; j < numelemattrib; j++) {
attrib = elemattribute(oldtet.tet, j);
setelemattribute(newtet.tet, j, attrib);
}
if (b->varvolume) {
volume = volumebound(oldtet.tet);
setvolumebound(newtet.tet, volume);
}
// Connect newtet <==> neightet, this also disconnect the old bond.
bond(newtet, neightet);
// oldtet still connects to neightet.
*cavetet = oldtet; // *cavetet = newtet;
} // i
// Set a handle for speeding point location.
recenttet = newtet;
//setpoint2tet(insertpt, encode(newtet));
setpoint2tet(insertpt, (tetrahedron) (newtet.tet));
// Re-use this list to save new interior cavity faces.
cavetetlist->restart();
// Connect adjacent new tetrahedra together.
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
// cavtet is an oldtet, get the newtet at this face.
oldtet = *cavetet;
fsym(oldtet, neightet);
fsym(neightet, newtet);
// Comment: oldtet and newtet must be at the same directed edge.
// Connect the three other faces of this newtet.
for (j = 0; j < 3; j++) {
esym(newtet, neightet); // Go to the face.
if (neightet.tet[neightet.ver & 3] == NULL) {
// Find the adjacent face of this newtet.
spintet = oldtet;
while (1) {
fnextself(spintet);
if (!infected(spintet)) break;
}
fsym(spintet, newneitet);
esymself(newneitet);
bond(neightet, newneitet);
if (ivf->lawson > 1) {
cavetetlist->newindex((void **) &parytet); *parytet = neightet;
}
}
//setpoint2tet(org(newtet), encode(newtet));
setpoint2tet(org(newtet), (tetrahedron) (newtet.tet));
enextself(newtet);
enextself(oldtet);
}
*cavetet = newtet; // Save the new tet.
} // i
if (checksubfaceflag) {
// Connect subfaces on the boundary of the cavity to the new tets.
for (i = 0; i < cavetetshlist->objects; i++) {
parysh = (face *) fastlookup(cavetetshlist, i);
// Connect it if it is not a missing subface.
if (!sinfected(*parysh)) {
stpivot(*parysh, neightet);
fsym(neightet, spintet);
sesymself(*parysh);
tsbond(spintet, *parysh);
}
}
}
if (checksubsegflag) {
// Connect segments on the boundary of the cavity to the new tets.
for (i = 0; i < cavetetseglist->objects; i++) {
paryseg = (face *) fastlookup(cavetetseglist, i);
// Connect it if it is not a missing segment.
if (!sinfected(*paryseg)) {
sstpivot1(*paryseg, neightet);
spintet = neightet;
while (1) {
tssbond1(spintet, *paryseg);
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
}
}
}
if (((splitsh != NULL) && (splitsh->sh != NULL)) ||
((splitseg != NULL) && (splitseg->sh != NULL))) {
// Split a subface or a segment.
sinsertvertex(insertpt, splitsh, splitseg, ivf->sloc, ivf->sbowywat, 0);
}
if (checksubfaceflag) {
if (ivf->splitbdflag) {
// Recover new subfaces in C(p).
for (i = 0; i < caveshbdlist->objects; i++) {
// Get an old subface at edge [a, b].
parysh = (face *) fastlookup(caveshbdlist, i);
spivot(*parysh, checksh); // The new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
// Note that the old subface still connects to adjacent old tets
// of C(p), which still connect to the tets outside C(p).
stpivot(*parysh, neightet);
// Find the adjacent tet containing the edge [a,b] outside C(p).
spintet = neightet;
while (1) {
fnextself(spintet);
if (!infected(spintet)) break;
}
// The adjacent tet connects to a new tet in C(p).
fsym(spintet, neightet);
// Find the tet containing the face [a, b, p].
spintet = neightet; while (1) {
fnextself(spintet);
if (apex(spintet) == insertpt) break;
}
// Adjust the edge direction in spintet and checksh.
if (sorg(checksh) != org(spintet)) {
sesymself(checksh);
}
// Connect the subface to two adjacent tets.
tsbond(spintet, checksh);
fsymself(spintet);
sesymself(checksh);
tsbond(spintet, checksh);
} // if (checksh.sh[3] != NULL)
}
} else {
// The Boundary recovery phase.
// Put all new subfaces into stack for recovery.
for (i = 0; i < caveshbdlist->objects; i++) {
// Get an old subface at edge [a, b].
parysh = (face *) fastlookup(caveshbdlist, i);
spivot(*parysh, checksh); // The new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
}
// Put all interior subfaces into stack for recovery.
for (i = 0; i < caveencshlist->objects; i++) {
parysh = (face *) fastlookup(caveencshlist, i);
// Some subfaces inside C(p) might be split in sinsertvertex().
// Only queue those faces which are not split.
if (!smarktested(*parysh)) {
checksh = *parysh;
suninfect(checksh);
stdissolve(checksh); // Detach connections to old tets.
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
}
}
} // if (checksubfaceflag)
if (checksubsegflag) {
if (ivf->splitbdflag) {
if (splitseg != NULL) {
// Recover the two new subsegments in C(p).
for (i = 0; i < cavesegshlist->objects; i++) {
paryseg = (face *) fastlookup(cavesegshlist, i);
// Insert this subsegment into C(p).
checkseg = *paryseg;
// Get the adjacent new subface.
checkseg.shver = 0;
spivot(checkseg, checksh);
if (checksh.sh != NULL) {
// Get the adjacent new tetrahedron.
stpivot(checksh, neightet);
} else {
// It's a dangling segment.
point2tetorg(sorg(checkseg), neightet);
finddirection(&neightet, sdest(checkseg));
}
sstbond1(checkseg, neightet);
spintet = neightet;
while (1) {
tssbond1(spintet, checkseg);
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
} }
} // if (splitseg != NULL)
} else {
// The Boundary Recovery Phase.
// Queue missing segments in C(p) for recovery.
if (splitseg != NULL) {
// Queue two new subsegments in C(p) for recovery.
for (i = 0; i < cavesegshlist->objects; i++) {
paryseg = (face *) fastlookup(cavesegshlist, i);
checkseg = *paryseg;
//sstdissolve1(checkseg); // It has not been connected yet.
s = randomnation(subsegstack->objects + 1);
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(subsegstack, s);
paryseg = (face *) fastlookup(subsegstack, s);
*paryseg = checkseg;
}
} // if (splitseg != NULL)
for (i = 0; i < caveencseglist->objects; i++) {
paryseg = (face *) fastlookup(caveencseglist, i);
if (!smarktested(*paryseg)) { // It may be split.
checkseg = *paryseg;
suninfect(checkseg);
sstdissolve1(checkseg); // Detach connections to old tets.
s = randomnation(subsegstack->objects + 1);
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(subsegstack, s);
paryseg = (face *) fastlookup(subsegstack, s);
*paryseg = checkseg;
}
}
}
} // if (checksubsegflag)
if (b->weighted
) {
// Some vertices may be completed inside the cavity. They must be
// detected and added to recovering list.
// Since every "live" vertex must contain a pointer to a non-dead
// tetrahedron, we can check for each vertex this pointer.
for (i = 0; i < cavetetvertlist->objects; i++) {
pts = (point *) fastlookup(cavetetvertlist, i);
decode(point2tet(*pts), *searchtet);
if (infected(*searchtet)) {
if (b->weighted) {
if (b->verbose > 1) {
printf(" Point #%d is non-regular after the insertion of #%d.\n",
pointmark(*pts), pointmark(insertpt));
}
setpointtype(*pts, NREGULARVERTEX);
nonregularcount++;
}
}
}
}
if (ivf->chkencflag & 1) {
// Queue all segment outside C(p).
for (i = 0; i < cavetetseglist->objects; i++) {
paryseg = (face *) fastlookup(cavetetseglist, i);
// Skip if it is the split segment.
if (!sinfected(*paryseg)) {
enqueuesubface(badsubsegs, paryseg);
}
}
if (splitseg != NULL) {
// Queue the two new subsegments inside C(p).
for (i = 0; i < cavesegshlist->objects; i++) {
paryseg = (face *) fastlookup(cavesegshlist, i);
enqueuesubface(badsubsegs, paryseg); }
}
} // if (chkencflag & 1)
if (ivf->chkencflag & 2) {
// Queue all subfaces outside C(p).
for (i = 0; i < cavetetshlist->objects; i++) {
parysh = (face *) fastlookup(cavetetshlist, i);
// Skip if it is a split subface.
if (!sinfected(*parysh)) {
enqueuesubface(badsubfacs, parysh);
}
}
// Queue all new subfaces inside C(p).
for (i = 0; i < caveshbdlist->objects; i++) {
// Get an old subface at edge [a, b].
parysh = (face *) fastlookup(caveshbdlist, i);
spivot(*parysh, checksh); // checksh is a new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
enqueuesubface(badsubfacs, &checksh);
}
}
} // if (chkencflag & 2)
if (ivf->chkencflag & 4) {
// Queue all new tetrahedra in C(p).
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
enqueuetetrahedron(cavetet);
}
}
// C(p) is re-meshed successfully.
// Delete the old tets in C(p).
for (i = 0; i < caveoldtetlist->objects; i++) {
searchtet = (triface *) fastlookup(caveoldtetlist, i);
if (ishulltet(*searchtet)) {
hullsize--;
}
tetrahedrondealloc(searchtet->tet);
}
if (((splitsh != NULL) && (splitsh->sh != NULL)) ||
((splitseg != NULL) && (splitseg->sh != NULL))) {
// Delete the old subfaces in sC(p).
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
if (checksubfaceflag) {//if (bowywat == 2) {
// It is possible that this subface still connects to adjacent
// tets which are not in C(p). If so, clear connections in the
// adjacent tets at this subface.
stpivot(*parysh, neightet);
if (neightet.tet != NULL) {
if (neightet.tet[4] != NULL) {
// Found an adjacent tet. It must be not in C(p).
tsdissolve(neightet);
fsymself(neightet);
tsdissolve(neightet);
}
}
}
shellfacedealloc(subfaces, parysh->sh);
}
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
// Delete the old segment in sC(p).
shellfacedealloc(subsegs, splitseg->sh);
}
}
if (ivf->lawson) {
for (i = 0; i < cavebdrylist->objects; i++) {
searchtet = (triface *) fastlookup(cavebdrylist, i);
flippush(flipstack, searchtet);
}
if (ivf->lawson > 1) {
for (i = 0; i < cavetetlist->objects; i++) {
searchtet = (triface *) fastlookup(cavetetlist, i);
flippush(flipstack, searchtet);
}
}
}
// Clean the working lists.
caveoldtetlist->restart();
cavebdrylist->restart();
cavetetlist->restart();
if (checksubsegflag) {
cavetetseglist->restart();
caveencseglist->restart();
}
if (checksubfaceflag) {
cavetetshlist->restart();
caveencshlist->restart();
}
if (b->weighted || ivf->smlenflag
) {
cavetetvertlist->restart();
}
if (((splitsh != NULL) && (splitsh->sh != NULL)) ||
((splitseg != NULL) && (splitseg->sh != NULL))) {
caveshlist->restart();
caveshbdlist->restart();
cavesegshlist->restart();
}
return 1; // Point is inserted.
}
///////////////////////////////////////////////////////////////////////////////
// //
// insertpoint_abort() Abort the insertion of a new vertex. //
// //
// The cavity will be restored. All working lists are cleared. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::insertpoint_abort(face *splitseg, insertvertexflags *ivf)
{
triface *cavetet;
face *parysh;
int i;
for (i = 0; i < caveoldtetlist->objects; i++) {
cavetet = (triface *) fastlookup(caveoldtetlist, i);
uninfect(*cavetet);
unmarktest(*cavetet);
}
for (i = 0; i < cavebdrylist->objects; i++) {
cavetet = (triface *) fastlookup(cavebdrylist, i);
unmarktest(*cavetet);
}
cavetetlist->restart(); cavebdrylist->restart();
caveoldtetlist->restart();
cavetetseglist->restart();
cavetetshlist->restart();
if (ivf->splitbdflag) {
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
sunmarktest(*splitseg);
}
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
sunmarktest(*parysh);
}
caveshlist->restart();
cavesegshlist->restart();
}
}
//// ////
//// ////
//// flip_cxx /////////////////////////////////////////////////////////////////
//// delaunay_cxx /////////////////////////////////////////////////////////////
//// ////
//// ////
///////////////////////////////////////////////////////////////////////////////
// //
// hilbert_init() Initialize the Gray code permutation table. //
// //
// The table 'transgc' has 8 x 3 x 8 entries. It contains all possible Gray //
// code sequences traveled by the 1st order Hilbert curve in 3 dimensions. //
// The first column is the Gray code of the entry point of the curve, and //
// the second column is the direction (0, 1, or 2, 0 means the x-axis) where //
// the exit point of curve lies. //
// //
// The table 'tsb1mod3' contains the numbers of trailing set '1' bits of the //
// indices from 0 to 7, modulo by '3'. The code for generating this table is //
// from: http://graphics.stanford.edu/~seander/bithacks.html. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::hilbert_init(int n)
{
int gc[8], N, mask, travel_bit;
int e, d, f, k, g;
int v, c;
int i;
N = (n == 2) ? 4 : 8;
mask = (n == 2) ? 3 : 7;
// Generate the Gray code sequence.
for (i = 0; i < N; i++) {
gc[i] = i ^ (i >> 1);
}
for (e = 0; e < N; e++) {
for (d = 0; d < n; d++) {
// Calculate the end point (f).
f = e ^ (1 << d); // Toggle the d-th bit of 'e'.
// travel_bit = 2**p, the bit we want to travel.
travel_bit = e ^ f;
for (i = 0; i < N; i++) {
// // Rotate gc[i] left by (p + 1) % n bits.
k = gc[i] * (travel_bit * 2);
g = ((k | (k / N)) & mask);
// Calculate the permuted Gray code by xor with the start point (e).
transgc[e][d][i] = (g ^ e);
} } // d
} // e
// Count the consecutive '1' bits (trailing) on the right.
tsb1mod3[0] = 0;
for (i = 1; i < N; i++) {
v = ~i; // Count the 0s.
v = (v ^ (v - 1)) >> 1; // Set v's trailing 0s to 1s and zero rest
for (c = 0; v; c++) {
v >>= 1;
}
tsb1mod3[i] = c % n;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// hilbert_sort3() Sort points using the 3d Hilbert curve. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::hilbert_split(point* vertexarray,int arraysize,int gc0,int gc1,
REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
REAL bzmin, REAL bzmax)
{
point swapvert;
int axis, d;
REAL split;
int i, j;
// Find the current splitting axis. 'axis' is a value 0, or 1, or 2, which
// correspoding to x-, or y- or z-axis.
axis = (gc0 ^ gc1) >> 1;
// Calulate the split position along the axis.
if (axis == 0) {
split = 0.5 * (bxmin + bxmax);
} else if (axis == 1) {
split = 0.5 * (bymin + bymax);
} else { // == 2
split = 0.5 * (bzmin + bzmax);
}
// Find the direction (+1 or -1) of the axis. If 'd' is +1, the direction
// of the axis is to the positive of the axis, otherwise, it is -1.
d = ((gc0 & (1<<axis)) == 0) ? 1 : -1;
// Partition the vertices into left- and right-arrays such that left points
// have Hilbert indices lower than the right points.
i = 0;
j = arraysize - 1;
// Partition the vertices into left- and right-arrays.
if (d > 0) {
do {
for (; i < arraysize; i++) {
if (vertexarray[i][axis] >= split) break;
}
for (; j >= 0; j--) {
if (vertexarray[j][axis] < split) break;
}
// Is the partition finished?
if (i == (j + 1)) break;
// Swap i-th and j-th vertices.
swapvert = vertexarray[i];
vertexarray[i] = vertexarray[j];
vertexarray[j] = swapvert;
// Continue patitioning the array; } while (true);
} else {
do {
for (; i < arraysize; i++) {
if (vertexarray[i][axis] <= split) break;
}
for (; j >= 0; j--) {
if (vertexarray[j][axis] > split) break;
}
// Is the partition finished?
if (i == (j + 1)) break;
// Swap i-th and j-th vertices.
swapvert = vertexarray[i];
vertexarray[i] = vertexarray[j];
vertexarray[j] = swapvert;
// Continue patitioning the array;
} while (true);
}
return i;
}
void tetgenmesh::hilbert_sort3(point* vertexarray, int arraysize, int e, int d,
REAL bxmin, REAL bxmax, REAL bymin, REAL bymax,
REAL bzmin, REAL bzmax, int depth)
{
REAL x1, x2, y1, y2, z1, z2;
int p[9], w, e_w, d_w, k, ei, di;
int n = 3, mask = 7;
p[0] = 0;
p[8] = arraysize;
// Sort the points according to the 1st order Hilbert curve in 3d.
p[4] = hilbert_split(vertexarray, p[8], transgc[e][d][3], transgc[e][d][4],
bxmin, bxmax, bymin, bymax, bzmin, bzmax);
p[2] = hilbert_split(vertexarray, p[4], transgc[e][d][1], transgc[e][d][2],
bxmin, bxmax, bymin, bymax, bzmin, bzmax);
p[1] = hilbert_split(vertexarray, p[2], transgc[e][d][0], transgc[e][d][1],
bxmin, bxmax, bymin, bymax, bzmin, bzmax);
p[3] = hilbert_split(&(vertexarray[p[2]]), p[4] - p[2],
transgc[e][d][2], transgc[e][d][3],
bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[2];
p[6] = hilbert_split(&(vertexarray[p[4]]), p[8] - p[4],
transgc[e][d][5], transgc[e][d][6],
bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[4];
p[5] = hilbert_split(&(vertexarray[p[4]]), p[6] - p[4],
transgc[e][d][4], transgc[e][d][5],
bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[4];
p[7] = hilbert_split(&(vertexarray[p[6]]), p[8] - p[6],
transgc[e][d][6], transgc[e][d][7],
bxmin, bxmax, bymin, bymax, bzmin, bzmax) + p[6];
if (b->hilbert_order > 0) {
// A maximum order is prescribed.
if ((depth + 1) == b->hilbert_order) {
// The maximum prescribed order is reached.
return;
}
}
// Recursively sort the points in sub-boxes.
for (w = 0; w < 8; w++) {
// w is the local Hilbert index (NOT Gray code).
// Sort into the sub-box either there are more than 2 points in it, or
// the prescribed order of the curve is not reached yet.
//if ((p[w+1] - p[w] > b->hilbert_limit) || (b->hilbert_order > 0)) {
if ((p[w+1] - p[w]) > b->hilbert_limit) {
// Calculcate the start point (ei) of the curve in this sub-box.
// update e = e ^ (e(w) left_rotate (d+1)). if (w == 0) {
e_w = 0;
} else {
// calculate e(w) = gc(2 * floor((w - 1) / 2)).
k = 2 * ((w - 1) / 2);
e_w = k ^ (k >> 1); // = gc(k).
}
k = e_w;
e_w = ((k << (d+1)) & mask) | ((k >> (n-d-1)) & mask);
ei = e ^ e_w;
// Calulcate the direction (di) of the curve in this sub-box.
// update d = (d + d(w) + 1) % n
if (w == 0) {
d_w = 0;
} else {
d_w = ((w % 2) == 0) ? tsb1mod3[w - 1] : tsb1mod3[w];
}
di = (d + d_w + 1) % n;
// Calculate the bounding box of the sub-box.
if (transgc[e][d][w] & 1) { // x-axis
x1 = 0.5 * (bxmin + bxmax);
x2 = bxmax;
} else {
x1 = bxmin;
x2 = 0.5 * (bxmin + bxmax);
}
if (transgc[e][d][w] & 2) { // y-axis
y1 = 0.5 * (bymin + bymax);
y2 = bymax;
} else {
y1 = bymin;
y2 = 0.5 * (bymin + bymax);
}
if (transgc[e][d][w] & 4) { // z-axis
z1 = 0.5 * (bzmin + bzmax);
z2 = bzmax;
} else {
z1 = bzmin;
z2 = 0.5 * (bzmin + bzmax);
}
hilbert_sort3(&(vertexarray[p[w]]), p[w+1] - p[w], ei, di,
x1, x2, y1, y2, z1, z2, depth+1);
} // if (p[w+1] - p[w] > 1)
} // w
}
///////////////////////////////////////////////////////////////////////////////
// //
// brio_multiscale_sort() Sort the points using BRIO and Hilbert curve. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::brio_multiscale_sort(point* vertexarray, int arraysize,
int threshold, REAL ratio, int *depth)
{
int middle;
middle = 0;
if (arraysize >= threshold) {
(*depth)++;
middle = arraysize * ratio;
brio_multiscale_sort(vertexarray, middle, threshold, ratio, depth);
}
// Sort the right-array (rnd-th round) using the Hilbert curve.
hilbert_sort3(&(vertexarray[middle]), arraysize - middle, 0, 0, // e, d
xmin, xmax, ymin, ymax, zmin, zmax, 0); // depth.
}
///////////////////////////////////////////////////////////////////////////////
// //// randomnation() Generate a random number between 0 and 'choices' - 1. //
// //
///////////////////////////////////////////////////////////////////////////////
unsigned long tetgenmesh::randomnation(unsigned int choices)
{
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;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// randomsample() Randomly sample the tetrahedra for point loation. //
// //
// Searching begins from one of handles: the input 'searchtet', a recently //
// encountered tetrahedron 'recenttet', or from one chosen from a random //
// sample. The choice is made by determining which one's origin is closest //
// to the point we are searching for. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::randomsample(point searchpt,triface *searchtet)
{
tetrahedron *firsttet, *tetptr;
point torg;
void **sampleblock;
uintptr_t alignptr;
long sampleblocks, samplesperblock, samplenum;
long tetblocks, i, j;
REAL searchdist, dist;
if (b->verbose > 2) {
printf(" Random sampling tetrahedra for searching point %d.\n",
pointmark(searchpt));
}
if (!nonconvex) {
if (searchtet->tet == NULL) {
// A null tet. Choose the recenttet as the starting tet.
*searchtet = recenttet;
}
// 'searchtet' should be a valid tetrahedron. Choose the base face
// whose vertices must not be 'dummypoint'.
searchtet->ver = 3;
// Record the distance from its origin to the searching point.
torg = org(*searchtet);
searchdist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) +
(searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
(searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
// If a recently encountered tetrahedron has been recorded and has not
// been deallocated, test it as a good starting point.
if (recenttet.tet != searchtet->tet) {
recenttet.ver = 3;
torg = org(recenttet);
dist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) + (searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
(searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
if (dist < searchdist) {
*searchtet = recenttet;
searchdist = dist;
}
}
} else {
// The mesh is non-convex. Do not use 'recenttet'.
searchdist = longest;
}
// Select "good" candidate using k random samples, taking the closest one.
// The number of random samples taken is proportional to the fourth root
// of the number of tetrahedra in the mesh.
while (samples * samples * samples * samples < tetrahedrons->items) {
samples++;
}
// Find how much blocks in current tet pool.
tetblocks = (tetrahedrons->maxitems + b->tetrahedraperblock - 1)
/ b->tetrahedraperblock;
// Find the average samples per block. Each block at least have 1 sample.
samplesperblock = 1 + (samples / tetblocks);
sampleblocks = samples / samplesperblock;
sampleblock = tetrahedrons->firstblock;
for (i = 0; i < sampleblocks; i++) {
alignptr = (uintptr_t) (sampleblock + 1);
firsttet = (tetrahedron *)
(alignptr + (uintptr_t) tetrahedrons->alignbytes
- (alignptr % (uintptr_t) tetrahedrons->alignbytes));
for (j = 0; j < samplesperblock; j++) {
if (i == tetblocks - 1) {
// This is the last block.
samplenum = randomnation((int)
(tetrahedrons->maxitems - (i * b->tetrahedraperblock)));
} else {
samplenum = randomnation(b->tetrahedraperblock);
}
tetptr = (tetrahedron *)
(firsttet + (samplenum * tetrahedrons->itemwords));
torg = (point) tetptr[4];
if (torg != (point) NULL) {
dist = (searchpt[0] - torg[0]) * (searchpt[0] - torg[0]) +
(searchpt[1] - torg[1]) * (searchpt[1] - torg[1]) +
(searchpt[2] - torg[2]) * (searchpt[2] - torg[2]);
if (dist < searchdist) {
searchtet->tet = tetptr;
searchtet->ver = 11; // torg = org(t);
searchdist = dist;
}
} else {
// A dead tet. Re-sample it.
if (i != tetblocks - 1) j--;
}
}
sampleblock = (void **) *sampleblock;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// locate() Find a tetrahedron containing a given point. //
// //
// Begins its search from 'searchtet', assume there is a line segment L from //
// a vertex of 'searchtet' to the query point 'searchpt', and simply walk //
// towards 'searchpt' by traversing all faces intersected by L. //
// //
// On completion, 'searchtet' is a tetrahedron that contains 'searchpt'. The //
// returned value indicates one of the following cases: //
// - ONVERTEX, the search point lies on the origin of 'searchtet'. //// - ONEDGE, the search point lies on an edge of 'searchtet'. //
// - ONFACE, the search point lies on a face of 'searchtet'. //
// - INTET, the search point lies in the interior of 'searchtet'. //
// - OUTSIDE, the search point lies outside the mesh. 'searchtet' is a //
// hull face which is visible by the search point. //
// //
// WARNING: This routine is designed for convex triangulations, and will not //
// generally work after the holes and concavities have been carved. //
// //
///////////////////////////////////////////////////////////////////////////////
enum tetgenmesh::locateresult
tetgenmesh::locate(point searchpt, triface* searchtet, int chkencflag)
{
point torg, tdest, tapex, toppo;
enum {ORGMOVE, DESTMOVE, APEXMOVE} nextmove;
REAL ori, oriorg, oridest, oriapex;
enum locateresult loc = OUTSIDE;
int t1ver;
int s;
if (searchtet->tet == NULL) {
// A null tet. Choose the recenttet as the starting tet.
searchtet->tet = recenttet.tet;
}
// Check if we are in the outside of the convex hull.
if (ishulltet(*searchtet)) {
// Get its adjacent tet (inside the hull).
searchtet->ver = 3;
fsymself(*searchtet);
}
// Let searchtet be the face such that 'searchpt' lies above to it.
for (searchtet->ver = 0; searchtet->ver < 4; searchtet->ver++) {
torg = org(*searchtet);
tdest = dest(*searchtet);
tapex = apex(*searchtet);
ori = orient3d(torg, tdest, tapex, searchpt);
if (ori < 0.0) break;
}
if (searchtet->ver == 4) {
terminatetetgen(this, 2);
}
// Walk through tetrahedra to locate the point.
while (true) {
toppo = oppo(*searchtet);
// Check if the vertex is we seek.
if (toppo == searchpt) {
// Adjust the origin of searchtet to be searchpt.
esymself(*searchtet);
eprevself(*searchtet);
loc = ONVERTEX; // return ONVERTEX;
break;
}
// We enter from one of serarchtet's faces, which face do we exit?
oriorg = orient3d(tdest, tapex, toppo, searchpt);
oridest = orient3d(tapex, torg, toppo, searchpt);
oriapex = orient3d(torg, tdest, toppo, searchpt);
// Now decide which face to move. It is possible there are more than one
// faces are viable moves. If so, randomly choose one.
if (oriorg < 0) {
if (oridest < 0) {
if (oriapex < 0) {
// All three faces are possible. s = randomnation(3); // 's' is in {0,1,2}.
if (s == 0) {
nextmove = ORGMOVE;
} else if (s == 1) {
nextmove = DESTMOVE;
} else {
nextmove = APEXMOVE;
}
} else {
// Two faces, opposite to origin and destination, are viable.
//s = randomnation(2); // 's' is in {0,1}.
if (randomnation(2)) {
nextmove = ORGMOVE;
} else {
nextmove = DESTMOVE;
}
}
} else {
if (oriapex < 0) {
// Two faces, opposite to origin and apex, are viable.
//s = randomnation(2); // 's' is in {0,1}.
if (randomnation(2)) {
nextmove = ORGMOVE;
} else {
nextmove = APEXMOVE;
}
} else {
// Only the face opposite to origin is viable.
nextmove = ORGMOVE;
}
}
} else {
if (oridest < 0) {
if (oriapex < 0) {
// Two faces, opposite to destination and apex, are viable.
//s = randomnation(2); // 's' is in {0,1}.
if (randomnation(2)) {
nextmove = DESTMOVE;
} else {
nextmove = APEXMOVE;
}
} else {
// Only the face opposite to destination is viable.
nextmove = DESTMOVE;
}
} else {
if (oriapex < 0) {
// Only the face opposite to apex is viable.
nextmove = APEXMOVE;
} else {
// The point we seek must be on the boundary of or inside this
// tetrahedron. Check for boundary cases.
if (oriorg == 0) {
// Go to the face opposite to origin.
enextesymself(*searchtet);
if (oridest == 0) {
eprevself(*searchtet); // edge oppo->apex
if (oriapex == 0) {
// oppo is duplicated with p.
loc = ONVERTEX; // return ONVERTEX;
break;
}
loc = ONEDGE; // return ONEDGE;
break;
}
if (oriapex == 0) {
enextself(*searchtet); // edge dest->oppo
loc = ONEDGE; // return ONEDGE;
break;
} loc = ONFACE; // return ONFACE;
break;
}
if (oridest == 0) {
// Go to the face opposite to destination.
eprevesymself(*searchtet);
if (oriapex == 0) {
eprevself(*searchtet); // edge oppo->org
loc = ONEDGE; // return ONEDGE;
break;
}
loc = ONFACE; // return ONFACE;
break;
}
if (oriapex == 0) {
// Go to the face opposite to apex
esymself(*searchtet);
loc = ONFACE; // return ONFACE;
break;
}
loc = INTETRAHEDRON; // return INTETRAHEDRON;
break;
}
}
}
// Move to the selected face.
if (nextmove == ORGMOVE) {
enextesymself(*searchtet);
} else if (nextmove == DESTMOVE) {
eprevesymself(*searchtet);
} else {
esymself(*searchtet);
}
if (chkencflag) {
// Check if we are walking across a subface.
if (issubface(*searchtet)) {
loc = ENCSUBFACE;
break;
}
}
// Move to the adjacent tetrahedron (maybe a hull tetrahedron).
fsymself(*searchtet);
if (oppo(*searchtet) == dummypoint) {
loc = OUTSIDE; // return OUTSIDE;
break;
}
// Retreat the three vertices of the base face.
torg = org(*searchtet);
tdest = dest(*searchtet);
tapex = apex(*searchtet);
} // while (true)
return loc;
}
///////////////////////////////////////////////////////////////////////////////
// //
// flippush() Push a face (possibly will be flipped) into flipstack. //
// //
// The face is marked. The flag is used to check the validity of the face on //
// its popup. Some other flips may change it already. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flippush(badface*& fstack, triface* flipface)
{
if (!facemarked(*flipface)) { badface *newflipface = (badface *) flippool->alloc();
newflipface->tt = *flipface;
markface(newflipface->tt);
// Push this face into stack.
newflipface->nextitem = fstack;
fstack = newflipface;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// incrementalflip() Incrementally flipping to construct DT. //
// //
// Faces need to be checked for flipping are already queued in 'flipstack'. //
// Return the total number of performed flips. //
// //
// Comment: This routine should be only used in the incremental Delaunay //
// construction. In other cases, lawsonflip3d() should be used. //
// //
// If the new point lies outside of the convex hull ('hullflag' is set). The //
// incremental flip algorithm still works as usual. However, we must ensure //
// that every flip (2-to-3 or 3-to-2) does not create a duplicated (existing)//
// edge or face. Otherwise, the underlying space of the triangulation becomes//
// non-manifold and it is not possible to flip further. //
// Thanks to Joerg Rambau and Frank Lutz for helping in this issue. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::incrementalflip(point newpt, int hullflag, flipconstraints *fc)
{
badface *popface;
triface fliptets[5], *parytet;
point *pts, *parypt, pe;
REAL sign, ori;
int flipcount = 0;
int t1ver;
int i;
if (b->verbose > 2) {
printf(" Lawson flip (%ld faces).\n", flippool->items);
}
if (hullflag) {
// 'newpt' lies in the outside of the convex hull.
// Mark all hull vertices which are connecting to it.
popface = flipstack;
while (popface != NULL) {
pts = (point *) popface->tt.tet;
for (i = 4; i < 8; i++) {
if ((pts[i] != newpt) && (pts[i] != dummypoint)) {
if (!pinfected(pts[i])) {
pinfect(pts[i]);
cavetetvertlist->newindex((void **) &parypt);
*parypt = pts[i];
}
}
}
popface = popface->nextitem;
}
}
// Loop until the queue is empty.
while (flipstack != NULL) {
// Pop a face from the stack.
popface = flipstack;
fliptets[0] = popface->tt;
flipstack = flipstack->nextitem; // The next top item in stack.
flippool->dealloc((void *) popface);
// Skip it if it is a dead tet (destroyed by previous flips).
if (isdeadtet(fliptets[0])) continue;
// Skip it if it is not the same tet as we saved.
if (!facemarked(fliptets[0])) continue;
unmarkface(fliptets[0]);
if ((point) fliptets[0].tet[7] == dummypoint) {
// It must be a hull edge.
fliptets[0].ver = epivot[fliptets[0].ver];
// A hull edge. The current convex hull may be enlarged.
fsym(fliptets[0], fliptets[1]);
pts = (point *) fliptets[1].tet;
ori = orient3d(pts[4], pts[5], pts[6], newpt);
if (ori < 0) {
// Visible. The convex hull will be enlarged.
// Decide which flip (2-to-3, 3-to-2, or 4-to-1) to use.
// Check if the tet [a,c,e,d] or [c,b,e,d] exists.
enext(fliptets[1], fliptets[2]);
eprev(fliptets[1], fliptets[3]);
fnextself(fliptets[2]); // [a,c,e,*]
fnextself(fliptets[3]); // [c,b,e,*]
if (oppo(fliptets[2]) == newpt) {
if (oppo(fliptets[3]) == newpt) {
// Both tets exist! A 4-to-1 flip is found.
terminatetetgen(this, 2); // Report a bug.
} else {
esym(fliptets[2], fliptets[0]);
fnext(fliptets[0], fliptets[1]);
fnext(fliptets[1], fliptets[2]);
// Perform a 3-to-2 flip. Replace edge [c,a] by face [d,e,b].
// This corresponds to my standard labels, where edge [e,d] is
// repalced by face [a,b,c], and a is the new vertex.
// [0] [c,a,d,e] (d = newpt)
// [1] [c,a,e,b] (c = dummypoint)
// [2] [c,a,b,d]
flip32(fliptets, 1, fc);
}
} else {
if (oppo(fliptets[3]) == newpt) {
fnext(fliptets[3], fliptets[0]);
fnext(fliptets[0], fliptets[1]);
fnext(fliptets[1], fliptets[2]);
// Perform a 3-to-2 flip. Replace edge [c,b] by face [d,a,e].
// [0] [c,b,d,a] (d = newpt)
// [1] [c,b,a,e] (c = dummypoint)
// [2] [c,b,e,d]
flip32(fliptets, 1, fc);
} else {
if (hullflag) {
// Reject this flip if pe is already marked.
pe = oppo(fliptets[1]);
if (!pinfected(pe)) {
pinfect(pe);
cavetetvertlist->newindex((void **) &parypt);
*parypt = pe;
// Perform a 2-to-3 flip.
flip23(fliptets, 1, fc);
} else {
// Reject this flip.
flipcount--;
}
} else {
// Perform a 2-to-3 flip. Replace face [a,b,c] by edge [e,d].
// [0] [a,b,c,d], d = newpt.
// [1] [b,a,c,e], c = dummypoint.
flip23(fliptets, 1, fc);
}
}
} flipcount++;
}
continue;
} // if (dummypoint)
fsym(fliptets[0], fliptets[1]);
if ((point) fliptets[1].tet[7] == dummypoint) {
// A hull face is locally Delaunay.
continue;
}
// Check if the adjacent tet has already been tested.
if (marktested(fliptets[1])) {
// It has been tested and it is Delaunay.
continue;
}
// Test whether the face is locally Delaunay or not.
pts = (point *) fliptets[1].tet;
if (b->weighted) {
sign = orient4d_s(pts[4], pts[5], pts[6], pts[7], newpt,
pts[4][3], pts[5][3], pts[6][3], pts[7][3],
newpt[3]);
} else {
sign = insphere_s(pts[4], pts[5], pts[6], pts[7], newpt);
}
if (sign < 0) {
point pd = newpt;
point pe = oppo(fliptets[1]);
// Check the convexity of its three edges. Stop checking either a
// locally non-convex edge (ori < 0) or a flat edge (ori = 0) is
// encountered, and 'fliptet' represents that edge.
for (i = 0; i < 3; i++) {
ori = orient3d(org(fliptets[0]), dest(fliptets[0]), pd, pe);
if (ori <= 0) break;
enextself(fliptets[0]);
}
if (ori > 0) {
// A 2-to-3 flip is found.
