1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
|
/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include <vector>
#include "triangulation/ntriangulation.h"
#include "utilities/memutils.h"
#include "utilities/stlutils.h"
namespace regina {
namespace {
// The indices of the new tetrahedra
int tetIndex[4][4][4] = {
{ {-1,-1,-1,-1}, {-1,-1,0,1}, {-1,2,-1,3}, {-1,4,5,-1} },
{ {-1,-1,6,7}, {-1,-1,-1,-1}, {8,-1,-1,9}, {10,-1,11,-1} },
{ {-1,12,-1,13}, {14,-1,-1,15}, {-1,-1,-1,-1}, {16,17,-1,-1} },
{ {-1,18,19,-1}, {20,-1,21,-1}, {22,23,-1,-1}, {-1,-1,-1,-1} } };
}
void NTriangulation::barycentricSubdivision() {
// (Initially written by Dave Letscher on 11/2/00)
unsigned long nOldTet = tetrahedra.size();
if (nOldTet == 0)
return;
ChangeEventBlock block(this);
NTetrahedron** newTet = new NTetrahedron*[nOldTet * 24];
NTetrahedron* oldTet;
NPerm p;
unsigned long tet;
int face, edge, corner, other;
for (tet=0; tet<24*nOldTet; tet++)
newTet[tet] = new NTetrahedron();
// Do all of the internal gluings
for (tet=0; tet<nOldTet; tet++) {
for (face=0; face<4; face++)
for (edge=0; edge<4; edge++)
if (edge != face)
for (corner=0; corner<4; corner++)
if ( (face != corner) && (edge != corner) ) {
other = 6-face-edge-corner;
// Glue to the tetrahedron on the same face and
// on the same edge
newTet[24*tet+tetIndex[face][edge][corner]]->
joinTo(corner,
newTet[24*tet+tetIndex[face][edge][other]],
NPerm(corner,other) );
// Glue to the tetrahedron on the same face and
// at the same corner
newTet[24*tet+tetIndex[face][edge][corner]]->
joinTo(other,
newTet[24*tet+tetIndex[face][other][corner]],
NPerm(edge,other) );
// Glue to the tetrahedron on the adjacent face
// sharing an edge and a vertex
newTet[24*tet+tetIndex[face][edge][corner]]->
joinTo(edge,
newTet[24*tet+tetIndex[edge][face][corner]],
NPerm(face, edge) );
// Glue to the new tetrahedron across an existing
// face
oldTet = getTetrahedron(tet);
if (oldTet->getAdjacentTetrahedron(face)) {
p = oldTet->getAdjacentTetrahedronGluing(face);
newTet[24*tet+tetIndex[face][edge][corner]]->
joinTo(face, newTet[24*tetrahedronIndex(
oldTet->getAdjacentTetrahedron(face))+
tetIndex[p[face]][p[edge]][p[corner]] ],
NPerm(p) );
}
}
}
// Delete the existing tetrahedra and put in the new ones.
removeAllTetrahedra();
for (tet=0; tet<24*nOldTet; tet++)
addTetrahedron(newTet[tet]);
delete[] newTet;
}
bool NTriangulation::idealToFinite(bool forceDivision) {
// The call to isValid() ensures the skeleton has been calculated.
if (isValid() && ! isIdeal())
if (! forceDivision)
return false;
int i,j,k,l;
int numOldTet = tetrahedra.size();
if (! numOldTet)
return false;
ChangeEventBlock block(this);
NTetrahedron **newTet = new NTetrahedron*[32*numOldTet];
for (i=0; i<32*numOldTet; i++)
newTet[i] = new NTetrahedron();
int tip[4];
int interior[4];
int edge[4][4];
int vertex[4][4];
int nDiv = 0;
for (j=0; j<4; j++) {
tip[j] = nDiv++;
interior[j] = nDiv++;
for (k=0; k<4; k++)
if (j != k) {
edge[j][k] = nDiv++;
vertex[j][k] = nDiv++;
}
}
// First glue all of the tetrahedra inside the same
// old tetrahedron together.
for (i=0; i<numOldTet; i++) {
// Glue the tip tetrahedra to the others.
for (j=0; j<4; j++)
newTet[tip[j] + i * nDiv]->joinTo(j,
newTet[interior[j] + i * nDiv], NPerm());
// Glue the interior tetrahedra to the others.
for (j=0; j<4; j++) {
for (k=0; k<4; k++)
if (j != k) {
newTet[interior[j] + i * nDiv]->joinTo(k,
newTet[vertex[k][j] + i * nDiv], NPerm());
}
}
// Glue the edge tetrahedra to the others.
for (j=0; j<4; j++)
for (k=0; k<4; k++)
if (j != k) {
newTet[edge[j][k] + i * nDiv]->joinTo(j,
newTet[edge[k][j] + i * nDiv], NPerm(j,k));
for (l=0; l<4; l++)
if ( (l != j) && (l != k) )
newTet[edge[j][k] + i * nDiv]->joinTo(l,
newTet[vertex[j][l] + i * nDiv], NPerm(k,l));
}
}
// Now deal with the gluings between the pieces inside adjacent tetrahedra.
