diff --git a/Mesh/bakmeshGRegionBoundaryRecovery.cpp b/Mesh/bakmeshGRegionBoundaryRecovery.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..5c3118dc95557d08d4c9a8f448f4be74371affc3
--- /dev/null
+++ b/Mesh/bakmeshGRegionBoundaryRecovery.cpp
@@ -0,0 +1 @@
+dummy file
diff --git a/Mesh/meshGRegionBoundaryRecovery.cpp b/Mesh/meshGRegionBoundaryRecovery.cpp
index 62b27c30e5275bf8ec373266cfaeabd00e86fa47..724358da0d858ddc64056cdeb60be0190e290554 100644
--- a/Mesh/meshGRegionBoundaryRecovery.cpp
+++ b/Mesh/meshGRegionBoundaryRecovery.cpp
@@ -33,27 +33,6 @@ bool meshGRegionBoundaryRecovery(GRegion *gr)
class tetgenio{
public:
- typedef struct {
- int *vertexlist;
- int numberofvertices;
- } polygon;
-
- // A "facet" describes a polygonal region possibly with holes, edges, and
- // points floating in it. Each facet consists of a list of polygons and
- // a list of hole points (which lie strictly inside holes).
- typedef struct {
- polygon *polygonlist;
- int numberofpolygons;
- REAL *holelist;
- int numberofholes;
- } facet;
-
- typedef struct{
- REAL uv[2];
- int tag;
- int type;
- } pointparam;
-
int firstnumber;
int numberofpointattributes;
@@ -68,7 +47,6 @@ public:
int numberofpoints;
int *pointlist;
int *pointattributelist;
- pointparam *pointparamlist;
int numberofpointmakers;
int *pointmarkerlist;
@@ -80,10 +58,6 @@ public:
int *edgelist;
int *edgemarkerlist;
- int numberoffacets;
- facet *facetlist;
- int *facetmarkerlist;
-
int numberofholes;
REAL *holelist;
@@ -104,7 +78,6 @@ public:
numberofpoints = 0;
pointlist = 0;
pointattributelist = 0;
- pointparamlist = 0;
numberofpointmakers = 0;
pointmarkerlist = 0;
numberofpointmtrs = 0;
@@ -112,9 +85,6 @@ public:
numberofedges = 0;
edgelist = 0;
edgemarkerlist = 0;
- numberoffacets = 0;
- facetlist = 0;
- facetmarkerlist = 0;
numberofholes = 0;
holelist = 0;
numberofregions = 0;
@@ -149,7 +119,7 @@ bool tetgenmesh::reconstructmesh(void *p)
in = new tetgenio();
b = new tetgenbehavior();
- char *opt = "pY";
+ char opt[] = "pY";
b->parse_commandline(opt);
bool returnValue (true);
@@ -537,7 +507,7 @@ bool tetgenmesh::reconstructmesh(void *p)
insegments = subsegs->items;
if (0) {
- //outsurfacemesh("dump");
+ outsurfacemesh("dump");
}
} // meshsurface()
@@ -624,7 +594,9 @@ bool tetgenmesh::reconstructmesh(void *p)
}
// Debug
- //outmesh2medit("dump");
+ if (0) {
+ //outmesh2medit("dump");
+ }
////////////////////////////////////////////////////////
{
@@ -869,4 +841,213 @@ bool tetgenmesh::reconstructmesh(void *p)
}
+// Dump the input surface mesh.
+// 'mfilename' is a filename without suffix.
+void tetgenmesh::outsurfacemesh(const char* mfilename)
+{
+ FILE *outfile = NULL;
+ char sfilename[256];
+ int firstindex;
+
+ point pointloop;
+ int pointnumber;
+ strcpy(sfilename, mfilename);
+ strcat(sfilename, ".node");
+ outfile = fopen(sfilename, "w");
+ if (!b->quiet) {
+ printf("Writing %s.\n", sfilename);
+ }
+ fprintf(outfile, "%ld 3 0 0\n", points->items);
+ // Determine the first index (0 or 1).
+ firstindex = b->zeroindex ? 0 : in->firstnumber;
+ points->traversalinit();
+ pointloop = pointtraverse();
+ pointnumber = firstindex; // in->firstnumber;
+ while (pointloop != (point) NULL) {
+ // Point number, x, y and z coordinates.
+ fprintf(outfile, "%4d %.17g %.17g %.17g", pointnumber,
+ pointloop[0], pointloop[1], pointloop[2]);
+ fprintf(outfile, "\n");
+ pointloop = pointtraverse();
+ pointnumber++;
+ }
+ fclose(outfile);
+
+ face faceloop;
+ point torg, tdest, tapex;
+ strcpy(sfilename, mfilename);
+ strcat(sfilename, ".smesh");
+ outfile = fopen(sfilename, "w");
+ if (!b->quiet) {
+ printf("Writing %s.\n", sfilename);
+ }
+ int shift = 0; // Default no shiftment.
+ if ((in->firstnumber == 1) && (firstindex == 0)) {
+ shift = 1; // Shift the output indices by 1.
+ }
+ fprintf(outfile, "0 3 0 0\n");
+ fprintf(outfile, "%ld 1\n", subfaces->items);
+ subfaces->traversalinit();
+ faceloop.sh = shellfacetraverse(subfaces);
+ while (faceloop.sh != (shellface *) NULL) {
+ torg = sorg(faceloop);
+ tdest = sdest(faceloop);
+ tapex = sapex(faceloop);
+ fprintf(outfile, "3 %4d %4d %4d %d\n",
+ pointmark(torg) - shift, pointmark(tdest) - shift,
+ pointmark(tapex) - shift, shellmark(faceloop));
+ faceloop.sh = shellfacetraverse(subfaces);
+ }
+ fprintf(outfile, "0\n");
+ fprintf(outfile, "0\n");
+ fclose(outfile);
+
+ face edgeloop;
+ int edgenumber;
+ strcpy(sfilename, mfilename);
+ strcat(sfilename, ".edge");
+ outfile = fopen(sfilename, "w");
+ if (!b->quiet) {
+ printf("Writing %s.\n", sfilename);
+ }
+ fprintf(outfile, "%ld 1\n", subsegs->items);
+ subsegs->traversalinit();
+ edgeloop.sh = shellfacetraverse(subsegs);
+ edgenumber = firstindex; // in->firstnumber;
+ while (edgeloop.sh != (shellface *) NULL) {
+ torg = sorg(edgeloop);
+ tdest = sdest(edgeloop);
+ fprintf(outfile, "%5d %4d %4d %d\n", edgenumber,
+ pointmark(torg) - shift, pointmark(tdest) - shift,
+ shellmark(edgeloop));
+ edgenumber++;
+ edgeloop.sh = shellfacetraverse(subsegs);
+ }
+ fclose(outfile);
+}
+
+void tetgenmesh::outmesh2medit(const char* mfilename)
+{
+ FILE *outfile;
+ char mefilename[256];
+ tetrahedron* tetptr;
+ triface tface, tsymface;
+ face segloop, checkmark;
+ point ptloop, p1, p2, p3, p4;
+ long ntets, faces;
+ int shift = 0;
+ int marker;
+
+ if (mfilename != (char *) NULL && mfilename[0] != '\0') {
+ strcpy(mefilename, mfilename);
+ } else {
+ strcpy(mefilename, "unnamed");
+ }
+ strcat(mefilename, ".mesh");
+
+ if (!b->quiet) {
+ printf("Writing %s.\n", mefilename);
+ }
+ outfile = fopen(mefilename, "w");
+ if (outfile == (FILE *) NULL) {
+ printf("File I/O Error: Cannot create file %s.\n", mefilename);
+ return;
+ }
+
+ fprintf(outfile, "MeshVersionFormatted 1\n");
+ fprintf(outfile, "\n");
+ fprintf(outfile, "Dimension\n");
+ fprintf(outfile, "3\n");
+ fprintf(outfile, "\n");
+
+ fprintf(outfile, "\n# Set of mesh vertices\n");
+ fprintf(outfile, "Vertices\n");
+ fprintf(outfile, "%ld\n", points->items);
+
+ points->traversalinit();
+ ptloop = pointtraverse();
+ //pointnumber = 1;
+ while (ptloop != (point) NULL) {
+ // Point coordinates.
+ fprintf(outfile, "%.17g %.17g %.17g", ptloop[0], ptloop[1], ptloop[2]);
+ fprintf(outfile, " 0\n");
+ //setpointmark(ptloop, pointnumber);
+ ptloop = pointtraverse();
+ //pointnumber++;
+ }
+
+ // Medit need start number form 1.
+ if (in->firstnumber == 1) {
+ shift = 0;
+ } else {
+ shift = 1;
+ }
+
+ // Compute the number of faces.
+ ntets = tetrahedrons->items - hullsize;
+ faces = (ntets * 4l + hullsize) / 2l;
+
+ /*
+ fprintf(outfile, "\n# Set of Triangles\n");
+ fprintf(outfile, "Triangles\n");
+ fprintf(outfile, "%ld\n", faces);
+
+ tetrahedrons->traversalinit();
+ tface.tet = tetrahedrontraverse();
+ while (tface.tet != (tetrahedron *) NULL) {
+ for (tface.ver = 0; tface.ver < 4; tface.ver ++) {
+ fsym(tface, tsymface);
+ if (ishulltet(tsymface) ||
+ (elemindex(tface.tet) < elemindex(tsymface.tet))) {
+ p1 = org (tface);
+ p2 = dest(tface);
+ p3 = apex(tface);
+ fprintf(outfile, "%5d %5d %5d",
+ pointmark(p1)+shift, pointmark(p2)+shift, pointmark(p3)+shift);
+ // Check if it is a subface.
+ tspivot(tface, checkmark);
+ if (checkmark.sh == NULL) {
+ marker = 0; // It is an inner face. It's marker is 0.
+ } else {
+ marker = 1; // The default marker for subface is 1.
+ }
+ fprintf(outfile, " %d\n", marker);
+ }
+ }
+ tface.tet = tetrahedrontraverse();
+ }
+ */
+
+ fprintf(outfile, "\n# Set of Tetrahedra\n");
+ fprintf(outfile, "Tetrahedra\n");
+ fprintf(outfile, "%ld\n", ntets);
+
+ tetrahedrons->traversalinit();
+ tetptr = tetrahedrontraverse();
+ while (tetptr != (tetrahedron *) NULL) {
+ if (!b->reversetetori) {
+ p1 = (point) tetptr[4];
+ p2 = (point) tetptr[5];
+ } else {
+ p1 = (point) tetptr[5];
+ p2 = (point) tetptr[4];
+ }
+ p3 = (point) tetptr[6];
+ p4 = (point) tetptr[7];
+ fprintf(outfile, "%5d %5d %5d %5d",
+ pointmark(p1)+shift, pointmark(p2)+shift,
+ pointmark(p3)+shift, pointmark(p4)+shift);
+ if (numelemattrib > 0) {
+ fprintf(outfile, " %.17g", elemattribute(tetptr, 0));
+ } else {
+ fprintf(outfile, " 0");
+ }
+ fprintf(outfile, "\n");
+ tetptr = tetrahedrontraverse();
+ }
+
+ fprintf(outfile, "\nEnd\n");
+ fclose(outfile);
+}
+
#endif
diff --git a/Mesh/tetgenBR.cxx b/Mesh/tetgenBR.cxx
new file mode 100644
index 0000000000000000000000000000000000000000..2a756fd206d348ffc80c25818d04ebaf24200b17
--- /dev/null
+++ b/Mesh/tetgenBR.cxx
@@ -0,0 +1,17056 @@
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// 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));
+ }
+
+ 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);
+ } 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);
+ }
+ } 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));
+ } 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);
+ } 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);
+ }
+ } 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);
+ } 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);
+ }
+ } 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));
+ } 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));
+ }
+ } 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);
+ } 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);
+ }
+ 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));
+ } 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));
+ }
+ 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);
+ } 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);
+ }
+ } 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);
+ } 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);
+ }
+ } 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);
+ } 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);
+ } 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;
+ 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--;
+
+ 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;
+}
+
+
diff --git a/Mesh/tetgenBR.h b/Mesh/tetgenBR.h
new file mode 100644
index 0000000000000000000000000000000000000000..849b185805c7aa3ba3b9d4dffd60eb669b89221e
--- /dev/null
+++ b/Mesh/tetgenBR.h
@@ -0,0 +1,2535 @@
+#ifndef tetgenBRH
+#define tetgenBRH
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// tetgenbehavior //
+// //
+// A structure for maintaining the switches and parameters used by TetGen's //
+// mesh data structure and algorithms. //
+// //
+// All switches and parameters are initialized with default values. They can //
+// be set by the command line arguments (a list of strings) of TetGen. //
+// //
+// NOTE: Some of the switches are incompatible. While some may depend on //
+// other switches. The routine parse_commandline() sets the switches from //
+// the command line (a list of strings) and checks the consistency of the //
+// applied switches. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+class tetgenbehavior {
+
+public:
+
+ // Switches of TetGen.