// [0] [a,b,c,d],
// [1] [b,a,c,e]. no dummypoint.
flip23(fliptets, 0, fc);
flipcount++;
} else { // ori <= 0
// The edge ('fliptets[0]' = [a',b',c',d]) is non-convex or flat,
// where the edge [a',b'] is one of [a,b], [b,c], and [c,a].
// Check if there are three or four tets sharing at this edge.
esymself(fliptets[0]); // [b,a,d,c]
for (i = 0; i < 3; i++) {
fnext(fliptets[i], fliptets[i+1]);
}
if (fliptets[3].tet == fliptets[0].tet) {
// A 3-to-2 flip is found. (No hull tet.)
flip32(fliptets, 0, fc);
flipcount++;
} else {
// There are more than 3 tets at this edge.
fnext(fliptets[3], fliptets[4]);
if (fliptets[4].tet == fliptets[0].tet) {
if (ori == 0) {
// A 4-to-4 flip is found. (Two hull tets may be involved.)
// Current tets in 'fliptets':
// [0] [b,a,d,c] (d may be newpt)
// [1] [b,a,c,e]
// [2] [b,a,e,f] (f may be dummypoint)
// [3] [b,a,f,d]
esymself(fliptets[0]); // [a,b,c,d]
// A 2-to-3 flip replaces face [a,b,c] by edge [e,d].
// This creates a degenerate tet [e,d,a,b] (tmpfliptets[0]). // It will be removed by the followed 3-to-2 flip.
flip23(fliptets, 0, fc); // No hull tet.
fnext(fliptets[3], fliptets[1]);
fnext(fliptets[1], fliptets[2]);
// Current tets in 'fliptets':
// [0] [...]
// [1] [b,a,d,e] (degenerated, d may be new point).
// [2] [b,a,e,f] (f may be dummypoint)
// [3] [b,a,f,d]
// A 3-to-2 flip replaces edge [b,a] by face [d,e,f].
// Hull tets may be involved (f may be dummypoint).
flip32(&(fliptets[1]), (apex(fliptets[3]) == dummypoint), fc);
flipcount++;
}
}
}
} // ori
} else {
// The adjacent tet is Delaunay. Mark it to avoid testing it again.
marktest(fliptets[1]);
// Save it for unmarking it later.
cavebdrylist->newindex((void **) &parytet);
*parytet = fliptets[1];
}
} // while (flipstack)
// Unmark saved tetrahedra.
for (i = 0; i < cavebdrylist->objects; i++) {
parytet = (triface *) fastlookup(cavebdrylist, i);
unmarktest(*parytet);
}
cavebdrylist->restart();
if (hullflag) {
// Unmark infected vertices.
for (i = 0; i < cavetetvertlist->objects; i++) {
parypt = (point *) fastlookup(cavetetvertlist, i);
puninfect(*parypt);
}
cavetetvertlist->restart();
}
return flipcount;
}
///////////////////////////////////////////////////////////////////////////////
// //
// initialdelaunay() Create an initial Delaunay tetrahedralization. //
// //
// The tetrahedralization contains only one tetrahedron abcd, and four hull //
// tetrahedra. The points pa, pb, pc, and pd must be linearly independent. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::initialdelaunay(point pa, point pb, point pc, point pd)
{
triface firsttet, tetopa, tetopb, tetopc, tetopd;
triface worktet, worktet1;
if (b->verbose > 2) {
printf(" Create init tet (%d, %d, %d, %d)\n", pointmark(pa),
pointmark(pb), pointmark(pc), pointmark(pd));
}
// Create the first tetrahedron.
maketetrahedron(&firsttet);
setvertices(firsttet, pa, pb, pc, pd);
// Create four hull tetrahedra. maketetrahedron(&tetopa);
setvertices(tetopa, pb, pc, pd, dummypoint);
maketetrahedron(&tetopb);
setvertices(tetopb, pc, pa, pd, dummypoint);
maketetrahedron(&tetopc);
setvertices(tetopc, pa, pb, pd, dummypoint);
maketetrahedron(&tetopd);
setvertices(tetopd, pb, pa, pc, dummypoint);
hullsize += 4;
// Connect hull tetrahedra to firsttet (at four faces of firsttet).
bond(firsttet, tetopd);
esym(firsttet, worktet);
bond(worktet, tetopc); // ab
enextesym(firsttet, worktet);
bond(worktet, tetopa); // bc
eprevesym(firsttet, worktet);
bond(worktet, tetopb); // ca
// Connect hull tetrahedra together (at six edges of firsttet).
esym(tetopc, worktet);
esym(tetopd, worktet1);
bond(worktet, worktet1); // ab
esym(tetopa, worktet);
eprevesym(tetopd, worktet1);
bond(worktet, worktet1); // bc
esym(tetopb, worktet);
enextesym(tetopd, worktet1);
bond(worktet, worktet1); // ca
eprevesym(tetopc, worktet);
enextesym(tetopb, worktet1);
bond(worktet, worktet1); // da
eprevesym(tetopa, worktet);
enextesym(tetopc, worktet1);
bond(worktet, worktet1); // db
eprevesym(tetopb, worktet);
enextesym(tetopa, worktet1);
bond(worktet, worktet1); // dc
// Set the vertex type.
if (pointtype(pa) == UNUSEDVERTEX) {
setpointtype(pa, VOLVERTEX);
}
if (pointtype(pb) == UNUSEDVERTEX) {
setpointtype(pb, VOLVERTEX);
}
if (pointtype(pc) == UNUSEDVERTEX) {
setpointtype(pc, VOLVERTEX);
}
if (pointtype(pd) == UNUSEDVERTEX) {
setpointtype(pd, VOLVERTEX);
}
setpoint2tet(pa, encode(firsttet));
setpoint2tet(pb, encode(firsttet));
setpoint2tet(pc, encode(firsttet));
setpoint2tet(pd, encode(firsttet));
// Remember the first tetrahedron.
recenttet = firsttet;
}
///////////////////////////////////////////////////////////////////////////////
// //
// incrementaldelaunay() Create a Delaunay tetrahedralization by //
// the incremental approach. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::incrementaldelaunay(clock_t& tv)
{
triface searchtet;
point *permutarray, swapvertex;
REAL v1[3], v2[3], n[3];
REAL bboxsize, bboxsize2, bboxsize3, ori;
int randindex;
int ngroup = 0;
int i, j;
if (!b->quiet) {
printf("Delaunizing vertices...\n");
}
// Form a random permuation (uniformly at random) of the set of vertices.
permutarray = new point[in->numberofpoints];
points->traversalinit();
if (b->no_sort) {
if (b->verbose) {
printf(" Using the input order.\n");
}
for (i = 0; i < in->numberofpoints; i++) {
permutarray[i] = (point) points->traverse();
}
} else {
if (b->verbose) {
printf(" Permuting vertices.\n");
}
srand(in->numberofpoints);
for (i = 0; i < in->numberofpoints; i++) {
randindex = rand() % (i + 1); // randomnation(i + 1);
permutarray[i] = permutarray[randindex];
permutarray[randindex] = (point) points->traverse();
}
if (b->brio_hilbert) { // -b option
if (b->verbose) {
printf(" Sorting vertices.\n");
}
hilbert_init(in->mesh_dim);
brio_multiscale_sort(permutarray, in->numberofpoints, b->brio_threshold,
b->brio_ratio, &ngroup);
}
}
tv = clock(); // Remember the time for sorting points.
// Calculate the diagonal size of its bounding box.
bboxsize = sqrt(norm2(xmax - xmin, ymax - ymin, zmax - zmin));
bboxsize2 = bboxsize * bboxsize;
bboxsize3 = bboxsize2 * bboxsize;
// Make sure the second vertex is not identical with the first one.
i = 1;
while ((distance(permutarray[0],permutarray[i])/bboxsize)<b->epsilon) {
i++;
if (i == in->numberofpoints - 1) {
printf("Exception: All vertices are (nearly) identical (Tol = %g).\n",
b->epsilon);
terminatetetgen(this, 10);
}
}
if (i > 1) {
// Swap to move the non-identical vertex from index i to index 1.
swapvertex = permutarray[i];
permutarray[i] = permutarray[1];
permutarray[1] = swapvertex;
}
// Make sure the third vertex is not collinear with the first two. // Acknowledgement: Thanks Jan Pomplun for his correction by using
// epsilon^2 and epsilon^3 (instead of epsilon). 2013-08-15.
i = 2;
for (j = 0; j < 3; j++) {
v1[j] = permutarray[1][j] - permutarray[0][j];
v2[j] = permutarray[i][j] - permutarray[0][j];
}
cross(v1, v2, n);
while ((sqrt(norm2(n[0], n[1], n[2])) / bboxsize2) <
(b->epsilon * b->epsilon)) {
i++;
if (i == in->numberofpoints - 1) {
printf("Exception: All vertices are (nearly) collinear (Tol = %g).\n",
b->epsilon);
terminatetetgen(this, 10);
}
for (j = 0; j < 3; j++) {
v2[j] = permutarray[i][j] - permutarray[0][j];
}
cross(v1, v2, n);
}
if (i > 2) {
// Swap to move the non-identical vertex from index i to index 1.
swapvertex = permutarray[i];
permutarray[i] = permutarray[2];
permutarray[2] = swapvertex;
}
// Make sure the fourth vertex is not coplanar with the first three.
i = 3;
ori = orient3dfast(permutarray[0], permutarray[1], permutarray[2],
permutarray[i]);
while ((fabs(ori) / bboxsize3) < (b->epsilon * b->epsilon * b->epsilon)) {
i++;
if (i == in->numberofpoints) {
printf("Exception: All vertices are coplanar (Tol = %g).\n",
b->epsilon);
terminatetetgen(this, 10);
}
ori = orient3dfast(permutarray[0], permutarray[1], permutarray[2],
permutarray[i]);
}
if (i > 3) {
// Swap to move the non-identical vertex from index i to index 1.
swapvertex = permutarray[i];
permutarray[i] = permutarray[3];
permutarray[3] = swapvertex;
}
// Orient the first four vertices in permutarray so that they follow the
// right-hand rule.
if (ori > 0.0) {
// Swap the first two vertices.
swapvertex = permutarray[0];
permutarray[0] = permutarray[1];
permutarray[1] = swapvertex;
}
// Create the initial Delaunay tetrahedralization.
initialdelaunay(permutarray[0], permutarray[1], permutarray[2],
permutarray[3]);
if (b->verbose) {
printf(" Incrementally inserting vertices.\n");
}
insertvertexflags ivf;
flipconstraints fc;
// Choose algorithm: Bowyer-Watson (default) or Incremental Flip
if (b->incrflip) { ivf.bowywat = 0;
ivf.lawson = 1;
fc.enqflag = 1;
} else {
ivf.bowywat = 1;
ivf.lawson = 0;
}
for (i = 4; i < in->numberofpoints; i++) {
if (pointtype(permutarray[i]) == UNUSEDVERTEX) {
setpointtype(permutarray[i], VOLVERTEX);
}
if (b->brio_hilbert || b->no_sort) { // -b or -b/1
// Start the last updated tet.
searchtet.tet = recenttet.tet;
} else { // -b0
// Randomly choose the starting tet for point location.
searchtet.tet = NULL;
}
ivf.iloc = (int) OUTSIDE;
// Insert the vertex.
if (insertpoint(permutarray[i], &searchtet, NULL, NULL, &ivf)) {
if (flipstack != NULL) {
// Perform flip to recover Delaunayness.
incrementalflip(permutarray[i], (ivf.iloc == (int) OUTSIDE), &fc);
}
} else {
if (ivf.iloc == (int) ONVERTEX) {
// The point already exists. Mark it and do nothing on it.
swapvertex = org(searchtet);
if (b->object != tetgenbehavior::STL) {
if (!b->quiet) {
printf("Warning: Point #%d is coincident with #%d. Ignored!\n",
pointmark(permutarray[i]), pointmark(swapvertex));
}
}
setpoint2ppt(permutarray[i], swapvertex);
setpointtype(permutarray[i], DUPLICATEDVERTEX);
dupverts++;
} else if (ivf.iloc == (int) NEARVERTEX) {
swapvertex = org(searchtet);
if (!b->quiet) {
printf("Warning: Point %d is replaced by point %d.\n",
pointmark(permutarray[i]), pointmark(swapvertex));
printf(" Avoid creating a very short edge (len = %g) (< %g).\n",
permutarray[i][3], minedgelength);
printf(" You may try a smaller tolerance (-T) (current is %g)\n",
b->epsilon);
printf(" or use the option -M0/1 to avoid such replacement.\n");
}
// Remember it is a duplicated point.
setpoint2ppt(permutarray[i], swapvertex);
setpointtype(permutarray[i], DUPLICATEDVERTEX);
dupverts++;
} else if (ivf.iloc == (int) NONREGULAR) {
// The point is non-regular. Skipped.
if (b->verbose) {
printf(" Point #%d is non-regular, skipped.\n",
pointmark(permutarray[i]));
}
setpointtype(permutarray[i], NREGULARVERTEX);
nonregularcount++;
}
}
}
delete [] permutarray;}
//// ////
//// ////
//// delaunay_cxx /////////////////////////////////////////////////////////////
//// surface_cxx //////////////////////////////////////////////////////////////
//// ////
//// ////
///////////////////////////////////////////////////////////////////////////////
// //
// flipshpush() Push a facet edge into flip stack. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flipshpush(face* flipedge)
{
badface *newflipface;
newflipface = (badface *) flippool->alloc();
newflipface->ss = *flipedge;
newflipface->forg = sorg(*flipedge);
newflipface->fdest = sdest(*flipedge);
newflipface->nextitem = flipstack;
flipstack = newflipface;
}
///////////////////////////////////////////////////////////////////////////////
// //
// flip22() Perform a 2-to-2 flip in surface mesh. //
// //
// 'flipfaces' is an array of two subfaces. On input, they are [a,b,c] and //
// [b,a,d]. On output, they are [c,d,b] and [d,c,a]. As a result, edge [a,b] //
// is replaced by edge [c,d]. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flip22(face* flipfaces, int flipflag, int chkencflag)
{
face bdedges[4], outfaces[4], infaces[4];
face bdsegs[4];
face checkface;
point pa, pb, pc, pd;
int i;
pa = sorg(flipfaces[0]);
pb = sdest(flipfaces[0]);
pc = sapex(flipfaces[0]);
pd = sapex(flipfaces[1]);
if (sorg(flipfaces[1]) != pb) {
sesymself(flipfaces[1]);
}
flip22count++;
// Collect the four boundary edges.
senext(flipfaces[0], bdedges[0]);
senext2(flipfaces[0], bdedges[1]);
senext(flipfaces[1], bdedges[2]);
senext2(flipfaces[1], bdedges[3]);
// Collect outer boundary faces.
for (i = 0; i < 4; i++) {
spivot(bdedges[i], outfaces[i]);
infaces[i] = outfaces[i];
sspivot(bdedges[i], bdsegs[i]);
if (outfaces[i].sh != NULL) {
if (isshsubseg(bdedges[i])) { spivot(infaces[i], checkface);
while (checkface.sh != bdedges[i].sh) {
infaces[i] = checkface;
spivot(infaces[i], checkface);
}
}
}
}
// The flags set in these two subfaces do not change.
// Shellmark does not change.
// area constraint does not change.
// Transform [a,b,c] -> [c,d,b].
setshvertices(flipfaces[0], pc, pd, pb);
// Transform [b,a,d] -> [d,c,a].
setshvertices(flipfaces[1], pd, pc, pa);
// Update the point-to-subface map.
if (pointtype(pa) == FREEFACETVERTEX) {
setpoint2sh(pa, sencode(flipfaces[1]));
}
if (pointtype(pb) == FREEFACETVERTEX) {
setpoint2sh(pb, sencode(flipfaces[0]));
}
if (pointtype(pc) == FREEFACETVERTEX) {
setpoint2sh(pc, sencode(flipfaces[0]));
}
if (pointtype(pd) == FREEFACETVERTEX) {
setpoint2sh(pd, sencode(flipfaces[0]));
}
// Reconnect boundary edges to outer boundary faces.
for (i = 0; i < 4; i++) {
if (outfaces[(3 + i) % 4].sh != NULL) {
// Make sure that the subface has the ori as the segment.
if (bdsegs[(3 + i) % 4].sh != NULL) {
bdsegs[(3 + i) % 4].shver = 0;
if (sorg(bdedges[i]) != sorg(bdsegs[(3 + i) % 4])) {
sesymself(bdedges[i]);
}
}
sbond1(bdedges[i], outfaces[(3 + i) % 4]);
sbond1(infaces[(3 + i) % 4], bdedges[i]);
} else {
sdissolve(bdedges[i]);
}
if (bdsegs[(3 + i) % 4].sh != NULL) {
ssbond(bdedges[i], bdsegs[(3 + i) % 4]);
if (chkencflag & 1) {
// Queue this segment for encroaching check.
enqueuesubface(badsubsegs, &(bdsegs[(3 + i) % 4]));
}
} else {
ssdissolve(bdedges[i]);
}
}
if (chkencflag & 2) {
// Queue the flipped subfaces for quality/encroaching checks.
for (i = 0; i < 2; i++) {
enqueuesubface(badsubfacs, &(flipfaces[i]));
}
}
recentsh = flipfaces[0];
if (flipflag) {
// Put the boundary edges into flip stack.
for (i = 0; i < 4; i++) { flipshpush(&(bdedges[i]));
}
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// flip31() Remove a vertex by transforming 3-to-1 subfaces. //
// //
// 'flipfaces' is an array of subfaces. Its length is at least 4. On input, //
// the first three faces are: [p,a,b], [p,b,c], and [p,c,a]. This routine //
// replaces them by one face [a,b,c], it is returned in flipfaces[3]. //
// //
// NOTE: The three old subfaces are not deleted within this routine. They //
// still hold pointers to their adjacent subfaces. These informations are //
// needed by the routine 'sremovevertex()' for recovering a segment. //
// The caller of this routine must delete the old subfaces after their uses. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::flip31(face* flipfaces, int flipflag)
{
face bdedges[3], outfaces[3], infaces[3];
face bdsegs[3];
face checkface;
point pa, pb, pc;
int i;
pa = sdest(flipfaces[0]);
pb = sdest(flipfaces[1]);
pc = sdest(flipfaces[2]);
flip31count++;
// Collect all infos at the three boundary edges.
for (i = 0; i < 3; i++) {
senext(flipfaces[i], bdedges[i]);
spivot(bdedges[i], outfaces[i]);
infaces[i] = outfaces[i];
sspivot(bdedges[i], bdsegs[i]);
if (outfaces[i].sh != NULL) {
if (isshsubseg(bdedges[i])) {
spivot(infaces[i], checkface);
while (checkface.sh != bdedges[i].sh) {
infaces[i] = checkface;
spivot(infaces[i], checkface);
}
}
}
} // i
// Create a new subface.
makeshellface(subfaces, &(flipfaces[3]));
setshvertices(flipfaces[3], pa, pb,pc);
setshellmark(flipfaces[3], shellmark(flipfaces[0]));
if (checkconstraints) {
//area = areabound(flipfaces[0]);
setareabound(flipfaces[3], areabound(flipfaces[0]));
}
if (useinsertradius) {
setfacetindex(flipfaces[3], getfacetindex(flipfaces[0]));
}
// Update the point-to-subface map.
if (pointtype(pa) == FREEFACETVERTEX) {
setpoint2sh(pa, sencode(flipfaces[3]));
}
if (pointtype(pb) == FREEFACETVERTEX) {
setpoint2sh(pb, sencode(flipfaces[3]));
} if (pointtype(pc) == FREEFACETVERTEX) {
setpoint2sh(pc, sencode(flipfaces[3]));
}
// Update the three new boundary edges.
bdedges[0] = flipfaces[3]; // [a,b]
senext(flipfaces[3], bdedges[1]); // [b,c]
senext2(flipfaces[3], bdedges[2]); // [c,a]
// Reconnect boundary edges to outer boundary faces.
for (i = 0; i < 3; i++) {
if (outfaces[i].sh != NULL) {
// Make sure that the subface has the ori as the segment.
if (bdsegs[i].sh != NULL) {
bdsegs[i].shver = 0;
if (sorg(bdedges[i]) != sorg(bdsegs[i])) {
sesymself(bdedges[i]);
}
}
sbond1(bdedges[i], outfaces[i]);
sbond1(infaces[i], bdedges[i]);
}
if (bdsegs[i].sh != NULL) {
ssbond(bdedges[i], bdsegs[i]);
}
}
recentsh = flipfaces[3];
if (flipflag) {
// Put the boundary edges into flip stack.
for (i = 0; i < 3; i++) {
flipshpush(&(bdedges[i]));
}
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// lawsonflip() Flip non-locally Delaunay edges. //
// //
///////////////////////////////////////////////////////////////////////////////
long tetgenmesh::lawsonflip()
{
badface *popface;
face flipfaces[2];
point pa, pb, pc, pd;
REAL sign;
long flipcount = 0;
if (b->verbose > 2) {
printf(" Lawson flip %ld edges.\n", flippool->items);
}
while (flipstack != (badface *) NULL) {
// Pop an edge from the stack.
popface = flipstack;
flipfaces[0] = popface->ss;
pa = popface->forg;
pb = popface->fdest;
flipstack = popface->nextitem; // The next top item in stack.
flippool->dealloc((void *) popface);
// Skip it if it is dead.
if (flipfaces[0].sh[3] == NULL) continue;
// Skip it if it is not the same edge as we saved.
if ((sorg(flipfaces[0]) != pa) || (sdest(flipfaces[0]) != pb)) continue;
// Skip it if it is a subsegment. if (isshsubseg(flipfaces[0])) continue;
// Get the adjacent face.
spivot(flipfaces[0], flipfaces[1]);
if (flipfaces[1].sh == NULL) continue; // Skip a hull edge.
pc = sapex(flipfaces[0]);
pd = sapex(flipfaces[1]);
sign = incircle3d(pa, pb, pc, pd);
if (sign < 0) {
// It is non-locally Delaunay. Flip it.
flip22(flipfaces, 1, 0);
flipcount++;
}
}
if (b->verbose > 2) {
printf(" Performed %ld flips.\n", flipcount);
}
return flipcount;
}
///////////////////////////////////////////////////////////////////////////////
// //
// sinsertvertex() Insert a vertex into a triangulation of a facet. //
// //
// This function uses three global arrays: 'caveshlist', 'caveshbdlist', and //
// 'caveshseglist'. On return, 'caveshlist' contains old subfaces in C(p), //
// 'caveshbdlist' contains new subfaces in C(p). If the new point lies on a //
// segment, 'cavesegshlist' returns the two new subsegments. //
// //
// 'iloc' suggests the location of the point. If it is OUTSIDE, this routine //
// will first locate the point. It starts searching from 'searchsh' or 'rec- //
// entsh' if 'searchsh' is NULL. //
// //
// If 'bowywat' is set (1), the Bowyer-Watson algorithm is used to insert //
// the vertex. Otherwise, only insert the vertex in the initial cavity. //
// //
// If 'iloc' is 'INSTAR', this means the cavity of this vertex was already //
// provided in the list 'caveshlist'. //
// //
// If 'splitseg' is not NULL, the new vertex lies on the segment and it will //
// be split. 'iloc' must be either 'ONEDGE' or 'INSTAR'. //
// //
// 'rflag' (rounding) is a parameter passed to slocate() function. If it is //
// set, after the location of the point is found, either ONEDGE or ONFACE, //
// round the result using an epsilon. //
// //
// NOTE: the old subfaces in C(p) are not deleted. They're needed in case we //
// want to remove the new point immediately. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::sinsertvertex(point insertpt, face *searchsh, face *splitseg,
int iloc, int bowywat, int rflag)
{
face cavesh, neighsh, *parysh;
face newsh, casout, casin;
face checkseg;
point pa, pb;
enum locateresult loc = OUTSIDE;
REAL sign, ori;
int i, j;
if (b->verbose > 2) {
printf(" Insert facet point %d.\n", pointmark(insertpt));
}
if (bowywat == 3) {
loc = INSTAR;
}
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
// A segment is going to be split, no point location.
spivot(*splitseg, *searchsh);
if (loc != INSTAR) loc = ONEDGE;
} else {
if (loc != INSTAR) loc = (enum locateresult) iloc;
if (loc == OUTSIDE) {
// Do point location in surface mesh.
if (searchsh->sh == NULL) {
*searchsh = recentsh;
}
// Search the vertex. An above point must be provided ('aflag' = 1).
loc = slocate(insertpt, searchsh, 1, 1, rflag);
}
}
// Form the initial sC(p).
if (loc == ONFACE) {
// Add the face into list (in B-W cavity).
smarktest(*searchsh);
caveshlist->newindex((void **) &parysh);
*parysh = *searchsh;
} else if (loc == ONEDGE) {
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
splitseg->shver = 0;
pa = sorg(*splitseg);
} else {
pa = sorg(*searchsh);
}
if (searchsh->sh != NULL) {
// Collect all subfaces share at this edge.
neighsh = *searchsh;
while (1) {
// Adjust the origin of its edge to be 'pa'.
if (sorg(neighsh) != pa) sesymself(neighsh);
// Add this face into list (in B-W cavity).
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
*parysh = neighsh;
// Add this face into face-at-splitedge list.
cavesegshlist->newindex((void **) &parysh);
*parysh = neighsh;
// Go to the next face at the edge.
spivotself(neighsh);
// Stop if all faces at the edge have been visited.
if (neighsh.sh == searchsh->sh) break;
if (neighsh.sh == NULL) break;
}
} // If (not a non-dangling segment).
} else if (loc == ONVERTEX) {
return (int) loc;
} else if (loc == OUTSIDE) {
// Comment: This should only happen during the surface meshing step.
// Enlarge the convex hull of the triangulation by including p.
// An above point of the facet is set in 'dummypoint' to replace
// orient2d tests by orient3d tests.
// Imagine that the current edge a->b (in 'searchsh') is horizontal in a
// plane, and a->b is directed from left to right, p lies above a->b.
// Find the right-most edge of the triangulation which is visible by p.
neighsh = *searchsh;
while (1) {
senext2self(neighsh);
spivot(neighsh, casout);
if (casout.sh == NULL) {
// A convex hull edge. Is it visible by p. ori = orient3d(sorg(neighsh), sdest(neighsh), dummypoint, insertpt);
if (ori < 0) {
*searchsh = neighsh; // Visible, update 'searchsh'.
} else {
break; // 'searchsh' is the right-most visible edge.
}
} else {
if (sorg(casout) != sdest(neighsh)) sesymself(casout);
neighsh = casout;
}
}
// Create new triangles for all visible edges of p (from right to left).
casin.sh = NULL; // No adjacent face at right.
pa = sorg(*searchsh);
pb = sdest(*searchsh);
while (1) {
// Create a new subface on top of the (visible) edge.
makeshellface(subfaces, &newsh);
setshvertices(newsh, pb, pa, insertpt);
setshellmark(newsh, shellmark(*searchsh));
if (checkconstraints) {
//area = areabound(*searchsh);
setareabound(newsh, areabound(*searchsh));
}
if (useinsertradius) {
setfacetindex(newsh, getfacetindex(*searchsh));
}
// Connect the new subface to the bottom subfaces.
sbond1(newsh, *searchsh);
sbond1(*searchsh, newsh);
// Connect the new subface to its right-adjacent subface.
if (casin.sh != NULL) {
senext(newsh, casout);
sbond1(casout, casin);
sbond1(casin, casout);
}
// The left-adjacent subface has not been created yet.
senext2(newsh, casin);
// Add the new face into list (inside the B-W cavity).
smarktest(newsh);
caveshlist->newindex((void **) &parysh);
*parysh = newsh;
// Move to the convex hull edge at the left of 'searchsh'.
neighsh = *searchsh;
while (1) {
senextself(neighsh);
spivot(neighsh, casout);
if (casout.sh == NULL) {
*searchsh = neighsh;
break;
}
if (sorg(casout) != sdest(neighsh)) sesymself(casout);
neighsh = casout;
}
// A convex hull edge. Is it visible by p.
pa = sorg(*searchsh);
pb = sdest(*searchsh);
ori = orient3d(pa, pb, dummypoint, insertpt);
// Finish the process if p is not visible by the hull edge.
if (ori >= 0) break;
}
} else if (loc == INSTAR) {
// Under this case, the sub-cavity sC(p) has already been formed in
// insertvertex().
}
// Form the Bowyer-Watson cavity sC(p).
for (i = 0; i < caveshlist->objects; i++) {
cavesh = * (face *) fastlookup(caveshlist, i);
for (j = 0; j < 3; j++) { if (!isshsubseg(cavesh)) {
spivot(cavesh, neighsh);
if (neighsh.sh != NULL) {
// The adjacent face exists.
if (!smarktested(neighsh)) {
if (bowywat) {
if (loc == INSTAR) { // if (bowywat > 2) {
// It must be a boundary edge.
sign = 1;
} else {
// Check if this subface is connected to adjacent tet(s).
if (!isshtet(neighsh)) {
// Check if the subface is non-Delaunay wrt. the new pt.
sign = incircle3d(sorg(neighsh), sdest(neighsh),
sapex(neighsh), insertpt);
} else {
// It is connected to an adjacent tet. A boundary edge.
sign = 1;
}
}
if (sign < 0) {
// Add the adjacent face in list (in B-W cavity).
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
*parysh = neighsh;
}
} else {
sign = 1; // A boundary edge.
}
} else {
sign = -1; // Not a boundary edge.
}
} else {
// No adjacent face. It is a hull edge.
if (loc == OUTSIDE) {
// It is a boundary edge if it does not contain p.
if ((sorg(cavesh) == insertpt) || (sdest(cavesh) == insertpt)) {
sign = -1; // Not a boundary edge.
} else {
sign = 1; // A boundary edge.
}
} else {
sign = 1; // A boundary edge.
}
}
} else {
// Do not across a segment. It is a boundary edge.
sign = 1;
}
if (sign >= 0) {
// Add a boundary edge.
caveshbdlist->newindex((void **) &parysh);
*parysh = cavesh;
}
senextself(cavesh);
} // j
} // i
// Creating new subfaces.
for (i = 0; i < caveshbdlist->objects; i++) {
parysh = (face *) fastlookup(caveshbdlist, i);
sspivot(*parysh, checkseg);
if ((parysh->shver & 01) != 0) sesymself(*parysh);
pa = sorg(*parysh);
pb = sdest(*parysh);
// Create a new subface.
makeshellface(subfaces, &newsh);
setshvertices(newsh, pa, pb, insertpt);
setshellmark(newsh, shellmark(*parysh)); if (checkconstraints) {
//area = areabound(*parysh);
setareabound(newsh, areabound(*parysh));
}
if (useinsertradius) {
setfacetindex(newsh, getfacetindex(*parysh));
}
// Update the point-to-subface map.
if (pointtype(pa) == FREEFACETVERTEX) {
setpoint2sh(pa, sencode(newsh));
}
if (pointtype(pb) == FREEFACETVERTEX) {
setpoint2sh(pb, sencode(newsh));
}
// Connect newsh to outer subfaces.
spivot(*parysh, casout);
if (casout.sh != NULL) {
casin = casout;
if (checkseg.sh != NULL) {
// Make sure that newsh has the right ori at this segment.
checkseg.shver = 0;
if (sorg(newsh) != sorg(checkseg)) {
sesymself(newsh);
sesymself(*parysh); // This side should also be inverse.
}
spivot(casin, neighsh);
while (neighsh.sh != parysh->sh) {
casin = neighsh;
spivot(casin, neighsh);
}
}
sbond1(newsh, casout);
sbond1(casin, newsh);
}
if (checkseg.sh != NULL) {
ssbond(newsh, checkseg);
}
// Connect oldsh <== newsh (for connecting adjacent new subfaces).
// *parysh and newsh point to the same edge and the same ori.
sbond1(*parysh, newsh);
}
if (newsh.sh != NULL) {
// Set a handle for searching.
recentsh = newsh;
}
// Update the point-to-subface map.
if (pointtype(insertpt) == FREEFACETVERTEX) {
setpoint2sh(insertpt, sencode(newsh));
}
// Connect adjacent new subfaces together.
for (i = 0; i < caveshbdlist->objects; i++) {
// Get an old subface at edge [a, b].
parysh = (face *) fastlookup(caveshbdlist, i);
spivot(*parysh, newsh); // The new subface [a, b, p].
senextself(newsh); // At edge [b, p].
spivot(newsh, neighsh);
if (neighsh.sh == NULL) {
// Find the adjacent new subface at edge [b, p].
pb = sdest(*parysh);
neighsh = *parysh;
while (1) {
senextself(neighsh);
spivotself(neighsh);
if (neighsh.sh == NULL) break;
if (!smarktested(neighsh)) break;
if (sdest(neighsh) != pb) sesymself(neighsh);
} if (neighsh.sh != NULL) {
// Now 'neighsh' is a new subface at edge [b, #].
if (sorg(neighsh) != pb) sesymself(neighsh);
senext2self(neighsh); // Go to the open edge [p, b].
sbond(newsh, neighsh);
}
}
spivot(*parysh, newsh); // The new subface [a, b, p].
senext2self(newsh); // At edge [p, a].
spivot(newsh, neighsh);
if (neighsh.sh == NULL) {
// Find the adjacent new subface at edge [p, a].
pa = sorg(*parysh);
neighsh = *parysh;
while (1) {
senext2self(neighsh);
spivotself(neighsh);
if (neighsh.sh == NULL) break;
if (!smarktested(neighsh)) break;
if (sorg(neighsh) != pa) sesymself(neighsh);
}
if (neighsh.sh != NULL) {
// Now 'neighsh' is a new subface at edge [#, a].
if (sdest(neighsh) != pa) sesymself(neighsh);
senextself(neighsh); // Go to the open edge [a, p].
sbond(newsh, neighsh);
}
}
}
if ((loc == ONEDGE) || ((splitseg != NULL) && (splitseg->sh != NULL))
|| (cavesegshlist->objects > 0l)) {
// An edge is being split. We distinguish two cases:
// (1) the edge is not on the boundary of the cavity;
// (2) the edge is on the boundary of the cavity.
// In case (2), the edge is either a segment or a hull edge. There are
// degenerated new faces in the cavity. They must be removed.
face aseg, bseg, aoutseg, boutseg;
for (i = 0; i < cavesegshlist->objects; i++) {
// Get the saved old subface.
parysh = (face *) fastlookup(cavesegshlist, i);
// Get a possible new degenerated subface.
spivot(*parysh, cavesh);
if (sapex(cavesh) == insertpt) {
// Found a degenerated new subface, i.e., case (2).
if (cavesegshlist->objects > 1) {
// There are more than one subface share at this edge.
j = (i + 1) % (int) cavesegshlist->objects;
parysh = (face *) fastlookup(cavesegshlist, j);
spivot(*parysh, neighsh);
// Adjust cavesh and neighsh both at edge a->b, and has p as apex.
if (sorg(neighsh) != sorg(cavesh)) {
sesymself(neighsh);
}
// Connect adjacent faces at two other edges of cavesh and neighsh.
// As a result, the two degenerated new faces are squeezed from the
// new triangulation of the cavity. Note that the squeezed faces
// still hold the adjacent informations which will be used in
// re-connecting subsegments (if they exist).
for (j = 0; j < 2; j++) {
senextself(cavesh);
senextself(neighsh);
spivot(cavesh, newsh);
spivot(neighsh, casout);
sbond1(newsh, casout); // newsh <- casout.
}
} else {
// There is only one subface containing this edge [a,b]. Squeeze the
// degenerated new face [a,b,c] by disconnecting it from its two // adjacent subfaces at edges [b,c] and [c,a]. Note that the face
// [a,b,c] still hold the connection to them.
for (j = 0; j < 2; j++) {
senextself(cavesh);
spivot(cavesh, newsh);
sdissolve(newsh);
}
}
//recentsh = newsh;
// Update the point-to-subface map.
if (pointtype(insertpt) == FREEFACETVERTEX) {
setpoint2sh(insertpt, sencode(newsh));
}
}
}
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
if (loc != INSTAR) { // if (bowywat < 3) {
smarktest(*splitseg); // Mark it as being processed.
}
aseg = *splitseg;
pa = sorg(*splitseg);
pb = sdest(*splitseg);
// Insert the new point p.
makeshellface(subsegs, &aseg);
makeshellface(subsegs, &bseg);
setshvertices(aseg, pa, insertpt, NULL);
setshvertices(bseg, insertpt, pb, NULL);
setshellmark(aseg, shellmark(*splitseg));
setshellmark(bseg, shellmark(*splitseg));
if (checkconstraints) {
setareabound(aseg, areabound(*splitseg));
setareabound(bseg, areabound(*splitseg));
}
if (useinsertradius) {
setfacetindex(aseg, getfacetindex(*splitseg));
setfacetindex(bseg, getfacetindex(*splitseg));
}
// Connect [#, a]<->[a, p].
senext2(*splitseg, boutseg); // Temporarily use boutseg.
spivotself(boutseg);
if (boutseg.sh != NULL) {
senext2(aseg, aoutseg);
sbond(boutseg, aoutseg);
}
// Connect [p, b]<->[b, #].
senext(*splitseg, aoutseg);
spivotself(aoutseg);
if (aoutseg.sh != NULL) {
senext(bseg, boutseg);
sbond(boutseg, aoutseg);
}
// Connect [a, p] <-> [p, b].
senext(aseg, aoutseg);
senext2(bseg, boutseg);
sbond(aoutseg, boutseg);
// Connect subsegs [a, p] and [p, b] to adjacent new subfaces.
