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
|
/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2011, 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 <algorithm>
#include <cstdlib>
#include "triangulation/nisomorphism.h"
#include "triangulation/ntriangulation.h"
namespace regina {
NIsomorphism::NIsomorphism(const NIsomorphism& cloneMe) :
nTetrahedra(cloneMe.nTetrahedra),
mTetImage(cloneMe.nTetrahedra > 0 ?
new int[cloneMe.nTetrahedra] : 0),
mFacePerm(cloneMe.nTetrahedra > 0 ?
new NPerm4[cloneMe.nTetrahedra] : 0) {
std::copy(cloneMe.mTetImage, cloneMe.mTetImage + nTetrahedra, mTetImage);
std::copy(cloneMe.mFacePerm, cloneMe.mFacePerm + nTetrahedra, mFacePerm);
}
void NIsomorphism::writeTextShort(std::ostream& out) const {
out << "Isomorphism between triangulations";
}
void NIsomorphism::writeTextLong(std::ostream& out) const {
for (unsigned i = 0; i < nTetrahedra; i++)
out << i << " -> " << mTetImage[i] << " (" << mFacePerm[i] << ")\n";
}
bool NIsomorphism::isIdentity() const {
for (unsigned t = 0; t < nTetrahedra; t++) {
if (mTetImage[t] != static_cast<int>(t))
return false;
if (! mFacePerm[t].isIdentity())
return false;
}
return true;
}
NTriangulation* NIsomorphism::apply(const NTriangulation* original) const {
if (original->getNumberOfTetrahedra() != nTetrahedra)
return 0;
if (nTetrahedra == 0)
return new NTriangulation();
NTriangulation* ans = new NTriangulation();
NTetrahedron** tet = new NTetrahedron*[nTetrahedra];
unsigned long t;
int f;
NPacket::ChangeEventSpan span(ans);
for (t = 0; t < nTetrahedra; t++)
tet[t] = ans->newTetrahedron();
for (t = 0; t < nTetrahedra; t++)
tet[mTetImage[t]]->setDescription(
original->getTetrahedron(t)->getDescription());
const NTetrahedron *myTet, *adjTet;
unsigned long adjTetIndex;
NPerm4 gluingPerm;
for (t = 0; t < nTetrahedra; t++) {
myTet = original->getTetrahedron(t);
for (f = 0; f < 4; f++)
if ((adjTet = myTet->adjacentTetrahedron(f))) {
// We have an adjacent tetrahedron.
adjTetIndex = original->tetrahedronIndex(adjTet);
gluingPerm = myTet->adjacentGluing(f);
// Make the gluing from one side only.
if (adjTetIndex > t || (adjTetIndex == t &&
gluingPerm[f] > f))
tet[mTetImage[t]]->joinTo(mFacePerm[t][f],
tet[mTetImage[adjTetIndex]],
mFacePerm[adjTetIndex] * gluingPerm *
mFacePerm[t].inverse());
}
}
return ans;
}
void NIsomorphism::applyInPlace(NTriangulation* tri) const {
if (tri->getNumberOfTetrahedra() != nTetrahedra)
return;
if (nTetrahedra == 0)
return;
NTriangulation staging;
NTetrahedron** tet = new NTetrahedron*[nTetrahedra];
unsigned long t;
int f;
NPacket::ChangeEventSpan span1(&staging);
for (t = 0; t < nTetrahedra; t++)
tet[t] = staging.newTetrahedron();
for (t = 0; t < nTetrahedra; t++)
tet[mTetImage[t]]->setDescription(
tri->getTetrahedron(t)->getDescription());
const NTetrahedron *myTet, *adjTet;
unsigned long adjTetIndex;
NPerm4 gluingPerm;
for (t = 0; t < nTetrahedra; t++) {
myTet = tri->getTetrahedron(t);
for (f = 0; f < 4; f++)
if ((adjTet = myTet->adjacentTetrahedron(f))) {
// We have an adjacent tetrahedron.
adjTetIndex = tri->tetrahedronIndex(adjTet);
gluingPerm = myTet->adjacentGluing(f);
// Make the gluing from one side only.
if (adjTetIndex > t || (adjTetIndex == t &&
gluingPerm[f] > f))
tet[mTetImage[t]]->joinTo(mFacePerm[t][f],
tet[mTetImage[adjTetIndex]],
mFacePerm[adjTetIndex] * gluingPerm *
mFacePerm[t].inverse());
}
}
NPacket::ChangeEventSpan span2(tri);
tri->removeAllTetrahedra();
tri->swapContents(staging);
}
NIsomorphism* NIsomorphism::random(unsigned nTetrahedra) {
NIsomorphism* ans = new NIsomorphism(nTetrahedra);
// Randomly choose the destination tetrahedra.
unsigned i;
for (i = 0; i < nTetrahedra; i++)
ans->mTetImage[i] = i;
std::random_shuffle(ans->mTetImage, ans->mTetImage + nTetrahedra);
// Randomly choose the individual permutations.
for (i = 0; i < nTetrahedra; i++)
ans->mFacePerm[i] = NPerm4::S4[rand() % 24];
return ans;
}
} // namespace regina
|