+ int plc; // '-p', 0.
+ int psc; // '-s', 0.
+ int refine; // '-r', 0.
+ int quality; // '-q', 0.
+ int nobisect; // '-Y', 0.
+ int coarsen; // '-R', 0.
+ int weighted; // '-w', 0.
+ int brio_hilbert; // '-b', 1.
+ int incrflip; // '-l', 0.
+ int flipinsert; // '-L', 0.
+ int metric; // '-m', 0.
+ int varvolume; // '-a', 0.
+ int fixedvolume; // '-a', 0.
+ int regionattrib; // '-A', 0.
+ int cdtrefine; // '-D', 0.
+ int insertaddpoints; // '-i', 0.
+ int diagnose; // '-d', 0.
+ int convex; // '-c', 0.
+ int nomergefacet; // '-M', 0.
+ int nomergevertex; // '-M', 0.
+ int noexact; // '-X', 0.
+ int nostaticfilter; // '-X', 0.
+ int zeroindex; // '-z', 0.
+ int facesout; // '-f', 0.
+ int edgesout; // '-e', 0.
+ int neighout; // '-n', 0.
+ int voroout; // '-v', 0.
+ int meditview; // '-g', 0.
+ int vtkview; // '-k', 0.
+ int nobound; // '-B', 0.
+ int nonodewritten; // '-N', 0.
+ int noelewritten; // '-E', 0.
+ int nofacewritten; // '-F', 0.
+ int noiterationnum; // '-I', 0.
+ int nojettison; // '-J', 0.
+ int docheck; // '-C', 0.
+ int quiet; // '-Q', 0.
+ int verbose; // '-V', 0.
+
+ // Parameters of TetGen.
+ int vertexperblock; // '-x', 4092.
+ int tetrahedraperblock; // '-x', 8188.
+ int shellfaceperblock; // '-x', 2044.
+ int nobisect_nomerge; // '-Y', 1.
+ int supsteiner_level; // '-Y/', 2.
+ int addsteiner_algo; // '-Y//', 1.
+ int coarsen_param; // '-R', 0.
+ int weighted_param; // '-w', 0.
+ int fliplinklevel; // -1.
+ int flipstarsize; // -1.
+ int fliplinklevelinc; // 1.
+ int reflevel; // '-D', 3.
+ int optlevel; // '-O', 2.
+ int optscheme; // '-O', 7.
+ int delmaxfliplevel; // 1.
+ int order; // '-o', 1.
+ int reversetetori; // '-o/', 0.
+ int steinerleft; // '-S', 0.
+ int no_sort; // 0.
+ int hilbert_order; // '-b///', 52.
+ int hilbert_limit; // '-b//' 8.
+ int brio_threshold; // '-b' 64.
+ REAL brio_ratio; // '-b/' 0.125.
+ REAL facet_separate_ang_tol; // '-p', 179.9.
+ REAL facet_overlap_ang_tol; // '-p/', 0.1.
+ REAL facet_small_ang_tol; // '-p//', 15.0.
+ REAL maxvolume; // '-a', -1.0.
+ REAL minratio; // '-q', 0.0.
+ REAL mindihedral; // '-q', 5.0.
+ REAL optmaxdihedral; // 165.0.
+ REAL optminsmtdihed; // 179.0.
+ REAL optminslidihed; // 179.0.
+ REAL epsilon; // '-T', 1.0e-8.
+ REAL coarsen_percent; // -R1/#, 1.0.
+
+ // Strings of command line arguments and input/output file names.
+ char commandline[1024];
+ char infilename[1024];
+ char outfilename[1024];
+ char addinfilename[1024];
+ char bgmeshfilename[1024];
+
+ // The input object of TetGen. They are recognized by either the input
+ // file extensions or by the specified options.
+ // Currently the following objects are supported:
+ // - NODES, a list of nodes (.node);
+ // - POLY, a piecewise linear complex (.poly or .smesh);
+ // - OFF, a polyhedron (.off, Geomview's file format);
+ // - PLY, a polyhedron (.ply, file format from gatech, only ASCII);
+ // - STL, a surface mesh (.stl, stereolithography format);
+ // - MEDIT, a surface mesh (.mesh, Medit's file format);
+ // - MESH, a tetrahedral mesh (.ele).
+ // If no extension is available, the imposed command line switch
+ // (-p or -r) implies the object.
+ enum objecttype {NODES, POLY, OFF, PLY, STL, MEDIT, VTK, MESH} object;
+
+
+ void syntax();
+ void usage();
+
+ // Command line parse routine.
+ bool parse_commandline(int argc, char **argv);
+ bool parse_commandline(char *switches) {
+ return parse_commandline(0, &switches);
+ }
+
+ // Initialize all variables.
+ tetgenbehavior()
+ {
+ plc = 0;
+ psc = 0;
+ refine = 0;
+ quality = 0;
+ nobisect = 0;
+ coarsen = 0;
+ metric = 0;
+ weighted = 0;
+ brio_hilbert = 1;
+ incrflip = 0;
+ flipinsert = 0;
+ varvolume = 0;
+ fixedvolume = 0;
+ noexact = 0;
+ nostaticfilter = 0;
+ insertaddpoints = 0;
+ regionattrib = 0;
+ cdtrefine = 0;
+ diagnose = 0;
+ convex = 0;
+ zeroindex = 0;
+ facesout = 0;
+ edgesout = 0;
+ neighout = 0;
+ voroout = 0;
+ meditview = 0;
+ vtkview = 0;
+ nobound = 0;
+ nonodewritten = 0;
+ noelewritten = 0;
+ nofacewritten = 0;
+ noiterationnum = 0;
+ nomergefacet = 0;
+ nomergevertex = 0;
+ nojettison = 0;
+ docheck = 0;
+ quiet = 0;
+ verbose = 0;
+
+ vertexperblock = 4092;
+ tetrahedraperblock = 8188;
+ shellfaceperblock = 4092;
+ nobisect_nomerge = 1;
+ supsteiner_level = 2;
+ addsteiner_algo = 1;
+ coarsen_param = 0;
+ weighted_param = 0;
+ fliplinklevel = -1;
+ flipstarsize = -1;
+ fliplinklevelinc = 1;
+ reflevel = 3;
+ optscheme = 7;
+ optlevel = 2;
+ delmaxfliplevel = 1;
+ order = 1;
+ reversetetori = 0;
+ steinerleft = -1;
+ no_sort = 0;
+ hilbert_order = 52; //-1;
+ hilbert_limit = 8;
+ brio_threshold = 64;
+ brio_ratio = 0.125;
+ facet_separate_ang_tol = 179.9;
+ facet_overlap_ang_tol = 0.1;
+ facet_small_ang_tol = 15.0;
+ maxvolume = -1.0;
+ minratio = 2.0;
+ mindihedral = 0.0;
+ optmaxdihedral = 165.00;
+ optminsmtdihed = 179.00;
+ optminslidihed = 179.00;
+ epsilon = 1.0e-8;
+ coarsen_percent = 1.0;
+ object = NODES;
+
+ commandline[0] = '\0';
+ infilename[0] = '\0';
+ outfilename[0] = '\0';
+ addinfilename[0] = '\0';
+ bgmeshfilename[0] = '\0';
+
+ }
+
+}; // class tetgenbehavior
+
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// tetgenmesh //
+// //
+// A structure for creating and updating tetrahedral meshes. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+class tetgenmesh {
+
+public:
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Mesh data structure //
+// //
+// A tetrahedral mesh T of a 3D piecewise linear complex (PLC) X is a 3D //
+// simplicial complex whose underlying space is equal to the space of X. T //
+// contains a 2D subcomplex S which is a triangular mesh of the boundary of //
+// X. S contains a 1D subcomplex L which is a linear mesh of the boundary of //
+// S. Faces and edges in S and L are respectively called subfaces and segme- //
+// nts to distinguish them from others in T. //
+// //
+// TetGen stores the tetrahedra and vertices of T. The basic structure of a //
+// tetrahedron contains pointers to its vertices and adjacent tetrahedra. A //
+// vertex stores its x-, y-, and z-coordinates, and a pointer to a tetrahed- //
+// ron containing it. Both tetrahedra and vertices may contain user data. //
+// //
+// Each face of T belongs to either two tetrahedra or one tetrahedron. In //
+// the latter case, the face is an exterior boundary face of T. TetGen adds //
+// fictitious tetrahedra (one-to-one) at such faces, and connects them to an //
+// "infinite vertex" (which has no geometric coordinates). One can imagine //
+// such a vertex lies in 4D space and is visible by all exterior boundary //
+// faces. The extended set of tetrahedra (including the infinite vertex) is //
+// a tetrahedralization of a 3-pseudomanifold without boundary. It has the //
+// property that every face is shared by exactly two tetrahedra. //
+// //
+// The current version of TetGen stores explicitly the subfaces and segments //
+// (which are in surface mesh S and the linear mesh L), respectively. Extra //
+// pointers are allocated in tetrahedra and subfaces to point each others. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ // The tetrahedron data structure. It includes the following fields:
+ // - a list of four adjoining tetrahedra;
+ // - a list of four vertices;
+ // - a pointer to a list of four subfaces (optional, for -p switch);
+ // - a pointer to a list of six segments (optional, for -p switch);
+ // - a list of user-defined floating-point attributes (optional);
+ // - a volume constraint (optional, for -a switch);
+ // - an integer of element marker (and flags);
+ // The structure of a tetrahedron is an array of pointers. Its actual size
+ // (the length of the array) is determined at runtime.
+
+ typedef REAL **tetrahedron;
+
+ // The subface data structure. It includes the following fields:
+ // - a list of three adjoining subfaces;
+ // - a list of three vertices;
+ // - a list of three adjoining segments;
+ // - two adjoining tetrahedra;
+ // - an area constraint (optional, for -q switch);
+ // - an integer for boundary marker;
+ // - an integer for type, flags, etc.
+
+ typedef REAL **shellface;
+
+ // The point data structure. It includes the following fields:
+ // - x, y and z coordinates;
+ // - a list of user-defined point attributes (optional);
+ // - u, v coordinates (optional, for -s switch);
+ // - a metric tensor (optional, for -q or -m switch);
+ // - a pointer to an adjacent tetrahedron;
+ // - a pointer to a parent (or a duplicate) point;
+ // - a pointer to an adjacent subface or segment (optional, -p switch);
+ // - a pointer to a tet in background mesh (optional, for -m switch);
+ // - an integer for boundary marker (point index);
+ // - an integer for point type (and flags).
+ // - an integer for geometry tag (optional, for -s switch).
+ // The structure of a point is an array of REALs. Its acutal size is
+ // determined at the runtime.
+
+ typedef REAL *point;
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Handles //
+// //
+// Navigation and manipulation in a tetrahedralization are accomplished by //
+// operating on structures referred as ``handles". A handle is a pair (t,v), //
+// where t is a pointer to a tetrahedron, and v is a 4-bit integer, in the //
+// range from 0 to 11. v is called the ``version'' of a tetrahedron, it rep- //
+// resents a directed edge of a specific face of the tetrahedron. //
+// //
+// There are 12 even permutations of the four vertices, each of them corres- //
+// ponds to a directed edge (a version) of the tetrahedron. The 12 versions //
+// can be grouped into 4 distinct ``edge rings'' in 4 ``oriented faces'' of //
+// this tetrahedron. One can encode each version (a directed edge) into a //
+// 4-bit integer such that the two upper bits encode the index (from 0 to 2) //
+// of this edge in the edge ring, and the two lower bits encode the index ( //
+// from 0 to 3) of the oriented face which contains this edge. //
+// //
+// The four vertices of a tetrahedron are indexed from 0 to 3 (according to //
+// their storage in the data structure). Give each face the same index as //
+// the node opposite it in the tetrahedron. Denote the edge connecting face //
+// i to face j as i/j. We number the twelve versions as follows: //
+// //
+// | edge 0 edge 1 edge 2 //
+// --------|-------------------------------- //
+// face 0 | 0 (0/1) 4 (0/3) 8 (0/2) //
+// face 1 | 1 (1/2) 5 (1/3) 9 (1/0) //
+// face 2 | 2 (2/3) 6 (2/1) 10 (2/0) //
+// face 3 | 3 (3/0) 7 (3/1) 11 (3/2) //
+// //
+// Similarly, navigation and manipulation in a (boundary) triangulation are //
+// done by using handles of triangles. Each handle is a pair (s, v), where s //
+// is a pointer to a triangle, and v is a version in the range from 0 to 5. //
+// Each version corresponds to a directed edge of this triangle. //
+// //
+// Number the three vertices of a triangle from 0 to 2 (according to their //
+// storage in the data structure). Give each edge the same index as the node //
+// opposite it in the triangle. The six versions of a triangle are: //
+// //
+// | edge 0 edge 1 edge 2 //
+// ---------------|-------------------------- //
+// ccw orieation | 0 2 4 //
+// cw orieation | 1 3 5 //
+// //
+// In the following, a 'triface' is a handle of tetrahedron, and a 'face' is //
+// a handle of a triangle. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class triface {
+ public:
+ tetrahedron *tet;
+ int ver; // Range from 0 to 11.