// Although the degenerated new faces have been squeezed. They still
// hold the connections to the actual new faces.
for (i = 0; i < cavesegshlist->objects; i++) {
parysh = (face *) fastlookup(cavesegshlist, i);
spivot(*parysh, neighsh);
// neighsh is a degenerated new face.
if (sorg(neighsh) != pa) {
sesymself(neighsh); }
senext2(neighsh, newsh);
spivotself(newsh); // The edge [p, a] in newsh
ssbond(newsh, aseg);
senext(neighsh, newsh);
spivotself(newsh); // The edge [b, p] in newsh
ssbond(newsh, bseg);
}
// Let the point remember the segment it lies on.
if (pointtype(insertpt) == FREESEGVERTEX) {
setpoint2sh(insertpt, sencode(aseg));
}
// Update the point-to-seg map.
if (pointtype(pa) == FREESEGVERTEX) {
setpoint2sh(pa, sencode(aseg));
}
if (pointtype(pb) == FREESEGVERTEX) {
setpoint2sh(pb, sencode(bseg));
}
} // if ((splitseg != NULL) && (splitseg->sh != NULL))
// Delete all degenerated new faces.
for (i = 0; i < cavesegshlist->objects; i++) {
parysh = (face *) fastlookup(cavesegshlist, i);
spivotself(*parysh);
if (sapex(*parysh) == insertpt) {
shellfacedealloc(subfaces, parysh->sh);
}
}
cavesegshlist->restart();
if ((splitseg != NULL) && (splitseg->sh != NULL)) {
// Return the two new subsegments (for further process).
// Re-use 'cavesegshlist'.
cavesegshlist->newindex((void **) &parysh);
*parysh = aseg;
cavesegshlist->newindex((void **) &parysh);
*parysh = bseg;
}
} // if (loc == ONEDGE)
return (int) loc;
}
///////////////////////////////////////////////////////////////////////////////
// //
// sremovevertex() Remove a vertex from the surface mesh. //
// //
// 'delpt' (p) is the vertex to be removed. If 'parentseg' is not NULL, p is //
// a segment vertex, and the origin of 'parentseg' is p. Otherwise, p is a //
// facet vertex, and the origin of 'parentsh' is p. //
// //
// Within each facet, we first use a sequence of 2-to-2 flips to flip any //
// edge at p, finally use a 3-to-1 flip to remove p. //
// //
// All new created subfaces are returned in the global array 'caveshbdlist'. //
// The new segment (when p is on segment) is returned in 'parentseg'. //
// //
// If 'lawson' > 0, the Lawson flip algorithm is used to recover Delaunay- //
// ness after p is removed. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::sremovevertex(point delpt, face* parentsh, face* parentseg,
int lawson)
{
face flipfaces[4], spinsh, *parysh; point pa, pb, pc, pd;
REAL ori1, ori2;
int it, i, j;
if (parentseg != NULL) {
// 'delpt' (p) should be a Steiner point inserted in a segment [a,b],
// where 'parentseg' should be [p,b]. Find the segment [a,p].
face startsh, neighsh, nextsh;
face abseg, prevseg, checkseg;
face adjseg1, adjseg2;
face fakesh;
senext2(*parentseg, prevseg);
spivotself(prevseg);
prevseg.shver = 0;
// Restore the original segment [a,b].
pa = sorg(prevseg);
pb = sdest(*parentseg);
if (b->verbose > 2) {
printf(" Remove vertex %d from segment [%d, %d].\n",
pointmark(delpt), pointmark(pa), pointmark(pb));
}
makeshellface(subsegs, &abseg);
setshvertices(abseg, pa, pb, NULL);
setshellmark(abseg, shellmark(*parentseg));
if (checkconstraints) {
setareabound(abseg, areabound(*parentseg));
}
if (useinsertradius) {
setfacetindex(abseg, getfacetindex(*parentseg));
}
// Connect [#, a]<->[a, b].
senext2(prevseg, adjseg1);
spivotself(adjseg1);
if (adjseg1.sh != NULL) {
adjseg1.shver = 0;
senextself(adjseg1);
senext2(abseg, adjseg2);
sbond(adjseg1, adjseg2);
}
// Connect [a, b]<->[b, #].
senext(*parentseg, adjseg1);
spivotself(adjseg1);
if (adjseg1.sh != NULL) {
adjseg1.shver = 0;
senext2self(adjseg1);
senext(abseg, adjseg2);
sbond(adjseg1, adjseg2);
}
// Update the point-to-segment map.
setpoint2sh(pa, sencode(abseg));
setpoint2sh(pb, sencode(abseg));
// Get the faces in face ring at segment [p, b].
// Re-use array 'caveshlist'.
spivot(*parentseg, *parentsh);
if (parentsh->sh != NULL) {
spinsh = *parentsh;
while (1) {
// Save this face in list.
caveshlist->newindex((void **) &parysh);
*parysh = spinsh;
// Go to the next face in the ring.
spivotself(spinsh);
if (spinsh.sh == NULL) {
break; // It is possible there is only one facet.
}
if (spinsh.sh == parentsh->sh) break;
}
}
// Create the face ring of the new segment [a,b]. Each face in the ring
// is [a,b,p] (degenerated!). It will be removed (automatically).
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
startsh = *parysh;
if (sorg(startsh) != delpt) {
sesymself(startsh);
}
// startsh is [p, b, #1], find the subface [a, p, #2].
neighsh = startsh;
while (1) {
senext2self(neighsh);
sspivot(neighsh, checkseg);
if (checkseg.sh != NULL) {
// It must be the segment [a, p].
break;
}
spivotself(neighsh);
if (sorg(neighsh) != delpt) sesymself(neighsh);
}
// Now neighsh is [a, p, #2].
if (neighsh.sh != startsh.sh) {
// Detach the two subsegments [a,p] and [p,b] from subfaces.
ssdissolve(startsh);
ssdissolve(neighsh);
// Create a degenerated subface [a,b,p]. It is used to: (1) hold the
// new segment [a,b]; (2) connect to the two adjacent subfaces
// [p,b,#] and [a,p,#].
makeshellface(subfaces, &fakesh);
setshvertices(fakesh, pa, pb, delpt);
setshellmark(fakesh, shellmark(startsh));
// Connect fakesh to the segment [a,b].
ssbond(fakesh, abseg);
// Connect fakesh to adjacent subfaces: [p,b,#1] and [a,p,#2].
senext(fakesh, nextsh);
sbond(nextsh, startsh);
senext2(fakesh, nextsh);
sbond(nextsh, neighsh);
smarktest(fakesh); // Mark it as faked.
} else {
// Special case. There exists already a degenerated face [a,b,p]!
// There is no need to create a faked subface here.
senext2self(neighsh); // [a,b,p]
// Since we will re-connect the face ring using the faked subfaces.
// We put the adjacent face of [a,b,p] to the list.
spivot(neighsh, startsh); // The original adjacent subface.
if (sorg(startsh) != pa) sesymself(startsh);
sdissolve(startsh);
// Connect fakesh to the segment [a,b].
ssbond(startsh, abseg);
fakesh = startsh; // Do not mark it!
// Delete the degenerated subface.
shellfacedealloc(subfaces, neighsh.sh);
}
// Save the fakesh in list (for re-creating the face ring).
cavesegshlist->newindex((void **) &parysh);
*parysh = fakesh;
} // i
caveshlist->restart();
// Re-create the face ring.
if (cavesegshlist->objects > 1) {
for (i = 0; i < cavesegshlist->objects; i++) {
parysh = (face *) fastlookup(cavesegshlist, i);
fakesh = *parysh;
// Get the next face in the ring.
j = (i + 1) % cavesegshlist->objects;
parysh = (face *) fastlookup(cavesegshlist, j);
nextsh = *parysh;
sbond1(fakesh, nextsh); }
}
// Delete the two subsegments containing p.
shellfacedealloc(subsegs, parentseg->sh);
shellfacedealloc(subsegs, prevseg.sh);
// Return the new segment.
*parentseg = abseg;
} else {
// p is inside the surface.
if (b->verbose > 2) {
printf(" Remove vertex %d from surface.\n", pointmark(delpt));
}
// Let 'delpt' be its apex.
senextself(*parentsh);
// For unifying the code, we add parentsh to list.
cavesegshlist->newindex((void **) &parysh);
*parysh = *parentsh;
}
// Remove the point (p).
for (it = 0; it < cavesegshlist->objects; it++) {
parentsh = (face *) fastlookup(cavesegshlist, it); // [a,b,p]
senextself(*parentsh); // [b,p,a].
spivotself(*parentsh);
if (sorg(*parentsh) != delpt) sesymself(*parentsh);
// now parentsh is [p,b,#].
if (sorg(*parentsh) != delpt) {
// The vertex has already been removed in above special case.
continue;
}
while (1) {
// Initialize the flip edge list. Re-use 'caveshlist'.
spinsh = *parentsh; // [p, b, #]
while (1) {
caveshlist->newindex((void **) &parysh);
*parysh = spinsh;
senext2self(spinsh);
spivotself(spinsh);
if (spinsh.sh == parentsh->sh) break;
if (sorg(spinsh) != delpt) sesymself(spinsh);
} // while (1)
if (caveshlist->objects == 3) {
// Delete the point by a 3-to-1 flip.
for (i = 0; i < 3; i++) {
parysh = (face *) fastlookup(caveshlist, i);
flipfaces[i] = *parysh;
}
flip31(flipfaces, lawson);
for (i = 0; i < 3; i++) {
shellfacedealloc(subfaces, flipfaces[i].sh);
}
caveshlist->restart();
// Save the new subface.
caveshbdlist->newindex((void **) &parysh);
*parysh = flipfaces[3];
// The vertex is removed.
break;
}
// Search an edge to flip.
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
flipfaces[0] = *parysh;
spivot(flipfaces[0], flipfaces[1]);
if (sorg(flipfaces[0]) != sdest(flipfaces[1]))
sesymself(flipfaces[1]); // Skip this edge if it belongs to a faked subface.
if (!smarktested(flipfaces[0]) && !smarktested(flipfaces[1])) {
pa = sorg(flipfaces[0]);
pb = sdest(flipfaces[0]);
pc = sapex(flipfaces[0]);
pd = sapex(flipfaces[1]);
calculateabovepoint4(pa, pb, pc, pd);
// Check if a 2-to-2 flip is possible.
ori1 = orient3d(pc, pd, dummypoint, pa);
ori2 = orient3d(pc, pd, dummypoint, pb);
if (ori1 * ori2 < 0) {
// A 2-to-2 flip is found.
flip22(flipfaces, lawson, 0);
// The i-th edge is flipped. The i-th and (i-1)-th subfaces are
// changed. The 'flipfaces[1]' contains p as its apex.
senext2(flipfaces[1], *parentsh);
// Save the new subface.
caveshbdlist->newindex((void **) &parysh);
*parysh = flipfaces[0];
break;
}
} //
} // i
if (i == caveshlist->objects) {
// Do a flip22 and a flip31 to remove p.
parysh = (face *) fastlookup(caveshlist, 0);
flipfaces[0] = *parysh;
spivot(flipfaces[0], flipfaces[1]);
if (sorg(flipfaces[0]) != sdest(flipfaces[1])) {
sesymself(flipfaces[1]);
}
flip22(flipfaces, lawson, 0);
senext2(flipfaces[1], *parentsh);
// Save the new subface.
caveshbdlist->newindex((void **) &parysh);
*parysh = flipfaces[0];
}
// The edge list at p are changed.
caveshlist->restart();
} // while (1)
} // it
cavesegshlist->restart();
if (b->verbose > 2) {
printf(" Created %ld new subfaces.\n", caveshbdlist->objects);
}
if (lawson) {
lawsonflip();
}
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// slocate() Locate a point in a surface triangulation. //
// //
// Staring the search from 'searchsh'(it should not be NULL). Perform a line //
// walk search for a subface containing the point (p). //
// //
// If 'aflag' is set, the 'dummypoint' is pre-calculated so that it lies //
// above the 'searchsh' in its current orientation. The test if c is CCW to //
// the line a->b can be done by the test if c is below the oriented plane //
// a->b->dummypoint. //// //
// If 'cflag' is not TRUE, the triangulation may not be convex. Stop search //
// when a segment is met and return OUTSIDE. //
// //
// If 'rflag' (rounding) is set, after the location of the point is found, //
// either ONEDGE or ONFACE, round the result using an epsilon. //
// //
// The returned value indicates the following cases: //
// - ONVERTEX, p is the origin of 'searchsh'. //
// - ONEDGE, p lies on the edge of 'searchsh'. //
// - ONFACE, p lies in the interior of 'searchsh'. //
// - OUTSIDE, p lies outside of the triangulation, p is on the left-hand //
// side of the edge 'searchsh'(s), i.e., org(s), dest(s), p are CW. //
// //
///////////////////////////////////////////////////////////////////////////////
enum tetgenmesh::locateresult tetgenmesh::slocate(point searchpt,
face* searchsh, int aflag, int cflag, int rflag)
{
face neighsh;
point pa, pb, pc;
enum locateresult loc;
enum {MOVE_BC, MOVE_CA} nextmove;
REAL ori, ori_bc, ori_ca;
int i;
pa = sorg(*searchsh);
pb = sdest(*searchsh);
pc = sapex(*searchsh);
if (!aflag) {
// No above point is given. Calculate an above point for this facet.
calculateabovepoint4(pa, pb, pc, searchpt);
}
// 'dummypoint' is given. Make sure it is above [a,b,c]
ori = orient3d(pa, pb, pc, dummypoint);
if (ori > 0) {
sesymself(*searchsh); // Reverse the face orientation.
} else if (ori == 0.0) {
// This case should not happen theoretically. But...
return UNKNOWN;
}
// Find an edge of the face s.t. p lies on its right-hand side (CCW).
for (i = 0; i < 3; i++) {
pa = sorg(*searchsh);
pb = sdest(*searchsh);
ori = orient3d(pa, pb, dummypoint, searchpt);
if (ori > 0) break;
senextself(*searchsh);
}
if (i == 3) {
return UNKNOWN;
}
pc = sapex(*searchsh);
if (pc == searchpt) {
senext2self(*searchsh);
return ONVERTEX;
}
while (1) {
ori_bc = orient3d(pb, pc, dummypoint, searchpt);
ori_ca = orient3d(pc, pa, dummypoint, searchpt);
if (ori_bc < 0) {
if (ori_ca < 0) { // (--) // Any of the edges is a viable move.
if (randomnation(2)) {
nextmove = MOVE_CA;
} else {
nextmove = MOVE_BC;
}
} else { // (-#)
// Edge [b, c] is viable.
nextmove = MOVE_BC;
}
} else {
if (ori_ca < 0) { // (#-)
// Edge [c, a] is viable.
nextmove = MOVE_CA;
} else {
if (ori_bc > 0) {
if (ori_ca > 0) { // (++)
loc = ONFACE; // Inside [a, b, c].
break;
} else { // (+0)
senext2self(*searchsh); // On edge [c, a].
loc = ONEDGE;
break;
}
} else { // ori_bc == 0
if (ori_ca > 0) { // (0+)
senextself(*searchsh); // On edge [b, c].
loc = ONEDGE;
break;
} else { // (00)
// p is coincident with vertex c.
senext2self(*searchsh);
return ONVERTEX;
}
}
}
}
// Move to the next face.
if (nextmove == MOVE_BC) {
senextself(*searchsh);
} else {
senext2self(*searchsh);
}
if (!cflag) {
// NON-convex case. Check if we will cross a boundary.
if (isshsubseg(*searchsh)) {
return ENCSEGMENT;
}
}
spivot(*searchsh, neighsh);
if (neighsh.sh == NULL) {
return OUTSIDE; // A hull edge.
}
// Adjust the edge orientation.
if (sorg(neighsh) != sdest(*searchsh)) {
sesymself(neighsh);
}
// Update the newly discovered face and its endpoints.
*searchsh = neighsh;
pa = sorg(*searchsh);
pb = sdest(*searchsh);
pc = sapex(*searchsh);
if (pc == searchpt) {
senext2self(*searchsh);
return ONVERTEX;
}
} // while (1)
// assert(loc == ONFACE || loc == ONEDGE);
if (rflag) {
// Round the locate result before return.
REAL n[3], area_abc, area_abp, area_bcp, area_cap;
pa = sorg(*searchsh);
pb = sdest(*searchsh);
pc = sapex(*searchsh);
facenormal(pa, pb, pc, n, 1, NULL);
area_abc = sqrt(dot(n, n));
facenormal(pb, pc, searchpt, n, 1, NULL);
area_bcp = sqrt(dot(n, n));
if ((area_bcp / area_abc) < b->epsilon) {
area_bcp = 0; // Rounding.
}
facenormal(pc, pa, searchpt, n, 1, NULL);
area_cap = sqrt(dot(n, n));
if ((area_cap / area_abc) < b->epsilon) {
area_cap = 0; // Rounding
}
if ((loc == ONFACE) || (loc == OUTSIDE)) {
facenormal(pa, pb, searchpt, n, 1, NULL);
area_abp = sqrt(dot(n, n));
if ((area_abp / area_abc) < b->epsilon) {
area_abp = 0; // Rounding
}
} else { // loc == ONEDGE
area_abp = 0;
}
if (area_abp == 0) {
if (area_bcp == 0) {
senextself(*searchsh);
loc = ONVERTEX; // p is close to b.
} else {
if (area_cap == 0) {
loc = ONVERTEX; // p is close to a.
} else {
loc = ONEDGE; // p is on edge [a,b].
}
}
} else if (area_bcp == 0) {
if (area_cap == 0) {
senext2self(*searchsh);
loc = ONVERTEX; // p is close to c.
} else {
senextself(*searchsh);
loc = ONEDGE; // p is on edge [b,c].
}
} else if (area_cap == 0) {
senext2self(*searchsh);
loc = ONEDGE; // p is on edge [c,a].
} else {
loc = ONFACE; // p is on face [a,b,c].
}
} // if (rflag)
return loc;
}
///////////////////////////////////////////////////////////////////////////////
// //// sscoutsegment() Look for a segment in the surface triangulation. //
// //
// The segment is given by the origin of 'searchsh' and 'endpt'. //
// //
// If an edge in T is found matching this segment, the segment is "locked" //
// in T at the edge. Otherwise, flip the first edge in T that the segment //
// crosses. Continue the search from the flipped face. //
// //
// This routine uses 'orisent3d' to determine the search direction. It uses //
// 'dummypoint' as the 'lifted point' in 3d, and it assumes that it (dummy- //
// point) lies above the 'searchsh' (w.r.t the Right-hand rule). //
// //
///////////////////////////////////////////////////////////////////////////////
enum tetgenmesh::interresult tetgenmesh::sscoutsegment(face *searchsh,
point endpt, int insertsegflag, int reporterrorflag, int chkencflag)
{
face flipshs[2], neighsh;
point startpt, pa, pb, pc, pd;
enum interresult dir;
enum {MOVE_AB, MOVE_CA} nextmove;
REAL ori_ab, ori_ca, len;
// The origin of 'searchsh' is fixed.
startpt = sorg(*searchsh);
nextmove = MOVE_AB; // Avoid compiler warning.
if (b->verbose > 2) {
printf(" Scout segment (%d, %d).\n", pointmark(startpt),
pointmark(endpt));
}
len = distance(startpt, endpt);
// Search an edge in 'searchsh' on the path of this segment.
while (1) {
pb = sdest(*searchsh);
if (pb == endpt) {
dir = SHAREEDGE; // Found!
break;
}
pc = sapex(*searchsh);
if (pc == endpt) {
senext2self(*searchsh);
sesymself(*searchsh);
dir = SHAREEDGE; // Found!
break;
}
// Round the results.
if ((sqrt(triarea(startpt, pb, endpt)) / len) < b->epsilon) {
ori_ab = 0.0;
} else {
ori_ab = orient3d(startpt, pb, dummypoint, endpt);
}
if ((sqrt(triarea(pc, startpt, endpt)) / len) < b->epsilon) {
ori_ca = 0.0;
} else {
ori_ca = orient3d(pc, startpt, dummypoint, endpt);
}
if (ori_ab < 0) {
if (ori_ca < 0) { // (--)
// Both sides are viable moves.
if (randomnation(2)) {
nextmove = MOVE_CA;
} else {
nextmove = MOVE_AB; }
} else { // (-#)
nextmove = MOVE_AB;
}
} else {
if (ori_ca < 0) { // (#-)
nextmove = MOVE_CA;
} else {
if (ori_ab > 0) {
if (ori_ca > 0) { // (++)
// The segment intersects with edge [b, c].
dir = ACROSSEDGE;
break;
} else { // (+0)
// The segment collinear with edge [c, a].
senext2self(*searchsh);
sesymself(*searchsh);
dir = ACROSSVERT;
break;
}
} else {
if (ori_ca > 0) { // (0+)
// The segment is collinear with edge [a, b].
dir = ACROSSVERT;
break;
} else { // (00)
// startpt == endpt. Not possible.
terminatetetgen(this, 2);
}
}
}
}
// Move 'searchsh' to the next face, keep the origin unchanged.
if (nextmove == MOVE_AB) {
if (chkencflag) {
// Do not cross boundary.
if (isshsubseg(*searchsh)) {
return ACROSSEDGE; // ACROSS_SEG
}
}
spivot(*searchsh, neighsh);
if (neighsh.sh != NULL) {
if (sorg(neighsh) != pb) sesymself(neighsh);
senext(neighsh, *searchsh);
} else {
// This side (startpt->pb) is outside. It is caused by rounding error.
// Try the next side, i.e., (pc->startpt).
senext2(*searchsh, neighsh);
if (chkencflag) {
// Do not cross boundary.
if (isshsubseg(neighsh)) {
*searchsh = neighsh;
return ACROSSEDGE; // ACROSS_SEG
}
}
spivotself(neighsh);
if (sdest(neighsh) != pc) sesymself(neighsh);
*searchsh = neighsh;
}
} else { // MOVE_CA
senext2(*searchsh, neighsh);
if (chkencflag) {
// Do not cross boundary.
if (isshsubseg(neighsh)) {
*searchsh = neighsh;
return ACROSSEDGE; // ACROSS_SEG
}
}
spivotself(neighsh); if (neighsh.sh != NULL) {
if (sdest(neighsh) != pc) sesymself(neighsh);
*searchsh = neighsh;
} else {
// The same reason as above.
// Try the next side, i.e., (startpt->pb).
if (chkencflag) {
// Do not cross boundary.
if (isshsubseg(*searchsh)) {
return ACROSSEDGE; // ACROSS_SEG
}
}
spivot(*searchsh, neighsh);
if (sorg(neighsh) != pb) sesymself(neighsh);
senext(neighsh, *searchsh);
}
}
} // while
if (dir == SHAREEDGE) {
if (insertsegflag) {
// Insert the segment into the triangulation.
face newseg;
makeshellface(subsegs, &newseg);
setshvertices(newseg, startpt, endpt, NULL);
// Set the default segment marker.
setshellmark(newseg, -1);
ssbond(*searchsh, newseg);
spivot(*searchsh, neighsh);
if (neighsh.sh != NULL) {
ssbond(neighsh, newseg);
}
}
return dir;
}
if (dir == ACROSSVERT) {
// A point is found collinear with this segment.
if (reporterrorflag) {
point pp = sdest(*searchsh);
printf("PLC Error: A vertex lies in a segment in facet #%d.\n",
shellmark(*searchsh));
printf(" Vertex: [%d] (%g,%g,%g).\n",pointmark(pp),pp[0],pp[1],pp[2]);
printf(" Segment: [%d, %d]\n", pointmark(startpt), pointmark(endpt));
}
return dir;
}
if (dir == ACROSSEDGE) {
// Edge [b, c] intersects with the segment.
senext(*searchsh, flipshs[0]);
if (isshsubseg(flipshs[0])) {
if (reporterrorflag) {
REAL P[3], Q[3], tp = 0, tq = 0;
linelineint(startpt, endpt, pb, pc, P, Q, &tp, &tq);
printf("PLC Error: Two segments intersect at point (%g,%g,%g),",
P[0], P[1], P[2]);
printf(" in facet #%d.\n", shellmark(*searchsh));
printf(" Segment 1: [%d, %d]\n", pointmark(pb), pointmark(pc));
printf(" Segment 2: [%d, %d]\n", pointmark(startpt),pointmark(endpt));
}
return dir; // ACROSS_SEG
}
// Flip edge [b, c], queue unflipped edges (for Delaunay checks).
spivot(flipshs[0], flipshs[1]);
if (sorg(flipshs[1]) != sdest(flipshs[0])) sesymself(flipshs[1]);
flip22(flipshs, 1, 0);
// The flip may create an inverted triangle, check it.
pa = sapex(flipshs[1]);
pb = sapex(flipshs[0]); pc = sorg(flipshs[0]);
pd = sdest(flipshs[0]);
// Check if pa and pb are on the different sides of [pc, pd].
// Re-use ori_ab, ori_ca for the tests.
ori_ab = orient3d(pc, pd, dummypoint, pb);
ori_ca = orient3d(pd, pc, dummypoint, pa);
if (ori_ab <= 0) {
flipshpush(&(flipshs[0]));
} else if (ori_ca <= 0) {
flipshpush(&(flipshs[1]));
}
// Set 'searchsh' s.t. its origin is 'startpt'.
*searchsh = flipshs[0];
}
return sscoutsegment(searchsh, endpt, insertsegflag, reporterrorflag,
chkencflag);
}
///////////////////////////////////////////////////////////////////////////////
// //
// scarveholes() Remove triangles not in the facet. //
// //
// This routine re-uses the two global arrays: caveshlist and caveshbdlist. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::scarveholes(int holes, REAL* holelist)
{
face *parysh, searchsh, neighsh;
enum locateresult loc;
int i, j;
// Get all triangles. Infect unprotected convex hull triangles.
smarktest(recentsh);
caveshlist->newindex((void **) &parysh);
*parysh = recentsh;
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
searchsh = *parysh;
searchsh.shver = 0;
for (j = 0; j < 3; j++) {
spivot(searchsh, neighsh);
// Is this side on the convex hull?
if (neighsh.sh != NULL) {
if (!smarktested(neighsh)) {
smarktest(neighsh);
caveshlist->newindex((void **) &parysh);
*parysh = neighsh;
}
} else {
// A hull side. Check if it is protected by a segment.
if (!isshsubseg(searchsh)) {
// Not protected. Save this face.
if (!sinfected(searchsh)) {
sinfect(searchsh);
caveshbdlist->newindex((void **) &parysh);
*parysh = searchsh;
}
}
}
senextself(searchsh);
}
}
// Infect the triangles in the holes.
for (i = 0; i < 3 * holes; i += 3) {
searchsh = recentsh;
loc = slocate(&(holelist[i]), &searchsh, 1, 1, 0);
if (loc != OUTSIDE) { sinfect(searchsh);
caveshbdlist->newindex((void **) &parysh);
*parysh = searchsh;
}
}
// Find and infect all exterior triangles.
for (i = 0; i < caveshbdlist->objects; i++) {
parysh = (face *) fastlookup(caveshbdlist, i);
searchsh = *parysh;
searchsh.shver = 0;
for (j = 0; j < 3; j++) {
spivot(searchsh, neighsh);
if (neighsh.sh != NULL) {
if (!isshsubseg(searchsh)) {
if (!sinfected(neighsh)) {
sinfect(neighsh);
caveshbdlist->newindex((void **) &parysh);
*parysh = neighsh;
}
} else {
sdissolve(neighsh); // Disconnect a protected face.
}
}
senextself(searchsh);
}
}
// Delete exterior triangles, unmark interior triangles.
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
if (sinfected(*parysh)) {
shellfacedealloc(subfaces, parysh->sh);
} else {
sunmarktest(*parysh);
}
}
caveshlist->restart();
caveshbdlist->restart();
}
///////////////////////////////////////////////////////////////////////////////
// //
// unifysegments() Remove redundant segments and create face links. //
// //
// After this routine, although segments are unique, but some of them may be //
// removed later by mergefacet(). All vertices still have type FACETVERTEX. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::unifysegments()
{
badface *facelink = NULL, *newlinkitem, *f1, *f2;
face *facperverlist, sface;
face subsegloop, testseg;
point torg, tdest;
REAL ori1, ori2, ori3;
REAL n1[3], n2[3];
REAL cosang, ang, ang_tol;
int *idx2faclist;
int idx, k, m;
if (b->verbose > 1) {
printf(" Unifying segments.\n");
}
// The limit dihedral angle that two facets are not overlapping.
ang_tol = b->facet_overlap_ang_tol / 180.0 * PI;
if (ang_tol < 0.0) ang_tol = 0.0;
// Create a mapping from vertices to subfaces.
makepoint2submap(subfaces, idx2faclist, facperverlist);
subsegloop.shver = 0;
subsegs->traversalinit();
subsegloop.sh = shellfacetraverse(subsegs);
while (subsegloop.sh != (shellface *) NULL) {
torg = sorg(subsegloop);
tdest = sdest(subsegloop);
idx = pointmark(torg) - in->firstnumber;
// Loop through the set of subfaces containing 'torg'. Get all the
// subfaces containing the edge (torg, tdest). Save and order them
// in 'sfacelist', the ordering is defined by the right-hand rule
// with thumb points from torg to tdest.
for (k = idx2faclist[idx]; k < idx2faclist[idx + 1]; k++) {
sface = facperverlist[k];
// The face may be deleted if it is a duplicated face.
if (sface.sh[3] == NULL) continue;
// Search the edge torg->tdest.
if (sdest(sface) != tdest) {
senext2self(sface);
sesymself(sface);
}
if (sdest(sface) != tdest) continue;
// Save the face f in facelink.
if (flippool->items >= 2) {
f1 = facelink;
for (m = 0; m < flippool->items - 1; m++) {
f2 = f1->nextitem;
ori1 = orient3d(torg, tdest, sapex(f1->ss), sapex(f2->ss));
ori2 = orient3d(torg, tdest, sapex(f1->ss), sapex(sface));
if (ori1 > 0) {
// apex(f2) is below f1.
if (ori2 > 0) {
// apex(f) is below f1 (see Fig.1).
ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface));
if (ori3 > 0) {
// apex(f) is below f2, insert it.
break;
} else if (ori3 < 0) {
// apex(f) is above f2, continue.
} else { // ori3 == 0;
// f is coplanar and codirection with f2.
report_overlapping_facets(&(f2->ss), &sface);
break;
}
} else if (ori2 < 0) {
// apex(f) is above f1 below f2, inset it (see Fig. 2).
break;
} else { // ori2 == 0;
// apex(f) is coplanar with f1 (see Fig. 5).
ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface));
if (ori3 > 0) {
// apex(f) is below f2, insert it.
break;
} else {
// f is coplanar and codirection with f1.
report_overlapping_facets(&(f1->ss), &sface);
break;
}
}
} else if (ori1 < 0) {
// apex(f2) is above f1.
if (ori2 > 0) {
// apex(f) is below f1, continue (see Fig. 3).
} else if (ori2 < 0) { // apex(f) is above f1 (see Fig.4).
ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface));
if (ori3 > 0) {
// apex(f) is below f2, insert it.
break;
} else if (ori3 < 0) {
// apex(f) is above f2, continue.
} else { // ori3 == 0;
// f is coplanar and codirection with f2.
report_overlapping_facets(&(f2->ss), &sface);
break;
}
} else { // ori2 == 0;
// f is coplanar and with f1 (see Fig. 6).
ori3 = orient3d(torg, tdest, sapex(f2->ss), sapex(sface));
if (ori3 > 0) {
// f is also codirection with f1.
report_overlapping_facets(&(f1->ss), &sface);
break;
} else {
// f is above f2, continue.
}
}
} else { // ori1 == 0;
// apex(f2) is coplanar with f1. By assumption, f1 is not
// coplanar and codirection with f2.
if (ori2 > 0) {
// apex(f) is below f1, continue (see Fig. 7).
} else if (ori2 < 0) {
// apex(f) is above f1, insert it (see Fig. 7).
break;
} else { // ori2 == 0.
// apex(f) is coplanar with f1 (see Fig. 8).
// f is either codirection with f1 or is codirection with f2.
facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL);
facenormal(torg, tdest, sapex(sface), n2, 1, NULL);
if (dot(n1, n2) > 0) {
report_overlapping_facets(&(f1->ss), &sface);
} else {
report_overlapping_facets(&(f2->ss), &sface);
}
break;
}
}
// Go to the next item;
f1 = f2;
} // for (m = 0; ...)
if (sface.sh[3] != NULL) {
// Insert sface between f1 and f2.
newlinkitem = (badface *) flippool->alloc();
newlinkitem->ss = sface;
newlinkitem->nextitem = f1->nextitem;
f1->nextitem = newlinkitem;
}
} else if (flippool->items == 1) {
f1 = facelink;
// Make sure that f is not coplanar and codirection with f1.
ori1 = orient3d(torg, tdest, sapex(f1->ss), sapex(sface));
if (ori1 == 0) {
// f is coplanar with f1 (see Fig. 8).
facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL);
facenormal(torg, tdest, sapex(sface), n2, 1, NULL);
if (dot(n1, n2) > 0) {
// The two faces are codirectional as well.
report_overlapping_facets(&(f1->ss), &sface);
}
}
// Add this face to link if it is not deleted.
if (sface.sh[3] != NULL) {
// Add this face into link. newlinkitem = (badface *) flippool->alloc();
newlinkitem->ss = sface;
newlinkitem->nextitem = NULL;
f1->nextitem = newlinkitem;
}
} else {
// The first face.
newlinkitem = (badface *) flippool->alloc();
newlinkitem->ss = sface;
newlinkitem->nextitem = NULL;
facelink = newlinkitem;
}
} // for (k = idx2faclist[idx]; ...)
// Set the connection between this segment and faces containing it,
// at the same time, remove redundant segments.
f1 = facelink;
for (k = 0; k < flippool->items; k++) {
sspivot(f1->ss, testseg);
// If 'testseg' is not 'subsegloop' and is not dead, it is redundant.
if ((testseg.sh != subsegloop.sh) && (testseg.sh[3] != NULL)) {
shellfacedealloc(subsegs, testseg.sh);
}
// Bonds the subface and the segment together.
ssbond(f1->ss, subsegloop);
f1 = f1->nextitem;
}
// Create the face ring at the segment.
if (flippool->items > 1) {
f1 = facelink;
for (k = 1; k <= flippool->items; k++) {
k < flippool->items ? f2 = f1->nextitem : f2 = facelink;
// Calculate the dihedral angle between the two facet.
facenormal(torg, tdest, sapex(f1->ss), n1, 1, NULL);
facenormal(torg, tdest, sapex(f2->ss), n2, 1, NULL);
cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2)));
// Rounding.
if (cosang > 1.0) cosang = 1.0;
else if (cosang < -1.0) cosang = -1.0;
ang = acos(cosang);
if (ang < ang_tol) {
// Two facets are treated as overlapping each other.
report_overlapping_facets(&(f1->ss), &(f2->ss), ang);
} else {
// Record the smallest input dihedral angle.
if (ang < minfacetdihed) {
minfacetdihed = ang;
}
sbond1(f1->ss, f2->ss);
}
f1 = f2;
}
}
flippool->restart();
// Are there length constraints?
if (b->quality && (in->segmentconstraintlist != (REAL *) NULL)) {
int e1, e2;
REAL len;
for (k = 0; k < in->numberofsegmentconstraints; k++) {
e1 = (int) in->segmentconstraintlist[k * 3];
e2 = (int) in->segmentconstraintlist[k * 3 + 1];
if (((pointmark(torg) == e1) && (pointmark(tdest) == e2)) ||
((pointmark(torg) == e2) && (pointmark(tdest) == e1))) {
len = in->segmentconstraintlist[k * 3 + 2];
setareabound(subsegloop, len);
break; }
}
}
subsegloop.sh = shellfacetraverse(subsegs);
}
delete [] idx2faclist;
delete [] facperverlist;
}
///////////////////////////////////////////////////////////////////////////////
// //
// identifyinputedges() Identify input edges. //
// //
// A set of input edges is provided in the 'in->edgelist'. We find these //
// edges in the surface mesh and make them segments of the mesh. //
// //
// It is possible that an input edge is not in any facet, i.e.,it is a float-//
// segment inside the volume. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::identifyinputedges(point *idx2verlist)
{
face* shperverlist;
int* idx2shlist;
face searchsh, neighsh;
face segloop, checkseg, newseg;
point checkpt, pa = NULL, pb = NULL;
int *endpts;
int edgemarker;
int idx, i, j;
int e1, e2;
REAL len;
if (!b->quiet) {
printf("Inserting edges ...\n");
}
// Construct a map from points to subfaces.
makepoint2submap(subfaces, idx2shlist, shperverlist);
// Process the set of input edges.
for (i = 0; i < in->numberofedges; i++) {
endpts = &(in->edgelist[(i << 1)]);
if (endpts[0] == endpts[1]) {
if (!b->quiet) {
printf("Warning: Edge #%d is degenerated. Skipped.\n", i);
}
continue; // Skip a degenerated edge.
