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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, 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. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* 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, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include "enumerate/enumconstraints.h"
#include "surfaces/nsvectororiented.h"
#include "maths/matrix.h"
#include "maths/rational.h"
#include "triangulation/dim3.h"
namespace regina {
LargeInteger NSVectorOriented::edgeWeight(
size_t edgeIndex, const Triangulation<3>& triang) const {
// Find a tetrahedron next to the edge in question.
const EdgeEmbedding<3>& emb = triang.edge(edgeIndex)->front();
long tetIndex = emb.tetrahedron()->index();
int start = emb.vertices()[0];
int end = emb.vertices()[1];
// Add up the triangles and quads meeting that edge.
// Triangles:
LargeInteger ans(triangles(tetIndex,start,triang));
ans += triangles(tetIndex,end,triang);
// Quads:
ans += quads(tetIndex, quadMeeting[start][end][0],triang);
ans += quads(tetIndex, quadMeeting[start][end][1],triang);
return ans;
}
LargeInteger NSVectorOriented::arcs(size_t triIndex,
int triVertex, const Triangulation<3>& triang) const {
// Find a tetrahedron next to the triangle in question.
const TriangleEmbedding<3>& emb = triang.triangles()[triIndex]->front();
long tetIndex = emb.tetrahedron()->index();
int vertex = emb.vertices()[triVertex];
int backOfFace = emb.vertices()[3];
// Add up the triangles and quads meeting that triangle in the required arc.
// Triangles:
LargeInteger ans(triangles(tetIndex,vertex,triang));
// Quads:
ans += quads(tetIndex, quadSeparating[vertex][backOfFace],triang);
return ans;
}
std::optional<MatrixInt> NSVectorOriented::makeMatchingEquations(
const Triangulation<3>& triangulation) {
size_t nCoords = 14 * triangulation.size();
// Six equations per non-boundary triangle.
// F_boundary + 2 F_internal = 4 T
long nEquations = 6 * (4 * long(triangulation.size()) -
long(triangulation.countTriangles()));
MatrixInt ans(nEquations, nCoords);
// Run through each internal triangle and add the corresponding three
// equations.
unsigned row = 0;
int i;
size_t tet0, tet1;
Perm<4> perm0, perm1;
bool natural;
for (Triangle<3>* t : triangulation.triangles()) {
if (! t->isBoundary()) {
tet0 = t->embedding(0).tetrahedron()->index();
tet1 = t->embedding(1).tetrahedron()->index();
perm0 = t->embedding(0).vertices();
perm1 = t->embedding(1).vertices();
for (i=0; i<3; i++) {
// row: oriented towards the vertex of the face
// row+1: oriented towards the opposite face
// Triangles:
ans.entry(row, 14*tet0 + 2*perm0[i]) += 1;
ans.entry(row+1, 14*tet0 + 2*perm0[i] + 1) += 1;
ans.entry(row, 14*tet1 + 2*perm1[i]) -= 1;
ans.entry(row+1, 14*tet1 + 2*perm1[i] + 1) -= 1;
// Quads:
natural = (perm0[i] == 0 || perm0[3] == 0);
ans.entry(row, 14*tet0 + 8 +
2*quadSeparating[perm0[i]][perm0[3]] +
(natural ? 0 : 1)) += 1;
ans.entry(row+1, 14*tet0 + 8 +
2*quadSeparating[perm0[i]][perm0[3]] +
(natural ? 1 : 0)) += 1;
natural = (perm1[i] == 0 || perm1[3] == 0);
ans.entry(row, 14*tet1 + 8 +
2*quadSeparating[perm1[i]][perm1[3]] +
(natural ? 0 : 1)) -= 1;
ans.entry(row+1, 14*tet1 + 8 +
2*quadSeparating[perm1[i]][perm1[3]] +
(natural ? 1 : 0)) -= 1;
row+=2;
}
}
}
return ans;
}
EnumConstraints NSVectorOriented::makeEmbeddedConstraints(
const Triangulation<3>& triangulation) {
// TODO: Must be a neater way of doing this, but might mean re-working
// bitmasks.
EnumConstraints ans(8 * triangulation.size());
unsigned base = 0;
unsigned c = 0;
while (c < ans.size()) {
for (unsigned d = 0; d < 2; d++) {
for (unsigned e = 0; e < 2; e++) {
for (unsigned f = 0; f < 2; f++) {
ans[c].insert(ans[c].end(), base + 8 + d);
ans[c].insert(ans[c].end(), base + 10 + e);
ans[c].insert(ans[c].end(), base + 12 + f);
++c;
}
}
}
base += 14;
}
return ans;
}
} // namespace regina
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