+ triface() : tet(0), ver(0) {}
+ triface& operator=(const triface& t) {
+ tet = t.tet; ver = t.ver;
+ return *this;
+ }
+ };
+
+ class face {
+ public:
+ shellface *sh;
+ int shver; // Range from 0 to 5.
+ face() : sh(0), shver(0) {}
+ face& operator=(const face& s) {
+ sh = s.sh; shver = s.shver;
+ return *this;
+ }
+ };
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Arraypool //
+// //
+// A dynamic linear array. (It is written by J. Shewchuk) //
+// //
+// Each arraypool contains an array of pointers to a number of blocks. Each //
+// block contains the same fixed number of objects. Each index of the array //
+// addresses a particular object in the pool. The most significant bits add- //
+// ress the index of the block containing the object. The less significant //
+// bits address this object within the block. //
+// //
+// 'objectbytes' is the size of one object in blocks; 'log2objectsperblock' //
+// is the base-2 logarithm of 'objectsperblock'; 'objects' counts the number //
+// of allocated objects; 'totalmemory' is the total memory in bytes. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class arraypool {
+
+ public:
+
+ int objectbytes;
+ int objectsperblock;
+ int log2objectsperblock;
+ int objectsperblockmark;
+ int toparraylen;
+ char **toparray;
+ long objects;
+ unsigned long totalmemory;
+
+ void restart();
+ void poolinit(int sizeofobject, int log2objperblk);
+ char* getblock(int objectindex);
+ void* lookup(int objectindex);
+ int newindex(void **newptr);
+
+ arraypool(int sizeofobject, int log2objperblk);
+ ~arraypool();
+ };
+
+// fastlookup() -- A fast, unsafe operation. Return the pointer to the object
+// with a given index. Note: The object's block must have been allocated,
+// i.e., by the function newindex().
+
+#define fastlookup(pool, index) \
+ (void *) ((pool)->toparray[(index) >> (pool)->log2objectsperblock] + \
+ ((index) & (pool)->objectsperblockmark) * (pool)->objectbytes)
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Memorypool //
+// //
+// A structure for memory allocation. (It is written by J. Shewchuk) //
+// //
+// firstblock is the first block of items. nowblock is the block from which //
+// items are currently being allocated. nextitem points to the next slab //
+// of free memory for an item. deaditemstack is the head of a linked list //
+// (stack) of deallocated items that can be recycled. unallocateditems is //
+// the number of items that remain to be allocated from nowblock. //
+// //
+// Traversal is the process of walking through the entire list of items, and //
+// is separate from allocation. Note that a traversal will visit items on //
+// the "deaditemstack" stack as well as live items. pathblock points to //
+// the block currently being traversed. pathitem points to the next item //
+// to be traversed. pathitemsleft is the number of items that remain to //
+// be traversed in pathblock. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class memorypool {
+
+ public:
+
+ void **firstblock, **nowblock;
+ void *nextitem;
+ void *deaditemstack;
+ void **pathblock;
+ void *pathitem;
+ int alignbytes;
+ int itembytes, itemwords;
+ int itemsperblock;
+ long items, maxitems;
+ int unallocateditems;
+ int pathitemsleft;
+
+ memorypool();
+ memorypool(int, int, int, int);
+ ~memorypool();
+
+ void poolinit(int, int, int, int);
+ void restart();
+ void *alloc();
+ void dealloc(void*);
+ void traversalinit();
+ void *traverse();
+ };
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// badface //
+// //
+// Despite of its name, a 'badface' can be used to represent one of the //
+// following objects: //
+// - a face of a tetrahedron which is (possibly) non-Delaunay; //
+// - an encroached subsegment or subface; //
+// - a bad-quality tetrahedron, i.e, has too large radius-edge ratio; //
+// - a sliver, i.e., has good radius-edge ratio but nearly zero volume; //
+// - a recently flipped face (saved for undoing the flip later). //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class badface {
+ public:
+ triface tt;
+ face ss;
+ REAL key, cent[6]; // circumcenter or cos(dihedral angles) at 6 edges.
+ point forg, fdest, fapex, foppo, noppo;
+ badface *nextitem;
+ badface() : key(0), forg(0), fdest(0), fapex(0), foppo(0), noppo(0),
+ nextitem(0) {}
+ };
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// insertvertexflags //
+// //
+// A collection of flags that pass to the routine insertvertex(). //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class insertvertexflags {
+
+ public:
+
+ int iloc; // input/output.
+ int bowywat, lawson;
+ int splitbdflag, validflag, respectbdflag;
+ int rejflag, chkencflag, cdtflag;
+ int assignmeshsize;
+ int sloc, sbowywat;
+
+ // Used by Delaunay refinement.
+ int refineflag; // 0, 1, 2, 3
+ triface refinetet;
+ face refinesh;
+ int smlenflag; // for useinsertradius.
+ REAL smlen; // for useinsertradius.
+ point parentpt;
+
+ insertvertexflags() {
+ iloc = bowywat = lawson = 0;
+ splitbdflag = validflag = respectbdflag = 0;
+ rejflag = chkencflag = cdtflag = 0;
+ assignmeshsize = 0;
+ sloc = sbowywat = 0;
+
+ refineflag = 0;
+ refinetet.tet = NULL;
+ refinesh.sh = NULL;
+ smlenflag = 0;
+ smlen = 0.0;
+ }
+ };
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// flipconstraints //
+// //
+// A structure of a collection of data (options and parameters) which pass //
+// to the edge flip function flipnm(). //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class flipconstraints {
+
+ public:
+
+ // Elementary flip flags.
+ int enqflag; // (= flipflag)
+ int chkencflag;
+
+ // Control flags
+ int unflip; // Undo the performed flips.
+ int collectnewtets; // Collect the new tets created by flips.
+ int collectencsegflag;
+
+ // Optimization flags.
+ int remove_ndelaunay_edge; // Remove a non-Delaunay edge.
+ REAL bak_tetprism_vol; // The value to be minimized.
+ REAL tetprism_vol_sum;
+ int remove_large_angle; // Remove a large dihedral angle at edge.
+ REAL cosdihed_in; // The input cosine of the dihedral angle (> 0).
+ REAL cosdihed_out; // The improved cosine of the dihedral angle.
+
+ // Boundary recovery flags.
+ int checkflipeligibility;
+ point seg[2]; // A constraining edge to be recovered.
+ point fac[3]; // A constraining face to be recovered.
+ point remvert; // A vertex to be removed.
+
+
+ flipconstraints() {
+ enqflag = 0;
+ chkencflag = 0;
+
+ unflip = 0;
+ collectnewtets = 0;
+ collectencsegflag = 0;
+
+ remove_ndelaunay_edge = 0;
+ bak_tetprism_vol = 0.0;
+ tetprism_vol_sum = 0.0;
+ remove_large_angle = 0;
+ cosdihed_in = 0.0;
+ cosdihed_out = 0.0;
+
+ checkflipeligibility = 0;
+ seg[0] = NULL;
+ fac[0] = NULL;
+ remvert = NULL;
+ }
+ };
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// optparameters //
+// //
+// Optimization options and parameters. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ class optparameters {
+
+ public:
+
+ // The one of goals of optimization.
+ int max_min_volume; // Maximize the minimum volume.
+ int min_max_aspectratio; // Minimize the maximum aspect ratio.
+ int min_max_dihedangle; // Minimize the maximum dihedral angle.
+
+ // The initial and improved value.
+ REAL initval, imprval;
+
+ int numofsearchdirs;
+ REAL searchstep;
+ int maxiter; // Maximum smoothing iterations (disabled by -1).
+ int smthiter; // Performed iterations.
+
+
+ optparameters() {
+ max_min_volume = 0;
+ min_max_aspectratio = 0;
+ min_max_dihedangle = 0;
+
+ initval = imprval = 0.0;
+
+ numofsearchdirs = 10;
+ searchstep = 0.01;
+ maxiter = -1; // Unlimited smoothing iterations.
+ smthiter = 0;
+
+ }
+ };
+
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Labels (enumeration declarations) used by TetGen. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ // Labels that signify the type of a vertex.
+ enum verttype {UNUSEDVERTEX, DUPLICATEDVERTEX, RIDGEVERTEX, ACUTEVERTEX,
+ FACETVERTEX, VOLVERTEX, FREESEGVERTEX, FREEFACETVERTEX,
+ FREEVOLVERTEX, NREGULARVERTEX, DEADVERTEX};
+
+ // Labels that signify the result of triangle-triangle intersection test.
+ enum interresult {DISJOINT, INTERSECT, SHAREVERT, SHAREEDGE, SHAREFACE,
+ TOUCHEDGE, TOUCHFACE, ACROSSVERT, ACROSSEDGE, ACROSSFACE};
+
+ // Labels that signify the result of point location.
+ enum locateresult {UNKNOWN, OUTSIDE, INTETRAHEDRON, ONFACE, ONEDGE, ONVERTEX,
+ ENCVERTEX, ENCSEGMENT, ENCSUBFACE, NEARVERTEX, NONREGULAR,
+ INSTAR, BADELEMENT};
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Variables of TetGen //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ // Pointer to the input data (a set of nodes, a PLC, or a mesh).
+ tetgenio *in, *addin;
+
+ // Pointer to the switches and parameters.
+ tetgenbehavior *b;
+
+ // Pointer to a background mesh (contains size specification map).
+ tetgenmesh *bgm;
+
+ // Memorypools to store mesh elements (points, tetrahedra, subfaces, and
+ // segments) and extra pointers between tetrahedra, subfaces, and segments.
+ memorypool *tetrahedrons, *subfaces, *subsegs, *points;
+ memorypool *tet2subpool, *tet2segpool;
+
+ // Memorypools to store bad-quality (or encroached) elements.
+ memorypool *badtetrahedrons, *badsubfacs, *badsubsegs;
+
+ // A memorypool to store faces to be flipped.
+ memorypool *flippool;
+ arraypool *unflipqueue;
+ badface *flipstack;
+
+ // Arrays used for point insertion (the Bowyer-Watson algorithm).
+ arraypool *cavetetlist, *cavebdrylist, *caveoldtetlist;
+ arraypool *cavetetshlist, *cavetetseglist, *cavetetvertlist;
+ arraypool *caveencshlist, *caveencseglist;
+ arraypool *caveshlist, *caveshbdlist, *cavesegshlist;
+
+ // Stacks used for CDT construction and boundary recovery.
+ arraypool *subsegstack, *subfacstack, *subvertstack;
+
+ // Arrays of encroached segments and subfaces (for mesh refinement).
+ arraypool *encseglist, *encshlist;
+
+ // The map between facets to their vertices (for mesh refinement).
+ int *idx2facetlist;
+ point *facetverticeslist;
+
+ // The map between segments to their endpoints (for mesh refinement).
+ point *segmentendpointslist;
+
+ // The infinite vertex.
+ point dummypoint;
+ // The recently visited tetrahedron, subface.
+ triface recenttet;
+ face recentsh;
+
+ // PI is the ratio of a circle's circumference to its diameter.
+ static REAL PI;
+
+ // Array (size = numberoftetrahedra * 6) for storing high-order nodes of
+ // tetrahedra (only used when -o2 switch is selected).
+ point *highordertable;
+
+ // Various variables.
+ int numpointattrib; // Number of point attributes.
+ int numelemattrib; // Number of tetrahedron attributes.
+ int sizeoftensor; // Number of REALs per metric tensor.
+ int pointmtrindex; // Index to find the metric tensor of a point.
+ int pointparamindex; // Index to find the u,v coordinates of a point.
+ int point2simindex; // Index to find a simplex adjacent to a point.
+ int pointmarkindex; // Index to find boundary marker of a point.
+ int pointinsradiusindex; // Index to find the insertion radius of a point.
+ int elemattribindex; // Index to find attributes of a tetrahedron.
+ int volumeboundindex; // Index to find volume bound of a tetrahedron.
+ int elemmarkerindex; // Index to find marker of a tetrahedron.
+ int shmarkindex; // Index to find boundary marker of a subface.
+ int areaboundindex; // Index to find area bound of a subface.
+ int checksubsegflag; // Are there segments in the tetrahedralization yet?
+ int checksubfaceflag; // Are there subfaces in the tetrahedralization yet?
+ int checkconstraints; // Are there variant (node, seg, facet) constraints?
+ int nonconvex; // Is current mesh non-convex?
+ int autofliplinklevel; // The increase of link levels, default is 1.
+ int useinsertradius; // Save the insertion radius for Steiner points.
+ long samples; // Number of random samples for point location.
+ unsigned long randomseed; // Current random number seed.
+ REAL cosmaxdihed, cosmindihed; // The cosine values of max/min dihedral.
+ REAL cossmtdihed; // The cosine value of a bad dihedral to be smoothed.
+ REAL cosslidihed; // The cosine value of the max dihedral of a sliver.
+ REAL minfaceang, minfacetdihed; // The minimum input (dihedral) angles.