}
// Recall that all existing segments have a default marker '-1'.
// We assign all identified segments a default marker '-2'.
edgemarker = in->edgemarkerlist ? in->edgemarkerlist[i] : -2;
// Find a face contains the edge.
newseg.sh = NULL;
searchsh.sh = NULL;
idx = endpts[0] - in->firstnumber;
for (j = idx2shlist[idx]; j < idx2shlist[idx + 1]; j++) {
checkpt = sdest(shperverlist[j]);
if (pointmark(checkpt) == endpts[1]) {
searchsh = shperverlist[j];
break; // Found.
} else {
checkpt = sapex(shperverlist[j]);
if (pointmark(checkpt) == endpts[1]) {
senext2(shperverlist[j], searchsh); sesymself(searchsh);
break;
}
}
} // j
if (searchsh.sh != NULL) {
// Check if this edge is already a segment of the mesh.
sspivot(searchsh, checkseg);
if (checkseg.sh != NULL) {
// This segment already exist.
newseg = checkseg;
} else {
// Create a new segment at this edge.
pa = sorg(searchsh);
pb = sdest(searchsh);
makeshellface(subsegs, &newseg);
setshvertices(newseg, pa, pb, NULL);
ssbond(searchsh, newseg);
spivot(searchsh, neighsh);
if (neighsh.sh != NULL) {
ssbond(neighsh, newseg);
}
}
} else {
// It is a dangling segment (not belong to any facets).
// Get the two endpoints of this segment.
pa = idx2verlist[endpts[0]];
pb = idx2verlist[endpts[1]];
if (pa == pb) {
if (!b->quiet) {
printf("Warning: Edge #%d is degenerated. Skipped.\n", i);
}
continue;
}
// Check if segment [a,b] already exists.
// TODO: Change the brute-force search. Slow!
point *ppt;
subsegs->traversalinit();
segloop.sh = shellfacetraverse(subsegs);
while (segloop.sh != NULL) {
ppt = (point *) &(segloop.sh[3]);
if (((ppt[0] == pa) && (ppt[1] == pb)) ||
((ppt[0] == pb) && (ppt[1] == pa))) {
// Found!
newseg = segloop;
break;
}
segloop.sh = shellfacetraverse(subsegs);
}
if (newseg.sh == NULL) {
makeshellface(subsegs, &newseg);
setshvertices(newseg, pa, pb, NULL);
}
}
setshellmark(newseg, edgemarker);
if (b->quality && (in->segmentconstraintlist != (REAL *) NULL)) {
for (i = 0; i < in->numberofsegmentconstraints; i++) {
e1 = (int) in->segmentconstraintlist[i * 3];
e2 = (int) in->segmentconstraintlist[i * 3 + 1];
if (((pointmark(pa) == e1) && (pointmark(pb) == e2)) ||
((pointmark(pa) == e2) && (pointmark(pb) == e1))) {
len = in->segmentconstraintlist[i * 3 + 2];
setareabound(newseg, len);
break;
}
}
} } // i
delete [] shperverlist;
delete [] idx2shlist;
}
///////////////////////////////////////////////////////////////////////////////
// //
// mergefacets() Merge adjacent facets. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::mergefacets()
{
face parentsh, neighsh, neineish;
face segloop;
point pa, pb, pc, pd;
REAL n1[3], n2[3];
REAL cosang, cosang_tol;
// Allocate an array to save calcaulated dihedral angles at segments.
arraypool *dihedangarray = new arraypool(sizeof(double), 10);
REAL *paryang = NULL;
// First, remove coplanar segments.
// The dihedral angle bound for two different facets.
cosang_tol = cos(b->facet_separate_ang_tol / 180.0 * PI);
subsegs->traversalinit();
segloop.sh = shellfacetraverse(subsegs);
while (segloop.sh != (shellface *) NULL) {
// Only remove a segment if it has a marker '-1'.
if (shellmark(segloop) != -1) {
segloop.sh = shellfacetraverse(subsegs);
continue;
}
spivot(segloop, parentsh);
if (parentsh.sh != NULL) {
spivot(parentsh, neighsh);
if (neighsh.sh != NULL) {
spivot(neighsh, neineish);
if (neineish.sh == parentsh.sh) {
// Exactly two subfaces at this segment.
// Only merge them if they have the same boundary marker.
if (shellmark(parentsh) == shellmark(neighsh)) {
pa = sorg(segloop);
pb = sdest(segloop);
pc = sapex(parentsh);
pd = sapex(neighsh);
// Calculate the dihedral angle at the segment [a,b].
facenormal(pa, pb, pc, n1, 1, NULL);
facenormal(pa, pb, pd, n2, 1, NULL);
cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2)));
if (cosang < cosang_tol) {
ssdissolve(parentsh);
ssdissolve(neighsh);
shellfacedealloc(subsegs, segloop.sh);
// Add the edge to flip stack.
flipshpush(&parentsh);
} else {
// Save 'cosang' to avoid re-calculate it.
// Re-use the pointer at the first segment.
dihedangarray->newindex((void **) &paryang);
*paryang = cosang;
segloop.sh[6] = (shellface) paryang;
}
}
} // if (neineish.sh == parentsh.sh)
} }
segloop.sh = shellfacetraverse(subsegs);
}
// Second, remove ridge segments at small angles.
// The dihedral angle bound for two different facets.
cosang_tol = cos(b->facet_small_ang_tol / 180.0 * PI);
REAL cosang_sep_tol = cos((b->facet_separate_ang_tol - 5.0) / 180.0 * PI);
face shloop;
face seg1, seg2;
REAL cosang1, cosang2;
int i, j;
subfaces->traversalinit();
shloop.sh = shellfacetraverse(subfaces);
while (shloop.sh != (shellface *) NULL) {
for (i = 0; i < 3; i++) {
if (isshsubseg(shloop)) {
senext(shloop, neighsh);
if (isshsubseg(neighsh)) {
// Found two segments sharing at one vertex.
// Check if they form a small angle.
pa = sorg(shloop);
pb = sdest(shloop);
pc = sapex(shloop);
for (j = 0; j < 3; j++) n1[j] = pa[j] - pb[j];
for (j = 0; j < 3; j++) n2[j] = pc[j] - pb[j];
cosang = dot(n1, n2) / (sqrt(dot(n1, n1)) * sqrt(dot(n2, n2)));
if (cosang > cosang_tol) {
// Found a small angle.
segloop.sh = NULL;
sspivot(shloop, seg1);
sspivot(neighsh, seg2);
if (seg1.sh[6] != NULL) {
paryang = (REAL *) (seg1.sh[6]);
cosang1 = *paryang;
} else {
cosang1 = 1.0; // 0 degree;
}
if (seg2.sh[6] != NULL) {
paryang = (REAL *) (seg2.sh[6]);
cosang2 = *paryang;
} else {
cosang2 = 1.0; // 0 degree;
}
if (cosang1 < cosang_sep_tol) {
if (cosang2 < cosang_sep_tol) {
if (cosang1 < cosang2) {
segloop = seg1;
} else {
segloop = seg2;
}
} else {
segloop = seg1;
}
} else {
if (cosang2 < cosang_sep_tol) {
segloop = seg2;
}
}
if (segloop.sh != NULL) {
// Remove this segment.
segloop.shver = 0;
spivot(segloop, parentsh);
spivot(parentsh, neighsh);
ssdissolve(parentsh);
ssdissolve(neighsh);
shellfacedealloc(subsegs, segloop.sh);
// Add the edge to flip stack.
flipshpush(&parentsh); break;
}
}
} // if (isshsubseg)
} // if (isshsubseg)
senextself(shloop);
}
shloop.sh = shellfacetraverse(subfaces);
}
delete dihedangarray;
if (flipstack != NULL) {
lawsonflip(); // Recover Delaunayness.
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// finddirection() Find the tet on the path from one point to another. //
// //
// The path starts from 'searchtet''s origin and ends at 'endpt'. On finish, //
// 'searchtet' contains a tet on the path, its origin does not change. //
// //
// The return value indicates one of the following cases (let 'searchtet' be //
// abcd, a is the origin of the path): //
// - ACROSSVERT, edge ab is collinear with the path; //
// - ACROSSEDGE, edge bc intersects with the path; //
// - ACROSSFACE, face bcd intersects with the path. //
// //
// WARNING: This routine is designed for convex triangulations, and will not //
// generally work after the holes and concavities have been carved. //
// //
///////////////////////////////////////////////////////////////////////////////
enum tetgenmesh::interresult
tetgenmesh::finddirection(triface* searchtet, point endpt)
{
triface neightet;
point pa, pb, pc, pd;
enum {HMOVE, RMOVE, LMOVE} nextmove;
REAL hori, rori, lori;
int t1ver;
int s;
// The origin is fixed.
pa = org(*searchtet);
if ((point) searchtet->tet[7] == dummypoint) {
// A hull tet. Choose the neighbor of its base face.
decode(searchtet->tet[3], *searchtet);
// Reset the origin to be pa.
if ((point) searchtet->tet[4] == pa) {
searchtet->ver = 11;
} else if ((point) searchtet->tet[5] == pa) {
searchtet->ver = 3;
} else if ((point) searchtet->tet[6] == pa) {
searchtet->ver = 7;
} else {
searchtet->ver = 0;
}
}
pb = dest(*searchtet);
// Check whether the destination or apex is 'endpt'.
if (pb == endpt) {
// pa->pb is the search edge.
return ACROSSVERT;
}
pc = apex(*searchtet);
if (pc == endpt) {
// pa->pc is the search edge.
eprevesymself(*searchtet);
return ACROSSVERT;
}
// Walk through tets around pa until the right one is found.
while (1) {
pd = oppo(*searchtet);
// Check whether the opposite vertex is 'endpt'.
if (pd == endpt) {
// pa->pd is the search edge.
esymself(*searchtet);
enextself(*searchtet);
return ACROSSVERT;
}
// Check if we have entered outside of the domain.
if (pd == dummypoint) {
// This is possible when the mesh is non-convex.
if (nonconvex) {
return ACROSSFACE; // return ACROSSSUB; // Hit a bounday.
} else {
terminatetetgen(this, 2);
}
}
// Now assume that the base face abc coincides with the horizon plane,
// and d lies above the horizon. The search point 'endpt' may lie
// above or below the horizon. We test the orientations of 'endpt'
// with respect to three planes: abc (horizon), bad (right plane),
// and acd (left plane).
hori = orient3d(pa, pb, pc, endpt);
rori = orient3d(pb, pa, pd, endpt);
lori = orient3d(pa, pc, pd, endpt);
// Now decide the tet to move. It is possible there are more than one
// tets are viable moves. Is so, randomly choose one.
if (hori > 0) {
if (rori > 0) {
if (lori > 0) {
// Any of the three neighbors is a viable move.
s = randomnation(3);
if (s == 0) {
nextmove = HMOVE;
} else if (s == 1) {
nextmove = RMOVE;
} else {
nextmove = LMOVE;
}
} else {
// Two tets, below horizon and below right, are viable.
if (randomnation(2)) {
nextmove = HMOVE;
} else {
nextmove = RMOVE;
}
}
} else {
if (lori > 0) {
// Two tets, below horizon and below left, are viable.
if (randomnation(2)) {
nextmove = HMOVE;
} else {
nextmove = LMOVE;
}
} else {
// The tet below horizon is chosen.
nextmove = HMOVE; }
}
} else {
if (rori > 0) {
if (lori > 0) {
// Two tets, below right and below left, are viable.
if (randomnation(2)) {
nextmove = RMOVE;
} else {
nextmove = LMOVE;
}
} else {
// The tet below right is chosen.
nextmove = RMOVE;
}
} else {
if (lori > 0) {
// The tet below left is chosen.
nextmove = LMOVE;
} else {
// 'endpt' lies either on the plane(s) or across face bcd.
if (hori == 0) {
if (rori == 0) {
// pa->'endpt' is COLLINEAR with pa->pb.
return ACROSSVERT;
}
if (lori == 0) {
// pa->'endpt' is COLLINEAR with pa->pc.
eprevesymself(*searchtet); // [a,c,d]
return ACROSSVERT;
}
// pa->'endpt' crosses the edge pb->pc.
return ACROSSEDGE;
}
if (rori == 0) {
if (lori == 0) {
// pa->'endpt' is COLLINEAR with pa->pd.
esymself(*searchtet); // face bad.
enextself(*searchtet); // face [a,d,b]
return ACROSSVERT;
}
// pa->'endpt' crosses the edge pb->pd.
esymself(*searchtet); // face bad.
enextself(*searchtet); // face adb
return ACROSSEDGE;
}
if (lori == 0) {
// pa->'endpt' crosses the edge pc->pd.
eprevesymself(*searchtet); // [a,c,d]
return ACROSSEDGE;
}
// pa->'endpt' crosses the face bcd.
return ACROSSFACE;
}
}
}
// Move to the next tet, fix pa as its origin.
if (nextmove == RMOVE) {
fnextself(*searchtet);
} else if (nextmove == LMOVE) {
eprevself(*searchtet);
fnextself(*searchtet);
enextself(*searchtet);
} else { // HMOVE
fsymself(*searchtet);
enextself(*searchtet);
}
pb = dest(*searchtet);
pc = apex(*searchtet);
} // while (1)
}
//// steiner_cxx //////////////////////////////////////////////////////////////
//// ////
//// ////
///////////////////////////////////////////////////////////////////////////////
// //
// checkflipeligibility() A call back function for boundary recovery. //
// //
// 'fliptype' indicates which elementary flip will be performed: 1 : 2-to-3, //
// and 2 : 3-to-2, respectively. //
// //
// 'pa, ..., pe' are the vertices involved in this flip, where [a,b,c] is //
// the flip face, and [d,e] is the flip edge. NOTE: 'pc' may be 'dummypoint',//
// other points must not be 'dummypoint'. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::checkflipeligibility(int fliptype, point pa, point pb,
point pc, point pd, point pe,
int level, int edgepivot,
flipconstraints* fc)
{
point tmppts[3];
enum interresult dir;
int types[2], poss[4];
int intflag;
int rejflag = 0;
int i;
if (fc->seg[0] != NULL) {
// A constraining edge is given (e.g., for edge recovery).
if (fliptype == 1) {
// A 2-to-3 flip: [a,b,c] => [e,d,a], [e,d,b], [e,d,c].
tmppts[0] = pa;
tmppts[1] = pb;
tmppts[2] = pc;
for (i = 0; i < 3 && !rejflag; i++) {
if (tmppts[i] != dummypoint) {
// Test if the face [e,d,#] intersects the edge.
intflag = tri_edge_test(pe, pd, tmppts[i], fc->seg[0], fc->seg[1],
NULL, 1, types, poss);
if (intflag == 2) {
// They intersect at a single point.
dir = (enum interresult) types[0];
if (dir == ACROSSFACE) {
// The interior of [e,d,#] intersect the segment.
rejflag = 1;
} else if (dir == ACROSSEDGE) {
if (poss[0] == 0) {
// The interior of [e,d] intersect the segment.
// Since [e,d] is the newly created edge. Reject this flip.
rejflag = 1;
}
}
} else if (intflag == 4) {
// They may intersect at either a point or a line segment.
dir = (enum interresult) types[0];
if (dir == ACROSSEDGE) {
if (poss[0] == 0) {
// The interior of [e,d] intersect the segment.
// Since [e,d] is the newly created edge. Reject this flip.
rejflag = 1;
}
} }
} // if (tmppts[0] != dummypoint)
} // i
} else if (fliptype == 2) {
// A 3-to-2 flip: [e,d,a], [e,d,b], [e,d,c] => [a,b,c]
if (pc != dummypoint) {
// Check if the new face [a,b,c] intersect the edge in its interior.
intflag = tri_edge_test(pa, pb, pc, fc->seg[0], fc->seg[1], NULL,
1, types, poss);
if (intflag == 2) {
// They intersect at a single point.
dir = (enum interresult) types[0];
if (dir == ACROSSFACE) {
// The interior of [a,b,c] intersect the segment.
rejflag = 1; // Do not flip.
}
} else if (intflag == 4) {
// [a,b,c] is coplanar with the edge.
dir = (enum interresult) types[0];
if (dir == ACROSSEDGE) {
// The boundary of [a,b,c] intersect the segment.
rejflag = 1; // Do not flip.
}
}
} // if (pc != dummypoint)
}
} // if (fc->seg[0] != NULL)
if ((fc->fac[0] != NULL) && !rejflag) {
// A constraining face is given (e.g., for face recovery).
if (fliptype == 1) {
// A 2-to-3 flip.
// Test if the new edge [e,d] intersects the face.
intflag = tri_edge_test(fc->fac[0], fc->fac[1], fc->fac[2], pe, pd,
NULL, 1, types, poss);
if (intflag == 2) {
// They intersect at a single point.
dir = (enum interresult) types[0];
if (dir == ACROSSFACE) {
rejflag = 1;
} else if (dir == ACROSSEDGE) {
rejflag = 1;
}
} else if (intflag == 4) {
// The edge [e,d] is coplanar with the face.
// There may be two intersections.
for (i = 0; i < 2 && !rejflag; i++) {
dir = (enum interresult) types[i];
if (dir == ACROSSFACE) {
rejflag = 1;
} else if (dir == ACROSSEDGE) {
rejflag = 1;
}
}
}
} // if (fliptype == 1)
} // if (fc->fac[0] != NULL)
if ((fc->remvert != NULL) && !rejflag) {
// The vertex is going to be removed. Do not create a new edge which
// contains this vertex.
if (fliptype == 1) {
// A 2-to-3 flip.
if ((pd == fc->remvert) || (pe == fc->remvert)) {
rejflag = 1;
}
}
}
if (fc->remove_large_angle && !rejflag) { // Remove a large dihedral angle. Do not create a new small angle.
REAL cosmaxd = 0, diff;
if (fliptype == 1) {
// We assume that neither 'a' nor 'b' is dummypoint.
// A 2-to-3 flip: [a,b,c] => [e,d,a], [e,d,b], [e,d,c].
// The new tet [e,d,a,b] will be flipped later. Only two new tets:
// [e,d,b,c] and [e,d,c,a] need to be checked.
if ((pc != dummypoint) && (pe != dummypoint) && (pd != dummypoint)) {
// Get the largest dihedral angle of [e,d,b,c].
tetalldihedral(pe, pd, pb, pc, NULL, &cosmaxd, NULL);
diff = cosmaxd - fc->cosdihed_in;
if (fabs(diff/fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding.
if (diff <= 0) { //if (cosmaxd <= fc->cosdihed_in) {
rejflag = 1;
} else {
// Record the largest new angle.
if (cosmaxd < fc->cosdihed_out) {
fc->cosdihed_out = cosmaxd;
}
// Get the largest dihedral angle of [e,d,c,a].
tetalldihedral(pe, pd, pc, pa, NULL, &cosmaxd, NULL);
diff = cosmaxd - fc->cosdihed_in;
if (fabs(diff/fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding.
if (diff <= 0) { //if (cosmaxd <= fc->cosdihed_in) {
rejflag = 1;
} else {
// Record the largest new angle.
if (cosmaxd < fc->cosdihed_out) {
fc->cosdihed_out = cosmaxd;
}
}
}
} // if (pc != dummypoint && ...)
} else if (fliptype == 2) {
// A 3-to-2 flip: [e,d,a], [e,d,b], [e,d,c] => [a,b,c]
// We assume that neither 'e' nor 'd' is dummypoint.
if (level == 0) {
// Both new tets [a,b,c,d] and [b,a,c,e] are new tets.
if ((pa != dummypoint) && (pb != dummypoint) && (pc != dummypoint)) {
// Get the largest dihedral angle of [a,b,c,d].
tetalldihedral(pa, pb, pc, pd, NULL, &cosmaxd, NULL);
diff = cosmaxd - fc->cosdihed_in;
if (fabs(diff/fc->cosdihed_in) < b->epsilon) diff = 0.0; // Rounding
if (diff <= 0) { //if (cosmaxd <= fc->cosdihed_in) {
rejflag = 1;
} else {
// Record the largest new angle.
if (cosmaxd < fc->cosdihed_out) {
fc->cosdihed_out = cosmaxd;
}
// Get the largest dihedral angle of [b,a,c,e].
tetalldihedral(pb, pa, pc, pe, NULL, &cosmaxd, NULL);
diff = cosmaxd - fc->cosdihed_in;
if (fabs(diff/fc->cosdihed_in) < b->epsilon) diff = 0.0;// Rounding
if (diff <= 0) { //if (cosmaxd <= fc->cosdihed_in) {
rejflag = 1;
} else {
// Record the largest new angle.
if (cosmaxd < fc->cosdihed_out) {
fc->cosdihed_out = cosmaxd;
}
}
}
}
} else { // level > 0
if (edgepivot == 1) {
// The new tet [a,b,c,d] will be flipped. Only check [b,a,c,e].
if ((pa != dummypoint) && (pb != dummypoint) && (pc != dummypoint)) {
// Get the largest dihedral angle of [b,a,c,e].
tetalldihedral(pb, pa, pc, pe, NULL, &cosmaxd, NULL); diff = cosmaxd - fc->cosdihed_in;
if (fabs(diff/fc->cosdihed_in) < b->epsilon) diff = 0.0;// Rounding
if (diff <= 0) { //if (cosmaxd <= fc->cosdihed_in) {
rejflag = 1;
} else {
// Record the largest new angle.
if (cosmaxd < fc->cosdihed_out) {
fc->cosdihed_out = cosmaxd;
}
}
}
} else {
// The new tet [b,a,c,e] will be flipped. Only check [a,b,c,d].
if ((pa != dummypoint) && (pb != dummypoint) && (pc != dummypoint)) {
// Get the largest dihedral angle of [b,a,c,e].
tetalldihedral(pa, pb, pc, pd, NULL, &cosmaxd, NULL);
diff = cosmaxd - fc->cosdihed_in;
if (fabs(diff/fc->cosdihed_in) < b->epsilon) diff = 0.0;// Rounding
if (diff <= 0) { //if (cosmaxd <= fc->cosdihed_in) {
rejflag = 1;
} else {
// Record the largest new angle.
if (cosmaxd < fc->cosdihed_out) {
fc->cosdihed_out = cosmaxd;
}
}
}
} // edgepivot
} // level
}
}
return rejflag;
}
///////////////////////////////////////////////////////////////////////////////
// //
// removeedgebyflips() Attempt to remove an edge by flips. //
// //
// 'flipedge' is a non-convex or flat edge [a,b,#,#] to be removed. //
// //
// The return value is a positive integer, it indicates whether the edge is //
// removed or not. A value "2" means the edge is removed, otherwise, the //
// edge is not removed and the value (must >= 3) is the current number of //
// tets in the edge star. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::removeedgebyflips(triface *flipedge, flipconstraints* fc)
{
triface *abtets, spintet;
int t1ver;
int n, nn, i;
if (checksubsegflag) {
// Do not flip a segment.
if (issubseg(*flipedge)) {
if (fc->collectencsegflag) {
face checkseg, *paryseg;
tsspivot1(*flipedge, checkseg);
if (!sinfected(checkseg)) {
// Queue this segment in list.
sinfect(checkseg);
caveencseglist->newindex((void **) &paryseg);
*paryseg = checkseg;
}
}
return 0;
} }
// Count the number of tets at edge [a,b].
n = 0;
spintet = *flipedge;
while (1) {
n++;
fnextself(spintet);
if (spintet.tet == flipedge->tet) break;
}
if (n < 3) {
// It is only possible when the mesh contains inverted tetrahedra.
terminatetetgen(this, 2); // Report a bug
}
if ((b->flipstarsize > 0) && (n > b->flipstarsize)) {
// The star size exceeds the limit.
return 0; // Do not flip it.
}
// Allocate spaces.
abtets = new triface[n];
// Collect the tets at edge [a,b].
spintet = *flipedge;
i = 0;
while (1) {
abtets[i] = spintet;
setelemcounter(abtets[i], 1);
i++;
fnextself(spintet);
if (spintet.tet == flipedge->tet) break;
}
// Try to flip the edge (level = 0, edgepivot = 0).
nn = flipnm(abtets, n, 0, 0, fc);
if (nn > 2) {
// Edge is not flipped. Unmarktest the remaining tets in Star(ab).
for (i = 0; i < nn; i++) {
setelemcounter(abtets[i], 0);
}
// Restore the input edge (needed by Lawson's flip).
*flipedge = abtets[0];
}
// Release the temporary allocated spaces.
// NOTE: fc->unflip must be 0.
int bakunflip = fc->unflip;
fc->unflip = 0;
flipnm_post(abtets, n, nn, 0, fc);
fc->unflip = bakunflip;
delete [] abtets;
return nn;
}
///////////////////////////////////////////////////////////////////////////////
// //
// removefacebyflips() Remove a face by flips. //
// //
// Return 1 if the face is removed. Otherwise, return 0. //
// //
// ASSUMPTIONS: //
// - 'flipface' must not be a subface. //
// - 'flipface' must not be a hull face. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::removefacebyflips(triface *flipface, flipconstraints* fc)
{
triface fliptets[3], flipedge;
point pa, pb, pc, pd, pe;
REAL ori;
int reducflag = 0;
fliptets[0] = *flipface;
fsym(*flipface, fliptets[1]);
pa = org(fliptets[0]);
pb = dest(fliptets[0]);
pc = apex(fliptets[0]);
pd = oppo(fliptets[0]);
pe = oppo(fliptets[1]);
ori = orient3d(pa, pb, pd, pe);
if (ori > 0) {
ori = orient3d(pb, pc, pd, pe);
if (ori > 0) {
ori = orient3d(pc, pa, pd, pe);
if (ori > 0) {
// Found a 2-to-3 flip.
reducflag = 1;
} else {
eprev(*flipface, flipedge); // [c,a]
}
} else {
enext(*flipface, flipedge); // [b,c]
}
} else {
flipedge = *flipface; // [a,b]
}
if (reducflag) {
// A 2-to-3 flip is found.
flip23(fliptets, 0, fc);
return 1;
} else {
// Try to flip the selected edge of this face.
if (removeedgebyflips(&flipedge, fc) == 2) {
return 1;
}
}
// Face is not removed.
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// recoveredge() Recover an edge in current tetrahedralization. //
// //
// If the edge is recovered, 'searchtet' returns a tet containing the edge. //
// //
// This edge may intersect a set of faces and edges in the mesh. All these //
// faces or edges are needed to be removed. //
// //
// If the parameter 'fullsearch' is set, it tries to flip any face or edge //
// that intersects the recovering edge. Otherwise, only the face or edge //
// which is visible by 'startpt' is tried. //
// //
// The parameter 'sedge' is used to report self-intersection. If it is not //
// a NULL, it is EITHER a segment OR a subface that contains this edge. //
// //
// Note that this routine assumes that the tetrahedralization is convex. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::recoveredgebyflips(point startpt, point endpt, face *sedge, triface* searchtet, int fullsearch)
{
flipconstraints fc;
enum interresult dir;
fc.seg[0] = startpt;
fc.seg[1] = endpt;
fc.checkflipeligibility = 1;
// The mainloop of the edge reocvery.
while (1) { // Loop I
// Search the edge from 'startpt'.
point2tetorg(startpt, *searchtet);
dir = finddirection(searchtet, endpt);
if (dir == ACROSSVERT) {
if (dest(*searchtet) == endpt) {
return 1; // Edge is recovered.
} else {
if (sedge) {
return report_selfint_edge(startpt, endpt, sedge, searchtet, dir);
} else {
return 0;
}
}
}
// The edge is missing.
// Try to remove the first intersecting face/edge.
enextesymself(*searchtet); // Go to the opposite face.
if (dir == ACROSSFACE) {
if (checksubfaceflag) {
if (issubface(*searchtet)) {
if (sedge) {
return report_selfint_edge(startpt, endpt, sedge, searchtet, dir);
} else {
return 0; // Cannot flip a subface.
}
}
}
// Try to flip a crossing face.
if (removefacebyflips(searchtet, &fc)) {
continue;
}
} else if (dir == ACROSSEDGE) {
if (checksubsegflag) {
if (issubseg(*searchtet)) {
if (sedge) {
return report_selfint_edge(startpt, endpt, sedge, searchtet, dir);
} else {
return 0; // Cannot flip a segment.
}
}
}
// Try to flip an intersecting edge.
if (removeedgebyflips(searchtet, &fc) == 2) {
continue;
}
}
// The edge is missing.
if (fullsearch) {
// Try to flip one of the faces/edges which intersects the edge.
triface neightet, spintet;
point pa, pb, pc, pd;
badface bakface;
enum interresult dir1;
int types[2], poss[4], pos = 0; int success = 0;
int t1ver;
int i, j;
// Loop through the sequence of intersecting faces/edges from
// 'startpt' to 'endpt'.
point2tetorg(startpt, *searchtet);
dir = finddirection(searchtet, endpt);
// Go to the face/edge intersecting the searching edge.
enextesymself(*searchtet); // Go to the opposite face.
// This face/edge has been tried in previous step.
while (1) { // Loop I-I
// Find the next intersecting face/edge.
fsymself(*searchtet);
if (dir == ACROSSFACE) {
neightet = *searchtet;
j = (neightet.ver & 3); // j is the current face number.
for (i = j + 1; i < j + 4; i++) {
neightet.ver = (i % 4);
pa = org(neightet);
pb = dest(neightet);
pc = apex(neightet);
pd = oppo(neightet); // The above point.
if (tri_edge_test(pa,pb,pc,startpt,endpt, pd, 1, types, poss)) {
dir = (enum interresult) types[0];
pos = poss[0];
break;
} else {
dir = DISJOINT;
pos = 0;
}
} // i
// There must be an intersection face/edge.
if (dir == DISJOINT) {
terminatetetgen(this, 2);
}
} else if (dir == ACROSSEDGE) {
while (1) { // Loop I-I-I
// Check the two opposite faces (of the edge) in 'searchtet'.
for (i = 0; i < 2; i++) {
if (i == 0) {
enextesym(*searchtet, neightet);
} else {
eprevesym(*searchtet, neightet);
}
pa = org(neightet);
pb = dest(neightet);
pc = apex(neightet);
pd = oppo(neightet); // The above point.
if (tri_edge_test(pa,pb,pc,startpt,endpt,pd,1, types, poss)) {
dir = (enum interresult) types[0];
pos = poss[0];
break; // for loop
} else {
dir = DISJOINT;
pos = 0;
}
} // i
if (dir != DISJOINT) {
// Find an intersection face/edge.
break; // Loop I-I-I
}
// No intersection. Rotate to the next tet at the edge.
fnextself(*searchtet);
} // while (1) // Loop I-I-I
} else {
terminatetetgen(this, 2); // Report a bug }
// Adjust to the intersecting edge/vertex.
for (i = 0; i < pos; i++) {
enextself(neightet);
}
if (dir == SHAREVERT) {
// Check if we have reached the 'endpt'.
pd = org(neightet);
if (pd == endpt) {
// Failed to recover the edge.
break; // Loop I-I
} else {
terminatetetgen(this, 2); // Report a bug
}
}
// The next to be flipped face/edge.
*searchtet = neightet;
// Bakup this face (tetrahedron).
bakface.forg = org(*searchtet);
bakface.fdest = dest(*searchtet);
bakface.fapex = apex(*searchtet);
bakface.foppo = oppo(*searchtet);
// Try to flip this intersecting face/edge.
if (dir == ACROSSFACE) {
if (checksubfaceflag) {
if (issubface(*searchtet)) {
if (sedge) {
return report_selfint_edge(startpt,endpt,sedge,searchtet,dir);
} else {
return 0; // Cannot flip a subface.
}
}
}
if (removefacebyflips(searchtet, &fc)) {
success = 1;
break; // Loop I-I
}
} else if (dir == ACROSSEDGE) {
if (checksubsegflag) {
if (issubseg(*searchtet)) {
if (sedge) {
return report_selfint_edge(startpt,endpt,sedge,searchtet,dir);
} else {
return 0; // Cannot flip a segment.
}
}
}
if (removeedgebyflips(searchtet, &fc) == 2) {
success = 1;
break; // Loop I-I
}
} else if (dir == ACROSSVERT) {
if (sedge) {
//return report_selfint_edge(startpt, endpt, sedge, searchtet, dir);
terminatetetgen(this, 2);
} else {
return 0;
}
} else {
terminatetetgen(this, 2);
}
// The face/edge is not flipped.
if ((searchtet->tet == NULL) ||
(org(*searchtet) != bakface.forg) || (dest(*searchtet) != bakface.fdest) ||
(apex(*searchtet) != bakface.fapex) ||
(oppo(*searchtet) != bakface.foppo)) {
// 'searchtet' was flipped. We must restore it.
point2tetorg(bakface.forg, *searchtet);
dir1 = finddirection(searchtet, bakface.fdest);
if (dir1 == ACROSSVERT) {
if (dest(*searchtet) == bakface.fdest) {
spintet = *searchtet;
while (1) {
if (apex(spintet) == bakface.fapex) {
// Found the face.
*searchtet = spintet;
break;
}
fnextself(spintet);
if (spintet.tet == searchtet->tet) {
searchtet->tet = NULL;
break; // Not find.
}
} // while (1)
if (searchtet->tet != NULL) {
if (oppo(*searchtet) != bakface.foppo) {
fsymself(*searchtet);
if (oppo(*searchtet) != bakface.foppo) {
// The original (intersecting) tet has been flipped.
searchtet->tet = NULL;
break; // Not find.
}
}
}
} else {
searchtet->tet = NULL; // Not find.
}
} else {
searchtet->tet = NULL; // Not find.
}
if (searchtet->tet == NULL) {
success = 0; // This face/edge has been destroyed.
break; // Loop I-I
}
}
} // while (1) // Loop I-I
if (success) {
// One of intersecting faces/edges is flipped.
continue;
}
} // if (fullsearch)
// The edge is missing.
break; // Loop I
} // while (1) // Loop I
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// add_steinerpt_in_schoenhardtpoly() Insert a Steiner point in a Schoen- //
// hardt polyhedron. //
// //
// 'abtets' is an array of n tets which all share at the edge [a,b]. Let the //
// tets are [a,b,p0,p1], [a,b,p1,p2], ..., [a,b,p_(n-2),p_(n-1)]. Moreover, //
// the edge [p0,p_(n-1)] intersects all of the tets in 'abtets'. A special //
// case is that the edge [p0,p_(n-1)] is coplanar with the edge [a,b]. //
// Such set of tets arises when we want to recover an edge from 'p0' to 'p_ //
// (n-1)', and the number of tets at [a,b] can not be reduced by any flip. //// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::add_steinerpt_in_schoenhardtpoly(triface *abtets, int n,
int chkencflag)
{
triface worktet, *parytet;
triface faketet1, faketet2;
point pc, pd, steinerpt;
insertvertexflags ivf;
optparameters opm;
REAL vcd[3], sampt[3], smtpt[3];
REAL maxminvol = 0.0, minvol = 0.0, ori;
int success, maxidx = 0;
int it, i;
pc = apex(abtets[0]); // pc = p0
pd = oppo(abtets[n-1]); // pd = p_(n-1)
// Find an optimial point in edge [c,d]. It is visible by all outer faces
// of 'abtets', and it maxmizes the min volume.
// initialize the list of 2n boundary faces.
for (i = 0; i < n; i++) {
edestoppo(abtets[i], worktet); // [p_i,p_i+1,a]
cavetetlist->newindex((void **) &parytet);
*parytet = worktet;
eorgoppo(abtets[i], worktet); // [p_i+1,p_i,b]
cavetetlist->newindex((void **) &parytet);
*parytet = worktet;
}
int N = 100;
REAL stepi = 0.01;
// Search the point along the edge [c,d].
for (i = 0; i < 3; i++) vcd[i] = pd[i] - pc[i];
// Sample N points in edge [c,d].
for (it = 1; it < N; it++) {
for (i = 0; i < 3; i++) {
sampt[i] = pc[i] + (stepi * (double) it) * vcd[i];
}
for (i = 0; i < cavetetlist->objects; i++) {
parytet = (triface *) fastlookup(cavetetlist, i);
ori = orient3d(dest(*parytet), org(*parytet), apex(*parytet), sampt);
if (i == 0) {
minvol = ori;
} else {
if (minvol > ori) minvol = ori;
}
} // i
if (it == 1) {
maxminvol = minvol;
maxidx = it;
} else {
if (maxminvol < minvol) {
maxminvol = minvol;
maxidx = it;
}
}
} // it
if (maxminvol <= 0) {
cavetetlist->restart();
return 0;
}
for (i = 0; i < 3; i++) {
smtpt[i] = pc[i] + (stepi * (double) maxidx) * vcd[i];
}
// Create two faked tets to hold the two non-existing boundary faces:
// [d,c,a] and [c,d,b].
maketetrahedron(&faketet1);
setvertices(faketet1, pd, pc, org(abtets[0]), dummypoint);
cavetetlist->newindex((void **) &parytet);
*parytet = faketet1;
maketetrahedron(&faketet2);
setvertices(faketet2, pc, pd, dest(abtets[0]), dummypoint);
cavetetlist->newindex((void **) &parytet);
*parytet = faketet2;
// Point smooth options.
opm.max_min_volume = 1;
opm.numofsearchdirs = 20;
opm.searchstep = 0.001;
opm.maxiter = 100; // Limit the maximum iterations.
opm.initval = 0.0; // Initial volume is zero.
