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
|
/**************************************************************************
* *
* 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 <queue>
#include "surfaces/ndisc.h"
namespace regina {
namespace {
/**
* Stores orientation and sides A/B for a normal disc.
*/
struct OrientData {
int orient;
/**< Specifies the orientation of the disc.
1 represents with the natural boundary orientation.
-1 represents against the natural boundary orientation.
0 means orientation is not yet determined. */
int sides;
/**< Specifies which sides of the disc are sides A/B.
If sides is 1, discs are numbered from side A to B.
If sides is -1, discs are numbered from side B to A.
A value of 0 means sides are not yet determined. */
/**
* Create a new structure with all values initialised to 0.
*/
OrientData() : orient(0), sides(0) {
}
};
}
void NNormalSurface::calculateOrientable() const {
// This is going to be ghastly.
// We will create an orientation and side selection for every disc.
// First check that the precondition (compactness) holds, since if
// it doesn't we'll have a rather nasty crash (thanks Nathan).
if (! isCompact()) {
orientable = NTriBool::Unknown;
twoSided = NTriBool::Unknown;
connected = NTriBool::Unknown;
orientable.clear();
twoSided.clear();
connected.clear();
return;
}
// TODO: First check that there aren't too many discs!
// All right. Off we go.
orientable.clear();
twoSided.clear();
connected.clear();
NDiscSetSurfaceData<OrientData> orients(*this);
// Stores the orientation of each disc.
std::queue<NDiscSpec> discQueue;
// A queue of discs whose orientations must be propagated.
NDiscSpecIterator it(orients);
// Runs through the discs whose orientations might not have yet
// been determined.
NDiscSpec use;
// The disc that currently holds our interest.
int nGluingArcs; // The number of arcs on the current disc to
// which an adjacent disc might may be glued.
NDiscSpec* adjDisc; // The disc to which the current disc is glued.
NPerm arc[8]; // Holds each gluing arc for the current disc.
NPerm adjArc; // Represents the corresponding gluing arc on the
// adjacent disc.
bool myOrient, yourOrient, sameOrient;
bool mySides, yourSides, sameSides;
int i;
bool noComponents = true;
while (true) {
// If there's no discs to propagate from, choose the next
// unoriented one.
while (discQueue.empty() && (! it.done())) {
if (orients.data(*it).orient == 0) {
orients.data(*it).orient = 1;
orients.data(*it).sides = 1;
discQueue.push(*it);
if (noComponents)
noComponents = false;
else
connected = false;
}
it++;
}
if (discQueue.empty())
break;
// At the head of the queue is the next already-oriented disc
// whose orientation must be propagated.
use = discQueue.front();
discQueue.pop();
// Determine along which arcs we may glue other discs.
if (use.type < 4) {
// Current disc is a triangle.
nGluingArcs = 3;
for (i = 0; i < 3; i++)
arc[i] = triDiscArcs(use.type, i);
} else if (use.type < 7) {
// Current disc is a quad.
nGluingArcs = 4;
for (i = 0; i < 4; i++)
arc[i] = quadDiscArcs(use.type - 4, i);
} else {
// Current disc is an octagon.
nGluingArcs = 8;
for (i = 0; i < 8; i++)
arc[i] = octDiscArcs(use.type - 7, i);
}
// Process any discs that might be adjacent to each of these
// gluing arcs.
for (i = 0; i < nGluingArcs; i++) {
// Establish which is the adjacent disc.
adjDisc = orients.adjacentDisc(use, arc[i], adjArc);
if (adjDisc == 0)
continue;
// There is actually a disc glued along this arc.
// Determine the desired properties of the adjacent disc.
if (! orientable.known()) {
myOrient = discOrientationFollowsEdge(use.type,
arc[i][0], arc[i][1], arc[i][2]);
yourOrient = discOrientationFollowsEdge(adjDisc->type,
adjArc[0], adjArc[2], adjArc[1]);
sameOrient = (myOrient && yourOrient) ||
((! myOrient) && (! yourOrient));
} else
sameOrient = true;
if (! twoSided.known()) {
mySides = numberDiscsAwayFromVertex(use.type, arc[i][0]);
yourSides = numberDiscsAwayFromVertex(
adjDisc->type, adjArc[0]);
sameSides = (mySides && yourSides) ||
((! mySides) && (! yourSides));
} else
sameSides = true;
// Propagate these properties.
if (orients.data(*adjDisc).orient == 0) {
orients.data(*adjDisc).orient = (sameOrient ?
orients.data(use).orient : -orients.data(use).orient);
orients.data(*adjDisc).sides = (sameSides ?
orients.data(use).sides : -orients.data(use).sides);
discQueue.push(*adjDisc);
} else {
if (! orientable.known()) {
if (sameOrient) {
if (orients.data(*adjDisc).orient !=
orients.data(use).orient)
orientable = false;
} else {
if (orients.data(*adjDisc).orient ==
orients.data(use).orient)
orientable = false;
}
}
if (! twoSided.known()) {
if (sameSides) {
if (orients.data(*adjDisc).sides !=
orients.data(use).sides)
twoSided = false;
} else {
if (orients.data(*adjDisc).sides ==
orients.data(use).sides)
twoSided = false;
}
}
}
// Tidy up.
delete adjDisc;
if (orientable.known() && twoSided.known() && connected.known())
return;
}
}
// We made it through! Any properties that weren't proven false
// must be true.
if (! orientable.known())
orientable = true;
if (! twoSided.known())
twoSided = true;
if (! connected.known())
connected = true;
}
} // namespace regina
|