+ REAL tetprism_vol_sum; // The total volume of tetrahedral-prisms (in 4D).
+ REAL longest; // The longest possible edge length.
+ REAL minedgelength; // = longest * b->epsion.
+ REAL xmax, xmin, ymax, ymin, zmax, zmin; // Bounding box of points.
+
+ // Counters.
+ long insegments; // Number of input segments.
+ long hullsize; // Number of exterior boundary faces.
+ long meshedges; // Number of mesh edges.
+ long meshhulledges; // Number of boundary mesh edges.
+ long steinerleft; // Number of Steiner points not yet used.
+ long dupverts; // Are there duplicated vertices?
+ long unuverts; // Are there unused vertices?
+ long nonregularcount; // Are there non-regular vertices?
+ long st_segref_count, st_facref_count, st_volref_count; // Steiner points.
+ long fillregioncount, cavitycount, cavityexpcount;
+ long flip14count, flip26count, flipn2ncount;
+ long flip23count, flip32count, flip44count, flip41count;
+ long flip31count, flip22count;
+ unsigned long totalworkmemory; // Total memory used by working arrays.
+
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Mesh manipulation primitives //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ // Fast lookup tables for mesh manipulation primitives.
+ static int bondtbl[12][12], fsymtbl[12][12];
+ static int esymtbl[12], enexttbl[12], eprevtbl[12];
+ static int enextesymtbl[12], eprevesymtbl[12];
+ static int eorgoppotbl[12], edestoppotbl[12];
+ static int facepivot1[12], facepivot2[12][12];
+ static int orgpivot[12], destpivot[12], apexpivot[12], oppopivot[12];
+ static int tsbondtbl[12][6], stbondtbl[12][6];
+ static int tspivottbl[12][6], stpivottbl[12][6];
+ static int ver2edge[12], edge2ver[6], epivot[12];
+ static int sorgpivot [6], sdestpivot[6], sapexpivot[6];
+ static int snextpivot[6];
+
+ void inittables();
+
+ // Primitives for tetrahedra.
+ inline tetrahedron encode(triface& t);
+ inline tetrahedron encode2(tetrahedron* ptr, int ver);
+ inline void decode(tetrahedron ptr, triface& t);
+ inline void bond(triface& t1, triface& t2);
+ inline void dissolve(triface& t);
+ inline void esym(triface& t1, triface& t2);
+ inline void esymself(triface& t);
+ inline void enext(triface& t1, triface& t2);
+ inline void enextself(triface& t);
+ inline void eprev(triface& t1, triface& t2);
+ inline void eprevself(triface& t);
+ inline void enextesym(triface& t1, triface& t2);
+ inline void enextesymself(triface& t);
+ inline void eprevesym(triface& t1, triface& t2);
+ inline void eprevesymself(triface& t);
+ inline void eorgoppo(triface& t1, triface& t2);
+ inline void eorgoppoself(triface& t);
+ inline void edestoppo(triface& t1, triface& t2);
+ inline void edestoppoself(triface& t);
+ inline void fsym(triface& t1, triface& t2);
+ inline void fsymself(triface& t);
+ inline void fnext(triface& t1, triface& t2);
+ inline void fnextself(triface& t);
+ inline point org (triface& t);
+ inline point dest(triface& t);
+ inline point apex(triface& t);
+ inline point oppo(triface& t);
+ inline void setorg (triface& t, point p);
+ inline void setdest(triface& t, point p);
+ inline void setapex(triface& t, point p);
+ inline void setoppo(triface& t, point p);
+ inline REAL elemattribute(tetrahedron* ptr, int attnum);
+ inline void setelemattribute(tetrahedron* ptr, int attnum, REAL value);
+ inline REAL volumebound(tetrahedron* ptr);
+ inline void setvolumebound(tetrahedron* ptr, REAL value);
+ inline int elemindex(tetrahedron* ptr);
+ inline void setelemindex(tetrahedron* ptr, int value);
+ inline int elemmarker(tetrahedron* ptr);
+ inline void setelemmarker(tetrahedron* ptr, int value);
+ inline void infect(triface& t);
+ inline void uninfect(triface& t);
+ inline bool infected(triface& t);
+ inline void marktest(triface& t);
+ inline void unmarktest(triface& t);
+ inline bool marktested(triface& t);
+ inline void markface(triface& t);
+ inline void unmarkface(triface& t);
+ inline bool facemarked(triface& t);
+ inline void markedge(triface& t);
+ inline void unmarkedge(triface& t);
+ inline bool edgemarked(triface& t);
+ inline void marktest2(triface& t);
+ inline void unmarktest2(triface& t);
+ inline bool marktest2ed(triface& t);
+ inline int elemcounter(triface& t);
+ inline void setelemcounter(triface& t, int value);
+ inline void increaseelemcounter(triface& t);
+ inline void decreaseelemcounter(triface& t);
+ inline bool ishulltet(triface& t);
+ inline bool isdeadtet(triface& t);
+
+ // Primitives for subfaces and subsegments.
+ inline void sdecode(shellface sptr, face& s);
+ inline shellface sencode(face& s);
+ inline shellface sencode2(shellface *sh, int shver);
+ inline void spivot(face& s1, face& s2);
+ inline void spivotself(face& s);
+ inline void sbond(face& s1, face& s2);
+ inline void sbond1(face& s1, face& s2);
+ inline void sdissolve(face& s);
+ inline point sorg(face& s);
+ inline point sdest(face& s);
+ inline point sapex(face& s);
+ inline void setsorg(face& s, point pointptr);
+ inline void setsdest(face& s, point pointptr);
+ inline void setsapex(face& s, point pointptr);
+ inline void sesym(face& s1, face& s2);
+ inline void sesymself(face& s);
+ inline void senext(face& s1, face& s2);
+ inline void senextself(face& s);
+ inline void senext2(face& s1, face& s2);
+ inline void senext2self(face& s);
+ inline REAL areabound(face& s);
+ inline void setareabound(face& s, REAL value);
+ inline int shellmark(face& s);
+ inline void setshellmark(face& s, int value);
+ inline void sinfect(face& s);
+ inline void suninfect(face& s);
+ inline bool sinfected(face& s);
+ inline void smarktest(face& s);
+ inline void sunmarktest(face& s);
+ inline bool smarktested(face& s);
+ inline void smarktest2(face& s);
+ inline void sunmarktest2(face& s);
+ inline bool smarktest2ed(face& s);
+ inline void smarktest3(face& s);
+ inline void sunmarktest3(face& s);
+ inline bool smarktest3ed(face& s);
+ inline void setfacetindex(face& f, int value);
+ inline int getfacetindex(face& f);
+
+ // Primitives for interacting tetrahedra and subfaces.
+ inline void tsbond(triface& t, face& s);
+ inline void tsdissolve(triface& t);
+ inline void stdissolve(face& s);
+ inline void tspivot(triface& t, face& s);
+ inline void stpivot(face& s, triface& t);
+
+ // Primitives for interacting tetrahedra and segments.
+ inline void tssbond1(triface& t, face& seg);
+ inline void sstbond1(face& s, triface& t);
+ inline void tssdissolve1(triface& t);
+ inline void sstdissolve1(face& s);
+ inline void tsspivot1(triface& t, face& s);
+ inline void sstpivot1(face& s, triface& t);
+
+ // Primitives for interacting subfaces and segments.
+ inline void ssbond(face& s, face& edge);
+ inline void ssbond1(face& s, face& edge);
+ inline void ssdissolve(face& s);
+ inline void sspivot(face& s, face& edge);
+
+ // Primitives for points.
+ inline int pointmark(point pt);
+ inline void setpointmark(point pt, int value);
+ inline enum verttype pointtype(point pt);
+ inline void setpointtype(point pt, enum verttype value);
+ inline int pointgeomtag(point pt);
+ inline void setpointgeomtag(point pt, int value);
+ inline REAL pointgeomuv(point pt, int i);
+ inline void setpointgeomuv(point pt, int i, REAL value);
+ inline void pinfect(point pt);
+ inline void puninfect(point pt);
+ inline bool pinfected(point pt);
+ inline void pmarktest(point pt);
+ inline void punmarktest(point pt);
+ inline bool pmarktested(point pt);
+ inline void pmarktest2(point pt);
+ inline void punmarktest2(point pt);
+ inline bool pmarktest2ed(point pt);
+ inline void pmarktest3(point pt);
+ inline void punmarktest3(point pt);
+ inline bool pmarktest3ed(point pt);
+ inline tetrahedron point2tet(point pt);
+ inline void setpoint2tet(point pt, tetrahedron value);
+ inline shellface point2sh(point pt);
+ inline void setpoint2sh(point pt, shellface value);
+ inline point point2ppt(point pt);
+ inline void setpoint2ppt(point pt, point value);
+ inline tetrahedron point2bgmtet(point pt);
+ inline void setpoint2bgmtet(point pt, tetrahedron value);
+ inline void setpointinsradius(point pt, REAL value);
+ inline REAL getpointinsradius(point pt);
+ inline bool issteinerpoint(point pt);
+
+ // Advanced primitives.
+ inline void point2tetorg(point pt, triface& t);
+ inline void point2shorg(point pa, face& s);
+ inline point farsorg(face& seg);
+ inline point farsdest(face& seg);
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Memory managment //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ void tetrahedrondealloc(tetrahedron*);
+ tetrahedron *tetrahedrontraverse();
+ tetrahedron *alltetrahedrontraverse();
+ void shellfacedealloc(memorypool*, shellface*);
+ shellface *shellfacetraverse(memorypool*);
+ void pointdealloc(point);
+ point pointtraverse();
+
+ void makeindex2pointmap(point*&);
+ void makepoint2submap(memorypool*, int*&, face*&);
+ void maketetrahedron(triface*);
+ void makeshellface(memorypool*, face*);
+ void makepoint(point*, enum verttype);
+
+ void initializepools();
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Advanced geometric predicates and calculations //
+// //
+// TetGen uses a simplified symbolic perturbation scheme from Edelsbrunner, //
+// et al [*]. Hence the point-in-sphere test never returns a zero. The idea //
+// is to perturb the weights of vertices in the fourth dimension. TetGen //
+// uses the indices of the vertices decide the amount of perturbation. It is //
+// implemented in the routine insphere_s().
+// //
+// The routine tri_edge_test() determines whether or not a triangle and an //
+// edge intersect in 3D. If they intersect, their intersection type is also //
+// reported. This test is a combination of n 3D orientation tests (n is bet- //
+// ween 3 and 9). It uses the robust orient3d() test to make the branch dec- //
+// isions. The routine tri_tri_test() determines whether or not two triang- //
+// les intersect in 3D. It also uses the robust orient3d() test. //
+// //
+// There are a number of routines to calculate geometrical quantities, e.g., //
+// circumcenters, angles, dihedral angles, face normals, face areas, etc. //
+// They are so far done by the default floating-point arithmetics which are //
+// non-robust. They should be improved in the future. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ // Symbolic perturbations (robust)
+ REAL insphere_s(REAL*, REAL*, REAL*, REAL*, REAL*);
+ REAL orient4d_s(REAL*, REAL*, REAL*, REAL*, REAL*,
+ REAL, REAL, REAL, REAL, REAL);
+
+ // Triangle-edge intersection test (robust)
+ int tri_edge_2d(point, point, point, point, point, point, int, int*, int*);
+ int tri_edge_tail(point, point, point, point, point, point, REAL, REAL, int,
+ int*, int*);
+ int tri_edge_test(point, point, point, point, point, point, int, int*, int*);
+
+ // Triangle-triangle intersection test (robust)
+ int tri_edge_inter_tail(point, point, point, point, point, REAL, REAL);
+ int tri_tri_inter(point, point, point, point, point, point);
+
+ // Linear algebra functions
+ inline REAL dot(REAL* v1, REAL* v2);
+ inline void cross(REAL* v1, REAL* v2, REAL* n);
+ bool lu_decmp(REAL lu[4][4], int n, int* ps, REAL* d, int N);
+ void lu_solve(REAL lu[4][4], int n, int* ps, REAL* b, int N);
+
+ // An embedded 2-dimensional geometric predicate (non-robust)
+ REAL incircle3d(point pa, point pb, point pc, point pd);
+
+ // Geometric calculations (non-robust)
+ REAL orient3dfast(REAL *pa, REAL *pb, REAL *pc, REAL *pd);
+ inline REAL norm2(REAL x, REAL y, REAL z);
+ inline REAL distance(REAL* p1, REAL* p2);
+ void facenormal(point pa, point pb, point pc, REAL *n, int pivot, REAL *lav);
+ REAL shortdistance(REAL* p, REAL* e1, REAL* e2);
+ REAL triarea(REAL* pa, REAL* pb, REAL* pc);
+ REAL interiorangle(REAL* o, REAL* p1, REAL* p2, REAL* n);
+ void projpt2edge(REAL* p, REAL* e1, REAL* e2, REAL* prj);
+ void projpt2face(REAL* p, REAL* f1, REAL* f2, REAL* f3, REAL* prj);
+ bool tetalldihedral(point, point, point, point, REAL*, REAL*, REAL*);
+ void tetallnormal(point, point, point, point, REAL N[4][3], REAL* volume);
+ REAL tetaspectratio(point, point, point, point);
+ bool circumsphere(REAL*, REAL*, REAL*, REAL*, REAL* cent, REAL* radius);
+ bool orthosphere(REAL*,REAL*,REAL*,REAL*,REAL,REAL,REAL,REAL,REAL*,REAL*);
+ void planelineint(REAL*, REAL*, REAL*, REAL*, REAL*, REAL*, REAL*);
+ int linelineint(REAL*, REAL*, REAL*, REAL*, REAL*, REAL*, REAL*, REAL*);
+ REAL tetprismvol(REAL* pa, REAL* pb, REAL* pc, REAL* pd);
+ bool calculateabovepoint(arraypool*, point*, point*, point*);
+ void calculateabovepoint4(point, point, point, point);
+
+ // PLC error reports.