// Try to relocate the point into the inside of the polyhedron.
success = smoothpoint(smtpt, cavetetlist, 1, &opm);
if (success) {
while (opm.smthiter == 100) {
// It was relocated and the prescribed maximum iteration reached.
// Try to increase the search stepsize.
opm.searchstep *= 10.0;
//opm.maxiter = 100; // Limit the maximum iterations.
opm.initval = opm.imprval;
opm.smthiter = 0; // Init.
smoothpoint(smtpt, cavetetlist, 1, &opm);
}
} // if (success)
// Delete the two faked tets.
tetrahedrondealloc(faketet1.tet);
tetrahedrondealloc(faketet2.tet);
cavetetlist->restart();
if (!success) {
return 0;
}
// Insert the Steiner point.
makepoint(&steinerpt, FREEVOLVERTEX);
for (i = 0; i < 3; i++) steinerpt[i] = smtpt[i];
// Insert the created Steiner point.
for (i = 0; i < n; i++) {
infect(abtets[i]);
caveoldtetlist->newindex((void **) &parytet);
*parytet = abtets[i];
}
worktet = abtets[0]; // No need point location.
ivf.iloc = (int) INSTAR;
ivf.chkencflag = chkencflag;
ivf.assignmeshsize = b->metric;
if (ivf.assignmeshsize) {
// Search the tet containing 'steinerpt' for size interpolation.
locate(steinerpt, &(abtets[0]));
worktet = abtets[0];
}
// Insert the new point into the tetrahedralization T.
// Note that T is convex (nonconvex = 0). if (insertpoint(steinerpt, &worktet, NULL, NULL, &ivf)) {
// The vertex has been inserted.
st_volref_count++;
if (steinerleft > 0) steinerleft--;
return 1;
} else {
// Not inserted.
pointdealloc(steinerpt);
return 0;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// add_steinerpt_in_segment() Add a Steiner point inside a segment. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::add_steinerpt_in_segment(face* misseg, int searchlevel)
{
triface searchtet;
face *paryseg, candseg;
point startpt, endpt, pc, pd;
flipconstraints fc;
enum interresult dir;
REAL P[3], Q[3], tp, tq;
REAL len, smlen = 0, split = 0, split_q = 0;
int success=0;
int i;
startpt = sorg(*misseg);
endpt = sdest(*misseg);
fc.seg[0] = startpt;
fc.seg[1] = endpt;
fc.checkflipeligibility = 1;
fc.collectencsegflag = 1;
point2tetorg(startpt, searchtet);
dir = finddirection(&searchtet, endpt);
// Try to flip the first intersecting face/edge.
enextesymself(searchtet); // Go to the opposite face.
int bak_fliplinklevel = b->fliplinklevel;
b->fliplinklevel = searchlevel;
if (dir == ACROSSFACE) {
// A face is intersected with the segment. Try to flip it.
success = removefacebyflips(&searchtet, &fc);
} else if (dir == ACROSSEDGE) {
// An edge is intersected with the segment. Try to flip it.
success = removeedgebyflips(&searchtet, &fc);
}
split = 0;
for (i = 0; i < caveencseglist->objects; i++) {
paryseg = (face *) fastlookup(caveencseglist, i);
suninfect(*paryseg);
// Calculate the shortest edge between the two lines.
pc = sorg(*paryseg);
pd = sdest(*paryseg);
tp = tq = 0;
if (linelineint(startpt, endpt, pc, pd, P, Q, &tp, &tq)) {
// Does the shortest edge lie between the two segments?
// Round tp and tq.
if ((tp > 0) && (tq < 1)) {
if (tp < 0.5) {
if (tp < (b->epsilon * 1e+3)) tp = 0.0;
} else {
if ((1.0 - tp) < (b->epsilon * 1e+3)) tp = 1.0; }
}
if ((tp <= 0) || (tp >= 1)) continue;
if ((tq > 0) && (tq < 1)) {
if (tq < 0.5) {
if (tq < (b->epsilon * 1e+3)) tq = 0.0;
} else {
if ((1.0 - tq) < (b->epsilon * 1e+3)) tq = 1.0;
}
}
if ((tq <= 0) || (tq >= 1)) continue;
// It is a valid shortest edge. Calculate its length.
len = distance(P, Q);
if (split == 0) {
smlen = len;
split = tp;
split_q = tq;
candseg = *paryseg;
} else {
if (len < smlen) {
smlen = len;
split = tp;
split_q = tq;
candseg = *paryseg;
}
}
}
}
caveencseglist->restart();
b->fliplinklevel = bak_fliplinklevel;
if (split == 0) {
// Found no crossing segment.
return 0;
}
face splitsh;
face splitseg;
point steinerpt, *parypt;
insertvertexflags ivf;
if (b->addsteiner_algo == 1) {
// Split the segment at the closest point to a near segment.
makepoint(&steinerpt, FREESEGVERTEX);
for (i = 0; i < 3; i++) {
steinerpt[i] = startpt[i] + split * (endpt[i] - startpt[i]);
}
} else { // b->addsteiner_algo == 2
for (i = 0; i < 3; i++) {
P[i] = startpt[i] + split * (endpt[i] - startpt[i]);
}
pc = sorg(candseg);
pd = sdest(candseg);
for (i = 0; i < 3; i++) {
Q[i] = pc[i] + split_q * (pd[i] - pc[i]);
}
makepoint(&steinerpt, FREEVOLVERTEX);
for (i = 0; i < 3; i++) {
steinerpt[i] = 0.5 * (P[i] + Q[i]);
}
}
// We need to locate the point. Start searching from 'searchtet'.
if (split < 0.5) {
point2tetorg(startpt, searchtet);
} else {
point2tetorg(endpt, searchtet);
}
if (b->addsteiner_algo == 1) { splitseg = *misseg;
spivot(*misseg, splitsh);
} else {
splitsh.sh = NULL;
splitseg.sh = NULL;
}
ivf.iloc = (int) OUTSIDE;
ivf.bowywat = 1;
ivf.lawson = 0;
ivf.rejflag = 0;
ivf.chkencflag = 0;
ivf.sloc = (int) ONEDGE;
ivf.sbowywat = 1;
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
ivf.assignmeshsize = b->metric;
if (!insertpoint(steinerpt, &searchtet, &splitsh, &splitseg, &ivf)) {
pointdealloc(steinerpt);
return 0;
}
if (b->addsteiner_algo == 1) {
// Save this Steiner point (for removal).
// Re-use the array 'subvertstack'.
subvertstack->newindex((void **) &parypt);
*parypt = steinerpt;
st_segref_count++;
} else { // b->addsteiner_algo == 2
// Queue the segment for recovery.
subsegstack->newindex((void **) &paryseg);
*paryseg = *misseg;
st_volref_count++;
}
if (steinerleft > 0) steinerleft--;
if (!success){
// error
}
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// addsteiner4recoversegment() Add a Steiner point for recovering a seg. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::addsteiner4recoversegment(face* misseg, int splitsegflag)
{
triface *abtets, searchtet, spintet;
face splitsh;
face *paryseg;
point startpt, endpt;
point pa, pb, pd, steinerpt, *parypt;
enum interresult dir;
insertvertexflags ivf;
int types[2], poss[4];
int n, endi, success;
int t1ver;
int i;
startpt = sorg(*misseg);
if (pointtype(startpt) == FREESEGVERTEX) {
sesymself(*misseg);
startpt = sorg(*misseg);
}
endpt = sdest(*misseg);
// Try to recover the edge by adding Steiner points.
point2tetorg(startpt, searchtet);
dir = finddirection(&searchtet, endpt);
enextself(searchtet);
if (dir == ACROSSFACE) {
// The segment is crossing at least 3 faces. Find the common edge of
// the first 3 crossing faces.
esymself(searchtet);
fsym(searchtet, spintet);
pd = oppo(spintet);
for (i = 0; i < 3; i++) {
pa = org(spintet);
pb = dest(spintet);
if (tri_edge_test(pa, pb, pd, startpt, endpt, NULL, 1, types, poss)) {
break; // Found the edge.
}
enextself(spintet);
eprevself(searchtet);
}
esymself(searchtet);
}
spintet = searchtet;
n = 0; endi = -1;
while (1) {
// Check if the endpt appears in the star.
if (apex(spintet) == endpt) {
endi = n; // Remember the position of endpt.
}
n++; // Count a tet in the star.
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
if (endi > 0) {
// endpt is also in the edge star
// Get all tets in the edge star.
abtets = new triface[n];
spintet = searchtet;
for (i = 0; i < n; i++) {
abtets[i] = spintet;
fnextself(spintet);
}
success = 0;
if (dir == ACROSSFACE) {
// Find a Steiner points inside the polyhedron.
if (add_steinerpt_in_schoenhardtpoly(abtets, endi, 0)) {
success = 1;
}
} else if (dir == ACROSSEDGE) {
// PLC check.
if (issubseg(searchtet)) {
terminatetetgen(this, 2);
}
if (n > 4) {
// In this case, 'abtets' is separated by the plane (containing the
// two intersecting edges) into two parts, P1 and P2, where P1
// consists of 'endi' tets: abtets[0], abtets[1], ...,
// abtets[endi-1], and P2 consists of 'n - endi' tets:
// abtets[endi], abtets[endi+1], abtets[n-1].
if (endi > 2) { // P1
// There are at least 3 tets in the first part.
if (add_steinerpt_in_schoenhardtpoly(abtets, endi, 0)) {
success++;
}
}
if ((n - endi) > 2) { // P2 // There are at least 3 tets in the first part.
if (add_steinerpt_in_schoenhardtpoly(&(abtets[endi]), n - endi, 0)) {
success++;
}
}
} else {
// In this case, a 4-to-4 flip should be re-cover the edge [c,d].
// However, there will be invalid tets (either zero or negtive
// volume). Otherwise, [c,d] should already be recovered by the
// recoveredge() function.
terminatetetgen(this, 2);
}
} else {
terminatetetgen(this, 2);
}
delete [] abtets;
if (success) {
// Add the missing segment back to the recovering list.
subsegstack->newindex((void **) &paryseg);
*paryseg = *misseg;
return 1;
}
} // if (endi > 0)
if (!splitsegflag) {
return 0;
}
if (b->verbose > 2) {
printf(" Splitting segment (%d, %d)\n", pointmark(startpt),
pointmark(endpt));
}
steinerpt = NULL;
if (b->addsteiner_algo > 0) { // -Y/1 or -Y/2
if (add_steinerpt_in_segment(misseg, 3)) {
return 1;
}
sesymself(*misseg);
if (add_steinerpt_in_segment(misseg, 3)) {
return 1;
}
sesymself(*misseg);
}
if (steinerpt == NULL) {
// Split the segment at its midpoint.
makepoint(&steinerpt, FREESEGVERTEX);
for (i = 0; i < 3; i++) {
steinerpt[i] = 0.5 * (startpt[i] + endpt[i]);
}
// We need to locate the point.
spivot(*misseg, splitsh);
ivf.iloc = (int) OUTSIDE;
ivf.bowywat = 1;
ivf.lawson = 0;
ivf.rejflag = 0;
ivf.chkencflag = 0;
ivf.sloc = (int) ONEDGE;
ivf.sbowywat = 1;
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
ivf.assignmeshsize = b->metric; if (!insertpoint(steinerpt, &searchtet, &splitsh, misseg, &ivf)) {
terminatetetgen(this, 2);
}
} // if (endi > 0)
// Save this Steiner point (for removal).
// Re-use the array 'subvertstack'.
subvertstack->newindex((void **) &parypt);
*parypt = steinerpt;
st_segref_count++;
if (steinerleft > 0) steinerleft--;
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// recoversegments() Recover all segments. //
// //
// All segments need to be recovered are in 'subsegstack'. //
// //
// This routine first tries to recover each segment by only using flips. If //
// no flip is possible, and the flag 'steinerflag' is set, it then tries to //
// insert Steiner points near or in the segment. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::recoversegments(arraypool *misseglist, int fullsearch,
int steinerflag)
{
triface searchtet, spintet;
face sseg, *paryseg;
point startpt, endpt;
int success;
int t1ver;
long bak_inpoly_count = st_volref_count;
long bak_segref_count = st_segref_count;
if (b->verbose > 1) {
printf(" Recover segments [%s level = %2d] #: %ld.\n",
(b->fliplinklevel > 0) ? "fixed" : "auto",
(b->fliplinklevel > 0) ? b->fliplinklevel : autofliplinklevel,
subsegstack->objects);
}
// Loop until 'subsegstack' is empty.
while (subsegstack->objects > 0l) {
// seglist is used as a stack.
subsegstack->objects--;
paryseg = (face *) fastlookup(subsegstack, subsegstack->objects);
sseg = *paryseg;
// Check if this segment has been recovered.
sstpivot1(sseg, searchtet);
if (searchtet.tet != NULL) {
continue; // Not a missing segment.
}
startpt = sorg(sseg);
endpt = sdest(sseg);
if (b->verbose > 2) {
printf(" Recover segment (%d, %d).\n", pointmark(startpt),
pointmark(endpt));
}
success = 0;
if (recoveredgebyflips(startpt, endpt, &sseg, &searchtet, 0)) {
success = 1;
} else {
// Try to recover it from the other direction.
if (recoveredgebyflips(endpt, startpt, &sseg, &searchtet, 0)) {
success = 1;
}
}
if (!success && fullsearch) {
if (recoveredgebyflips(startpt, endpt, &sseg, &searchtet, fullsearch)) {
success = 1;
}
}
if (success) {
// Segment is recovered. Insert it.
// Let the segment remember an adjacent tet.
sstbond1(sseg, searchtet);
// Bond the segment to all tets containing it.
spintet = searchtet;
do {
tssbond1(spintet, sseg);
fnextself(spintet);
} while (spintet.tet != searchtet.tet);
} else {
if (steinerflag > 0) {
// Try to recover the segment but do not split it.
if (addsteiner4recoversegment(&sseg, 0)) {
success = 1;
}
if (!success && (steinerflag > 1)) {
// Split the segment.
addsteiner4recoversegment(&sseg, 1);
success = 1;
}
}
if (!success) {
if (misseglist != NULL) {
// Save this segment.
misseglist->newindex((void **) &paryseg);
*paryseg = sseg;
}
}
}
} // while (subsegstack->objects > 0l)
if (steinerflag) {
if (b->verbose > 1) {
// Report the number of added Steiner points.
if (st_volref_count > bak_inpoly_count) {
printf(" Add %ld Steiner points in volume.\n",
st_volref_count - bak_inpoly_count);
}
if (st_segref_count > bak_segref_count) {
printf(" Add %ld Steiner points in segments.\n",
st_segref_count - bak_segref_count);
}
}
}
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// recoverfacebyflips() Recover a face by flips. //
// //
// 'pa', 'pb', and 'pc' are the three vertices of this face. This routine //// tries to recover it in the tetrahedral mesh. It is assumed that the three //
// edges, i.e., pa->pb, pb->pc, and pc->pa all exist. //
// //
// If the face is recovered, it is returned by 'searchtet'. //
// //
// If 'searchsh' is not NULL, it is a subface to be recovered. Its vertices //
// must be pa, pb, and pc. It is mainly used to check self-intersections. //
// Another use of this subface is to split it when a Steiner point is found //
// inside this subface. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::recoverfacebyflips(point pa, point pb, point pc,
face *searchsh, triface* searchtet)
{
triface spintet, flipedge;
point pd, pe;
flipconstraints fc;
int types[2], poss[4], intflag;
int success;
int t1ver;
int i, j;
fc.fac[0] = pa;
fc.fac[1] = pb;
fc.fac[2] = pc;
fc.checkflipeligibility = 1;
success = 0;
for (i = 0; i < 3 && !success; i++) {
while (1) {
// Get a tet containing the edge [a,b].
point2tetorg(fc.fac[i], *searchtet);
finddirection(searchtet, fc.fac[(i+1)%3]);
// Search the face [a,b,c]
spintet = *searchtet;
while (1) {
if (apex(spintet) == fc.fac[(i+2)%3]) {
// Found the face.
*searchtet = spintet;
// Return the face [a,b,c].
for (j = i; j > 0; j--) {
eprevself(*searchtet);
}
success = 1;
break;
}
fnextself(spintet);
if (spintet.tet == searchtet->tet) break;
} // while (1)
if (success) break;
// The face is missing. Try to recover it.
flipedge.tet = NULL;
// Find a crossing edge of this face.
spintet = *searchtet;
while (1) {
pd = apex(spintet);
pe = oppo(spintet);
if ((pd != dummypoint) && (pe != dummypoint)) {
// Check if [d,e] intersects [a,b,c]
intflag = tri_edge_test(pa, pb, pc, pd, pe, NULL, 1, types, poss);
if (intflag > 0) {
// By the assumption that all edges of the face exist, they can
// only intersect at a single point.
if (intflag == 2) {
// Go to the edge [d,e].
edestoppo(spintet, flipedge); // [d,e,a,b]
if (searchsh != NULL) {
// Check the intersection type. if ((types[0] == (int) ACROSSFACE) ||
(types[0] == (int) ACROSSEDGE)) {
// Check if [e,d] is a segment.
if (issubseg(flipedge)) {
return report_selfint_face(pa, pb, pc, searchsh, &flipedge,
intflag, types, poss);
} else {
// Check if [e,d] is an edge of a subface.
triface chkface = flipedge;
while (1) {
if (issubface(chkface)) break;
fsymself(chkface);
if (chkface.tet == flipedge.tet) break;
}
if (issubface(chkface)) {
// Two subfaces are intersecting.
return report_selfint_face(pa, pb, pc,searchsh,&chkface,
intflag, types, poss);
}
}
} else if (types[0] == TOUCHFACE) {
// This is possible when a Steiner point was added on it.
point touchpt, *parypt;
if (poss[1] == 0) {
touchpt = pd; // pd is a coplanar vertex.
} else {
touchpt = pe; // pe is a coplanar vertex.
}
if (pointtype(touchpt) == FREEVOLVERTEX) {
// A volume Steiner point was added in this subface.
// Split this subface by this point.
face checksh, *parysh;
int siloc = (int) ONFACE;
int sbowat = 0; // Only split this subface. A 1-to-3 flip.
setpointtype(touchpt, FREEFACETVERTEX);
sinsertvertex(touchpt, searchsh, NULL, siloc, sbowat, 0);
st_volref_count--;
st_facref_count++;
// Queue this vertex for removal.
subvertstack->newindex((void **) &parypt);
*parypt = touchpt;
// Queue new subfaces for recovery.
// Put all new subfaces into stack for recovery.
for (i = 0; i < caveshbdlist->objects; i++) {
// Get an old subface at edge [a, b].
parysh = (face *) fastlookup(caveshbdlist, i);
spivot(*parysh, checksh); // The new subface [a, b, p].
// Do not recover a deleted new face (degenerated).
if (checksh.sh[3] != NULL) {
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
}
// Delete the old subfaces in sC(p).
for (i = 0; i < caveshlist->objects; i++) {
parysh = (face *) fastlookup(caveshlist, i);
shellfacedealloc(subfaces, parysh->sh);
}
// Clear working lists.
caveshlist->restart();
caveshbdlist->restart();
cavesegshlist->restart();
// We can return this function.
searchsh->sh = NULL; // It has been split.
return 1;
} else {
// Other cases may be due to a bug or a PLC error.
return report_selfint_face(pa, pb, pc, searchsh, &flipedge,
intflag, types, poss);
} } else {
// The other intersection types: ACROSSVERT, TOUCHEDGE,
// SHAREVERTEX should not be possible or due to a PLC error.
return report_selfint_face(pa, pb, pc, searchsh, &flipedge,
intflag, types, poss);
}
} // if (searchsh != NULL)
} else { // intflag == 4. Coplanar case.
terminatetetgen(this, 2);
}
break;
} // if (intflag > 0)
}
fnextself(spintet);
if (spintet.tet == searchtet->tet) {
terminatetetgen(this, 2);
}
} // while (1)
// Try to flip the edge [d,e].
if (removeedgebyflips(&flipedge, &fc) == 2) {
// A crossing edge is removed.
continue;
}
break;
} // while (1)
} // i
return success;
}
///////////////////////////////////////////////////////////////////////////////
// //
// recoversubfaces() Recover all subfaces. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::recoversubfaces(arraypool *misshlist, int steinerflag)
{
triface searchtet, neightet, spintet;
face searchsh, neighsh, neineish, *parysh;
face bdsegs[3];
point startpt, endpt, apexpt, *parypt;
point steinerpt;
insertvertexflags ivf;
int success;
int t1ver;
int i, j;
if (b->verbose > 1) {
printf(" Recover subfaces [%s level = %2d] #: %ld.\n",
(b->fliplinklevel > 0) ? "fixed" : "auto",
(b->fliplinklevel > 0) ? b->fliplinklevel : autofliplinklevel,
subfacstack->objects);
}
// Loop until 'subfacstack' is empty.
while (subfacstack->objects > 0l) {
subfacstack->objects--;
parysh = (face *) fastlookup(subfacstack, subfacstack->objects);
searchsh = *parysh;
if (searchsh.sh[3] == NULL) continue; // Skip a dead subface.
stpivot(searchsh, neightet);
if (neightet.tet != NULL) continue; // Skip a recovered subface.
if (b->verbose > 2) {
printf(" Recover subface (%d, %d, %d).\n",pointmark(sorg(searchsh)), pointmark(sdest(searchsh)), pointmark(sapex(searchsh)));
}
// The three edges of the face need to be existed first.
for (i = 0; i < 3; i++) {
sspivot(searchsh, bdsegs[i]);
if (bdsegs[i].sh != NULL) {
// The segment must exist.
sstpivot1(bdsegs[i], searchtet);
if (searchtet.tet == NULL) {
terminatetetgen(this, 2);
}
} else {
// This edge is not a segment (due to a Steiner point).
// Check whether it exists or not.
success = 0;
startpt = sorg(searchsh);
endpt = sdest(searchsh);
point2tetorg(startpt, searchtet);
finddirection(&searchtet, endpt);
if (dest(searchtet) == endpt) {
success = 1;
} else {
// The edge is missing. Try to recover it.
if (recoveredgebyflips(startpt, endpt, &searchsh, &searchtet, 0)) {
success = 1;
} else {
if (recoveredgebyflips(endpt, startpt, &searchsh, &searchtet, 0)) {
success = 1;
}
}
}
if (success) {
// Insert a temporary segment to protect this edge.
makeshellface(subsegs, &(bdsegs[i]));
setshvertices(bdsegs[i], startpt, endpt, NULL);
smarktest2(bdsegs[i]); // It's a temporary segment.
// Insert this segment into surface mesh.
ssbond(searchsh, bdsegs[i]);
spivot(searchsh, neighsh);
if (neighsh.sh != NULL) {
ssbond(neighsh, bdsegs[i]);
}
// Insert this segment into tetrahedralization.
sstbond1(bdsegs[i], searchtet);
// Bond the segment to all tets containing it.
spintet = searchtet;
do {
tssbond1(spintet, bdsegs[i]);
fnextself(spintet);
} while (spintet.tet != searchtet.tet);
} else {
// An edge of this subface is missing. Can't recover this subface.
// Delete any temporary segment that has been created.
for (j = (i - 1); j >= 0; j--) {
if (smarktest2ed(bdsegs[j])) {
spivot(bdsegs[j], neineish);
ssdissolve(neineish);
spivot(neineish, neighsh);
if (neighsh.sh != NULL) {
ssdissolve(neighsh);
}
sstpivot1(bdsegs[j], searchtet);
spintet = searchtet;
while (1) {
tssdissolve1(spintet);
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
shellfacedealloc(subsegs, bdsegs[j].sh); }
} // j
if (steinerflag) {
// Add a Steiner point at the midpoint of this edge.
if (b->verbose > 2) {
printf(" Add a Steiner point in subedge (%d, %d).\n",
pointmark(startpt), pointmark(endpt));
}
makepoint(&steinerpt, FREEFACETVERTEX);
for (j = 0; j < 3; j++) {
steinerpt[j] = 0.5 * (startpt[j] + endpt[j]);
}
point2tetorg(startpt, searchtet); // Start from 'searchtet'.
ivf.iloc = (int) OUTSIDE; // Need point location.
ivf.bowywat = 1;
ivf.lawson = 0;
ivf.rejflag = 0;
ivf.chkencflag = 0;
ivf.sloc = (int) ONEDGE;
ivf.sbowywat = 1; // Allow flips in facet.
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
ivf.assignmeshsize = b->metric;
if (!insertpoint(steinerpt, &searchtet, &searchsh, NULL, &ivf)) {
terminatetetgen(this, 2);
}
// Save this Steiner point (for removal).
// Re-use the array 'subvertstack'.
subvertstack->newindex((void **) &parypt);
*parypt = steinerpt;
st_facref_count++;
if (steinerleft > 0) steinerleft--;
} // if (steinerflag)
break;
}
}
senextself(searchsh);
} // i
if (i == 3) {
// Recover the subface.
startpt = sorg(searchsh);
endpt = sdest(searchsh);
apexpt = sapex(searchsh);
success = recoverfacebyflips(startpt,endpt,apexpt,&searchsh,&searchtet);
// Delete any temporary segment that has been created.
for (j = 0; j < 3; j++) {
if (smarktest2ed(bdsegs[j])) {
spivot(bdsegs[j], neineish);
ssdissolve(neineish);
spivot(neineish, neighsh);
if (neighsh.sh != NULL) {
ssdissolve(neighsh);
}
sstpivot1(bdsegs[j], neightet);
spintet = neightet;
while (1) {
tssdissolve1(spintet);
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
shellfacedealloc(subsegs, bdsegs[j].sh);
}
} // j
if (success) {
if (searchsh.sh != NULL) {
// Face is recovered. Insert it.
tsbond(searchtet, searchsh);
fsymself(searchtet);
sesymself(searchsh);
tsbond(searchtet, searchsh);
}
} else {
if (steinerflag) {
// Add a Steiner point at the barycenter of this subface.
if (b->verbose > 2) {
printf(" Add a Steiner point in subface (%d, %d, %d).\n",
pointmark(startpt), pointmark(endpt), pointmark(apexpt));
}
makepoint(&steinerpt, FREEFACETVERTEX);
for (j = 0; j < 3; j++) {
steinerpt[j] = (startpt[j] + endpt[j] + apexpt[j]) / 3.0;
}
point2tetorg(startpt, searchtet); // Start from 'searchtet'.
ivf.iloc = (int) OUTSIDE; // Need point location.
ivf.bowywat = 1;
ivf.lawson = 0;
ivf.rejflag = 0;
ivf.chkencflag = 0;
ivf.sloc = (int) ONFACE;
ivf.sbowywat = 1; // Allow flips in facet.
ivf.splitbdflag = 0;
ivf.validflag = 1;
ivf.respectbdflag = 1;
ivf.assignmeshsize = b->metric;
if (!insertpoint(steinerpt, &searchtet, &searchsh, NULL, &ivf)) {
terminatetetgen(this, 2);
}
// Save this Steiner point (for removal).
// Re-use the array 'subvertstack'.
subvertstack->newindex((void **) &parypt);
*parypt = steinerpt;
st_facref_count++;
if (steinerleft > 0) steinerleft--;
} // if (steinerflag)
}
} else {
success = 0;
}
if (!success) {
if (misshlist != NULL) {
// Save this subface.
misshlist->newindex((void **) &parysh);
*parysh = searchsh;
}
}
} // while (subfacstack->objects > 0l)
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// getvertexstar() Return the star of a vertex. //
// //
// If the flag 'fullstar' is set, return the complete star of this vertex. //
// Otherwise, only a part of the star which is bounded by facets is returned.//
// //
// 'tetlist' returns the list of tets in the star of the vertex 'searchpt'. //
// Every tet in 'tetlist' is at the face opposing to 'searchpt'. //// //
// 'vertlist' returns the list of vertices in the star (exclude 'searchpt'). //
// //
// 'shlist' returns the list of subfaces in the star. Each subface must face //
// to the interior of this star. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::getvertexstar(int fullstar, point searchpt, arraypool* tetlist,
arraypool* vertlist, arraypool* shlist)
{
triface searchtet, neightet, *parytet;
face checksh, *parysh;
point pt, *parypt;
int collectflag;
int t1ver;
int i, j;
point2tetorg(searchpt, searchtet);
// Go to the opposite face (the link face) of the vertex.
enextesymself(searchtet);
//assert(oppo(searchtet) == searchpt);
infect(searchtet); // Collect this tet (link face).
tetlist->newindex((void **) &parytet);
*parytet = searchtet;
if (vertlist != NULL) {
// Collect three (link) vertices.
j = (searchtet.ver & 3); // The current vertex index.
for (i = 1; i < 4; i++) {
pt = (point) searchtet.tet[4 + ((j + i) % 4)];
pinfect(pt);
vertlist->newindex((void **) &parypt);
*parypt = pt;
}
}
collectflag = 1;
esym(searchtet, neightet);
if (issubface(neightet)) {
if (shlist != NULL) {
tspivot(neightet, checksh);
if (!sinfected(checksh)) {
// Collect this subface (link edge).
sinfected(checksh);
shlist->newindex((void **) &parysh);
*parysh = checksh;
}
}
if (!fullstar) {
collectflag = 0;
}
}
if (collectflag) {
fsymself(neightet); // Goto the adj tet of this face.
esymself(neightet); // Goto the oppo face of this vertex.
// assert(oppo(neightet) == searchpt);
infect(neightet); // Collect this tet (link face).
tetlist->newindex((void **) &parytet);
*parytet = neightet;
if (vertlist != NULL) {
// Collect its apex.
pt = apex(neightet);
pinfect(pt);
vertlist->newindex((void **) &parypt);
*parypt = pt;
}
} // if (collectflag)
// Continue to collect all tets in the star. for (i = 0; i < tetlist->objects; i++) {
searchtet = * (triface *) fastlookup(tetlist, i);
// Note that 'searchtet' is a face opposite to 'searchpt', and the neighbor
// tet at the current edge is already collected.
// Check the neighbors at the other two edges of this face.
for (j = 0; j < 2; j++) {
collectflag = 1;
enextself(searchtet);
esym(searchtet, neightet);
if (issubface(neightet)) {
if (shlist != NULL) {
tspivot(neightet, checksh);
if (!sinfected(checksh)) {
// Collect this subface (link edge).
sinfected(checksh);
shlist->newindex((void **) &parysh);
*parysh = checksh;
}
}
if (!fullstar) {
collectflag = 0;
}
}
if (collectflag) {
fsymself(neightet);
if (!infected(neightet)) {
esymself(neightet); // Go to the face opposite to 'searchpt'.
infect(neightet);
tetlist->newindex((void **) &parytet);
*parytet = neightet;
if (vertlist != NULL) {
// Check if a vertex is collected.
pt = apex(neightet);
if (!pinfected(pt)) {
pinfect(pt);
vertlist->newindex((void **) &parypt);
*parypt = pt;
}
}
} // if (!infected(neightet))
} // if (collectflag)
} // j
} // i
// Uninfect the list of tets and vertices.
for (i = 0; i < tetlist->objects; i++) {
parytet = (triface *) fastlookup(tetlist, i);
uninfect(*parytet);
}
if (vertlist != NULL) {
for (i = 0; i < vertlist->objects; i++) {
parypt = (point *) fastlookup(vertlist, i);
puninfect(*parypt);
}
}
if (shlist != NULL) {
for (i = 0; i < shlist->objects; i++) {
parysh = (face *) fastlookup(shlist, i);
suninfect(*parysh);
}
}
return (int) tetlist->objects;
}
///////////////////////////////////////////////////////////////////////////////
// //// getedge() Get a tetrahedron having the two endpoints. //
// //
// The method here is to search the second vertex in the link faces of the //
// first vertex. The global array 'cavetetlist' is re-used for searching. //
// //
// This function is used for the case when the mesh is non-convex. Otherwise,//
// the function finddirection() should be faster than this. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::getedge(point e1, point e2, triface *tedge)
{
triface searchtet, neightet, *parytet;
point pt;
int done;
int i, j;
if (b->verbose > 2) {
printf(" Get edge from %d to %d.\n", pointmark(e1), pointmark(e2));
}
// Quickly check if 'tedge' is just this edge.
if (!isdeadtet(*tedge)) {
if (org(*tedge) == e1) {
if (dest(*tedge) == e2) {
return 1;
}
} else if (org(*tedge) == e2) {
if (dest(*tedge) == e1) {
esymself(*tedge);
return 1;
}
}
}
// Search for the edge [e1, e2].
point2tetorg(e1, *tedge);
finddirection(tedge, e2);
if (dest(*tedge) == e2) {
return 1;
} else {
// Search for the edge [e2, e1].
point2tetorg(e2, *tedge);
finddirection(tedge, e1);
if (dest(*tedge) == e1) {
esymself(*tedge);
return 1;
}
}
// Go to the link face of e1.
point2tetorg(e1, searchtet);
enextesymself(searchtet);
arraypool *tetlist = cavebdrylist;
// Search e2.
for (i = 0; i < 3; i++) {
pt = apex(searchtet);
if (pt == e2) {
// Found. 'searchtet' is [#,#,e2,e1].
eorgoppo(searchtet, *tedge); // [e1,e2,#,#].
return 1;
}
enextself(searchtet);
}
// Get the adjacent link face at 'searchtet'.
fnext(searchtet, neightet);
esymself(neightet); // assert(oppo(neightet) == e1);
pt = apex(neightet);
if (pt == e2) {
// Found. 'neightet' is [#,#,e2,e1].
eorgoppo(neightet, *tedge); // [e1,e2,#,#].
return 1;
}
// Continue searching in the link face of e1.
infect(searchtet);
tetlist->newindex((void **) &parytet);
*parytet = searchtet;
infect(neightet);
tetlist->newindex((void **) &parytet);
*parytet = neightet;
done = 0;
for (i = 0; (i < tetlist->objects) && !done; i++) {
parytet = (triface *) fastlookup(tetlist, i);
searchtet = *parytet;
for (j = 0; (j < 2) && !done; j++) {
enextself(searchtet);
fnext(searchtet, neightet);
if (!infected(neightet)) {
esymself(neightet);
pt = apex(neightet);
if (pt == e2) {
// Found. 'neightet' is [#,#,e2,e1].
eorgoppo(neightet, *tedge);
done = 1;
} else {
infect(neightet);
tetlist->newindex((void **) &parytet);
*parytet = neightet;
}
}
} // j
} // i
// Uninfect the list of visited tets.
for (i = 0; i < tetlist->objects; i++) {
parytet = (triface *) fastlookup(tetlist, i);
uninfect(*parytet);
}
tetlist->restart();
return done;
}
///////////////////////////////////////////////////////////////////////////////
// //
// reduceedgesatvertex() Reduce the number of edges at a given vertex. //
// //
// 'endptlist' contains the endpoints of edges connecting at the vertex. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::reduceedgesatvertex(point startpt, arraypool* endptlist)
{
triface searchtet;
point *pendpt, *parypt;
enum interresult dir;
flipconstraints fc;
int reduceflag;
int count;
int n, i, j;
fc.remvert = startpt; fc.checkflipeligibility = 1;
while (1) {
count = 0;
for (i = 0; i < endptlist->objects; i++) {
pendpt = (point *) fastlookup(endptlist, i);
if (*pendpt == dummypoint) {
continue; // Do not reduce a virtual edge.
