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
|
////////////////////////////////////////////////////////////////////////////////
//
// CheckTriang.cc
//
// produced: 22 Nov 1999 jr
// last change: 22 Nov 1999 jr
//
////////////////////////////////////////////////////////////////////////////////
#include "LabelSet.hh"
#include "SimplicialComplex.hh"
#include "Permutation.hh"
#include "Chirotope.hh"
#include "CheckTriang.hh"
#include "CommandlineOptions.hh"
namespace topcom {
const bool CheckTriang::operator()() const {
const size_type no(_chiroptr->no());
const size_type rank(_chiroptr->rank());
const size_type dim(rank - 1);
// first check unique conver of a lexicographic extension:
if (!_check_extension_cover()) {
std::cerr << "Triangulation covers an interior extension twice." << std::endl;
return false;
}
// then check intersection of adjacent simplices:
size_type countdown(_triang.card());
if (_fine_only && (_triang.support() != LabelSet(0, no))) {
if (CommandlineOptions::verbose()) {
std::cerr << "Triangulation does not use all vertices." << std::endl;
}
return false;
}
// HashSet<Simplex> done_facets;
SimplicialComplex done_facets;
SimplicialComplex done_simplices;
for (SimplicialComplex::const_iterator iter = _triang.begin();
iter != _triang.end();
++iter) {
--countdown;
const Simplex simp(*iter);
if (simp.card() != rank) {
if (CommandlineOptions::verbose()) {
std::cerr << "Triangulation contains simplex with too few vertices." << std::endl;
}
return false;
}
if (done_simplices.contains(simp, rank)) {
continue;
}
done_simplices.insert(simp, rank);
for (symmetryptr_iterdata::const_iterator sym_iter = _triang_symmetryptrs.first.begin();
sym_iter != _triang_symmetryptrs.first.end();
++sym_iter) {
const Symmetry& g(**sym_iter);
done_simplices.insert(g.map(simp), rank);
}
Simplex facet(simp);
if (CommandlineOptions::verbose()) {
std::cerr << "... still facets of " << countdown << " simplices to check for correctness ..."
<< std::endl;
}
for (Simplex::const_iterator simp_iter = simp.begin();
simp_iter != simp.end();
++simp_iter) {
facet -= *simp_iter;
// if (done_facets.member(facet, dim)) {
if (done_facets.contains(facet, dim)) {
facet += *simp_iter;
continue;
}
if (!_check(facet)) {
return false;
}
done_facets.insert(facet, dim);
for (symmetryptr_iterdata::const_iterator sym_iter = _triang_symmetryptrs.first.begin();
sym_iter != _triang_symmetryptrs.first.end();
++sym_iter) {
const Symmetry& g(**sym_iter);
done_facets.insert(g.map(facet), dim);
}
facet += *simp_iter;
}
}
return true;
}
const bool CheckTriang::_check(const Simplex& facet) const {
// we know already that the link of facet contains only vertices:
Simplex facet_lk;
size_type facet_lk_card(0);
for (SimplicialComplex::const_iterator iter = _triang.begin();
iter != _triang.end();
++iter) {
const Simplex simp(*iter);
if (iter->superset(facet)) {
facet_lk += simp;
++facet_lk_card;
}
}
facet_lk -= facet;
if (facet_lk_card == 0) {
if (CommandlineOptions::verbose()) {
std::cerr << facet << " lies in no simplex." << std::endl;
}
return false;
}
Simplex::const_iterator iter(facet_lk.begin());
size_type i(*iter);
if (facet_lk.card() == 1) {
for (size_type j = 0; j < _chiroptr->no(); ++j) {
if (_opposite_sides(facet, i, j)) {
if (CommandlineOptions::verbose()) {
std::cerr << facet << " lies in exactly one simplex "
<< facet + i << std::endl
<< "but is not contained in a facet because "
<< j << " and " << i << " are on opposite sides." << std::endl;
}
return false;
}
}
return true;
}
else if (facet_lk_card == 2) {
size_type j(*(++iter));
if (!_opposite_sides(facet, i, j)) {
if (CommandlineOptions::verbose()) {
std::cerr << facet << " lies in two simplices "
<< facet + i << " and " << facet + j << std::endl
<< "but " << i << " and " << j
<< " do not lie on opposite sides." << std::endl;
}
return false;
}
return true;
}
else {
if (CommandlineOptions::verbose()) {
std::cerr << facet << " lies in more than two simplices." << std::endl;
}
return false;
}
}
const bool CheckTriang::_opposite_sides(const Simplex& facet,
const size_type i,
const size_type j) const {
if (facet.contains(i) || facet.contains(j)) {
return false;
}
Permutation perm_i(facet);
perm_i.push_back(i);
const int perm_i_sign(perm_i.sign());
const basis_type basis_i(perm_i);
const int basis_i_sign((*_chiroptr)(basis_i));
Permutation perm_j(facet);
perm_j.push_back(j);
const int perm_j_sign(perm_j.sign());
const basis_type basis_j(perm_j);
const int basis_j_sign((*_chiroptr)(basis_j));
return (perm_i_sign * basis_i_sign == -perm_j_sign * basis_j_sign);
}
const bool CheckTriang::_check_extension_cover() const {
size_type countdown(_triang.card());
if (_triang.empty()) {
return false;
}
SimplicialComplex::const_iterator iter(_triang.begin());
// this is the simplex we check for an interior lexicographic extension in
// the reference simplex; no other simplex may contain this extension in its
// convex hull; unfortunately, we cannot make use of the symmetries,
// but the check is fast, anyway:
const Simplex& reference_simp(*iter);
// form the permutation for the lexicographic extension:
const Permutation extension_lex_perm(_chiroptr->no(), _chiroptr->rank(), reference_simp);
while (++iter != _triang.end()) {
if (CommandlineOptions::verbose()) {
std::cerr << "... still " << --countdown << " simplices to check for unique extension cover ..."
<< std::endl;
}
const Simplex& checksimp(*iter);
Simplex facet(checksimp);
bool checksimp_okay = false;
// check all signs of facets of checksimp plus the extension point:
int pm((*_chiroptr)(checksimp));
if (_chiroptr->rank() % 2) {
pm = -pm;
}
for (Simplex::const_iterator simp_iter = checksimp.begin();
simp_iter != checksimp.end();
++simp_iter) {
facet -= *simp_iter;
if ((*_chiroptr)(facet, extension_lex_perm) == pm) {
// checksimp is okay:
checksimp_okay = true;
}
pm = -pm;
facet += *simp_iter;
}
if (!checksimp_okay) {
if (CommandlineOptions::verbose()) {
std::cerr << "lexicographic extension in " << reference_simp
<< " is also covered by " << checksimp
<< std::endl;
}
return false;
}
}
return true;
}
};
// eof CheckTriang.cc
|