+ void report_overlapping_facets(face*, face*, REAL dihedang = 0.0);
+ int report_selfint_edge(point, point, face* sedge, triface* searchtet,
+ enum interresult);
+ int report_selfint_face(point, point, point, face* sface, triface* iedge,
+ int intflag, int* types, int* poss);
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Local mesh transformations //
+// //
+// A local transformation replaces a small set of tetrahedra with another //
+// set of tetrahedra which fills the same space and the same boundaries. //
+// In 3D, the most simplest local transformations are the elementary flips //
+// performed within the convex hull of five vertices: 2-to-3, 3-to-2, 1-to-4,//
+// and 4-to-1 flips, where the numbers indicate the number of tetrahedra //
+// before and after each flip. The 1-to-4 and 4-to-1 flip involve inserting //
+// or deleting a vertex, respectively. //
+// There are complex local transformations which can be decomposed as a //
+// combination of elementary flips. For example,a 4-to-4 flip which replaces //
+// two coplanar edges can be regarded by a 2-to-3 flip and a 3-to-2 flip. //
+// Note that the first 2-to-3 flip will temporarily create a degenerate tet- //
+// rahedron which is removed immediately by the followed 3-to-2 flip. More //
+// generally, a n-to-m flip, where n > 3, m = (n - 2) * 2, which removes an //
+// edge can be done by first performing a sequence of (n - 3) 2-to-3 flips //
+// followed by a 3-to-2 flip. //
+// //
+// The routines flip23(), flip32(), and flip41() perform the three element- //
+// ray flips. The flip14() is available inside the routine insertpoint(). //
+// //
+// The routines flipnm() and flipnm_post() implement a generalized edge flip //
+// algorithm which uses a combination of elementary flips. //
+// //
+// The routine insertpoint() implements a variant of Bowyer-Watson's cavity //
+// algorithm to insert a vertex. It works for arbitrary tetrahedralization, //
+// either Delaunay, or constrained Delaunay, or non-Delaunay. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ // The elementary flips.
+ void flip23(triface*, int, flipconstraints* fc);
+ void flip32(triface*, int, flipconstraints* fc);
+ void flip41(triface*, int, flipconstraints* fc);
+
+ // A generalized edge flip.
+ int flipnm(triface*, int n, int level, int, flipconstraints* fc);
+ int flipnm_post(triface*, int n, int nn, int, flipconstraints* fc);
+
+ // Point insertion.
+ int insertpoint(point, triface*, face*, face*, insertvertexflags*);
+ void insertpoint_abort(face*, insertvertexflags*);
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Delaunay tetrahedralization //
+// //
+// The routine incrementaldelaunay() implemented two incremental algorithms //
+// for constructing Delaunay tetrahedralizations (DTs): the Bowyer-Watson //
+// (B-W) algorithm and the incremental flip algorithm of Edelsbrunner and //
+// Shah, "Incremental topological flipping works for regular triangulation," //
+// Algorithmica, 15:233-241, 1996. //
+// //
+// The routine incrementalflip() implements the flip algorithm of [Edelsbru- //
+// nner and Shah, 1996]. It flips a queue of locally non-Delaunay faces (in //
+// an arbitrary order). The success is guaranteed when the Delaunay tetrah- //
+// edralization is constructed incrementally by adding one vertex at a time. //
+// //
+// The routine locate() finds a tetrahedron contains a new point in current //
+// DT. It uses a simple stochastic walk algorithm: starting from an arbitr- //
+// ary tetrahedron in DT, it finds the destination by visit one tetrahedron //
+// at a time, randomly chooses a tetrahedron if there are more than one //
+// choices. This algorithm terminates due to Edelsbrunner's acyclic theorem. //
+// Choose a good starting tetrahedron is crucial to the speed of the walk. //
+// TetGen originally uses the "jump-and-walk" algorithm of Muecke, E.P., //
+// Saias, I., and Zhu, B. "Fast Randomized Point Location Without Preproces- //
+// sing." In Proceedings of the 12th ACM Symposium on Computational Geometry,//
+// 274-283, 1996. It first randomly samples several tetrahedra in the DT //
+// and then choosing the closet one to start walking. //
+// The above algorithm slows download dramatically as the number of points //
+// grows -- reported in Amenta, N., Choi, S. and Rote, G., "Incremental //
+// construction con {BRIO}," In Proceedings of 19th ACM Symposium on //
+// Computational Geometry, 211-219, 2003. On the other hand, Liu and //
+// Snoeyink showed that the point location can be made in constant time if //
+// the points are pre-sorted so that the nearby points in space have nearby //
+// indices, then adding the points in this order. They sorted the points //
+// along the 3D Hilbert curve. //
+// //
+// The routine hilbert_sort3() sorts a set of 3D points along the 3D Hilbert //
+// curve. It recursively splits a point set according to the Hilbert indices //
+// mapped to the subboxes of the bounding box of the point set. //
+// The Hilbert indices is calculated by Butz's algorithm in 1971. A nice //
+// exposition of this algorithm can be found in the paper of Hamilton, C., //
+// "Compact Hilbert Indices", Technical Report CS-2006-07, Computer Science, //
+// Dalhousie University, 2006 (the Section 2). My implementation also refer- //
+// enced Steven Witham's implementation of "Hilbert walk" (hopefully, it is //
+// still available at: http://www.tiac.net/~sw/2008/10/Hilbert/). //
+// //
+// TetGen sorts the points using the method in the paper of Boissonnat,J.-D.,//
+// Devillers, O. and Hornus, S. "Incremental Construction of the Delaunay //
+// Triangulation and the Delaunay Graph in Medium Dimension," In Proceedings //
+// of the 25th ACM Symposium on Computational Geometry, 2009. //
+// It first randomly sorts the points into subgroups using the Biased Rand-//
+// omized Insertion Ordering (BRIO) of Amenta et al 2003, then sorts the //
+// points in each subgroup along the 3D Hilbert curve. Inserting points in //
+// this order ensures a randomized "sprinkling" of the points over the //
+// domain, while sorting of each subset ensures locality. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ void transfernodes();
+
+ // Point sorting.
+ int transgc[8][3][8], tsb1mod3[8];
+ void hilbert_init(int n);
+ int hilbert_split(point* vertexarray, int arraysize, int gc0, int gc1,
+ REAL, REAL, REAL, REAL, REAL, REAL);
+ void hilbert_sort3(point* vertexarray, int arraysize, int e, int d,
+ REAL, REAL, REAL, REAL, REAL, REAL, int depth);
+ void brio_multiscale_sort(point*,int,int threshold,REAL ratio,int* depth);
+
+ // Point location.
+ unsigned long randomnation(unsigned int choices);
+ void randomsample(point searchpt, triface *searchtet);
+ enum locateresult locate(point searchpt, triface *searchtet,
+ int chkencflag = 0);
+
+ // Incremental flips.
+ void flippush(badface*&, triface*);
+ int incrementalflip(point newpt, int, flipconstraints *fc);
+
+ // Incremental Delaunay construction.
+ void initialdelaunay(point pa, point pb, point pc, point pd);
+ void incrementaldelaunay(clock_t&);
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Surface triangulation //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ void flipshpush(face*);
+ void flip22(face*, int, int);
+ void flip31(face*, int);
+ long lawsonflip();
+ int sinsertvertex(point newpt, face*, face*, int iloc, int bowywat, int);
+ int sremovevertex(point delpt, face*, face*, int lawson);
+
+ enum locateresult slocate(point, face*, int, int, int);
+ enum interresult sscoutsegment(face*, point, int, int, int);
+ void scarveholes(int, REAL*);
+
+ void unifysegments();
+ void identifyinputedges(point*);
+ void mergefacets();
+
+ enum interresult finddirection(triface* searchtet, point endpt);
+
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Constrained tetrahedralizations. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ int checkflipeligibility(int fliptype, point, point, point, point, point,
+ int level, int edgepivot, flipconstraints* fc);
+
+ int removeedgebyflips(triface*, flipconstraints*);
+ int removefacebyflips(triface*, flipconstraints*);
+
+ int recoveredgebyflips(point, point, face*, triface*, int fullsearch);
+ int add_steinerpt_in_schoenhardtpoly(triface*, int, int chkencflag);
+ int add_steinerpt_in_segment(face*, int searchlevel);
+ int addsteiner4recoversegment(face*, int);
+ int recoversegments(arraypool*, int fullsearch, int steinerflag);
+
+ int recoverfacebyflips(point, point, point, face*, triface*);
+ int recoversubfaces(arraypool*, int steinerflag);
+
+ int getvertexstar(int, point searchpt, arraypool*, arraypool*, arraypool*);
+ int getedge(point, point, triface*);
+ int reduceedgesatvertex(point startpt, arraypool* endptlist);
+ int removevertexbyflips(point steinerpt);
+
+ int suppressbdrysteinerpoint(point steinerpt);
+ int suppresssteinerpoints();
+
+ void recoverboundary(clock_t&);
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Mesh reconstruction //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ void carveholes();
+
+ // Comment: These three functions are implemented directly in:
+ // gmsh_wrk/Mesh/meshGRegionBoundaryRecovery.cpp
+ bool reconstructmesh(void *);
+ void outsurfacemesh(const char* mfilename);
+ void outmesh2medit(const char* mfilename);
+
+ void enqueuesubface(memorypool*, face*);
+ void enqueuetetrahedron(triface*);
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Mesh optimization //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ long lawsonflip3d(flipconstraints *fc);
+ void recoverdelaunay();
+
+ int gettetrahedron(point, point, point, point, triface *);
+ long improvequalitybyflips();
+
+ int smoothpoint(point smtpt, arraypool*, int ccw, optparameters *opm);
+ long improvequalitybysmoothing(optparameters *opm);
+
+ int splitsliver(triface *, REAL, int);
+ long removeslivers(int);
+
+ void optimizemesh();
+
+ void jettisonnodes();
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Constructor & destructor //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+ void initializetetgenmesh()
+ {
+ in = addin = NULL;
+ b = NULL;
+ bgm = NULL;
+
+ tetrahedrons = subfaces = subsegs = points = NULL;
+ badtetrahedrons = badsubfacs = badsubsegs = NULL;
+ tet2segpool = tet2subpool = NULL;
+ flippool = NULL;
+
+ dummypoint = NULL;
+ flipstack = NULL;
+ unflipqueue = NULL;
+
+ cavetetlist = cavebdrylist = caveoldtetlist = NULL;
+ cavetetshlist = cavetetseglist = cavetetvertlist = NULL;
+ caveencshlist = caveencseglist = NULL;
+ caveshlist = caveshbdlist = cavesegshlist = NULL;
+
+ subsegstack = subfacstack = subvertstack = NULL;
+ encseglist = encshlist = NULL;
+ idx2facetlist = NULL;
+ facetverticeslist = NULL;
+ segmentendpointslist = NULL;
+
+ highordertable = NULL;
+
+ numpointattrib = numelemattrib = 0;
+ sizeoftensor = 0;
+ pointmtrindex = 0;
+ pointparamindex = 0;
+ pointmarkindex = 0;
+ point2simindex = 0;
+ pointinsradiusindex = 0;
+ elemattribindex = 0;
+ volumeboundindex = 0;
+ shmarkindex = 0;
+ areaboundindex = 0;
+ checksubsegflag = 0;
+ checksubfaceflag = 0;
+ checkconstraints = 0;
+ nonconvex = 0;
+ autofliplinklevel = 1;
+ useinsertradius = 0;
+ samples = 0l;
+ randomseed = 1l;
+ minfaceang = minfacetdihed = PI;
+ tetprism_vol_sum = 0.0;
+ longest = minedgelength = 0.0;
+ xmax = xmin = ymax = ymin = zmax = zmin = 0.0;
+
+ insegments = 0l;
+ hullsize = 0l;
+ meshedges = meshhulledges = 0l;
+ steinerleft = -1;
+ dupverts = 0l;
+ unuverts = 0l;
+ nonregularcount = 0l;
+ st_segref_count = st_facref_count = st_volref_count = 0l;
+ fillregioncount = cavitycount = cavityexpcount = 0l;
+ flip14count = flip26count = flipn2ncount = 0l;
+ flip23count = flip32count = flip44count = flip41count = 0l;
+ flip22count = flip31count = 0l;
+ totalworkmemory = 0l;
+
+
+ } // tetgenmesh()
+
+ void freememory()
+ {
+ if (bgm != NULL) {
+ delete bgm;
+ }
+
+ if (points != (memorypool *) NULL) {
+ delete points;
+ delete [] dummypoint;
+ }
+ if (tetrahedrons != (memorypool *) NULL) {
+ delete tetrahedrons;
+ }
+ if (subfaces != (memorypool *) NULL) {
+ delete subfaces;
+ delete subsegs;
+ }
+ if (tet2segpool != NULL) {
+ delete tet2segpool;
+ delete tet2subpool;
+ }
+
+ if (badtetrahedrons) {
+ delete badtetrahedrons;
+ }
+ if (badsubfacs) {
+ delete badsubfacs;
+ }
+ if (badsubsegs) {
+ delete badsubsegs;
+ }
+ if (encseglist) {
+ delete encseglist;
+ }
+ if (encshlist) {
+ delete encshlist;
+ }
+
+ if (flippool != NULL) {
+ delete flippool;
+ delete unflipqueue;
+ }
+
+ if (cavetetlist != NULL) {
+ delete cavetetlist;
+ delete cavebdrylist;
+ delete caveoldtetlist;
+ delete cavetetvertlist;
+ }
+
+ if (caveshlist != NULL) {
+ delete caveshlist;
+ delete caveshbdlist;
+ delete cavesegshlist;
+ delete cavetetshlist;
+ delete cavetetseglist;
+ delete caveencshlist;
+ delete caveencseglist;
+ }
+
+ if (subsegstack != NULL) {
+ delete subsegstack;
+ delete subfacstack;
+ delete subvertstack;
+ }
+
+ if (idx2facetlist != NULL) {
+ delete [] idx2facetlist;
+ delete [] facetverticeslist;
+ }
+
+ if (segmentendpointslist != NULL) {
+ delete [] segmentendpointslist;
+ }
+
+ if (highordertable != NULL) {
+ delete [] highordertable;
+ }
+
+ initializetetgenmesh();
+ }
+
+ tetgenmesh()
+ {
+ initializetetgenmesh();
+ }
+
+ ~tetgenmesh()
+ {
+ freememory();
+ } // ~tetgenmesh()
+
+}; // End of class tetgenmesh.