}
reduceflag = 0;
// Find the edge.
if (nonconvex) {
if (getedge(startpt, *pendpt, &searchtet)) {
dir = ACROSSVERT;
} else {
// The edge does not exist (was flipped).
dir = INTERSECT;
}
} else {
point2tetorg(startpt, searchtet);
dir = finddirection(&searchtet, *pendpt);
}
if (dir == ACROSSVERT) {
if (dest(searchtet) == *pendpt) {
// Do not flip a segment.
if (!issubseg(searchtet)) {
n = removeedgebyflips(&searchtet, &fc);
if (n == 2) {
reduceflag = 1;
}
}
}
} else {
// The edge has been flipped.
reduceflag = 1;
}
if (reduceflag) {
count++;
// Move the last vertex into this slot.
j = endptlist->objects - 1;
parypt = (point *) fastlookup(endptlist, j);
*pendpt = *parypt;
endptlist->objects--;
i--;
}
} // i
if (count == 0) {
// No edge is reduced.
break;
}
} // while (1)
return (int) endptlist->objects;
}
///////////////////////////////////////////////////////////////////////////////
// //
// removevertexbyflips() Remove a vertex by flips. //
// //
// This routine attempts to remove the given vertex 'rempt' (p) from the //
// tetrahedralization (T) by a sequence of flips. //
// //
// The algorithm used here is a simple edge reduce method. Suppose there are //
// n edges connected at p. We try to reduce the number of edges by flipping //
// any edge (not a segment) that is connecting at p. //
// //// Unless T is a Delaunay tetrahedralization, there is no guarantee that 'p' //
// can be successfully removed. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::removevertexbyflips(point steinerpt)
{
triface *fliptets = NULL, wrktets[4];
triface searchtet, spintet, neightet;
face parentsh, spinsh, checksh;
face leftseg, rightseg, checkseg;
point lpt = NULL, rpt = NULL, apexpt; //, *parypt;
flipconstraints fc;
enum verttype vt;
enum locateresult loc;
int valence, removeflag;
int slawson;
int t1ver;
int n, i;
vt = pointtype(steinerpt);
if (vt == FREESEGVERTEX) {
sdecode(point2sh(steinerpt), leftseg);
leftseg.shver = 0;
if (sdest(leftseg) == steinerpt) {
senext(leftseg, rightseg);
spivotself(rightseg);
rightseg.shver = 0;
} else {
rightseg = leftseg;
senext2(rightseg, leftseg);
spivotself(leftseg);
leftseg.shver = 0;
}
lpt = sorg(leftseg);
rpt = sdest(rightseg);
if (b->verbose > 2) {
printf(" Removing Steiner point %d in segment (%d, %d).\n",
pointmark(steinerpt), pointmark(lpt), pointmark(rpt));
}
} else if (vt == FREEFACETVERTEX) {
if (b->verbose > 2) {
printf(" Removing Steiner point %d in facet.\n",
pointmark(steinerpt));
}
} else if (vt == FREEVOLVERTEX) {
if (b->verbose > 2) {
printf(" Removing Steiner point %d in volume.\n",
pointmark(steinerpt));
}
} else if (vt == VOLVERTEX) {
if (b->verbose > 2) {
printf(" Removing a point %d in volume.\n",
pointmark(steinerpt));
}
} else {
// It is not a Steiner point.
return 0;
}
// Try to reduce the number of edges at 'p' by flips.
getvertexstar(1, steinerpt, cavetetlist, cavetetvertlist, NULL);
cavetetlist->restart(); // This list may be re-used.
if (cavetetvertlist->objects > 3l) {
valence = reduceedgesatvertex(steinerpt, cavetetvertlist);
} else {
valence = cavetetvertlist->objects;
} cavetetvertlist->restart();
removeflag = 0;
if (valence == 4) {
// Only 4 vertices (4 tets) left! 'p' is inside the convex hull of the 4
// vertices. This case is due to that 'p' is not exactly on the segment.
point2tetorg(steinerpt, searchtet);
loc = INTETRAHEDRON;
removeflag = 1;
} else if (valence == 5) {
// There are 5 edges.
if (vt == FREESEGVERTEX) {
sstpivot1(leftseg, searchtet);
if (org(searchtet) != steinerpt) {
esymself(searchtet);
}
i = 0; // Count the numbe of tet at the edge [p,lpt].
neightet.tet = NULL; // Init the face.
spintet = searchtet;
while (1) {
i++;
if (apex(spintet) == rpt) {
// Remember the face containing the edge [lpt, rpt].
neightet = spintet;
}
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
if (i == 3) {
// This case has been checked below.
} else if (i == 4) {
// There are 4 tets sharing at [p,lpt]. There must be 4 tets sharing
// at [p,rpt]. There must be a face [p, lpt, rpt].
if (apex(neightet) == rpt) {
// The edge (segment) has been already recovered!
// Check if a 6-to-2 flip is possible (to remove 'p').
// Let 'searchtet' be [p,d,a,b]
esym(neightet, searchtet);
enextself(searchtet);
// Check if there are exactly three tets at edge [p,d].
wrktets[0] = searchtet; // [p,d,a,b]
for (i = 0; i < 2; i++) {
fnext(wrktets[i], wrktets[i+1]); // [p,d,b,c], [p,d,c,a]
}
if (apex(wrktets[0]) == oppo(wrktets[2])) {
loc = ONFACE;
removeflag = 1;
}
}
}
} else if (vt == FREEFACETVERTEX) {
// It is possible to do a 6-to-2 flip to remove the vertex.
point2tetorg(steinerpt, searchtet);
// Get the three faces of 'searchtet' which share at p.
// All faces has p as origin.
wrktets[0] = searchtet;
wrktets[1] = searchtet;
esymself(wrktets[1]);
enextself(wrktets[1]);
wrktets[2] = searchtet;
eprevself(wrktets[2]);
esymself(wrktets[2]);
// All internal edges of the six tets have valance either 3 or 4.
// Get one edge which has valance 3.
searchtet.tet = NULL;
for (i = 0; i < 3; i++) {
spintet = wrktets[i];
valence = 0;
while (1) { valence++;
fnextself(spintet);
if (spintet.tet == wrktets[i].tet) break;
}
if (valence == 3) {
// Found the edge.
searchtet = wrktets[i];
break;
}
}
// Note, we do not detach the three subfaces at p.
// They will be removed within a 4-to-1 flip.
loc = ONFACE;
removeflag = 1;
}
//removeflag = 1;
}
if (!removeflag) {
if (vt == FREESEGVERTEX) {
// Check is it possible to recover the edge [lpt,rpt].
// The condition to check is: Whether each tet containing 'leftseg' is
// adjacent to a tet containing 'rightseg'.
sstpivot1(leftseg, searchtet);
if (org(searchtet) != steinerpt) {
esymself(searchtet);
}
spintet = searchtet;
while (1) {
// Go to the bottom face of this tet.
eprev(spintet, neightet);
esymself(neightet); // [steinerpt, p1, p2, lpt]
// Get the adjacent tet.
fsymself(neightet); // [p1, steinerpt, p2, rpt]
if (oppo(neightet) != rpt) {
// Found a non-matching adjacent tet.
break;
}
fnextself(spintet);
if (spintet.tet == searchtet.tet) {
// 'searchtet' is [p,d,p1,p2].
loc = ONEDGE;
removeflag = 1;
break;
}
}
} // if (vt == FREESEGVERTEX)
}
if (!removeflag) {
if (vt == FREESEGVERTEX) {
// Check if the edge [lpt, rpt] exists.
if (getedge(lpt, rpt, &searchtet)) {
// We have recovered this edge. Shift the vertex into the volume.
// We can recover this edge if the subfaces are not recovered yet.
if (!checksubfaceflag) {
// Remove the vertex from the surface mesh.
// This will re-create the segment [lpt, rpt] and re-triangulate
// all the facets at the segment.
// Detach the subsegments from their surrounding tets.
for (i = 0; i < 2; i++) {
checkseg = (i == 0) ? leftseg : rightseg;
sstpivot1(checkseg, neightet);
spintet = neightet;
while (1) {
tssdissolve1(spintet);
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
sstdissolve1(checkseg); } // i
slawson = 1; // Do lawson flip after removal.
spivot(rightseg, parentsh); // 'rightseg' has p as its origin.
sremovevertex(steinerpt, &parentsh, &rightseg, slawson);
// Clear the list for new subfaces.
caveshbdlist->restart();
// Insert the new segment.
sstbond1(rightseg, searchtet);
spintet = searchtet;
while (1) {
tssbond1(spintet, rightseg);
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
// The Steiner point has been shifted into the volume.
setpointtype(steinerpt, FREEVOLVERTEX);
st_segref_count--;
st_volref_count++;
return 1;
} // if (!checksubfaceflag)
} // if (getedge(...))
} // if (vt == FREESEGVERTEX)
} // if (!removeflag)
if (!removeflag) {
return 0;
}
if (vt == FREESEGVERTEX) {
// Detach the subsegments from their surronding tets.
for (i = 0; i < 2; i++) {
checkseg = (i == 0) ? leftseg : rightseg;
sstpivot1(checkseg, neightet);
spintet = neightet;
while (1) {
tssdissolve1(spintet);
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
sstdissolve1(checkseg);
} // i
if (checksubfaceflag) {
// Detach the subfaces at the subsegments from their attached tets.
for (i = 0; i < 2; i++) {
checkseg = (i == 0) ? leftseg : rightseg;
spivot(checkseg, parentsh);
if (parentsh.sh != NULL) {
spinsh = parentsh;
while (1) {
stpivot(spinsh, neightet);
if (neightet.tet != NULL) {
tsdissolve(neightet);
}
sesymself(spinsh);
stpivot(spinsh, neightet);
if (neightet.tet != NULL) {
tsdissolve(neightet);
}
stdissolve(spinsh);
spivotself(spinsh); // Go to the next subface.
if (spinsh.sh == parentsh.sh) break;
}
}
} // i
} // if (checksubfaceflag)
}
if (loc == INTETRAHEDRON) {
// Collect the four tets containing 'p'.
fliptets = new triface[4]; fliptets[0] = searchtet; // [p,d,a,b]
for (i = 0; i < 2; i++) {
fnext(fliptets[i], fliptets[i+1]); // [p,d,b,c], [p,d,c,a]
}
eprev(fliptets[0], fliptets[3]);
fnextself(fliptets[3]); // it is [a,p,b,c]
eprevself(fliptets[3]);
esymself(fliptets[3]); // [a,b,c,p].
// Remove p by a 4-to-1 flip.
//flip41(fliptets, 1, 0, 0);
flip41(fliptets, 1, &fc);
//recenttet = fliptets[0];
} else if (loc == ONFACE) {
// Let the original two tets be [a,b,c,d] and [b,a,c,e]. And p is in
// face [a,b,c]. Let 'searchtet' be the tet [p,d,a,b].
// Collect the six tets containing 'p'.
fliptets = new triface[6];
fliptets[0] = searchtet; // [p,d,a,b]
for (i = 0; i < 2; i++) {
fnext(fliptets[i], fliptets[i+1]); // [p,d,b,c], [p,d,c,a]
}
eprev(fliptets[0], fliptets[3]);
fnextself(fliptets[3]); // [a,p,b,e]
esymself(fliptets[3]); // [p,a,e,b]
eprevself(fliptets[3]); // [e,p,a,b]
for (i = 3; i < 5; i++) {
fnext(fliptets[i], fliptets[i+1]); // [e,p,b,c], [e,p,c,a]
}
if (vt == FREEFACETVERTEX) {
// We need to determine the location of three subfaces at p.
valence = 0; // Re-use it.
// Check if subfaces are all located in the lower three tets.
// i.e., [e,p,a,b], [e,p,b,c], and [e,p,c,a].
for (i = 3; i < 6; i++) {
if (issubface(fliptets[i])) valence++;
}
if (valence > 0) {
// We must do 3-to-2 flip in the upper part. We simply re-arrange
// the six tets.
for (i = 0; i < 3; i++) {
esym(fliptets[i+3], wrktets[i]);
esym(fliptets[i], fliptets[i+3]);
fliptets[i] = wrktets[i];
}
// Swap the last two pairs, i.e., [1]<->[[2], and [4]<->[5]
wrktets[1] = fliptets[1];
fliptets[1] = fliptets[2];
fliptets[2] = wrktets[1];
wrktets[1] = fliptets[4];
fliptets[4] = fliptets[5];
fliptets[5] = wrktets[1];
}
}
// Remove p by a 6-to-2 flip, which is a combination of two flips:
// a 3-to-2 (deletes the edge [e,p]), and
// a 4-to-1 (deletes the vertex p).
// First do a 3-to-2 flip on [e,p,a,b],[e,p,b,c],[e,p,c,a]. It creates
// two new tets: [a,b,c,p] and [b,a,c,e]. The new tet [a,b,c,p] is
// degenerate (has zero volume). It will be deleted in the followed
// 4-to-1 flip.
//flip32(&(fliptets[3]), 1, 0, 0);
flip32(&(fliptets[3]), 1, &fc);
// Second do a 4-to-1 flip on [p,d,a,b],[p,d,b,c],[p,d,c,a],[a,b,c,p].
// This creates a new tet [a,b,c,d].
//flip41(fliptets, 1, 0, 0);
flip41(fliptets, 1, &fc);
//recenttet = fliptets[0];
} else if (loc == ONEDGE) {
// Let the original edge be [e,d] and p is in [e,d]. Assume there are n
// tets sharing at edge [e,d] originally. We number the link vertices // of [e,d]: p_0, p_1, ..., p_n-1. 'searchtet' is [p,d,p_0,p_1].
// Count the number of tets at edge [e,p] and [p,d] (this is n).
n = 0;
spintet = searchtet;
while (1) {
n++;
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
// Collect the 2n tets containing 'p'.
fliptets = new triface[2 * n];
fliptets[0] = searchtet; // [p,b,p_0,p_1]
for (i = 0; i < (n - 1); i++) {
fnext(fliptets[i], fliptets[i+1]); // [p,d,p_i,p_i+1].
}
eprev(fliptets[0], fliptets[n]);
fnextself(fliptets[n]); // [p_0,p,p_1,e]
esymself(fliptets[n]); // [p,p_0,e,p_1]
eprevself(fliptets[n]); // [e,p,p_0,p_1]
for (i = n; i < (2 * n - 1); i++) {
fnext(fliptets[i], fliptets[i+1]); // [e,p,p_i,p_i+1].
}
// Remove p by a 2n-to-n flip, it is a sequence of n flips:
// - Do a 2-to-3 flip on
// [p_0,p_1,p,d] and
// [p,p_1,p_0,e].
// This produces:
// [e,d,p_0,p_1],
// [e,d,p_1,p] (degenerated), and
// [e,d,p,p_0] (degenerated).
wrktets[0] = fliptets[0]; // [p,d,p_0,p_1]
eprevself(wrktets[0]); // [p_0,p,d,p_1]
esymself(wrktets[0]); // [p,p_0,p_1,d]
enextself(wrktets[0]); // [p_0,p_1,p,d] [0]
wrktets[1] = fliptets[n]; // [e,p,p_0,p_1]
enextself(wrktets[1]); // [p,p_0,e,p_1]
esymself(wrktets[1]); // [p_0,p,p_1,e]
eprevself(wrktets[1]); // [p_1,p_0,p,e] [1]
//flip23(wrktets, 1, 0, 0);
flip23(wrktets, 1, &fc);
// Save the new tet [e,d,p,p_0] (degenerated).
fliptets[n] = wrktets[2];
// Save the new tet [e,d,p_0,p_1].
fliptets[0] = wrktets[0];
// - Repeat from i = 1 to n-2: (n - 2) flips
// - Do a 3-to-2 flip on
// [p,p_i,d,e],
// [p,p_i,e,p_i+1], and
// [p,p_i,p_i+1,d].
// This produces:
// [d,e,p_i+1,p_i], and
// [e,d,p_i+1,p] (degenerated).
for (i = 1; i < (n - 1); i++) {
wrktets[0] = wrktets[1]; // [e,d,p_i,p] (degenerated).
enextself(wrktets[0]); // [d,p_i,e,p] (...)
esymself(wrktets[0]); // [p_i,d,p,e] (...)
eprevself(wrktets[0]); // [p,p_i,d,e] (degenerated) [0].
wrktets[1] = fliptets[n+i]; // [e,p,p_i,p_i+1]
enextself(wrktets[1]); // [p,p_i,e,p_i+1] [1]
wrktets[2] = fliptets[i]; // [p,d,p_i,p_i+1]
eprevself(wrktets[2]); // [p_i,p,d,p_i+1]
esymself(wrktets[2]); // [p,p_i,p_i+1,d] [2]
//flip32(wrktets, 1, 0, 0);
flip32(wrktets, 1, &fc);
// Save the new tet [e,d,p_i,p_i+1]. // FOR DEBUG ONLY
fliptets[i] = wrktets[0]; // [d,e,p_i+1,p_i] // FOR DEBUG ONLY
esymself(fliptets[i]); // [e,d,p_i,p_i+1] // FOR DEBUG ONLY
}
// - Do a 4-to-1 flip on
// [p,p_0,e,d], [d,e,p_0,p], // [p,p_0,d,p_n-1], [e,p_n-1,p_0,p],
// [p,p_0,p_n-1,e], [p_0,p_n-1,d,p], and
// [e,d,p_n-1,p].
// This produces
// [e,d,p_n-1,p_0] and
// deletes p.
wrktets[3] = wrktets[1]; // [e,d,p_n-1,p] (degenerated) [3]
wrktets[0] = fliptets[n]; // [e,d,p,p_0] (degenerated)
eprevself(wrktets[0]); // [p,e,d,p_0] (...)
esymself(wrktets[0]); // [e,p,p_0,d] (...)
enextself(wrktets[0]); // [p,p_0,e,d] (degenerated) [0]
wrktets[1] = fliptets[n-1]; // [p,d,p_n-1,p_0]
esymself(wrktets[1]); // [d,p,p_0,p_n-1]
enextself(wrktets[1]); // [p,p_0,d,p_n-1] [1]
wrktets[2] = fliptets[2*n-1]; // [e,p,p_n-1,p_0]
enextself(wrktets[2]); // [p_p_n-1,e,p_0]
esymself(wrktets[2]); // [p_n-1,p,p_0,e]
enextself(wrktets[2]); // [p,p_0,p_n-1,e] [2]
//flip41(wrktets, 1, 0, 0);
flip41(wrktets, 1, &fc);
// Save the new tet [e,d,p_n-1,p_0] // FOR DEBUG ONLY
fliptets[n-1] = wrktets[0]; // [e,d,p_n-1,p_0] // FOR DEBUG ONLY
//recenttet = fliptets[0];
}
delete [] fliptets;
if (vt == FREESEGVERTEX) {
// Remove the vertex from the surface mesh.
// This will re-create the segment [lpt, rpt] and re-triangulate
// all the facets at the segment.
// Only do lawson flip when subfaces are not recovery yet.
slawson = (checksubfaceflag ? 0 : 1);
spivot(rightseg, parentsh); // 'rightseg' has p as its origin.
sremovevertex(steinerpt, &parentsh, &rightseg, slawson);
// The original segment is returned in 'rightseg'.
rightseg.shver = 0;
// Insert the new segment.
point2tetorg(lpt, searchtet);
finddirection(&searchtet, rpt);
sstbond1(rightseg, searchtet);
spintet = searchtet;
while (1) {
tssbond1(spintet, rightseg);
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
if (checksubfaceflag) {
// Insert subfaces at segment [lpt,rpt] into the tetrahedralization.
spivot(rightseg, parentsh);
if (parentsh.sh != NULL) {
spinsh = parentsh;
while (1) {
if (sorg(spinsh) != lpt) {
sesymself(spinsh);
}
apexpt = sapex(spinsh);
// Find the adjacent tet of [lpt,rpt,apexpt];
spintet = searchtet;
while (1) {
if (apex(spintet) == apexpt) {
tsbond(spintet, spinsh);
sesymself(spinsh); // Get to another side of this face.
fsym(spintet, neightet);
tsbond(neightet, spinsh);
sesymself(spinsh); // Get back to the original side.
break;
} fnextself(spintet);
}
spivotself(spinsh);
if (spinsh.sh == parentsh.sh) break;
}
}
} // if (checksubfaceflag)
// Clear the set of new subfaces.
caveshbdlist->restart();
} // if (vt == FREESEGVERTEX)
// The point has been removed.
if (pointtype(steinerpt) != UNUSEDVERTEX) {
setpointtype(steinerpt, UNUSEDVERTEX);
unuverts++;
}
if (vt != VOLVERTEX) {
// Update the correspinding counters.
if (vt == FREESEGVERTEX) {
st_segref_count--;
} else if (vt == FREEFACETVERTEX) {
st_facref_count--;
} else if (vt == FREEVOLVERTEX) {
st_volref_count--;
}
if (steinerleft > 0) steinerleft++;
}
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// suppressbdrysteinerpoint() Suppress a boundary Steiner point //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::suppressbdrysteinerpoint(point steinerpt)
{
face parentsh, spinsh, *parysh;
face leftseg, rightseg;
point lpt = NULL, rpt = NULL;
int i;
verttype vt = pointtype(steinerpt);
if (vt == FREESEGVERTEX) {
sdecode(point2sh(steinerpt), leftseg);
leftseg.shver = 0;
if (sdest(leftseg) == steinerpt) {
senext(leftseg, rightseg);
spivotself(rightseg);
rightseg.shver = 0;
} else {
rightseg = leftseg;
senext2(rightseg, leftseg);
spivotself(leftseg);
leftseg.shver = 0;
}
lpt = sorg(leftseg);
rpt = sdest(rightseg);
if (b->verbose > 2) {
printf(" Suppressing Steiner point %d in segment (%d, %d).\n",
pointmark(steinerpt), pointmark(lpt), pointmark(rpt));
}
// Get all subfaces at the left segment [lpt, steinerpt].
spivot(leftseg, parentsh);
if (parentsh.sh != NULL) {
// It is not a dangling segment. spinsh = parentsh;
while (1) {
cavesegshlist->newindex((void **) &parysh);
*parysh = spinsh;
// Orient the face consistently.
if (sorg(*parysh)!= sorg(parentsh)) sesymself(*parysh);
spivotself(spinsh);
if (spinsh.sh == NULL) break;
if (spinsh.sh == parentsh.sh) break;
}
}
if (cavesegshlist->objects < 2) {
// It is a single segment. Not handle it yet.
cavesegshlist->restart();
return 0;
}
} else if (vt == FREEFACETVERTEX) {
if (b->verbose > 2) {
printf(" Suppressing Steiner point %d from facet.\n",
pointmark(steinerpt));
}
sdecode(point2sh(steinerpt), parentsh);
// A facet Steiner point. There are exactly two sectors.
for (i = 0; i < 2; i++) {
cavesegshlist->newindex((void **) &parysh);
*parysh = parentsh;
sesymself(parentsh);
}
} else {
return 0;
}
triface searchtet, neightet, *parytet;
point pa, pb, pc, pd;
REAL v1[3], v2[3], len, u;
REAL startpt[3] = {0,}, samplept[3] = {0,}, candpt[3] = {0,};
REAL ori, minvol, smallvol;
int samplesize;
int it, j, k;
int n = (int) cavesegshlist->objects;
point *newsteiners = new point[n];
for (i = 0; i < n; i++) newsteiners[i] = NULL;
// Search for each sector an interior vertex.
for (i = 0; i < cavesegshlist->objects; i++) {
parysh = (face *) fastlookup(cavesegshlist, i);
stpivot(*parysh, searchtet);
// Skip it if it is outside.
if (ishulltet(searchtet)) continue;
// Get the "half-ball". Tets in 'cavetetlist' all contain 'steinerpt' as
// opposite. Subfaces in 'caveshlist' all contain 'steinerpt' as apex.
// Moreover, subfaces are oriented towards the interior of the ball.
setpoint2tet(steinerpt, encode(searchtet));
getvertexstar(0, steinerpt, cavetetlist, NULL, caveshlist);
// Calculate the searching vector.
pa = sorg(*parysh);
pb = sdest(*parysh);
pc = sapex(*parysh);
facenormal(pa, pb, pc, v1, 1, NULL);
len = sqrt(dot(v1, v1));
v1[0] /= len;
v1[1] /= len;
v1[2] /= len;
if (vt == FREESEGVERTEX) {
parysh = (face *) fastlookup(cavesegshlist, (i + 1) % n);
pd = sapex(*parysh);
facenormal(pb, pa, pd, v2, 1, NULL);
len = sqrt(dot(v2, v2)); v2[0] /= len;
v2[1] /= len;
v2[2] /= len;
// Average the two vectors.
v1[0] = 0.5 * (v1[0] + v2[0]);
v1[1] = 0.5 * (v1[1] + v2[1]);
v1[2] = 0.5 * (v1[2] + v2[2]);
}
// Search the intersection of the ray starting from 'steinerpt' to
// the search direction 'v1' and the shell of the half-ball.
// - Construct an endpoint.
len = distance(pa, pb);
v2[0] = steinerpt[0] + len * v1[0];
v2[1] = steinerpt[1] + len * v1[1];
v2[2] = steinerpt[2] + len * v1[2];
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
pa = org(*parytet);
pb = dest(*parytet);
pc = apex(*parytet);
// Test if the ray startpt->v2 lies in the cone: where 'steinerpt'
// is the apex, and three sides are defined by the triangle
// [pa, pb, pc].
ori = orient3d(steinerpt, pa, pb, v2);
if (ori >= 0) {
ori = orient3d(steinerpt, pb, pc, v2);
if (ori >= 0) {
ori = orient3d(steinerpt, pc, pa, v2);
if (ori >= 0) {
// Found! Calculate the intersection.
planelineint(pa, pb, pc, steinerpt, v2, startpt, &u);
break;
}
}
}
} // j
// Close the ball by adding the subfaces.
for (j = 0; j < caveshlist->objects; j++) {
parysh = (face *) fastlookup(caveshlist, j);
stpivot(*parysh, neightet);
cavetetlist->newindex((void **) &parytet);
*parytet = neightet;
}
// Search a best point inside the segment [startpt, steinerpt].
it = 0;
samplesize = 100;
v1[0] = steinerpt[0] - startpt[0];
v1[1] = steinerpt[1] - startpt[1];
v1[2] = steinerpt[2] - startpt[2];
minvol = -1.0;
while (it < 3) {
for (j = 1; j < samplesize - 1; j++) {
samplept[0] = startpt[0] + ((REAL) j / (REAL) samplesize) * v1[0];
samplept[1] = startpt[1] + ((REAL) j / (REAL) samplesize) * v1[1];
samplept[2] = startpt[2] + ((REAL) j / (REAL) samplesize) * v1[2];
// Find the minimum volume for 'samplept'.
smallvol = -1;
for (k = 0; k < cavetetlist->objects; k++) {
parytet = (triface *) fastlookup(cavetetlist, k);
pa = org(*parytet);
pb = dest(*parytet);
pc = apex(*parytet);
ori = orient3d(pb, pa, pc, samplept);
if (ori <= 0) {
break; // An invalid tet.
}
if (smallvol == -1) {
smallvol = ori;
} else {
if (ori < smallvol) smallvol = ori; }
} // k
if (k == cavetetlist->objects) {
// Found a valid point. Remember it.
if (minvol == -1.0) {
candpt[0] = samplept[0];
candpt[1] = samplept[1];
candpt[2] = samplept[2];
minvol = smallvol;
} else {
if (minvol < smallvol) {
// It is a better location. Remember it.
candpt[0] = samplept[0];
candpt[1] = samplept[1];
candpt[2] = samplept[2];
minvol = smallvol;
} else {
// No improvement of smallest volume.
// Since we are searching along the line [startpt, steinerpy],
// The smallest volume can only be decreased later.
break;
}
}
}
} // j
if (minvol > 0) break;
samplesize *= 10;
it++;
} // while (it < 3)
if (minvol == -1.0) {
// Failed to find a valid point.
cavetetlist->restart();
caveshlist->restart();
break;
}
// Create a new Steiner point inside this section.
makepoint(&(newsteiners[i]), FREEVOLVERTEX);
newsteiners[i][0] = candpt[0];
newsteiners[i][1] = candpt[1];
newsteiners[i][2] = candpt[2];
cavetetlist->restart();
caveshlist->restart();
} // i
if (i < cavesegshlist->objects) {
// Failed to suppress the vertex.
for (; i > 0; i--) {
if (newsteiners[i - 1] != NULL) {
pointdealloc(newsteiners[i - 1]);
}
}
delete [] newsteiners;
cavesegshlist->restart();
return 0;
}
// Remove p from the segment or the facet.
triface newtet, newface, spintet;
face newsh, neighsh;
face *splitseg, checkseg;
int slawson = 0; // Do not do flip afterword.
int t1ver;
if (vt == FREESEGVERTEX) {
// Detach 'leftseg' and 'rightseg' from their adjacent tets.
// These two subsegments will be deleted.
sstpivot1(leftseg, neightet);
spintet = neightet;
while (1) {
tssdissolve1(spintet); fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
sstpivot1(rightseg, neightet);
spintet = neightet;
while (1) {
tssdissolve1(spintet);
fnextself(spintet);
if (spintet.tet == neightet.tet) break;
}
}
// Loop through all sectors bounded by facets at this segment.
// Within each sector, create a new Steiner point 'np', and replace 'p'
// by 'np' for all tets in this sector.
for (i = 0; i < cavesegshlist->objects; i++) {
parysh = (face *) fastlookup(cavesegshlist, i);
// 'parysh' is the face [lpt, steinerpt, #].
stpivot(*parysh, neightet);
// Get all tets in this sector.
setpoint2tet(steinerpt, encode(neightet));
getvertexstar(0, steinerpt, cavetetlist, NULL, caveshlist);
if (!ishulltet(neightet)) {
// Within each tet in the ball, replace 'p' by 'np'.
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
setoppo(*parytet, newsteiners[i]);
} // j
// Point to a parent tet.
parytet = (triface *) fastlookup(cavetetlist, 0);
setpoint2tet(newsteiners[i], (tetrahedron) (parytet->tet));
st_volref_count++;
if (steinerleft > 0) steinerleft--;
}
// Disconnect the set of boundary faces. They're temporarily open faces.
// They will be connected to the new tets after 'p' is removed.
for (j = 0; j < caveshlist->objects; j++) {
// Get a boundary face.
parysh = (face *) fastlookup(caveshlist, j);
stpivot(*parysh, neightet);
//assert(apex(neightet) == newpt);
// Clear the connection at this face.
dissolve(neightet);
tsdissolve(neightet);
}
// Clear the working lists.
cavetetlist->restart();
caveshlist->restart();
} // i
cavesegshlist->restart();
if (vt == FREESEGVERTEX) {
spivot(rightseg, parentsh); // 'rightseg' has p as its origin.
splitseg = &rightseg;
} else {
if (sdest(parentsh) == steinerpt) {
senextself(parentsh);
} else if (sapex(parentsh) == steinerpt) {
senext2self(parentsh);
}
splitseg = NULL;
}
sremovevertex(steinerpt, &parentsh, splitseg, slawson);
if (vt == FREESEGVERTEX) {
// The original segment is returned in 'rightseg'.
rightseg.shver = 0;
}
// For each new subface, create two new tets at each side of it. // Both of the two new tets have its opposite be dummypoint.
for (i = 0; i < caveshbdlist->objects; i++) {
parysh = (face *) fastlookup(caveshbdlist, i);
sinfect(*parysh); // Mark it for connecting new tets.
newsh = *parysh;
pa = sorg(newsh);
pb = sdest(newsh);
pc = sapex(newsh);
maketetrahedron(&newtet);
maketetrahedron(&neightet);
setvertices(newtet, pa, pb, pc, dummypoint);
setvertices(neightet, pb, pa, pc, dummypoint);
bond(newtet, neightet);
tsbond(newtet, newsh);
sesymself(newsh);
tsbond(neightet, newsh);
}
// Temporarily increase the hullsize.
hullsize += (caveshbdlist->objects * 2l);
if (vt == FREESEGVERTEX) {
// Connecting new tets at the recovered segment.
spivot(rightseg, parentsh);
spinsh = parentsh;
while (1) {
if (sorg(spinsh) != lpt) sesymself(spinsh);
// Get the new tet at this subface.
stpivot(spinsh, newtet);
tssbond1(newtet, rightseg);
// Go to the other face at this segment.
spivot(spinsh, neighsh);
if (sorg(neighsh) != lpt) sesymself(neighsh);
sesymself(neighsh);
stpivot(neighsh, neightet);
tssbond1(neightet, rightseg);
sstbond1(rightseg, neightet);
// Connecting two adjacent tets at this segment.
esymself(newtet);
esymself(neightet);
// Connect the two tets (at rightseg) together.
bond(newtet, neightet);
// Go to the next subface.
spivotself(spinsh);
if (spinsh.sh == parentsh.sh) break;
}
}
// Connecting new tets at new subfaces together.
for (i = 0; i < caveshbdlist->objects; i++) {
parysh = (face *) fastlookup(caveshbdlist, i);
newsh = *parysh;
//assert(sinfected(newsh));
// Each new subface contains two new tets.
for (k = 0; k < 2; k++) {
stpivot(newsh, newtet);
for (j = 0; j < 3; j++) {
// Check if this side is open.
esym(newtet, newface);
if (newface.tet[newface.ver & 3] == NULL) {
// An open face. Connect it to its adjacent tet.
sspivot(newsh, checkseg);
if (checkseg.sh != NULL) {
// A segment. It must not be the recovered segment.
tssbond1(newtet, checkseg);
sstbond1(checkseg, newtet);
}
spivot(newsh, neighsh);
if (neighsh.sh != NULL) {
// The adjacent subface exists. It's not a dangling segment.
if (sorg(neighsh) != sdest(newsh)) sesymself(neighsh); stpivot(neighsh, neightet);
if (sinfected(neighsh)) {
esymself(neightet);
} else {
// Search for an open face at this edge.
spintet = neightet;
while (1) {
esym(spintet, searchtet);
fsym(searchtet, spintet);
if (spintet.tet == NULL) break;
}
// Found an open face at 'searchtet'.
neightet = searchtet;
}
} else {
// The edge (at 'newsh') is a dangling segment.
// Get an adjacent tet at this segment.
sstpivot1(checkseg, neightet);
if (org(neightet) != sdest(newsh)) esymself(neightet);
// Search for an open face at this edge.
spintet = neightet;
while (1) {
esym(spintet, searchtet);
fsym(searchtet, spintet);
if (spintet.tet == NULL) break;
}
// Found an open face at 'searchtet'.
neightet = searchtet;
}
pc = apex(newface);
if (apex(neightet) == steinerpt) {
// Exterior case. The 'neightet' is a hull tet which contain
// 'steinerpt'. It will be deleted after 'steinerpt' is removed.
caveoldtetlist->newindex((void **) &parytet);
*parytet = neightet;
// Connect newface to the adjacent hull tet of 'neightet', which
// has the same edge as 'newface', and does not has 'steinerpt'.
fnextself(neightet);
} else {
if (pc == dummypoint) {
if (apex(neightet) != dummypoint) {
setapex(newface, apex(neightet));
// A hull tet has turned into an interior tet.
hullsize--; // Must update the hullsize.
}
}
}
bond(newface, neightet);
} // if (newface.tet[newface.ver & 3] == NULL)
enextself(newtet);
senextself(newsh);
} // j
sesymself(newsh);
} // k
} // i
// Unmark all new subfaces.
for (i = 0; i < caveshbdlist->objects; i++) {
parysh = (face *) fastlookup(caveshbdlist, i);
suninfect(*parysh);
}
caveshbdlist->restart();
if (caveoldtetlist->objects > 0l) {
// Delete hull tets which contain 'steinerpt'.
for (i = 0; i < caveoldtetlist->objects; i++) {
parytet = (triface *) fastlookup(caveoldtetlist, i);
tetrahedrondealloc(parytet->tet);
}
// Must update the hullsize. hullsize -= caveoldtetlist->objects;
caveoldtetlist->restart();
}
setpointtype(steinerpt, UNUSEDVERTEX);
unuverts++;
if (vt == FREESEGVERTEX) {
st_segref_count--;
} else { // vt == FREEFACETVERTEX
st_facref_count--;
}
if (steinerleft > 0) steinerleft++; // We've removed a Steiner points.
point *parypt;
int steinercount = 0;
int bak_fliplinklevel = b->fliplinklevel;
b->fliplinklevel = 100000; // Unlimited flip level.
// Try to remove newly added Steiner points.
for (i = 0; i < n; i++) {
if (newsteiners[i] != NULL) {
if (!removevertexbyflips(newsteiners[i])) {
if (b->supsteiner_level > 0) { // Not -Y/0
// Save it in subvertstack for removal.
subvertstack->newindex((void **) &parypt);
*parypt = newsteiners[i];
}
steinercount++;
}
}
}
b->fliplinklevel = bak_fliplinklevel;
if (steinercount > 0) {
if (b->verbose > 2) {
printf(" Added %d interior Steiner points.\n", steinercount);
}
}
delete [] newsteiners;
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //
// suppresssteinerpoints() Suppress Steiner points. //
// //
// All Steiner points have been saved in 'subvertstack' in the routines //
// carveholes() and suppresssteinerpoint(). //
// Each Steiner point is either removed or shifted into the interior. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::suppresssteinerpoints()
{
if (!b->quiet) {
printf("Suppressing Steiner points ...\n");
}
point rempt, *parypt;
int bak_fliplinklevel = b->fliplinklevel;
b->fliplinklevel = 100000; // Unlimited flip level.
int suppcount = 0, remcount = 0; int i;
// Try to suppress boundary Steiner points.
for (i = 0; i < subvertstack->objects; i++) {
parypt = (point *) fastlookup(subvertstack, i);
rempt = *parypt;
if (pointtype(rempt) != UNUSEDVERTEX) {
if ((pointtype(rempt) == FREESEGVERTEX) ||
(pointtype(rempt) == FREEFACETVERTEX)) {
if (suppressbdrysteinerpoint(rempt)) {
suppcount++;
}
}
}
} // i
if (suppcount > 0) {
if (b->verbose) {
printf(" Suppressed %d boundary Steiner points.\n", suppcount);
}
}
if (b->supsteiner_level > 0) { // -Y/1
for (i = 0; i < subvertstack->objects; i++) {
parypt = (point *) fastlookup(subvertstack, i);
rempt = *parypt;
if (pointtype(rempt) != UNUSEDVERTEX) {
if (pointtype(rempt) == FREEVOLVERTEX) {
if (removevertexbyflips(rempt)) {
remcount++;
}
}
}
}
}
if (remcount > 0) {
if (b->verbose) {
printf(" Removed %d interior Steiner points.\n", remcount);
}
}
b->fliplinklevel = bak_fliplinklevel;
if (b->supsteiner_level > 1) { // -Y/2
// Smooth interior Steiner points.
optparameters opm;
triface *parytet;
point *ppt;
REAL ori;
int smtcount, count, ivcount;
int nt, j;
// Point smooth options.
opm.max_min_volume = 1;
opm.numofsearchdirs = 20;
opm.searchstep = 0.001;
opm.maxiter = 30; // Limit the maximum iterations.
smtcount = 0;
do {
nt = 0;
while (1) {
count = 0;
ivcount = 0; // Clear the inverted count.
for (i = 0; i < subvertstack->objects; i++) { parypt = (point *) fastlookup(subvertstack, i);
rempt = *parypt;
if (pointtype(rempt) == FREEVOLVERTEX) {
getvertexstar(1, rempt, cavetetlist, NULL, NULL);
// Calculate the initial smallest volume (maybe zero or negative).