NTetrahedron *ot;
int oppTet;
NPerm p;
for (i=0; i<numOldTet; i++) {
ot = getTetrahedron(i);
for (j=0; j<4; j++)
if (ot->getAdjacentTetrahedron(j)) {
oppTet = tetrahedronIndex(ot->getAdjacentTetrahedron(j));
p = ot->getAdjacentTetrahedronGluing(j);
// First deal with the tip tetrahedra.
for (k=0; k<4; k++)
if (j != k)
newTet[tip[k] + i * nDiv]->joinTo(j,
newTet[tip[p[k]] + oppTet * nDiv], p);
// Next the edge tetrahedra.
for (k=0; k<4; k++)
if (j != k)
newTet[edge[j][k] + i * nDiv]->joinTo(k,
newTet[edge[p[j]][p[k]] + oppTet * nDiv], p);
// Finally, the vertex tetrahedra.
for (k=0; k<4; k++)
if (j != k)
newTet[vertex[j][k] + i * nDiv]->joinTo(k,
newTet[vertex[p[j]][p[k]] + oppTet * nDiv], p);
}
}
removeAllTetrahedra();
for (i=0; i<32*numOldTet; i++)
addTetrahedron(newTet[i]);
calculateSkeleton();
// Remove the tetrahedra that meet any of the non-standard or
// ideal vertices.
// First we make a list of the tetrahedra.
stdhash::hash_set<NTetrahedron*, HashPointer> tetList;
std::vector<NVertexEmbedding>::const_iterator vembit;
for (VertexIterator vIter = vertices.begin();
vIter != vertices.end(); vIter++)
if ((*vIter)->isIdeal() || ! (*vIter)->isStandard())
for (vembit = (*vIter)->getEmbeddings().begin();
vembit != (*vIter)->getEmbeddings().end(); vembit++)
tetList.insert((*vembit).getTetrahedron());
// Now remove the tetrahedra.
// For each tetrahedron, remove it and delete it.
for_each(tetList.begin(), tetList.end(),
regina::stl::compose1(FuncDelete<NTetrahedron>(),
std::bind1st(std::mem_fun(&NTriangulation::removeTetrahedron), this)));
gluingsHaveChanged();
return true;
}
bool NTriangulation::finiteToIdeal() {
if (! hasBoundaryFaces())
return false;
// Get a list of all boundary faces.
std::vector<NFace*> boundaryFaces;
BoundaryComponentIterator bit;
unsigned long nFaces;
unsigned long i;
for (bit = boundaryComponents.begin(); bit != boundaryComponents.end();
bit++) {
nFaces = (*bit)->getNumberOfFaces();
for (i = 0; i < nFaces; i++)
boundaryFaces.push_back((*bit)->getFace(i));
}
// There should be at least one boundary face. But just in case.
if (boundaryFaces.empty())
return false;
// Here's where we start changing things.
ChangeEventBlock block(this);
nFaces = boundaryFaces.size();
NTetrahedron** newTet = new NTetrahedron*[nFaces];
// Create the new tetrahedra and join them to the boundary faces.
for (i = 0; i < nFaces; i++) {
newTet[i] = new NTetrahedron();
NFaceEmbedding emb = boundaryFaces[i]->getEmbedding(0);
newTet[i]->joinTo(3, emb.getTetrahedron(), emb.getVertices());
}
// Now join the new tetrahedra to each other.
NEdge* edge;
NTetrahedron* t1;
NTetrahedron* t2;
NPerm t1Face;
NPerm t2Face;
for (bit = boundaryComponents.begin(); bit != boundaryComponents.end();
bit++)
for (i = 0; i < (*bit)->getNumberOfEdges(); i++) {
edge = (*bit)->getEdge(i);
// This must be a valid boundary edge.
// Find the boundary faces at either end.
NEdgeEmbedding e1 = edge->getEmbeddings().front();
NEdgeEmbedding e2 = edge->getEmbeddings().back();
t1 = e1.getTetrahedron()->getAdjacentTetrahedron(
e1.getVertices()[3]);
t2 = e2.getTetrahedron()->getAdjacentTetrahedron(
e2.getVertices()[2]);
t1Face = e1.getTetrahedron()->getAdjacentTetrahedronGluing(
e1.getVertices()[3]) * e1.getVertices();
t2Face = e2.getTetrahedron()->getAdjacentTetrahedronGluing(
e2.getVertices()[2]) * e2.getVertices() * NPerm(2, 3);
t1->joinTo(t1Face[2], t2, t2Face * t1Face.inverse());
}
// Finally add the new tetrahedra into the triangulation.
for (i = 0; i < nFaces; i++)
addTetrahedron(newTet[i]);
delete[] newTet;
return true;
}
} // namespace regina
|