+
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// terminatetetgen() Terminate TetGen with a given exit code. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+inline void terminatetetgen(tetgenmesh *m, int x)
+{
+#ifdef TETLIBRARY
+ throw x;
+#else
+ switch (x) {
+ case 1: // Out of memory.
+ printf("Error: Out of memory.\n");
+ break;
+ case 2: // Encounter an internal error.
+ printf("Please report this bug to Hang.Si@wias-berlin.de. Include\n");
+ printf(" the message above, your input data set, and the exact\n");
+ printf(" command line you used to run this program, thank you.\n");
+ break;
+ case 3:
+ printf("A self-intersection was detected. Program stopped.\n");
+ printf("Hint: use -d option to detect all self-intersections.\n");
+ break;
+ case 4:
+ printf("A very small input feature size was detected. Program stopped.\n");
+ if (m) {
+ printf("Hint: use -T option to set a smaller tolerance. Current is %g\n",
+ m->b->epsilon);
+ }
+ break;
+ case 5:
+ printf("Two very close input facets were detected. Program stopped.\n");
+ printf("Hint: use -Y option to avoid adding Steiner points in boundary.\n");
+ break;
+ case 10:
+ printf("An input error was detected. Program stopped.\n");
+ break;
+ } // switch (x)
+ exit(x);
+#endif // #ifdef TETLIBRARY
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for tetrahedra //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+// encode() compress a handle into a single pointer. It relies on the
+// assumption that all addresses of tetrahedra are aligned to sixteen-
+// byte boundaries, so that the last four significant bits are zero.
+
+inline tetgenmesh::tetrahedron tetgenmesh::encode(triface& t) {
+ return (tetrahedron) ((uintptr_t) (t).tet | (uintptr_t) (t).ver);
+}
+
+inline tetgenmesh::tetrahedron tetgenmesh::encode2(tetrahedron* ptr, int ver) {
+ return (tetrahedron) ((uintptr_t) (ptr) | (uintptr_t) (ver));
+}
+
+// decode() converts a pointer to a handle. The version is extracted from
+// the four least significant bits of the pointer.
+
+inline void tetgenmesh::decode(tetrahedron ptr, triface& t) {
+ (t).ver = (int) ((uintptr_t) (ptr) & (uintptr_t) 15);
+ (t).tet = (tetrahedron *) ((uintptr_t) (ptr) ^ (uintptr_t) (t).ver);
+}
+
+// bond() connects two tetrahedra together. (t1,v1) and (t2,v2) must
+// refer to the same face and the same edge.
+
+inline void tetgenmesh::bond(triface& t1, triface& t2) {
+ t1.tet[t1.ver & 3] = encode2(t2.tet, bondtbl[t1.ver][t2.ver]);
+ t2.tet[t2.ver & 3] = encode2(t1.tet, bondtbl[t2.ver][t1.ver]);
+}
+
+
+// dissolve() a bond (from one side).
+
+inline void tetgenmesh::dissolve(triface& t) {
+ t.tet[t.ver & 3] = NULL;
+}
+
+// enext() finds the next edge (counterclockwise) in the same face.
+
+inline void tetgenmesh::enext(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = enexttbl[t1.ver];
+}
+
+inline void tetgenmesh::enextself(triface& t) {
+ t.ver = enexttbl[t.ver];
+}
+
+// eprev() finds the next edge (clockwise) in the same face.
+
+inline void tetgenmesh::eprev(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = eprevtbl[t1.ver];
+}
+
+inline void tetgenmesh::eprevself(triface& t) {
+ t.ver = eprevtbl[t.ver];
+}
+
+// esym() finds the reversed edge. It is in the other face of the
+// same tetrahedron.
+
+inline void tetgenmesh::esym(triface& t1, triface& t2) {
+ (t2).tet = (t1).tet;
+ (t2).ver = esymtbl[(t1).ver];
+}
+
+inline void tetgenmesh::esymself(triface& t) {
+ (t).ver = esymtbl[(t).ver];
+}
+
+// enextesym() finds the reversed edge of the next edge. It is in the other
+// face of the same tetrahedron. It is the combination esym() * enext().
+
+inline void tetgenmesh::enextesym(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = enextesymtbl[t1.ver];
+}
+
+inline void tetgenmesh::enextesymself(triface& t) {
+ t.ver = enextesymtbl[t.ver];
+}
+
+// eprevesym() finds the reversed edge of the previous edge.
+
+inline void tetgenmesh::eprevesym(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = eprevesymtbl[t1.ver];
+}
+
+inline void tetgenmesh::eprevesymself(triface& t) {
+ t.ver = eprevesymtbl[t.ver];
+}
+
+// eorgoppo() Finds the opposite face of the origin of the current edge.
+// Return the opposite edge of the current edge.
+
+inline void tetgenmesh::eorgoppo(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = eorgoppotbl[t1.ver];
+}
+
+inline void tetgenmesh::eorgoppoself(triface& t) {
+ t.ver = eorgoppotbl[t.ver];
+}
+
+// edestoppo() Finds the opposite face of the destination of the current
+// edge. Return the opposite edge of the current edge.
+
+inline void tetgenmesh::edestoppo(triface& t1, triface& t2) {
+ t2.tet = t1.tet;
+ t2.ver = edestoppotbl[t1.ver];
+}
+
+inline void tetgenmesh::edestoppoself(triface& t) {
+ t.ver = edestoppotbl[t.ver];
+}
+
+// fsym() finds the adjacent tetrahedron at the same face and the same edge.
+
+inline void tetgenmesh::fsym(triface& t1, triface& t2) {
+ decode((t1).tet[(t1).ver & 3], t2);
+ t2.ver = fsymtbl[t1.ver][t2.ver];
+}
+
+
+#define fsymself(t) \
+ t1ver = (t).ver; \
+ decode((t).tet[(t).ver & 3], (t));\
+ (t).ver = fsymtbl[t1ver][(t).ver]
+
+// fnext() finds the next face while rotating about an edge according to
+// a right-hand rule. The face is in the adjacent tetrahedron. It is
+// the combination: fsym() * esym().
+
+inline void tetgenmesh::fnext(triface& t1, triface& t2) {
+ decode(t1.tet[facepivot1[t1.ver]], t2);
+ t2.ver = facepivot2[t1.ver][t2.ver];
+}
+
+
+#define fnextself(t) \
+ t1ver = (t).ver; \
+ decode((t).tet[facepivot1[(t).ver]], (t)); \
+ (t).ver = facepivot2[t1ver][(t).ver]
+
+
+// The following primtives get or set the origin, destination, face apex,
+// or face opposite of an ordered tetrahedron.
+
+inline tetgenmesh::point tetgenmesh::org(triface& t) {
+ return (point) (t).tet[orgpivot[(t).ver]];
+}
+
+inline tetgenmesh::point tetgenmesh:: dest(triface& t) {
+ return (point) (t).tet[destpivot[(t).ver]];
+}
+
+inline tetgenmesh::point tetgenmesh:: apex(triface& t) {
+ return (point) (t).tet[apexpivot[(t).ver]];
+}
+
+inline tetgenmesh::point tetgenmesh:: oppo(triface& t) {
+ return (point) (t).tet[oppopivot[(t).ver]];
+}
+
+inline void tetgenmesh:: setorg(triface& t, point p) {
+ (t).tet[orgpivot[(t).ver]] = (tetrahedron) (p);
+}
+
+inline void tetgenmesh:: setdest(triface& t, point p) {
+ (t).tet[destpivot[(t).ver]] = (tetrahedron) (p);
+}
+
+inline void tetgenmesh:: setapex(triface& t, point p) {
+ (t).tet[apexpivot[(t).ver]] = (tetrahedron) (p);
+}
+
+inline void tetgenmesh:: setoppo(triface& t, point p) {
+ (t).tet[oppopivot[(t).ver]] = (tetrahedron) (p);
+}
+
+#define setvertices(t, torg, tdest, tapex, toppo) \
+ (t).tet[orgpivot[(t).ver]] = (tetrahedron) (torg);\
+ (t).tet[destpivot[(t).ver]] = (tetrahedron) (tdest); \
+ (t).tet[apexpivot[(t).ver]] = (tetrahedron) (tapex); \
+ (t).tet[oppopivot[(t).ver]] = (tetrahedron) (toppo)
+
+// Check or set a tetrahedron's attributes.
+
+inline REAL tetgenmesh::elemattribute(tetrahedron* ptr, int attnum) {
+ return ((REAL *) (ptr))[elemattribindex + attnum];
+}
+
+inline void tetgenmesh::setelemattribute(tetrahedron* ptr, int attnum,
+ REAL value) {
+ ((REAL *) (ptr))[elemattribindex + attnum] = value;
+}
+
+// Check or set a tetrahedron's maximum volume bound.
+
+inline REAL tetgenmesh::volumebound(tetrahedron* ptr) {
+ return ((REAL *) (ptr))[volumeboundindex];
+}
+
+inline void tetgenmesh::setvolumebound(tetrahedron* ptr, REAL value) {
+ ((REAL *) (ptr))[volumeboundindex] = value;
+}
+
+// Get or set a tetrahedron's index (only used for output).
+// These two routines use the reserved slot ptr[10].
+
+inline int tetgenmesh::elemindex(tetrahedron* ptr) {
+ int *iptr = (int *) &(ptr[10]);
+ return iptr[0];
+}
+
+inline void tetgenmesh::setelemindex(tetrahedron* ptr, int value) {
+ int *iptr = (int *) &(ptr[10]);
+ iptr[0] = value;
+}
+
+// Get or set a tetrahedron's marker.
+// Set 'value = 0' cleans all the face/edge flags.
+
+inline int tetgenmesh::elemmarker(tetrahedron* ptr) {
+ return ((int *) (ptr))[elemmarkerindex];
+}
+
+inline void tetgenmesh::setelemmarker(tetrahedron* ptr, int value) {
+ ((int *) (ptr))[elemmarkerindex] = value;
+}
+
+// infect(), infected(), uninfect() -- primitives to flag or unflag a
+// tetrahedron. The last bit of the element marker is flagged (1)
+// or unflagged (0).
+
+inline void tetgenmesh::infect(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] |= 1;
+}
+
+inline void tetgenmesh::uninfect(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] &= ~1;
+}
+
+inline bool tetgenmesh::infected(triface& t) {
+ return (((int *) (t.tet))[elemmarkerindex] & 1) != 0;
+}
+
+// marktest(), marktested(), unmarktest() -- primitives to flag or unflag a
+// tetrahedron. Use the second lowerest bit of the element marker.