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
ppt = (point *) &(parytet->tet[4]);
ori = orient3dfast(ppt[1], ppt[0], ppt[2], ppt[3]);
if (j == 0) {
opm.initval = ori;
} else {
if (opm.initval > ori) opm.initval = ori;
}
}
if (smoothpoint(rempt, cavetetlist, 1, &opm)) {
count++;
}
if (opm.imprval <= 0.0) {
ivcount++; // The mesh contains inverted elements.
}
cavetetlist->restart();
}
} // i
smtcount += count;
if (count == 0) {
// No point has been smoothed.
break;
}
nt++;
if (nt > 2) {
break; // Already three iterations.
}
} // while
if (ivcount > 0) {
// There are inverted elements!
if (opm.maxiter > 0) {
// Set unlimited smoothing steps. Try again.
opm.numofsearchdirs = 30;
opm.searchstep = 0.0001;
opm.maxiter = -1;
continue;
}
}
break;
} while (1); // Additional loop for (ivcount > 0)
if (ivcount > 0) {
printf("BUG Report! The mesh contain inverted elements.\n");
}
if (b->verbose) {
if (smtcount > 0) {
printf(" Smoothed %d Steiner points.\n", smtcount);
}
}
} // -Y2
subvertstack->restart();
return 1;
}
///////////////////////////////////////////////////////////////////////////////
// //// recoverboundary() Recover segments and facets. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::recoverboundary(clock_t& tv)
{
arraypool *misseglist, *misshlist;
arraypool *bdrysteinerptlist;
face searchsh, *parysh;
face searchseg, *paryseg;
point rempt, *parypt;
long ms; // The number of missing segments/subfaces.
int nit; // The number of iterations.
int s, i;
// Counters.
long bak_segref_count, bak_facref_count, bak_volref_count;
if (!b->quiet) {
printf("Recovering boundaries...\n");
}
if (b->verbose) {
printf(" Recovering segments.\n");
}
// Segments will be introduced.
checksubsegflag = 1;
misseglist = new arraypool(sizeof(face), 8);
bdrysteinerptlist = new arraypool(sizeof(point), 8);
// In random order.
subsegs->traversalinit();
for (i = 0; i < subsegs->items; i++) {
s = randomnation(i + 1);
// Move the s-th seg to the i-th.
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(subsegstack, s);
// Put i-th seg to be the s-th.
searchseg.sh = shellfacetraverse(subsegs);
paryseg = (face *) fastlookup(subsegstack, s);
*paryseg = searchseg;
}
// The init number of missing segments.
ms = subsegs->items;
nit = 0;
if (b->fliplinklevel < 0) {
autofliplinklevel = 1; // Init value.
}
// First, trying to recover segments by only doing flips.
while (1) {
recoversegments(misseglist, 0, 0);
if (misseglist->objects > 0) {
if (b->fliplinklevel >= 0) {
break;
} else {
if (misseglist->objects >= ms) {
nit++;
if (nit >= 3) {
//break;
// Do the last round with unbounded flip link level.
b->fliplinklevel = 100000;
}
} else {
ms = misseglist->objects; if (nit > 0) {
nit--;
}
}
for (i = 0; i < misseglist->objects; i++) {
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(misseglist, i);
}
misseglist->restart();
autofliplinklevel+=b->fliplinklevelinc;
}
} else {
// All segments are recovered.
break;
}
} // while (1)
if (b->verbose) {
printf(" %ld (%ld) segments are recovered (missing).\n",
subsegs->items - misseglist->objects, misseglist->objects);
}
if (misseglist->objects > 0) {
// Second, trying to recover segments by doing more flips (fullsearch).
while (misseglist->objects > 0) {
ms = misseglist->objects;
for (i = 0; i < misseglist->objects; i++) {
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(misseglist, i);
}
misseglist->restart();
recoversegments(misseglist, 1, 0);
if (misseglist->objects < ms) {
// The number of missing segments is reduced.
continue;
} else {
break;
}
}
if (b->verbose) {
printf(" %ld (%ld) segments are recovered (missing).\n",
subsegs->items - misseglist->objects, misseglist->objects);
}
}
if (misseglist->objects > 0) {
// Third, trying to recover segments by doing more flips (fullsearch)
// and adding Steiner points in the volume.
while (misseglist->objects > 0) {
ms = misseglist->objects;
for (i = 0; i < misseglist->objects; i++) {
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(misseglist, i);
}
misseglist->restart();
recoversegments(misseglist, 1, 1);
if (misseglist->objects < ms) {
// The number of missing segments is reduced.
continue;
} else {
break;
}
}
if (b->verbose) {
printf(" Added %ld Steiner points in volume.\n", st_volref_count);
} }
if (misseglist->objects > 0) {
// Last, trying to recover segments by doing more flips (fullsearch),
// and adding Steiner points in the volume, and splitting segments.
long bak_inpoly_count = st_volref_count; //st_inpoly_count;
for (i = 0; i < misseglist->objects; i++) {
subsegstack->newindex((void **) &paryseg);
*paryseg = * (face *) fastlookup(misseglist, i);
}
misseglist->restart();
recoversegments(misseglist, 1, 2);
if (b->verbose) {
printf(" Added %ld Steiner points in segments.\n", st_segref_count);
if (st_volref_count > bak_inpoly_count) {
printf(" Added another %ld Steiner points in volume.\n",
st_volref_count - bak_inpoly_count);
}
}
}
if (st_segref_count > 0) {
// Try to remove the Steiner points added in segments.
bak_segref_count = st_segref_count;
bak_volref_count = st_volref_count;
for (i = 0; i < subvertstack->objects; i++) {
// Get the Steiner point.
parypt = (point *) fastlookup(subvertstack, i);
rempt = *parypt;
if (!removevertexbyflips(rempt)) {
// Save it in list.
bdrysteinerptlist->newindex((void **) &parypt);
*parypt = rempt;
}
}
if (b->verbose) {
if (st_segref_count < bak_segref_count) {
if (bak_volref_count < st_volref_count) {
printf(" Suppressed %ld Steiner points in segments.\n",
st_volref_count - bak_volref_count);
}
if ((st_segref_count + (st_volref_count - bak_volref_count)) <
bak_segref_count) {
printf(" Removed %ld Steiner points in segments.\n",
bak_segref_count -
(st_segref_count + (st_volref_count - bak_volref_count)));
}
}
}
subvertstack->restart();
}
tv = clock();
if (b->verbose) {
printf(" Recovering facets.\n");
}
// Subfaces will be introduced.
checksubfaceflag = 1;
misshlist = new arraypool(sizeof(face), 8);
// Randomly order the subfaces.
subfaces->traversalinit();
for (i = 0; i < subfaces->items; i++) { s = randomnation(i + 1);
// Move the s-th subface to the i-th.
subfacstack->newindex((void **) &parysh);
*parysh = * (face *) fastlookup(subfacstack, s);
// Put i-th subface to be the s-th.
searchsh.sh = shellfacetraverse(subfaces);
parysh = (face *) fastlookup(subfacstack, s);
*parysh = searchsh;
}
ms = subfaces->items;
nit = 0;
b->fliplinklevel = -1; // Init.
if (b->fliplinklevel < 0) {
autofliplinklevel = 1; // Init value.
}
while (1) {
recoversubfaces(misshlist, 0);
if (misshlist->objects > 0) {
if (b->fliplinklevel >= 0) {
break;
} else {
if (misshlist->objects >= ms) {
nit++;
if (nit >= 3) {
//break;
// Do the last round with unbounded flip link level.
b->fliplinklevel = 100000;
}
} else {
ms = misshlist->objects;
if (nit > 0) {
nit--;
}
}
for (i = 0; i < misshlist->objects; i++) {
subfacstack->newindex((void **) &parysh);
*parysh = * (face *) fastlookup(misshlist, i);
}
misshlist->restart();
autofliplinklevel+=b->fliplinklevelinc;
}
} else {
// All subfaces are recovered.
break;
}
} // while (1)
if (b->verbose) {
printf(" %ld (%ld) subfaces are recovered (missing).\n",
subfaces->items - misshlist->objects, misshlist->objects);
}
if (misshlist->objects > 0) {
// There are missing subfaces. Add Steiner points.
for (i = 0; i < misshlist->objects; i++) {
subfacstack->newindex((void **) &parysh);
*parysh = * (face *) fastlookup(misshlist, i);
}
misshlist->restart();
recoversubfaces(NULL, 1);
if (b->verbose) {
printf(" Added %ld Steiner points in facets.\n", st_facref_count);
}
}
if (st_facref_count > 0) {
// Try to remove the Steiner points added in facets.
bak_facref_count = st_facref_count;
for (i = 0; i < subvertstack->objects; i++) {
// Get the Steiner point.
parypt = (point *) fastlookup(subvertstack, i);
rempt = *parypt;
if (!removevertexbyflips(*parypt)) {
// Save it in list.
bdrysteinerptlist->newindex((void **) &parypt);
*parypt = rempt;
}
}
if (b->verbose) {
if (st_facref_count < bak_facref_count) {
printf(" Removed %ld Steiner points in facets.\n",
bak_facref_count - st_facref_count);
}
}
subvertstack->restart();
}
if (bdrysteinerptlist->objects > 0) {
if (b->verbose) {
printf(" %ld Steiner points remained in boundary.\n",
bdrysteinerptlist->objects);
}
} // if
// Accumulate the dynamic memory.
totalworkmemory += (misseglist->totalmemory + misshlist->totalmemory +
bdrysteinerptlist->totalmemory);
delete bdrysteinerptlist;
delete misseglist;
delete misshlist;
}
//// ////
//// ////
//// steiner_cxx //////////////////////////////////////////////////////////////
//// reconstruct_cxx //////////////////////////////////////////////////////////
//// ////
//// ////
///////////////////////////////////////////////////////////////////////////////
// //
// carveholes() Remove tetrahedra not in the mesh domain. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::carveholes()
{
arraypool *tetarray, *hullarray;
triface tetloop, neightet, *parytet, *parytet1;
triface *regiontets = NULL;
face checksh, *parysh;
face checkseg;
point ptloop, *parypt;
int t1ver;
int i, j, k;
if (!b->quiet) {
if (b->convex) { printf("Marking exterior tetrahedra ...\n");
} else {
printf("Removing exterior tetrahedra ...\n");
}
}
// Initialize the pool of exterior tets.
tetarray = new arraypool(sizeof(triface), 10);
hullarray = new arraypool(sizeof(triface), 10);
// Collect unprotected tets and hull tets.
tetrahedrons->traversalinit();
tetloop.ver = 11; // The face opposite to dummypoint.
tetloop.tet = alltetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
if (ishulltet(tetloop)) {
// Is this side protected by a subface?
if (!issubface(tetloop)) {
// Collect an unprotected hull tet and tet.
infect(tetloop);
hullarray->newindex((void **) &parytet);
*parytet = tetloop;
// tetloop's face number is 11 & 3 = 3.
decode(tetloop.tet[3], neightet);
if (!infected(neightet)) {
infect(neightet);
tetarray->newindex((void **) &parytet);
*parytet = neightet;
}
}
}
tetloop.tet = alltetrahedrontraverse();
}
if (in->numberofholes > 0) {
// Mark as infected any tets inside volume holes.
for (i = 0; i < 3 * in->numberofholes; i += 3) {
// Search a tet containing the i-th hole point.
neightet.tet = NULL;
randomsample(&(in->holelist[i]), &neightet);
if (locate(&(in->holelist[i]), &neightet) != OUTSIDE) {
// The tet 'neightet' contain this point.
if (!infected(neightet)) {
infect(neightet);
tetarray->newindex((void **) &parytet);
*parytet = neightet;
// Add its adjacent tet if it is not protected.
if (!issubface(neightet)) {
decode(neightet.tet[neightet.ver & 3], tetloop);
if (!infected(tetloop)) {
infect(tetloop);
if (ishulltet(tetloop)) {
hullarray->newindex((void **) &parytet);
} else {
tetarray->newindex((void **) &parytet);
}
*parytet = tetloop;
}
}
else {
// It is protected. Check if its adjacent tet is a hull tet.
decode(neightet.tet[neightet.ver & 3], tetloop);
if (ishulltet(tetloop)) {
// It is hull tet, add it into the list. Moreover, the subface
// is dead, i.e., both sides are in exterior.
if (!infected(tetloop)) {
infect(tetloop);
hullarray->newindex((void **) &parytet);
*parytet = tetloop;
} }
if (infected(tetloop)) {
// Both sides of this subface are in exterior.
tspivot(neightet, checksh);
sinfect(checksh); // Only queue it once.
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
}
} // if (!infected(neightet))
} else {
// A hole point locates outside of the convex hull.
if (!b->quiet) {
printf("Warning: The %d-th hole point ", i/3 + 1);
printf("lies outside the convex hull.\n");
}
}
} // i
} // if (in->numberofholes > 0)
if (b->regionattrib && (in->numberofregions > 0)) { // -A option.
// Record the tetrahedra that contains the region points for assigning
// region attributes after the holes have been carved.
regiontets = new triface[in->numberofregions];
// Mark as marktested any tetrahedra inside volume regions.
for (i = 0; i < 5 * in->numberofregions; i += 5) {
// Search a tet containing the i-th region point.
neightet.tet = NULL;
randomsample(&(in->regionlist[i]), &neightet);
if (locate(&(in->regionlist[i]), &neightet) != OUTSIDE) {
regiontets[i/5] = neightet;
} else {
if (!b->quiet) {
printf("Warning: The %d-th region point ", i/5+1);
printf("lies outside the convex hull.\n");
}
regiontets[i/5].tet = NULL;
}
}
}
// Collect all exterior tets (in concave place and in holes).
for (i = 0; i < tetarray->objects; i++) {
parytet = (triface *) fastlookup(tetarray, i);
j = (parytet->ver & 3); // j is the current face number.
// Check the other three adjacent tets.
for (k = 1; k < 4; k++) {
decode(parytet->tet[(j + k) % 4], neightet);
// neightet may be a hull tet.
if (!infected(neightet)) {
// Is neightet protected by a subface.
if (!issubface(neightet)) {
// Not proected. Collect it. (It must not be a hull tet).
infect(neightet);
tetarray->newindex((void **) &parytet1);
*parytet1 = neightet;
} else {
// Protected. Check if it is a hull tet.
if (ishulltet(neightet)) {
// A hull tet. Collect it.
infect(neightet);
hullarray->newindex((void **) &parytet1);
*parytet1 = neightet;
// Both sides of this subface are exterior.
tspivot(neightet, checksh);
// Queue this subface (to be deleted later).
sinfect(checksh); // Only queue it once.
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
} }
} else {
// Both sides of this face are in exterior.
// If there is a subface. It should be collected.
if (issubface(neightet)) {
tspivot(neightet, checksh);
if (!sinfected(checksh)) {
sinfect(checksh);
subfacstack->newindex((void **) &parysh);
*parysh = checksh;
}
}
}
} // j, k
} // i
if (b->regionattrib && (in->numberofregions > 0)) {
// Re-check saved region tets to see if they lie outside.
for (i = 0; i < in->numberofregions; i++) {
if (infected(regiontets[i])) {
if (b->verbose) {
printf("Warning: The %d-th region point ", i+1);
printf("lies in the exterior of the domain.\n");
}
regiontets[i].tet = NULL;
}
}
}
// Collect vertices which point to infected tets. These vertices
// may get deleted after the removal of exterior tets.
// If -Y1 option is used, collect all Steiner points for removal.
// The lists 'cavetetvertlist' and 'subvertstack' are re-used.
points->traversalinit();
ptloop = pointtraverse();
while (ptloop != NULL) {
if ((pointtype(ptloop) != UNUSEDVERTEX) &&
(pointtype(ptloop) != DUPLICATEDVERTEX)) {
decode(point2tet(ptloop), neightet);
if (infected(neightet)) {
cavetetvertlist->newindex((void **) &parypt);
*parypt = ptloop;
}
if (b->nobisect && (b->supsteiner_level > 0)) { // -Y/1
// Queue it if it is a Steiner point.
if (pointmark(ptloop) >
(in->numberofpoints - (in->firstnumber ? 0 : 1))) {
subvertstack->newindex((void **) &parypt);
*parypt = ptloop;
}
}
}
ptloop = pointtraverse();
}
if (!b->convex && (tetarray->objects > 0l)) { // No -c option.
// Remove exterior tets. Hull tets are updated.
arraypool *newhullfacearray;
triface hulltet, casface;
face segloop, *paryseg;
point pa, pb, pc;
long delsegcount = 0l;
// Collect segments which point to infected tets. Some segments
// may get deleted after the removal of exterior tets.
subsegs->traversalinit();
segloop.sh = shellfacetraverse(subsegs);
while (segloop.sh != NULL) {
sstpivot1(segloop, neightet);
if (infected(neightet)) { subsegstack->newindex((void **) &paryseg);
*paryseg = segloop;
}
segloop.sh = shellfacetraverse(subsegs);
}
newhullfacearray = new arraypool(sizeof(triface), 10);
// Create and save new hull tets.
for (i = 0; i < tetarray->objects; i++) {
parytet = (triface *) fastlookup(tetarray, i);
for (j = 0; j < 4; j++) {
decode(parytet->tet[j], tetloop);
if (!infected(tetloop)) {
// Found a new hull face (must be a subface).
tspivot(tetloop, checksh);
maketetrahedron(&hulltet);
pa = org(tetloop);
pb = dest(tetloop);
pc = apex(tetloop);
setvertices(hulltet, pb, pa, pc, dummypoint);
bond(tetloop, hulltet);
// Update the subface-to-tet map.
sesymself(checksh);
tsbond(hulltet, checksh);
// Update the segment-to-tet map.
for (k = 0; k < 3; k++) {
if (issubseg(tetloop)) {
tsspivot1(tetloop, checkseg);
tssbond1(hulltet, checkseg);
sstbond1(checkseg, hulltet);
}
enextself(tetloop);
eprevself(hulltet);
}
// Update the point-to-tet map.
setpoint2tet(pa, (tetrahedron) tetloop.tet);
setpoint2tet(pb, (tetrahedron) tetloop.tet);
setpoint2tet(pc, (tetrahedron) tetloop.tet);
// Save the exterior tet at this hull face. It still holds pointer
// to the adjacent interior tet. Use it to connect new hull tets.
newhullfacearray->newindex((void **) &parytet1);
parytet1->tet = parytet->tet;
parytet1->ver = j;
} // if (!infected(tetloop))
} // j
} // i
// Connect new hull tets.
for (i = 0; i < newhullfacearray->objects; i++) {
parytet = (triface *) fastlookup(newhullfacearray, i);
fsym(*parytet, neightet);
// Get the new hull tet.
fsym(neightet, hulltet);
for (j = 0; j < 3; j++) {
esym(hulltet, casface);
if (casface.tet[casface.ver & 3] == NULL) {
// Since the boundary of the domain may not be a manifold, we
// find the adjacent hull face by traversing the tets in the
// exterior (which are all infected tets).
neightet = *parytet;
while (1) {
fnextself(neightet);
if (!infected(neightet)) break;
}
if (!ishulltet(neightet)) {
// An interior tet. Get the new hull tet.
fsymself(neightet);
esymself(neightet);
} // Bond them together.
bond(casface, neightet);
}
enextself(hulltet);
enextself(*parytet);
} // j
} // i
if (subfacstack->objects > 0l) {
// Remove all subfaces which do not attach to any tetrahedron.
// Segments which are not attached to any subfaces and tets
// are deleted too.
face casingout, casingin;
for (i = 0; i < subfacstack->objects; i++) {
parysh = (face *) fastlookup(subfacstack, i);
if (i == 0) {
if (b->verbose) {
printf("Warning: Removed an exterior face (%d, %d, %d) #%d\n",
pointmark(sorg(*parysh)), pointmark(sdest(*parysh)),
pointmark(sapex(*parysh)), shellmark(*parysh));
}
}
// Dissolve this subface from face links.
for (j = 0; j < 3; j++) {
spivot(*parysh, casingout);
sspivot(*parysh, checkseg);
if (casingout.sh != NULL) {
casingin = casingout;
while (1) {
spivot(casingin, checksh);
if (checksh.sh == parysh->sh) break;
casingin = checksh;
}
if (casingin.sh != casingout.sh) {
// Update the link: ... -> casingin -> casingout ->...
sbond1(casingin, casingout);
} else {
// Only one subface at this edge is left.
sdissolve(casingout);
}
if (checkseg.sh != NULL) {
// Make sure the segment does not connect to a dead one.
ssbond(casingout, checkseg);
}
} else {
if (checkseg.sh != NULL) {
//if (checkseg.sh[3] != NULL) {
if (delsegcount == 0) {
if (b->verbose) {
printf("Warning: Removed an exterior segment (%d, %d) #%d\n",
pointmark(sorg(checkseg)), pointmark(sdest(checkseg)),
shellmark(checkseg));
}
}
shellfacedealloc(subsegs, checkseg.sh);
delsegcount++;
}
}
senextself(*parysh);
} // j
// Delete this subface.
shellfacedealloc(subfaces, parysh->sh);
} // i
if (b->verbose) {
printf(" Deleted %ld subfaces.\n", subfacstack->objects);
}
subfacstack->restart();
} // if (subfacstack->objects > 0l)
if (subsegstack->objects > 0l) {
for (i = 0; i < subsegstack->objects; i++) {
paryseg = (face *) fastlookup(subsegstack, i);
if (paryseg->sh && (paryseg->sh[3] != NULL)) {
sstpivot1(*paryseg, neightet);
if (infected(neightet)) {
if (b->verbose) {
printf("Warning: Removed an exterior segment (%d, %d) #%d\n",
pointmark(sorg(*paryseg)), pointmark(sdest(*paryseg)),
shellmark(*paryseg));
}
shellfacedealloc(subsegs, paryseg->sh);
delsegcount++;
}
}
}
subsegstack->restart();
} // if (subsegstack->objects > 0l)
if (delsegcount > 0) {
if (b->verbose) {
printf(" Deleted %ld segments.\n", delsegcount);
}
}
if (cavetetvertlist->objects > 0l) {
// Some vertices may lie in exterior. Marke them as UNUSEDVERTEX.
long delvertcount = unuverts;
long delsteinercount = 0l;
for (i = 0; i < cavetetvertlist->objects; i++) {
parypt = (point *) fastlookup(cavetetvertlist, i);
decode(point2tet(*parypt), neightet);
if (infected(neightet)) {
// Found an exterior vertex.
if (pointmark(*parypt) >
(in->numberofpoints - (in->firstnumber ? 0 : 1))) {
// A Steiner point.
if (pointtype(*parypt) == FREESEGVERTEX) {
st_segref_count--;
} else if (pointtype(*parypt) == FREEFACETVERTEX) {
st_facref_count--;
} else {
st_volref_count--;
}
delsteinercount++;
if (steinerleft > 0) steinerleft++;
}
setpointtype(*parypt, UNUSEDVERTEX);
unuverts++;
}
}
if (b->verbose) {
if (unuverts > delvertcount) {
if (delsteinercount > 0l) {
if (unuverts > (delvertcount + delsteinercount)) {
printf(" Removed %ld exterior input vertices.\n",
unuverts - delvertcount - delsteinercount);
}
printf(" Removed %ld exterior Steiner vertices.\n",
delsteinercount);
} else {
printf(" Removed %ld exterior input vertices.\n",
unuverts - delvertcount);
}
}
}
cavetetvertlist->restart();
// Comment: 'subvertstack' will be cleaned in routine // suppresssteinerpoints().
} // if (cavetetvertlist->objects > 0l)
// Update the hull size.
hullsize += (newhullfacearray->objects - hullarray->objects);
// Delete all exterior tets and old hull tets.
for (i = 0; i < tetarray->objects; i++) {
parytet = (triface *) fastlookup(tetarray, i);
tetrahedrondealloc(parytet->tet);
}
tetarray->restart();
for (i = 0; i < hullarray->objects; i++) {
parytet = (triface *) fastlookup(hullarray, i);
tetrahedrondealloc(parytet->tet);
}
hullarray->restart();
delete newhullfacearray;
} // if (!b->convex && (tetarray->objects > 0l))
if (b->convex && (tetarray->objects > 0l)) { // With -c option
// In this case, all exterior tets get a region marker '-1'.
int attrnum = numelemattrib - 1;
for (i = 0; i < tetarray->objects; i++) {
parytet = (triface *) fastlookup(tetarray, i);
setelemattribute(parytet->tet, attrnum, -1);
}
tetarray->restart();
for (i = 0; i < hullarray->objects; i++) {
parytet = (triface *) fastlookup(hullarray, i);
uninfect(*parytet);
}
hullarray->restart();
if (subfacstack->objects > 0l) {
for (i = 0; i < subfacstack->objects; i++) {
parysh = (face *) fastlookup(subfacstack, i);
suninfect(*parysh);
}
subfacstack->restart();
}
if (cavetetvertlist->objects > 0l) {
cavetetvertlist->restart();
}
} // if (b->convex && (tetarray->objects > 0l))
if (b->regionattrib) { // With -A option.
if (!b->quiet) {
printf("Spreading region attributes.\n");
}
REAL volume;
int attr, maxattr = 0; // Choose a small number here.
int attrnum = numelemattrib - 1;
// Comment: The element region marker is at the end of the list of
// the element attributes.
int regioncount = 0;
// If has user-defined region attributes.
if (in->numberofregions > 0) {
// Spread region attributes.
for (i = 0; i < 5 * in->numberofregions; i += 5) {
if (regiontets[i/5].tet != NULL) {
attr = (int) in->regionlist[i + 3];
if (attr > maxattr) {
maxattr = attr; }
volume = in->regionlist[i + 4];
tetarray->restart(); // Re-use this array.
infect(regiontets[i/5]);
tetarray->newindex((void **) &parytet);
*parytet = regiontets[i/5];
// Collect and set attrs for all tets of this region.
for (j = 0; j < tetarray->objects; j++) {
parytet = (triface *) fastlookup(tetarray, j);
tetloop = *parytet;
setelemattribute(tetloop.tet, attrnum, attr);
if (b->varvolume) { // If has -a option.
setvolumebound(tetloop.tet, volume);
}
for (k = 0; k < 4; k++) {
decode(tetloop.tet[k], neightet);
// Is the adjacent already checked?
if (!infected(neightet)) {
// Is this side protected by a subface?
if (!issubface(neightet)) {
infect(neightet);
tetarray->newindex((void **) &parytet);
*parytet = neightet;
}
}
} // k
} // j
regioncount++;
} // if (regiontets[i/5].tet != NULL)
} // i
}
// Set attributes for all tetrahedra.
attr = maxattr + 1;
tetrahedrons->traversalinit();
tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
if (!infected(tetloop)) {
// An unmarked region.
tetarray->restart(); // Re-use this array.
infect(tetloop);
tetarray->newindex((void **) &parytet);
*parytet = tetloop;
// Find and mark all tets.
for (j = 0; j < tetarray->objects; j++) {
parytet = (triface *) fastlookup(tetarray, j);
tetloop = *parytet;
setelemattribute(tetloop.tet, attrnum, attr);
for (k = 0; k < 4; k++) {
decode(tetloop.tet[k], neightet);
// Is the adjacent tet already checked?
if (!infected(neightet)) {
// Is this side protected by a subface?
if (!issubface(neightet)) {
infect(neightet);
tetarray->newindex((void **) &parytet);
*parytet = neightet;
}
}
} // k
} // j
attr++; // Increase the attribute.
regioncount++;
}
tetloop.tet = tetrahedrontraverse();
}
// Until here, every tet has a region attribute.
// Uninfect processed tets.
tetrahedrons->traversalinit(); tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
uninfect(tetloop);
tetloop.tet = tetrahedrontraverse();
}
if (b->verbose) {
//assert(regioncount > 0);
if (regioncount > 1) {
printf(" Found %d subdomains.\n", regioncount);
} else {
printf(" Found %d domain.\n", regioncount);
}
}
} // if (b->regionattrib)
if (regiontets != NULL) {
delete [] regiontets;
}
delete tetarray;
delete hullarray;
if (!b->convex) { // No -c option
// The mesh is non-convex now.
nonconvex = 1;
// Push all hull tets into 'flipstack'.
tetrahedrons->traversalinit();
tetloop.ver = 11; // The face opposite to dummypoint.
tetloop.tet = alltetrahedrontraverse();
while (tetloop.tet != (tetrahedron *) NULL) {
if ((point) tetloop.tet[7] == dummypoint) {
fsym(tetloop, neightet);
flippush(flipstack, &neightet);
}
tetloop.tet = alltetrahedrontraverse();
}
flipconstraints fc;
fc.enqflag = 2;
long sliver_peel_count = lawsonflip3d(&fc);
if (sliver_peel_count > 0l) {
if (b->verbose) {
printf(" Removed %ld hull slivers.\n", sliver_peel_count);
}
}
unflipqueue->restart();
} // if (!b->convex)
}
///////////////////////////////////////////////////////////////////////////////
// //
// enqueuesubface() Queue a subface or a subsegment for encroachment chk. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::enqueuesubface(memorypool *pool, face *chkface)
{
if (!smarktest2ed(*chkface)) {
smarktest2(*chkface); // Only queue it once.
face *queface = (face *) pool->alloc();
*queface = *chkface;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// enqueuetetrahedron() Queue a tetrahedron for quality check. //
// /////////////////////////////////////////////////////////////////////////////////
void tetgenmesh::enqueuetetrahedron(triface *chktet)
{
if (!marktest2ed(*chktet)) {
marktest2(*chktet); // Only queue it once.
triface *quetet = (triface *) badtetrahedrons->alloc();
*quetet = *chktet;
}
}
//// optimize_cxx /////////////////////////////////////////////////////////////
//// ////
//// ////
///////////////////////////////////////////////////////////////////////////////
// //
// lawsonflip3d() A three-dimensional Lawson's algorithm. //
// //
///////////////////////////////////////////////////////////////////////////////
long tetgenmesh::lawsonflip3d(flipconstraints *fc)
{
triface fliptets[5], neightet, hulltet;
face checksh, casingout;
badface *popface, *bface;
point pd, pe, *pts;
REAL sign, ori;
REAL vol, len3;
long flipcount, totalcount = 0l;
long sliver_peels = 0l;
int t1ver;
int i;
while (1) {
if (b->verbose > 2) {
printf(" Lawson flip %ld faces.\n", flippool->items);
}
flipcount = 0l;
while (flipstack != (badface *) NULL) {
// Pop a face from the stack.
popface = flipstack;
fliptets[0] = popface->tt;
flipstack = flipstack->nextitem; // The next top item in stack.
flippool->dealloc((void *) popface);
// Skip it if it is a dead tet (destroyed by previous flips).
if (isdeadtet(fliptets[0])) continue;
// Skip it if it is not the same tet as we saved.
if (!facemarked(fliptets[0])) continue;
unmarkface(fliptets[0]);
if (ishulltet(fliptets[0])) continue;
fsym(fliptets[0], fliptets[1]);
if (ishulltet(fliptets[1])) {
if (nonconvex) {
// Check if 'fliptets[0]' it is a hull sliver.
tspivot(fliptets[0], checksh);
for (i = 0; i < 3; i++) {
if (!isshsubseg(checksh)) {
spivot(checksh, casingout);
//assert(casingout.sh != NULL);
if (sorg(checksh) != sdest(casingout)) sesymself(casingout);
stpivot(casingout, neightet);
if (neightet.tet == fliptets[0].tet) { // Found a hull sliver 'neightet'. Let it be [e,d,a,b], where
// [e,d,a] and [d,e,b] are hull faces.
edestoppo(neightet, hulltet); // [a,b,e,d]
fsymself(hulltet); // [b,a,e,#]
if (oppo(hulltet) == dummypoint) {
pe = org(neightet);
if ((pointtype(pe) == FREEFACETVERTEX) ||
(pointtype(pe) == FREESEGVERTEX)) {
removevertexbyflips(pe);
}
} else {
eorgoppo(neightet, hulltet); // [b,a,d,e]
fsymself(hulltet); // [a,b,d,#]
if (oppo(hulltet) == dummypoint) {
pd = dest(neightet);
if ((pointtype(pd) == FREEFACETVERTEX) ||
(pointtype(pd) == FREESEGVERTEX)) {
removevertexbyflips(pd);
}
} else {
// Perform a 3-to-2 flip to remove the sliver.
fliptets[0] = neightet; // [e,d,a,b]
fnext(fliptets[0], fliptets[1]); // [e,d,b,c]
fnext(fliptets[1], fliptets[2]); // [e,d,c,a]
flip32(fliptets, 1, fc);
// Update counters.
flip32count--;
flip22count--;
sliver_peels++;
if (fc->remove_ndelaunay_edge) {
// Update the volume (must be decreased).
//assert(fc->tetprism_vol_sum <= 0);
tetprism_vol_sum += fc->tetprism_vol_sum;
fc->tetprism_vol_sum = 0.0; // Clear it.
}
}
}
break;
} // if (neightet.tet == fliptets[0].tet)
} // if (!isshsubseg(checksh))
senextself(checksh);
} // i
} // if (nonconvex)
continue;
}
if (checksubfaceflag) {
// Do not flip if it is a subface.
if (issubface(fliptets[0])) continue;
}
// Test whether the face is locally Delaunay or not.
pts = (point *) fliptets[1].tet;
sign = insphere_s(pts[4], pts[5], pts[6], pts[7], oppo(fliptets[0]));
if (sign < 0) {
// A non-Delaunay face. Try to flip it.
pd = oppo(fliptets[0]);
pe = oppo(fliptets[1]);
// Use the length of the edge [d,e] as a reference to determine
// a nearly degenerated new tet.
len3 = distance(pd, pe);
len3 = (len3 * len3 * len3);
// Check the convexity of its three edges. Stop checking either a
// locally non-convex edge (ori < 0) or a flat edge (ori = 0) is
// encountered, and 'fliptet' represents that edge.
for (i = 0; i < 3; i++) {
ori = orient3d(org(fliptets[0]), dest(fliptets[0]), pd, pe); if (ori > 0) {
// Avoid creating a nearly degenerated new tet at boundary.
// Re-use fliptets[2], fliptets[3];
esym(fliptets[0], fliptets[2]);
esym(fliptets[1], fliptets[3]);
if (issubface(fliptets[2]) || issubface(fliptets[3])) {
vol = orient3dfast(org(fliptets[0]), dest(fliptets[0]), pd, pe);
if ((fabs(vol) / len3) < b->epsilon) {
ori = 0.0; // Do rounding.
}
}
} // Rounding check
if (ori <= 0) break;
enextself(fliptets[0]);
eprevself(fliptets[1]);
}
if (ori > 0) {
// A 2-to-3 flip is found.
// [0] [a,b,c,d],
// [1] [b,a,c,e]. no dummypoint.
flip23(fliptets, 0, fc);
flipcount++;
if (fc->remove_ndelaunay_edge) {
// Update the volume (must be decreased).
//assert(fc->tetprism_vol_sum <= 0);
tetprism_vol_sum += fc->tetprism_vol_sum;
fc->tetprism_vol_sum = 0.0; // Clear it.
}
continue;
} else { // ori <= 0
// The edge ('fliptets[0]' = [a',b',c',d]) is non-convex or flat,
// where the edge [a',b'] is one of [a,b], [b,c], and [c,a].
if (checksubsegflag) {
// Do not flip if it is a segment.
if (issubseg(fliptets[0])) continue;
}
// Check if there are three or four tets sharing at this edge.
esymself(fliptets[0]); // [b,a,d,c]
for (i = 0; i < 3; i++) {
fnext(fliptets[i], fliptets[i+1]);
}
if (fliptets[3].tet == fliptets[0].tet) {
// A 3-to-2 flip is found. (No hull tet.)
flip32(fliptets, 0, fc);
flipcount++;
if (fc->remove_ndelaunay_edge) {
// Update the volume (must be decreased).
//assert(fc->tetprism_vol_sum <= 0);
tetprism_vol_sum += fc->tetprism_vol_sum;
fc->tetprism_vol_sum = 0.0; // Clear it.
}
continue;
} else {
// There are more than 3 tets at this edge.
fnext(fliptets[3], fliptets[4]);
if (fliptets[4].tet == fliptets[0].tet) {
// There are exactly 4 tets at this edge.
if (nonconvex) {
if (apex(fliptets[3]) == dummypoint) {
// This edge is locally non-convex on the hull.