+
+inline void tetgenmesh::marktest(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] |= 2;
+}
+
+inline void tetgenmesh::unmarktest(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] &= ~2;
+}
+
+inline bool tetgenmesh::marktested(triface& t) {
+ return (((int *) (t.tet))[elemmarkerindex] & 2) != 0;
+}
+
+// markface(), unmarkface(), facemarked() -- primitives to flag or unflag a
+// face of a tetrahedron. From the last 3rd to 6th bits are used for
+// face markers, e.g., the last third bit corresponds to loc = 0.
+
+inline void tetgenmesh::markface(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] |= (4 << (t.ver & 3));
+}
+
+inline void tetgenmesh::unmarkface(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] &= ~(4 << (t.ver & 3));
+}
+
+inline bool tetgenmesh::facemarked(triface& t) {
+ return (((int *) (t.tet))[elemmarkerindex] & (4 << (t.ver & 3))) != 0;
+}
+
+// markedge(), unmarkedge(), edgemarked() -- primitives to flag or unflag an
+// edge of a tetrahedron. From the last 7th to 12th bits are used for
+// edge markers, e.g., the last 7th bit corresponds to the 0th edge, etc.
+// Remark: The last 7th bit is marked by 2^6 = 64.
+
+inline void tetgenmesh::markedge(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] |= (int) (64 << ver2edge[(t).ver]);
+}
+
+inline void tetgenmesh::unmarkedge(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] &= ~(int) (64 << ver2edge[(t).ver]);
+}
+
+inline bool tetgenmesh::edgemarked(triface& t) {
+ return (((int *) (t.tet))[elemmarkerindex] &
+ (int) (64 << ver2edge[(t).ver])) != 0;
+}
+
+// marktest2(), unmarktest2(), marktest2ed() -- primitives to flag and unflag
+// a tetrahedron. The 13th bit (2^12 = 4096) is used for this flag.
+
+inline void tetgenmesh::marktest2(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] |= (int) (4096);
+}
+
+inline void tetgenmesh::unmarktest2(triface& t) {
+ ((int *) (t.tet))[elemmarkerindex] &= ~(int) (4096);
+}
+
+inline bool tetgenmesh::marktest2ed(triface& t) {
+ return (((int *) (t.tet))[elemmarkerindex] & (int) (4096)) != 0;
+}
+
+// elemcounter(), setelemcounter() -- primitives to read or ser a (small)
+// integer counter in this tet. It is saved from the 16th bit. On 32 bit
+// system, the range of the counter is [0, 2^15 = 32768].
+
+inline int tetgenmesh::elemcounter(triface& t) {
+ return (((int *) (t.tet))[elemmarkerindex]) >> 16;
+}
+
+inline void tetgenmesh::setelemcounter(triface& t, int value) {
+ int c = ((int *) (t.tet))[elemmarkerindex];
+ // Clear the old counter while keep the other flags.
+ c &= 65535; // sum_{i=0^15} 2^i
+ c |= (value << 16);
+ ((int *) (t.tet))[elemmarkerindex] = c;
+}
+
+inline void tetgenmesh::increaseelemcounter(triface& t) {
+ int c = elemcounter(t);
+ setelemcounter(t, c + 1);
+}
+
+inline void tetgenmesh::decreaseelemcounter(triface& t) {
+ int c = elemcounter(t);
+ setelemcounter(t, c - 1);
+}
+
+// ishulltet() tests if t is a hull tetrahedron.
+
+inline bool tetgenmesh::ishulltet(triface& t) {
+ return (point) (t).tet[7] == dummypoint;
+}
+
+// isdeadtet() tests if t is a tetrahedron is dead.
+
+inline bool tetgenmesh::isdeadtet(triface& t) {
+ return ((t.tet == NULL) || (t.tet[4] == NULL));
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for subfaces and subsegments //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+// Each subface contains three pointers to its neighboring subfaces, with
+// edge versions. To save memory, both information are kept in a single
+// pointer. To make this possible, all subfaces are aligned to eight-byte
+// boundaries, so that the last three bits of each pointer are zeros. An
+// edge version (in the range 0 to 5) is compressed into the last three
+// bits of each pointer by 'sencode()'. 'sdecode()' decodes a pointer,
+// extracting an edge version and a pointer to the beginning of a subface.
+
+inline void tetgenmesh::sdecode(shellface sptr, face& s) {
+ s.shver = (int) ((uintptr_t) (sptr) & (uintptr_t) 7);
+ s.sh = (shellface *) ((uintptr_t) (sptr) ^ (uintptr_t) (s.shver));
+}
+
+inline tetgenmesh::shellface tetgenmesh::sencode(face& s) {
+ return (shellface) ((uintptr_t) s.sh | (uintptr_t) s.shver);
+}
+
+inline tetgenmesh::shellface tetgenmesh::sencode2(shellface *sh, int shver) {
+ return (shellface) ((uintptr_t) sh | (uintptr_t) shver);
+}
+
+// sbond() bonds two subfaces (s1) and (s2) together. s1 and s2 must refer
+// to the same edge. No requirement is needed on their orientations.
+
+inline void tetgenmesh::sbond(face& s1, face& s2)
+{
+ s1.sh[s1.shver >> 1] = sencode(s2);
+ s2.sh[s2.shver >> 1] = sencode(s1);
+}
+
+// sbond1() bonds s1 <== s2, i.e., after bonding, s1 is pointing to s2,
+// but s2 is not pointing to s1. s1 and s2 must refer to the same edge.
+// No requirement is needed on their orientations.
+
+inline void tetgenmesh::sbond1(face& s1, face& s2)
+{
+ s1.sh[s1.shver >> 1] = sencode(s2);
+}
+
+// Dissolve a subface bond (from one side). Note that the other subface
+// will still think it's connected to this subface.
+
+inline void tetgenmesh::sdissolve(face& s)
+{
+ s.sh[s.shver >> 1] = NULL;
+}
+
+// spivot() finds the adjacent subface (s2) for a given subface (s1).
+// s1 and s2 share at the same edge.
+
+inline void tetgenmesh::spivot(face& s1, face& s2)
+{
+ shellface sptr = s1.sh[s1.shver >> 1];
+ sdecode(sptr, s2);
+}
+
+inline void tetgenmesh::spivotself(face& s)
+{
+ shellface sptr = s.sh[s.shver >> 1];
+ sdecode(sptr, s);
+}
+
+// These primitives determine or set the origin, destination, or apex
+// of a subface with respect to the edge version.
+
+inline tetgenmesh::point tetgenmesh::sorg(face& s)
+{
+ return (point) s.sh[sorgpivot[s.shver]];
+}
+
+inline tetgenmesh::point tetgenmesh::sdest(face& s)
+{
+ return (point) s.sh[sdestpivot[s.shver]];
+}
+
+inline tetgenmesh::point tetgenmesh::sapex(face& s)
+{
+ return (point) s.sh[sapexpivot[s.shver]];
+}
+
+inline void tetgenmesh::setsorg(face& s, point pointptr)
+{
+ s.sh[sorgpivot[s.shver]] = (shellface) pointptr;
+}
+
+inline void tetgenmesh::setsdest(face& s, point pointptr)
+{
+ s.sh[sdestpivot[s.shver]] = (shellface) pointptr;
+}
+
+inline void tetgenmesh::setsapex(face& s, point pointptr)
+{
+ s.sh[sapexpivot[s.shver]] = (shellface) pointptr;
+}
+
+#define setshvertices(s, pa, pb, pc)\
+ setsorg(s, pa);\
+ setsdest(s, pb);\
+ setsapex(s, pc)
+
+// sesym() reserves the direction of the lead edge.
+
+inline void tetgenmesh::sesym(face& s1, face& s2)
+{
+ s2.sh = s1.sh;
+ s2.shver = (s1.shver ^ 1); // Inverse the last bit.
+}
+
+inline void tetgenmesh::sesymself(face& s)
+{
+ s.shver ^= 1;
+}
+
+// senext() finds the next edge (counterclockwise) in the same orientation
+// of this face.
+
+inline void tetgenmesh::senext(face& s1, face& s2)
+{
+ s2.sh = s1.sh;
+ s2.shver = snextpivot[s1.shver];
+}
+
+inline void tetgenmesh::senextself(face& s)
+{
+ s.shver = snextpivot[s.shver];
+}
+
+inline void tetgenmesh::senext2(face& s1, face& s2)
+{
+ s2.sh = s1.sh;
+ s2.shver = snextpivot[snextpivot[s1.shver]];
+}
+
+inline void tetgenmesh::senext2self(face& s)
+{
+ s.shver = snextpivot[snextpivot[s.shver]];
+}
+
+
+// Check or set a subface's maximum area bound.
+
+inline REAL tetgenmesh::areabound(face& s)
+{
+ return ((REAL *) (s.sh))[areaboundindex];
+}
+
+inline void tetgenmesh::setareabound(face& s, REAL value)
+{
+ ((REAL *) (s.sh))[areaboundindex] = value;
+}
+
+// These two primitives read or set a shell marker. Shell markers are used
+// to hold user boundary information.
+
+inline int tetgenmesh::shellmark(face& s)
+{
+ return ((int *) (s.sh))[shmarkindex];
+}
+
+inline void tetgenmesh::setshellmark(face& s, int value)
+{
+ ((int *) (s.sh))[shmarkindex] = value;
+}
+
+
+
+// sinfect(), sinfected(), suninfect() -- primitives to flag or unflag a
+// subface. The last bit of ((int *) ((s).sh))[shmarkindex+1] is flagged.
+
+inline void tetgenmesh::sinfect(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *) ((s).sh))[shmarkindex+1] | (int) 1);
+}
+
+inline void tetgenmesh::suninfect(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *) ((s).sh))[shmarkindex+1] & ~(int) 1);
+}
+
+// Test a subface for viral infection.
+
+inline bool tetgenmesh::sinfected(face& s)
+{
+ return (((int *) ((s).sh))[shmarkindex+1] & (int) 1) != 0;
+}
+
+// smarktest(), smarktested(), sunmarktest() -- primitives to flag or unflag
+// a subface. The last 2nd bit of the integer is flagged.
+
+inline void tetgenmesh::smarktest(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *)((s).sh))[shmarkindex+1] | (int) 2);
+}
+
+inline void tetgenmesh::sunmarktest(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *)((s).sh))[shmarkindex+1] & ~(int)2);
+}
+
+inline bool tetgenmesh::smarktested(face& s)
+{
+ return ((((int *) ((s).sh))[shmarkindex+1] & (int) 2) != 0);
+}
+
+// smarktest2(), smarktest2ed(), sunmarktest2() -- primitives to flag or
+// unflag a subface. The last 3rd bit of the integer is flagged.
+
+inline void tetgenmesh::smarktest2(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *)((s).sh))[shmarkindex+1] | (int) 4);
+}
+
+inline void tetgenmesh::sunmarktest2(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *)((s).sh))[shmarkindex+1] & ~(int)4);
+}
+
+inline bool tetgenmesh::smarktest2ed(face& s)
+{
+ return ((((int *) ((s).sh))[shmarkindex+1] & (int) 4) != 0);
+}
+
+// The last 4th bit of ((int *) ((s).sh))[shmarkindex+1] is flagged.
+
+inline void tetgenmesh::smarktest3(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *)((s).sh))[shmarkindex+1] | (int) 8);
+}
+
+inline void tetgenmesh::sunmarktest3(face& s)
+{
+ ((int *) ((s).sh))[shmarkindex+1] =
+ (((int *)((s).sh))[shmarkindex+1] & ~(int)8);
+}
+
+inline bool tetgenmesh::smarktest3ed(face& s)
+{
+ return ((((int *) ((s).sh))[shmarkindex+1] & (int) 8) != 0);
+}
+
+
+// Each facet has a unique index (automatically indexed). Starting from '0'.
+// We save this index in the same field of the shell type.
+
+inline void tetgenmesh::setfacetindex(face& s, int value)
+{
+ ((int *) (s.sh))[shmarkindex + 2] = value;
+}
+
+inline int tetgenmesh::getfacetindex(face& s)
+{
+ return ((int *) (s.sh))[shmarkindex + 2];
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for interacting between tetrahedra and subfaces //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+// tsbond() bond a tetrahedron (t) and a subface (s) together.
+// Note that t and s must be the same face and the same edge. Moreover,
+// t and s have the same orientation.
+// Since the edge number in t and in s can be any number in {0,1,2}. We bond
+// the edge in s which corresponds to t's 0th edge, and vice versa.
+
+inline void tetgenmesh::tsbond(triface& t, face& s)
+{
+ if ((t).tet[9] == NULL) {
+ // Allocate space for this tet.
+ (t).tet[9] = (tetrahedron) tet2subpool->alloc();
+ // Initialize.
+ for (int i = 0; i < 4; i++) {
+ ((shellface *) (t).tet[9])[i] = NULL;
+ }
+ }
+ // Bond t <== s.
+ ((shellface *) (t).tet[9])[(t).ver & 3] =
+ sencode2((s).sh, tsbondtbl[t.ver][s.shver]);
+ // Bond s <== t.