// It can be removed by a 4-to-4 flip.
ori = 0;
}
} // if (nonconvex)
if (ori == 0) {
// A 4-to-4 flip is found. (Two hull tets may be involved.)
// Current tets in 'fliptets':
// [0] [b,a,d,c] (d may be newpt)
// [1] [b,a,c,e] // [2] [b,a,e,f] (f may be dummypoint)
// [3] [b,a,f,d]
esymself(fliptets[0]); // [a,b,c,d]
// A 2-to-3 flip replaces face [a,b,c] by edge [e,d].
// This creates a degenerate tet [e,d,a,b] (tmpfliptets[0]).
// It will be removed by the followed 3-to-2 flip.
flip23(fliptets, 0, fc); // No hull tet.
fnext(fliptets[3], fliptets[1]);
fnext(fliptets[1], fliptets[2]);
// Current tets in 'fliptets':
// [0] [...]
// [1] [b,a,d,e] (degenerated, d may be new point).
// [2] [b,a,e,f] (f may be dummypoint)
// [3] [b,a,f,d]
// A 3-to-2 flip replaces edge [b,a] by face [d,e,f].
// Hull tets may be involved (f may be dummypoint).
flip32(&(fliptets[1]), (apex(fliptets[3]) == dummypoint), fc);
flipcount++;
flip23count--;
flip32count--;
flip44count++;
if (fc->remove_ndelaunay_edge) {
// Update the volume (must be decreased).
//assert(fc->tetprism_vol_sum <= 0);
tetprism_vol_sum += fc->tetprism_vol_sum;
fc->tetprism_vol_sum = 0.0; // Clear it.
}
continue;
} // if (ori == 0)
}
}
} // if (ori <= 0)
// This non-Delaunay face is unflippable. Save it.
unflipqueue->newindex((void **) &bface);
bface->tt = fliptets[0];
bface->forg = org(fliptets[0]);
bface->fdest = dest(fliptets[0]);
bface->fapex = apex(fliptets[0]);
} // if (sign < 0)
} // while (flipstack)
if (b->verbose > 2) {
if (flipcount > 0) {
printf(" Performed %ld flips.\n", flipcount);
}
}
// Accumulate the counter of flips.
totalcount += flipcount;
// Return if no unflippable faces left.
if (unflipqueue->objects == 0l) break;
// Return if no flip has been performed.
if (flipcount == 0l) break;
// Try to flip the unflippable faces.
for (i = 0; i < unflipqueue->objects; i++) {
bface = (badface *) fastlookup(unflipqueue, i);
if (!isdeadtet(bface->tt) &&
(org(bface->tt) == bface->forg) &&
(dest(bface->tt) == bface->fdest) &&
(apex(bface->tt) == bface->fapex)) {
flippush(flipstack, &(bface->tt));
}
}
unflipqueue->restart();
} // while (1)
if (b->verbose > 2) { if (totalcount > 0) {
printf(" Performed %ld flips.\n", totalcount);
}
if (sliver_peels > 0) {
printf(" Removed %ld hull slivers.\n", sliver_peels);
}
if (unflipqueue->objects > 0l) {
printf(" %ld unflippable edges remained.\n", unflipqueue->objects);
}
}
return totalcount + sliver_peels;
}
///////////////////////////////////////////////////////////////////////////////
// //
// recoverdelaunay() Recovery the locally Delaunay property. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::recoverdelaunay()
{
arraypool *flipqueue, *nextflipqueue, *swapqueue;
triface tetloop, neightet, *parytet;
badface *bface, *parybface;
point *ppt;
flipconstraints fc;
int i, j;
if (!b->quiet) {
printf("Recovering Delaunayness...\n");
}
tetprism_vol_sum = 0.0; // Initialize it.
// Put all interior faces of the mesh into 'flipstack'.
tetrahedrons->traversalinit();
tetloop.tet = tetrahedrontraverse();
while (tetloop.tet != NULL) {
for (tetloop.ver = 0; tetloop.ver < 4; tetloop.ver++) {
decode(tetloop.tet[tetloop.ver], neightet);
if (!facemarked(neightet)) {
flippush(flipstack, &tetloop);
}
}
ppt = (point *) &(tetloop.tet[4]);
tetprism_vol_sum += tetprismvol(ppt[0], ppt[1], ppt[2], ppt[3]);
tetloop.tet = tetrahedrontraverse();
}
// Calulate a relatively lower bound for small improvement.
// Used to avoid rounding error in volume calculation.
fc.bak_tetprism_vol = tetprism_vol_sum * b->epsilon * 1e-3;
if (b->verbose) {
printf(" Initial obj = %.17g\n", tetprism_vol_sum);
}
if (b->verbose > 1) {
printf(" Recover Delaunay [Lawson] : %ld\n", flippool->items);
}
// First only use the basic Lawson's flip.
fc.remove_ndelaunay_edge = 1;
fc.enqflag = 2;
lawsonflip3d(&fc);
if (b->verbose > 1) {
printf(" obj (after Lawson) = %.17g\n", tetprism_vol_sum); }
if (unflipqueue->objects == 0l) {
return; // The mesh is Delaunay.
}
fc.unflip = 1; // Unflip if the edge is not flipped.
fc.collectnewtets = 1; // new tets are returned in 'cavetetlist'.
fc.enqflag = 0;
autofliplinklevel = 1; // Init level.
b->fliplinklevel = -1; // No fixed level.
// For efficiency reason, we limit the maximium size of the edge star.
int bakmaxflipstarsize = b->flipstarsize;
b->flipstarsize = 10; // default
flipqueue = new arraypool(sizeof(badface), 10);
nextflipqueue = new arraypool(sizeof(badface), 10);
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
while (flipqueue->objects > 0l) {
if (b->verbose > 1) {
printf(" Recover Delaunay [level = %2d] #: %ld.\n",
autofliplinklevel, flipqueue->objects);
}
for (i = 0; i < flipqueue->objects; i++) {
bface = (badface *) fastlookup(flipqueue, i);
if (getedge(bface->forg, bface->fdest, &bface->tt)) {
if (removeedgebyflips(&(bface->tt), &fc) == 2) {
tetprism_vol_sum += fc.tetprism_vol_sum;
fc.tetprism_vol_sum = 0.0; // Clear it.
// Queue new faces for flips.
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
// A queued new tet may be dead.
if (!isdeadtet(*parytet)) {
for (parytet->ver = 0; parytet->ver < 4; parytet->ver++) {
// Avoid queue a face twice.
decode(parytet->tet[parytet->ver], neightet);
if (!facemarked(neightet)) {
flippush(flipstack, parytet);
}
} // parytet->ver
}
} // j
cavetetlist->restart();
// Remove locally non-Delaunay faces. New non-Delaunay edges
// may be found. They are saved in 'unflipqueue'.
fc.enqflag = 2;
lawsonflip3d(&fc);
fc.enqflag = 0;
// There may be unflipable faces. Add them in flipqueue.
for (j = 0; j < unflipqueue->objects; j++) {
bface = (badface *) fastlookup(unflipqueue, j);
flipqueue->newindex((void **) &parybface);
*parybface = *bface;
}
unflipqueue->restart();
} else {
// Unable to remove this edge. Save it.
nextflipqueue->newindex((void **) &parybface);
*parybface = *bface;
// Normally, it should be zero. //assert(fc.tetprism_vol_sum == 0.0);
// However, due to rounding errors, a tiny value may appear.
fc.tetprism_vol_sum = 0.0;
}
}
} // i
if (b->verbose > 1) {
printf(" obj (after level %d) = %.17g.\n", autofliplinklevel,
tetprism_vol_sum);
}
flipqueue->restart();
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = nextflipqueue;
nextflipqueue = swapqueue;
if (flipqueue->objects > 0l) {
// default 'b->delmaxfliplevel' is 1.
if (autofliplinklevel >= b->delmaxfliplevel) {
// For efficiency reason, we do not search too far.
break;
}
autofliplinklevel+=b->fliplinklevelinc;
}
} // while (flipqueue->objects > 0l)
if (flipqueue->objects > 0l) {
if (b->verbose > 1) {
printf(" %ld non-Delaunay edges remained.\n", flipqueue->objects);
}
}
if (b->verbose) {
printf(" Final obj = %.17g\n", tetprism_vol_sum);
}
b->flipstarsize = bakmaxflipstarsize;
delete flipqueue;
delete nextflipqueue;
}
///////////////////////////////////////////////////////////////////////////////
// //
// gettetrahedron() Get a tetrahedron which have the given vertices. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::gettetrahedron(point pa, point pb, point pc, point pd,
triface *searchtet)
{
triface spintet;
int t1ver;
if (getedge(pa, pb, searchtet)) {
spintet = *searchtet;
while (1) {
if (apex(spintet) == pc) {
*searchtet = spintet;
break;
}
fnextself(spintet);
if (spintet.tet == searchtet->tet) break;
}
if (apex(*searchtet) == pc) {
if (oppo(*searchtet) == pd) {
return 1;
} else {
fsymself(*searchtet); if (oppo(*searchtet) == pd) {
return 1;
}
}
}
}
return 0;
}
///////////////////////////////////////////////////////////////////////////////
// //
// improvequalitybyflips() Improve the mesh quality by flips. //
// //
///////////////////////////////////////////////////////////////////////////////
long tetgenmesh::improvequalitybyflips()
{
arraypool *flipqueue, *nextflipqueue, *swapqueue;
badface *bface, *parybface;
triface *parytet;
point *ppt;
flipconstraints fc;
REAL *cosdd, ncosdd[6], maxdd;
long totalremcount, remcount;
int remflag;
int n, i, j, k;
//assert(unflipqueue->objects > 0l);
flipqueue = new arraypool(sizeof(badface), 10);
nextflipqueue = new arraypool(sizeof(badface), 10);
// Backup flip edge options.
int bakautofliplinklevel = autofliplinklevel;
int bakfliplinklevel = b->fliplinklevel;
int bakmaxflipstarsize = b->flipstarsize;
// Set flip edge options.
autofliplinklevel = 1;
b->fliplinklevel = -1;
b->flipstarsize = 10; // b->optmaxflipstarsize;
fc.remove_large_angle = 1;
fc.unflip = 1;
fc.collectnewtets = 1;
fc.checkflipeligibility = 1;
totalremcount = 0l;
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
while (flipqueue->objects > 0l) {
remcount = 0l;
while (flipqueue->objects > 0l) {
if (b->verbose > 1) {
printf(" Improving mesh qualiy by flips [%d]#: %ld.\n",
autofliplinklevel, flipqueue->objects);
}
for (k = 0; k < flipqueue->objects; k++) {
bface = (badface *) fastlookup(flipqueue, k);
if (gettetrahedron(bface->forg, bface->fdest, bface->fapex,
bface->foppo, &bface->tt)) {
//assert(!ishulltet(bface->tt));
// There are bad dihedral angles in this tet. if (bface->tt.ver != 11) {
// The dihedral angles are permuted.
// Here we simply re-compute them. Slow!!.
ppt = (point *) & (bface->tt.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
&bface->key, NULL);
bface->forg = ppt[0];
bface->fdest = ppt[1];
bface->fapex = ppt[2];
bface->foppo = ppt[3];
bface->tt.ver = 11;
}
if (bface->key == 0) {
// Re-comput the quality values. Due to smoothing operations.
ppt = (point *) & (bface->tt.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
&bface->key, NULL);
}
cosdd = bface->cent;
remflag = 0;
for (i = 0; (i < 6) && !remflag; i++) {
if (cosdd[i] < cosmaxdihed) {
// Found a large dihedral angle.
bface->tt.ver = edge2ver[i]; // Go to the edge.
fc.cosdihed_in = cosdd[i];
fc.cosdihed_out = 0.0; // 90 degree.
n = removeedgebyflips(&(bface->tt), &fc);
if (n == 2) {
// Edge is flipped.
remflag = 1;
if (fc.cosdihed_out < cosmaxdihed) {
// Queue new bad tets for further improvements.
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
if (!isdeadtet(*parytet)) {
ppt = (point *) & (parytet->tet[4]);
// Do not test a hull tet.
if (ppt[3] != dummypoint) {
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], ncosdd,
&maxdd, NULL);
if (maxdd < cosmaxdihed) {
// There are bad dihedral angles in this tet.
nextflipqueue->newindex((void **) &parybface);
parybface->tt.tet = parytet->tet;
parybface->tt.ver = 11;
parybface->forg = ppt[0];
parybface->fdest = ppt[1];
parybface->fapex = ppt[2];
parybface->foppo = ppt[3];
parybface->key = maxdd;
for (n = 0; n < 6; n++) {
parybface->cent[n] = ncosdd[n];
}
}
} // if (ppt[3] != dummypoint)
}
} // j
} // if (fc.cosdihed_out < cosmaxdihed)
cavetetlist->restart();
remcount++;
}
}
} // i
if (!remflag) {
// An unremoved bad tet. Queue it again.
unflipqueue->newindex((void **) &parybface);
*parybface = *bface;
}
} // if (gettetrahedron(...))
} // k
flipqueue->restart();
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = nextflipqueue;
nextflipqueue = swapqueue;
} // while (flipqueues->objects > 0)
if (b->verbose > 1) {
printf(" Removed %ld bad tets.\n", remcount);
}
totalremcount += remcount;
if (unflipqueue->objects > 0l) {
//if (autofliplinklevel >= b->optmaxfliplevel) {
if (autofliplinklevel >= b->optlevel) {
break;
}
autofliplinklevel+=b->fliplinklevelinc;
//b->flipstarsize = 10 + (1 << (b->optlevel - 1));
}
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
} // while (flipqueues->objects > 0)
// Restore original flip edge options.
autofliplinklevel = bakautofliplinklevel;
b->fliplinklevel = bakfliplinklevel;
b->flipstarsize = bakmaxflipstarsize;
delete flipqueue;
delete nextflipqueue;
return totalremcount;
}
///////////////////////////////////////////////////////////////////////////////
// //
// smoothpoint() Moving a vertex to improve the mesh quality. //
// //
// 'smtpt' (p) is a point to be smoothed. Generally, it is a Steiner point. //
// It may be not a vertex of the mesh. //
// //
// This routine tries to move 'p' inside its star until a selected objective //
// function over all tetrahedra in the star is improved. The function may be //
// the some quality measures, i.e., aspect ratio, maximum dihedral angel, or //
// simply the volume of the tetrahedra. //
// //
// 'linkfacelist' contains the list of link faces of 'p'. Since a link face //
// has two orientations, ccw or cw, with respect to 'p'. 'ccw' indicates //
// the orientation is ccw (1) or not (0). //
// //
// 'opm' is a structure contains the parameters of the objective function. //
// It is needed by the evaluation of the function value. //
// //
// The return value indicates weather the point is smoothed or not. //
// //
// ASSUMPTION: This routine assumes that all link faces are true faces, i.e, //
// no face has 'dummypoint' as its vertex. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::smoothpoint(point smtpt, arraypool *linkfacelist, int ccw,
optparameters *opm)
{
triface *parytet, *parytet1, swaptet; point pa, pb, pc;
REAL fcent[3], startpt[3], nextpt[3], bestpt[3];
REAL oldval, minval = 0.0, val;
REAL maxcosd; // oldang, newang;
REAL ori, diff;
int numdirs, iter;
int i, j, k;
// Decide the number of moving directions.
numdirs = (int) linkfacelist->objects;
if (numdirs > opm->numofsearchdirs) {
numdirs = opm->numofsearchdirs; // Maximum search directions.
}
// Set the initial value.
opm->imprval = opm->initval;
iter = 0;
for (i = 0; i < 3; i++) {
bestpt[i] = startpt[i] = smtpt[i];
}
// Iterate until the obj function is not improved.
while (1) {
// Find the best next location.
oldval = opm->imprval;
for (i = 0; i < numdirs; i++) {
// Randomly pick a link face (0 <= k <= objects - i - 1).
k = (int) randomnation(linkfacelist->objects - i);
parytet = (triface *) fastlookup(linkfacelist, k);
// Calculate a new position from 'p' to the center of this face.
pa = org(*parytet);
pb = dest(*parytet);
pc = apex(*parytet);
for (j = 0; j < 3; j++) {
fcent[j] = (pa[j] + pb[j] + pc[j]) / 3.0;
}
for (j = 0; j < 3; j++) {
nextpt[j] = startpt[j] + opm->searchstep * (fcent[j] - startpt[j]);
}
// Calculate the largest minimum function value for the new location.
for (j = 0; j < linkfacelist->objects; j++) {
parytet = (triface *) fastlookup(linkfacelist, j);
if (ccw) {
pa = org(*parytet);
pb = dest(*parytet);
} else {
pb = org(*parytet);
pa = dest(*parytet);
}
pc = apex(*parytet);
ori = orient3d(pa, pb, pc, nextpt);
if (ori < 0.0) {
// Calcuate the objective function value.
if (opm->max_min_volume) {
//val = -ori;
val = - orient3dfast(pa, pb, pc, nextpt);
} else if (opm->min_max_aspectratio) {
val = 1.0 / tetaspectratio(pa, pb, pc, nextpt);
} else if (opm->min_max_dihedangle) {
tetalldihedral(pa, pb, pc, nextpt, NULL, &maxcosd, NULL);
if (maxcosd < -1) maxcosd = -1.0; // Rounding.
val = maxcosd + 1.0; // Make it be positive.
} else {
// Unknown objective function.
val = 0.0;
}
} else { // ori >= 0.0; // An invalid new tet.
// This may happen if the mesh contains inverted elements.
if (opm->max_min_volume) {
//val = -ori;
val = - orient3dfast(pa, pb, pc, nextpt);
} else {
// Discard this point.
break; // j
}
} // if (ori >= 0.0)
// Stop looping when the object value is not improved.
if (val <= opm->imprval) {
break; // j
} else {
// Remember the smallest improved value.
if (j == 0) {
minval = val;
} else {
minval = (val < minval) ? val : minval;
}
}
} // j
if (j == linkfacelist->objects) {
// The function value has been improved.
opm->imprval = minval;
// Save the new location of the point.
for (j = 0; j < 3; j++) bestpt[j] = nextpt[j];
}
// Swap k-th and (object-i-1)-th entries.
j = linkfacelist->objects - i - 1;
parytet = (triface *) fastlookup(linkfacelist, k);
parytet1 = (triface *) fastlookup(linkfacelist, j);
swaptet = *parytet1;
*parytet1 = *parytet;
*parytet = swaptet;
} // i
diff = opm->imprval - oldval;
if (diff > 0.0) {
// Is the function value improved effectively?
if (opm->max_min_volume) {
//if ((diff / oldval) < b->epsilon) diff = 0.0;
} else if (opm->min_max_aspectratio) {
if ((diff / oldval) < 1e-3) diff = 0.0;
} else if (opm->min_max_dihedangle) {
//oldang = acos(oldval - 1.0);
//newang = acos(opm->imprval - 1.0);
//if ((oldang - newang) < 0.00174) diff = 0.0; // about 0.1 degree.
} else {
// Unknown objective function.
terminatetetgen(this, 2);
}
}
if (diff > 0.0) {
// Yes, move p to the new location and continue.
for (j = 0; j < 3; j++) startpt[j] = bestpt[j];
iter++;
if ((opm->maxiter > 0) && (iter >= opm->maxiter)) {
// Maximum smoothing iterations reached.
break;
}
} else {
break;
}
} // while (1)
if (iter > 0) {
// The point has been smoothed. opm->smthiter = iter; // Remember the number of iterations.
// The point has been smoothed. Update it to its new position.
for (i = 0; i < 3; i++) smtpt[i] = startpt[i];
}
return iter;
}
///////////////////////////////////////////////////////////////////////////////
// //
// improvequalitysmoothing() Improve mesh quality by smoothing. //
// //
///////////////////////////////////////////////////////////////////////////////
long tetgenmesh::improvequalitybysmoothing(optparameters *opm)
{
arraypool *flipqueue, *swapqueue;
triface *parytet;
badface *bface, *parybface;
point *ppt;
long totalsmtcount, smtcount;
int smtflag;
int iter, i, j, k;
//assert(unflipqueue->objects > 0l);
flipqueue = new arraypool(sizeof(badface), 10);
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
totalsmtcount = 0l;
iter = 0;
while (flipqueue->objects > 0l) {
smtcount = 0l;
if (b->verbose > 1) {
printf(" Improving mesh quality by smoothing [%d]#: %ld.\n",
iter, flipqueue->objects);
}
for (k = 0; k < flipqueue->objects; k++) {
bface = (badface *) fastlookup(flipqueue, k);
if (gettetrahedron(bface->forg, bface->fdest, bface->fapex,
bface->foppo, &bface->tt)) {
// Operate on it if it is not in 'unflipqueue'.
if (!marktested(bface->tt)) {
// Here we simply re-compute the quality. Since other smoothing
// operation may have moved the vertices of this tet.
ppt = (point *) & (bface->tt.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
&bface->key, NULL);
if (bface->key < cossmtdihed) { // if (maxdd < cosslidihed) {
// It is a sliver. Try to smooth its vertices.
smtflag = 0;
opm->initval = bface->key + 1.0;
for (i = 0; (i < 4) && !smtflag; i++) {
if (pointtype(ppt[i]) == FREEVOLVERTEX) {
getvertexstar(1, ppt[i], cavetetlist, NULL, NULL);
opm->searchstep = 0.001; // Search step size
smtflag = smoothpoint(ppt[i], cavetetlist, 1, opm);
if (smtflag) {
while (opm->smthiter == opm->maxiter) {
opm->searchstep *= 10.0; // Increase the step size.
opm->initval = opm->imprval;
opm->smthiter = 0; // reset smoothpoint(ppt[i], cavetetlist, 1, opm);
}
// This tet is modifed.
smtcount++;
if ((opm->imprval - 1.0) < cossmtdihed) {
// There are slivers in new tets. Queue them.
for (j = 0; j < cavetetlist->objects; j++) {
parytet = (triface *) fastlookup(cavetetlist, j);
// Operate it if it is not in 'unflipqueue'.
if (!marktested(*parytet)) {
// Evaluate its quality.
// Re-use ppt, bface->key, bface->cent.
ppt = (point *) & (parytet->tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3],
bface->cent, &bface->key, NULL);
if (bface->key < cossmtdihed) {
// A new sliver. Queue it.
marktest(*parytet); // It is in unflipqueue.
unflipqueue->newindex((void **) &parybface);
parybface->tt = *parytet;
parybface->forg = ppt[0];
parybface->fdest = ppt[1];
parybface->fapex = ppt[2];
parybface->foppo = ppt[3];
parybface->tt.ver = 11;
parybface->key = 0.0;
}
}
} // j
} // if ((opm->imprval - 1.0) < cossmtdihed)
} // if (smtflag)
cavetetlist->restart();
} // if (pointtype(ppt[i]) == FREEVOLVERTEX)
} // i
if (!smtflag) {
// Didn't smooth. Queue it again.
marktest(bface->tt); // It is in unflipqueue.
unflipqueue->newindex((void **) &parybface);
parybface->tt = bface->tt;
parybface->forg = ppt[0];
parybface->fdest = ppt[1];
parybface->fapex = ppt[2];
parybface->foppo = ppt[3];
parybface->tt.ver = 11;
parybface->key = 0.0;
}
} // if (maxdd < cosslidihed)
} // if (!marktested(...))
} // if (gettetrahedron(...))
} // k
flipqueue->restart();
// Unmark the tets in unflipqueue.
for (i = 0; i < unflipqueue->objects; i++) {
bface = (badface *) fastlookup(unflipqueue, i);
unmarktest(bface->tt);
}
if (b->verbose > 1) {
printf(" Smooth %ld points.\n", smtcount);
}
totalsmtcount += smtcount;
if (smtcount == 0l) {
// No point has been smoothed.
break;
} else {
iter++;
if (iter == 2) { //if (iter >= b->optpasses) { break;
}
}
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
} // while
delete flipqueue;
return totalsmtcount;
}
///////////////////////////////////////////////////////////////////////////////
// //
// splitsliver() Split a sliver. //
// //
///////////////////////////////////////////////////////////////////////////////
int tetgenmesh::splitsliver(triface *slitet, REAL cosd, int chkencflag)
{
triface *abtets;
triface searchtet, spintet, *parytet;
point pa, pb, steinerpt;
optparameters opm;
insertvertexflags ivf;
REAL smtpt[3], midpt[3];
int success;
int t1ver;
int n, i;
// 'slitet' is [c,d,a,b], where [c,d] has a big dihedral angle.
// Go to the opposite edge [a,b].
edestoppo(*slitet, searchtet); // [a,b,c,d].
// Do not split a segment.
if (issubseg(searchtet)) {
return 0;
}
// Count the number of tets shared at [a,b].
// Do not split it if it is a hull edge.
spintet = searchtet;
n = 0;
while (1) {
if (ishulltet(spintet)) break;
n++;
fnextself(spintet);
if (spintet.tet == searchtet.tet) break;
}
if (ishulltet(spintet)) {
return 0; // It is a hull edge.
}
// Get all tets at edge [a,b].
abtets = new triface[n];
spintet = searchtet;
for (i = 0; i < n; i++) {
abtets[i] = spintet;
fnextself(spintet);
}
// Initialize the list of 2n boundary faces.
for (i = 0; i < n; i++) {
eprev(abtets[i], searchtet);
esymself(searchtet); // [a,p_i,p_i+1].
cavetetlist->newindex((void **) &parytet);
*parytet = searchtet; enext(abtets[i], searchtet);
esymself(searchtet); // [p_i,b,p_i+1].
cavetetlist->newindex((void **) &parytet);
*parytet = searchtet;
}
// Init the Steiner point at the midpoint of edge [a,b].
pa = org(abtets[0]);
pb = dest(abtets[0]);
for (i = 0; i < 3; i++) {
smtpt[i] = midpt[i] = 0.5 * (pa[i] + pb[i]);
}
// Point smooth options.
opm.min_max_dihedangle = 1;
opm.initval = cosd + 1.0; // Initial volume is zero.
opm.numofsearchdirs = 20;
opm.searchstep = 0.001;
opm.maxiter = 100; // Limit the maximum iterations.
success = smoothpoint(smtpt, cavetetlist, 1, &opm);
if (success) {
while (opm.smthiter == opm.maxiter) {
// It was relocated and the prescribed maximum iteration reached.
// Try to increase the search stepsize.
opm.searchstep *= 10.0;
//opm.maxiter = 100; // Limit the maximum iterations.
opm.initval = opm.imprval;
opm.smthiter = 0; // Init.
smoothpoint(smtpt, cavetetlist, 1, &opm);
}
} // if (success)
cavetetlist->restart();
if (!success) {
delete [] abtets;
return 0;
}
// Insert the Steiner point.
makepoint(&steinerpt, FREEVOLVERTEX);
for (i = 0; i < 3; i++) steinerpt[i] = smtpt[i];
// Insert the created Steiner point.
for (i = 0; i < n; i++) {
infect(abtets[i]);
caveoldtetlist->newindex((void **) &parytet);
*parytet = abtets[i];
}
searchtet = abtets[0]; // No need point location.
if (b->metric) {
locate(steinerpt, &searchtet); // For size interpolation.
}
delete [] abtets;
ivf.iloc = (int) INSTAR;
ivf.chkencflag = chkencflag;
ivf.assignmeshsize = b->metric;
if (insertpoint(steinerpt, &searchtet, NULL, NULL, &ivf)) {
// The vertex has been inserted.
st_volref_count++;
if (steinerleft > 0) steinerleft--;
return 1; } else {
// The Steiner point is too close to an existing vertex. Reject it.
pointdealloc(steinerpt);
return 0;
}
}
///////////////////////////////////////////////////////////////////////////////
// //
// removeslivers() Remove slivers by adding Steiner points. //
// //
///////////////////////////////////////////////////////////////////////////////
long tetgenmesh::removeslivers(int chkencflag)
{
arraypool *flipqueue, *swapqueue;
badface *bface, *parybface;
triface slitet, *parytet;
point *ppt;
REAL cosdd[6], maxcosd;
long totalsptcount, sptcount;
int iter, i, j, k;
//assert(unflipqueue->objects > 0l);
flipqueue = new arraypool(sizeof(badface), 10);
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
totalsptcount = 0l;
iter = 0;
while ((flipqueue->objects > 0l) && (steinerleft != 0)) {
sptcount = 0l;
if (b->verbose > 1) {
printf(" Splitting bad quality tets [%d]#: %ld.\n",
iter, flipqueue->objects);
}
for (k = 0; (k < flipqueue->objects) && (steinerleft != 0); k++) {
bface = (badface *) fastlookup(flipqueue, k);
if (gettetrahedron(bface->forg, bface->fdest, bface->fapex,
bface->foppo, &bface->tt)) {
if ((bface->key == 0) || (bface->tt.ver != 11)) {
// Here we need to re-compute the quality. Since other smoothing
// operation may have moved the vertices of this tet.
ppt = (point *) & (bface->tt.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], bface->cent,
&bface->key, NULL);
}
if (bface->key < cosslidihed) {
// It is a sliver. Try to split it.
slitet.tet = bface->tt.tet;
//cosdd = bface->cent;
for (j = 0; j < 6; j++) {
if (bface->cent[j] < cosslidihed) {
// Found a large dihedral angle.
slitet.ver = edge2ver[j]; // Go to the edge.
if (splitsliver(&slitet, bface->cent[j], chkencflag)) {
sptcount++;
break;
}
}
} // j
if (j < 6) {
// A sliver is split. Queue new slivers. badtetrahedrons->traversalinit();
parytet = (triface *) badtetrahedrons->traverse();
while (parytet != NULL) {
unmarktest2(*parytet);
ppt = (point *) & (parytet->tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], cosdd,
&maxcosd, NULL);
if (maxcosd < cosslidihed) {
// A new sliver. Queue it.
unflipqueue->newindex((void **) &parybface);
parybface->forg = ppt[0];
parybface->fdest = ppt[1];
parybface->fapex = ppt[2];
parybface->foppo = ppt[3];
parybface->tt.tet = parytet->tet;
parybface->tt.ver = 11;
parybface->key = maxcosd;
for (i = 0; i < 6; i++) {
parybface->cent[i] = cosdd[i];
}
}
parytet = (triface *) badtetrahedrons->traverse();
}
badtetrahedrons->restart();
} else {
// Didn't split. Queue it again.
unflipqueue->newindex((void **) &parybface);
*parybface = *bface;
} // if (j == 6)
} // if (bface->key < cosslidihed)
} // if (gettetrahedron(...))
} // k
flipqueue->restart();
if (b->verbose > 1) {
printf(" Split %ld tets.\n", sptcount);
}
totalsptcount += sptcount;
if (sptcount == 0l) {
// No point has been smoothed.
break;
} else {
iter++;
if (iter == 2) { //if (iter >= b->optpasses) {
break;
}
}
// Swap the two flip queues.
swapqueue = flipqueue;
flipqueue = unflipqueue;
unflipqueue = swapqueue;
} // while
delete flipqueue;
return totalsptcount;
}
///////////////////////////////////////////////////////////////////////////////
// //
// optimizemesh() Optimize mesh for specified objective functions. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::optimizemesh()
{
badface *parybface; triface checktet;
point *ppt;
int optpasses;
optparameters opm;
REAL ncosdd[6], maxdd;
long totalremcount, remcount;
long totalsmtcount, smtcount;
long totalsptcount, sptcount;
int chkencflag;
int iter;
int n;
if (!b->quiet) {
printf("Optimizing mesh...\n");
}
optpasses = ((1 << b->optlevel) - 1);
if (b->verbose) {
printf(" Optimization level = %d.\n", b->optlevel);
printf(" Optimization scheme = %d.\n", b->optscheme);
printf(" Number of iteration = %d.\n", optpasses);
printf(" Min_Max dihed angle = %g.\n", b->optmaxdihedral);
}
totalsmtcount = totalsptcount = totalremcount = 0l;
cosmaxdihed = cos(b->optmaxdihedral / 180.0 * PI);
cossmtdihed = cos(b->optminsmtdihed / 180.0 * PI);
cosslidihed = cos(b->optminslidihed / 180.0 * PI);
int attrnum = numelemattrib - 1;
// Put all bad tetrahedra into array.
tetrahedrons->traversalinit();
checktet.tet = tetrahedrontraverse();
while (checktet.tet != NULL) {
if (b->convex) { // -c
// Skip this tet if it lies in the exterior.
if (elemattribute(checktet.tet, attrnum) == -1.0) {
checktet.tet = tetrahedrontraverse();
continue;
}
}
ppt = (point *) & (checktet.tet[4]);
tetalldihedral(ppt[0], ppt[1], ppt[2], ppt[3], ncosdd, &maxdd, NULL);
if (maxdd < cosmaxdihed) {
// There are bad dihedral angles in this tet.
unflipqueue->newindex((void **) &parybface);
parybface->tt.tet = checktet.tet;
parybface->tt.ver = 11;
parybface->forg = ppt[0];
parybface->fdest = ppt[1];
parybface->fapex = ppt[2];
parybface->foppo = ppt[3];
parybface->key = maxdd;
for (n = 0; n < 6; n++) {
parybface->cent[n] = ncosdd[n];
}
}
checktet.tet = tetrahedrontraverse();
}
totalremcount = improvequalitybyflips();
if ((unflipqueue->objects > 0l) &&
((b->optscheme & 2) || (b->optscheme & 4))) {
// The pool is only used by removeslivers().
badtetrahedrons = new memorypool(sizeof(triface), b->tetrahedraperblock,
sizeof(void *), 0);
// Smoothing options.
opm.min_max_dihedangle = 1;
opm.numofsearchdirs = 10;
// opm.searchstep = 0.001;
opm.maxiter = 30; // Limit the maximum iterations.
//opm.checkencflag = 4; // Queue affected tets after smoothing.
chkencflag = 4; // Queue affected tets after splitting a sliver.
iter = 0;
while (iter < optpasses) {
smtcount = sptcount = remcount = 0l;
if (b->optscheme & 2) {
smtcount += improvequalitybysmoothing(&opm);
totalsmtcount += smtcount;
if (smtcount > 0l) {
remcount = improvequalitybyflips();
totalremcount += remcount;
}
}
if (unflipqueue->objects > 0l) {
if (b->optscheme & 4) {
sptcount += removeslivers(chkencflag);
totalsptcount += sptcount;
if (sptcount > 0l) {
remcount = improvequalitybyflips();
totalremcount += remcount;
}
}
}
if (unflipqueue->objects > 0l) {
if (remcount > 0l) {
iter++;
} else {
break;
}
} else {
break;
}
} // while (iter)
delete badtetrahedrons;
badtetrahedrons = NULL;
}
if (unflipqueue->objects > 0l) {
if (b->verbose > 1) {
printf(" %ld bad tets remained.\n", unflipqueue->objects);
}
unflipqueue->restart();
}
if (b->verbose) {
if (totalremcount > 0l) {
printf(" Removed %ld edges.\n", totalremcount);
}
if (totalsmtcount > 0l) {
printf(" Smoothed %ld points.\n", totalsmtcount);
}
if (totalsptcount > 0l) {
printf(" Split %ld slivers.\n", totalsptcount);
}
}
}
//// ////
//// ////
//// optimize_cxx /////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
// //
// jettisonnodes() Jettison unused or duplicated vertices. //
// //
// Unused points are those input points which are outside the mesh domain or //
// have no connection (isolated) to the mesh. Duplicated points exist for //
// example if the input PLC is read from a .stl mesh file (marked during the //
// Delaunay tetrahedralization step. This routine remove these points from //
// points list. All existing points are reindexed. //
// //
///////////////////////////////////////////////////////////////////////////////
void tetgenmesh::jettisonnodes()
{
point pointloop;
bool jetflag;
int oldidx, newidx;
int remcount;
if (!b->quiet) {
printf("Jettisoning redundant points.\n");
}
points->traversalinit();
pointloop = pointtraverse();
oldidx = newidx = 0; // in->firstnumber;
remcount = 0;
while (pointloop != (point) NULL) {
jetflag = (pointtype(pointloop) == DUPLICATEDVERTEX) ||
(pointtype(pointloop) == UNUSEDVERTEX);
if (jetflag) {
// It is a duplicated or unused point, delete it.
pointdealloc(pointloop);
remcount++;
} else {
// Re-index it.
setpointmark(pointloop, newidx + in->firstnumber);
if (in->pointmarkerlist != (int *) NULL) {
if (oldidx < in->numberofpoints) {
// Re-index the point marker as well.
in->pointmarkerlist[newidx] = in->pointmarkerlist[oldidx];
}
}
newidx++;
}
oldidx++;
pointloop = pointtraverse();
}
if (b->verbose) {
printf(" %ld duplicated vertices are removed.\n", dupverts);
printf(" %ld unused vertices are removed.\n", unuverts);
}
dupverts = 0l;
unuverts = 0l;
// The following line ensures that dead items in the pool of nodes cannot
// be allocated for the new created nodes. This ensures that the input
// nodes will occur earlier in the output files, and have lower indices.
points->deaditemstack = (void *) NULL;
}