+ s.sh[9 + ((s).shver & 1)] =
+ (shellface) encode2((t).tet, stbondtbl[t.ver][s.shver]);
+}
+
+// tspivot() finds a subface (s) abutting on the given tetrahdera (t).
+// Return s.sh = NULL if there is no subface at t. Otherwise, return
+// the subface s, and s and t must be at the same edge wth the same
+// orientation.
+
+inline void tetgenmesh::tspivot(triface& t, face& s)
+{
+ if ((t).tet[9] == NULL) {
+ (s).sh = NULL;
+ return;
+ }
+ // Get the attached subface s.
+ sdecode(((shellface *) (t).tet[9])[(t).ver & 3], (s));
+ (s).shver = tspivottbl[t.ver][s.shver];
+}
+
+// Quickly check if the handle (t, v) is a subface.
+#define issubface(t) \
+ ((t).tet[9] && ((t).tet[9])[(t).ver & 3])
+
+// stpivot() finds a tetrahedron (t) abutting a given subface (s).
+// Return the t (if it exists) with the same edge and the same
+// orientation of s.
+
+inline void tetgenmesh::stpivot(face& s, triface& t)
+{
+ decode((tetrahedron) s.sh[9 + (s.shver & 1)], t);
+ if ((t).tet == NULL) {
+ return;
+ }
+ (t).ver = stpivottbl[t.ver][s.shver];
+}
+
+// Quickly check if this subface is attached to a tetrahedron.
+
+#define isshtet(s) \
+ ((s).sh[9 + ((s).shver & 1)])
+
+// tsdissolve() dissolve a bond (from the tetrahedron side).
+
+inline void tetgenmesh::tsdissolve(triface& t)
+{
+ if ((t).tet[9] != NULL) {
+ ((shellface *) (t).tet[9])[(t).ver & 3] = NULL;
+ }
+}
+
+// stdissolve() dissolve a bond (from the subface side).
+
+inline void tetgenmesh::stdissolve(face& s)
+{
+ (s).sh[9] = NULL;
+ (s).sh[10] = NULL;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for interacting between subfaces and segments //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+// ssbond() bond a subface to a subsegment.
+
+inline void tetgenmesh::ssbond(face& s, face& edge)
+{
+ s.sh[6 + (s.shver >> 1)] = sencode(edge);
+ edge.sh[0] = sencode(s);
+}
+
+inline void tetgenmesh::ssbond1(face& s, face& edge)
+{
+ s.sh[6 + (s.shver >> 1)] = sencode(edge);
+ //edge.sh[0] = sencode(s);
+}
+
+// ssdisolve() dissolve a bond (from the subface side)
+
+inline void tetgenmesh::ssdissolve(face& s)
+{
+ s.sh[6 + (s.shver >> 1)] = NULL;
+}
+
+// sspivot() finds a subsegment abutting a subface.
+
+inline void tetgenmesh::sspivot(face& s, face& edge)
+{
+ sdecode((shellface) s.sh[6 + (s.shver >> 1)], edge);
+}
+
+// Quickly check if the edge is a subsegment.
+
+#define isshsubseg(s) \
+ ((s).sh[6 + ((s).shver >> 1)])
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for interacting between tetrahedra and segments //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+inline void tetgenmesh::tssbond1(triface& t, face& s)
+{
+ if ((t).tet[8] == NULL) {
+ // Allocate space for this tet.
+ (t).tet[8] = (tetrahedron) tet2segpool->alloc();
+ // Initialization.
+ for (int i = 0; i < 6; i++) {
+ ((shellface *) (t).tet[8])[i] = NULL;
+ }
+ }
+ ((shellface *) (t).tet[8])[ver2edge[(t).ver]] = sencode((s));
+}
+
+inline void tetgenmesh::sstbond1(face& s, triface& t)
+{
+ ((tetrahedron *) (s).sh)[9] = encode(t);
+}
+
+inline void tetgenmesh::tssdissolve1(triface& t)
+{
+ if ((t).tet[8] != NULL) {
+ ((shellface *) (t).tet[8])[ver2edge[(t).ver]] = NULL;
+ }
+}
+
+inline void tetgenmesh::sstdissolve1(face& s)
+{
+ ((tetrahedron *) (s).sh)[9] = NULL;
+}
+
+inline void tetgenmesh::tsspivot1(triface& t, face& s)
+{
+ if ((t).tet[8] != NULL) {
+ sdecode(((shellface *) (t).tet[8])[ver2edge[(t).ver]], s);
+ } else {
+ (s).sh = NULL;
+ }
+}
+
+// Quickly check whether 't' is a segment or not.
+
+#define issubseg(t) \
+ ((t).tet[8] && ((t).tet[8])[ver2edge[(t).ver]])
+
+inline void tetgenmesh::sstpivot1(face& s, triface& t)
+{
+ decode((tetrahedron) s.sh[9], t);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Primitives for points //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+inline int tetgenmesh::pointmark(point pt) {
+ return ((int *) (pt))[pointmarkindex];
+}
+
+inline void tetgenmesh::setpointmark(point pt, int value) {
+ ((int *) (pt))[pointmarkindex] = value;
+}
+
+
+// These two primitives set and read the type of the point.
+
+inline enum tetgenmesh::verttype tetgenmesh::pointtype(point pt) {
+ return (enum verttype) (((int *) (pt))[pointmarkindex + 1] >> (int) 8);
+}
+
+inline void tetgenmesh::setpointtype(point pt, enum verttype value) {
+ ((int *) (pt))[pointmarkindex + 1] =
+ ((int) value << 8) + (((int *) (pt))[pointmarkindex + 1] & (int) 255);
+}
+
+// Read and set the geometry tag of the point (used by -s option).
+
+inline int tetgenmesh::pointgeomtag(point pt) {
+ return ((int *) (pt))[pointmarkindex + 2];
+}
+
+inline void tetgenmesh::setpointgeomtag(point pt, int value) {
+ ((int *) (pt))[pointmarkindex + 2] = value;
+}
+
+// Read and set the u,v coordinates of the point (used by -s option).
+
+inline REAL tetgenmesh::pointgeomuv(point pt, int i) {
+ return pt[pointparamindex + i];
+}
+
+inline void tetgenmesh::setpointgeomuv(point pt, int i, REAL value) {
+ pt[pointparamindex + i] = value;
+}
+
+// pinfect(), puninfect(), pinfected() -- primitives to flag or unflag
+// a point. The last bit of the integer '[pointindex+1]' is flagged.
+
+inline void tetgenmesh::pinfect(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] |= (int) 1;
+}
+
+inline void tetgenmesh::puninfect(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] &= ~(int) 1;
+}
+
+inline bool tetgenmesh::pinfected(point pt) {
+ return (((int *) (pt))[pointmarkindex + 1] & (int) 1) != 0;
+}
+
+// pmarktest(), punmarktest(), pmarktested() -- more primitives to
+// flag or unflag a point.
+
+inline void tetgenmesh::pmarktest(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] |= (int) 2;
+}
+
+inline void tetgenmesh::punmarktest(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] &= ~(int) 2;
+}
+
+inline bool tetgenmesh::pmarktested(point pt) {
+ return (((int *) (pt))[pointmarkindex + 1] & (int) 2) != 0;
+}
+
+inline void tetgenmesh::pmarktest2(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] |= (int) 4;
+}
+
+inline void tetgenmesh::punmarktest2(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] &= ~(int) 4;
+}
+
+inline bool tetgenmesh::pmarktest2ed(point pt) {
+ return (((int *) (pt))[pointmarkindex + 1] & (int) 4) != 0;
+}
+
+inline void tetgenmesh::pmarktest3(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] |= (int) 8;
+}
+
+inline void tetgenmesh::punmarktest3(point pt) {
+ ((int *) (pt))[pointmarkindex + 1] &= ~(int) 8;
+}
+
+inline bool tetgenmesh::pmarktest3ed(point pt) {
+ return (((int *) (pt))[pointmarkindex + 1] & (int) 8) != 0;
+}
+
+// These following primitives set and read a pointer to a tetrahedron
+// a subface/subsegment, a point, or a tet of background mesh.
+
+inline tetgenmesh::tetrahedron tetgenmesh::point2tet(point pt) {
+ return ((tetrahedron *) (pt))[point2simindex];
+}
+
+inline void tetgenmesh::setpoint2tet(point pt, tetrahedron value) {
+ ((tetrahedron *) (pt))[point2simindex] = value;
+}
+
+inline tetgenmesh::point tetgenmesh::point2ppt(point pt) {
+ return (point) ((tetrahedron *) (pt))[point2simindex + 1];
+}
+
+inline void tetgenmesh::setpoint2ppt(point pt, point value) {
+ ((tetrahedron *) (pt))[point2simindex + 1] = (tetrahedron) value;
+}
+
+inline tetgenmesh::shellface tetgenmesh::point2sh(point pt) {
+ return (shellface) ((tetrahedron *) (pt))[point2simindex + 2];
+}
+
+inline void tetgenmesh::setpoint2sh(point pt, shellface value) {
+ ((tetrahedron *) (pt))[point2simindex + 2] = (tetrahedron) value;
+}
+
+
+inline tetgenmesh::tetrahedron tetgenmesh::point2bgmtet(point pt) {
+ return ((tetrahedron *) (pt))[point2simindex + 3];
+}
+
+inline void tetgenmesh::setpoint2bgmtet(point pt, tetrahedron value) {
+ ((tetrahedron *) (pt))[point2simindex + 3] = value;
+}
+
+
+// The primitives for saving and getting the insertion radius.
+inline void tetgenmesh::setpointinsradius(point pt, REAL value)
+{
+ pt[pointinsradiusindex] = value;
+}
+
+inline REAL tetgenmesh::getpointinsradius(point pt)
+{
+ return pt[pointinsradiusindex];
+}
+
+inline bool tetgenmesh::issteinerpoint(point pt) {
+ return (pointtype(pt) == FREESEGVERTEX) || (pointtype(pt) == FREEFACETVERTEX)
+ || (pointtype(pt) == FREEVOLVERTEX);
+}
+
+// point2tetorg() Get the tetrahedron whose origin is the point.
+
+inline void tetgenmesh::point2tetorg(point pa, triface& searchtet)
+{
+ decode(point2tet(pa), searchtet);
+ 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;
+ }
+}
+
+// point2shorg() Get the subface/segment whose origin is the point.
+
+inline void tetgenmesh::point2shorg(point pa, face& searchsh)
+{
+ sdecode(point2sh(pa), searchsh);
+ if ((point) searchsh.sh[3] == pa) {
+ searchsh.shver = 0;
+ } else if ((point) searchsh.sh[4] == pa) {
+ searchsh.shver = (searchsh.sh[5] != NULL ? 2 : 1);
+ } else {
+ searchsh.shver = 4;
+ }
+}
+
+// farsorg() Return the origin of the subsegment.
+// farsdest() Return the destination of the subsegment.
+
+inline tetgenmesh::point tetgenmesh::farsorg(face& s)
+{
+ face travesh, neighsh;
+
+ travesh = s;
+ while (1) {
+ senext2(travesh, neighsh);
+ spivotself(neighsh);
+ if (neighsh.sh == NULL) break;
+ if (sorg(neighsh) != sorg(travesh)) sesymself(neighsh);
+ senext2(neighsh, travesh);
+ }
+ return sorg(travesh);
+}
+
+inline tetgenmesh::point tetgenmesh::farsdest(face& s)
+{
+ face travesh, neighsh;
+
+ travesh = s;
+ while (1) {
+ senext(travesh, neighsh);
+ spivotself(neighsh);
+ if (neighsh.sh == NULL) break;
+ if (sdest(neighsh) != sdest(travesh)) sesymself(neighsh);
+ senext(neighsh, travesh);
+ }
+ return sdest(travesh);
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// //
+// Linear algebra operators. //
+// //
+///////////////////////////////////////////////////////////////////////////////
+
+// dot() returns the dot product: v1 dot v2.
+inline REAL tetgenmesh::dot(REAL* v1, REAL* v2)
+{
+ return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
+}
+
+// cross() computes the cross product: n = v1 cross v2.
+inline void tetgenmesh::cross(REAL* v1, REAL* v2, REAL* n)
+{
+ n[0] = v1[1] * v2[2] - v2[1] * v1[2];
+ n[1] = -(v1[0] * v2[2] - v2[0] * v1[2]);
+ n[2] = v1[0] * v2[1] - v2[0] * v1[1];
+}
+
+// distance() computes the Euclidean distance between two points.
+inline REAL tetgenmesh::distance(REAL* p1, REAL* p2)
+{
+ return sqrt((p2[0] - p1[0]) * (p2[0] - p1[0]) +
+ (p2[1] - p1[1]) * (p2[1] - p1[1]) +
+ (p2[2] - p1[2]) * (p2[2] - p1[2]));
+}
+
+inline REAL tetgenmesh::norm2(REAL x, REAL y, REAL z)
+{
+ return (x) * (x) + (y) * (y) + (z) * (z);
+}
+
+#endif // tetgenBRH