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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 "hypersurface/normalhypersurface.h"
#include "triangulation/dim4.h"
#include <stack>
namespace regina {
template <int subdim>
std::pair<NormalHypersurface, bool> Triangulation<4>::linkingSurface(
const Face<4, subdim>& face) const {
static_assert(0 <= subdim && subdim < 4,
"Triangulation<4>::linkingSurface() requires a face of dimension "
"0, 1, 2 or 3.");
Vector<LargeInteger> coords(15 * size());
bool thin = true;
if constexpr (subdim == 0) {
// Vertex links are trivial to construct.
for (auto& emb : face)
coords[15 * emb.simplex()->index() + emb.vertex()] = 1;
} else {
// In general, face links can require normalisation.
//
// However, this normalisation always involves expanding the face
// into a larger subcomplex using the following rules:
// 1) at least two edges of a triangle -> absorb the full triangle;
// 2) at least two triangles of a tetrahedron -> absorb the full
// tetrahedron;
// 3) at least two tetrahedra of a pentachoron -> absorb the full
// pentachoron.
//
// The resulting face link is then the frontier of a regular
// neighbourhood of the resulting subcomplex.
//
// So: our main job is to build the subcomplex.
// We track the subcomplex with an array of booleans for each facial
// dimension, indicating which of the faces is currently included.
bool* use0 = new bool[countVertices()];
bool* use1 = new bool[countEdges()];
bool* use2 = new bool[countTriangles()];
bool* use3 = new bool[countTetrahedra()];
bool* use4 = new bool[size()];
std::fill(use0, use0 + countVertices(), false);
std::fill(use1, use1 + countEdges(), false);
std::fill(use2, use2 + countTriangles(), false);
std::fill(use3, use3 + countTetrahedra(), false);
std::fill(use4, use4 + size(), false);
if constexpr (subdim == 1) {
use1[face.index()] = true;
use0[face.vertex(0)->index()] = true;
use0[face.vertex(1)->index()] = true;
} else if constexpr (subdim == 2) {
use2[face.index()] = true;
for (int i = 0; i < 3; ++i)
use1[face.edge(i)->index()] = true;
for (int i = 0; i < 3; ++i)
use0[face.vertex(i)->index()] = true;
} else {
use3[face.index()] = true;
for (int i = 0; i < 4; ++i)
use2[face.triangle(i)->index()] = true;
for (int i = 0; i < 6; ++i)
use1[face.edge(i)->index()] = true;
for (int i = 0; i < 4; ++i)
use0[face.vertex(i)->index()] = true;
}
// Faces that were recently incorporated into the subcomplex,
// for which we need to now check for any follow-up larger faces
// that will need to be incorporated also as a result:
std::stack<const Edge<4>*> process1;
std::stack<const Triangle<4>*> process2;
std::stack<const Tetrahedron<4>*> process3;
if constexpr (subdim == 1) {
process1.push(std::addressof(face));
} else if constexpr (subdim == 2) {
process2.push(std::addressof(face));
for (int i = 0; i < 3; ++i)
process1.push(face.edge(i));
} else {
process3.push(std::addressof(face));
for (int i = 0; i < 4; ++i)
process2.push(face.triangle(i));
for (int i = 0; i < 6; ++i)
process1.push(face.edge(i));
}
while (true) {
if (! process3.empty()) {
const Tetrahedron<4>* t = process3.top();
process3.pop();
for (const auto& emb : *t) {
const Pentachoron<4>* pent = emb.pentachoron();
if (use4[pent->index()])
continue;
int found = 0;
for (int j = 0; j < 5; ++j)
if (use3[pent->tetrahedron(j)->index()]) {
++found;
if (found == 2)
break;
}
if (found == 2) {
// Absorb the entire pentachoron.
thin = false;
use4[pent->index()] = true;
for (int j = 0; j < 5; ++j) {
const Tetrahedron<4>* next = pent->tetrahedron(j);
if (! use3[next->index()]) {
use3[next->index()] = true;
process3.push(next);
}
}
for (int j = 0; j < 10; ++j) {
const Triangle<4>* next = pent->triangle(j);
if (! use2[next->index()]) {
use2[next->index()] = true;
process2.push(next);
}
}
for (int j = 0; j < 10; ++j) {
const Edge<4>* next = pent->edge(j);
if (! use1[next->index()]) {
use1[next->index()] = true;
process1.push(next);
}
}
}
}
continue;
}
if (! process2.empty()) {
const Triangle<4>* t = process2.top();
process2.pop();
bool bothSides = t->isBoundary();
for (const auto& emb : *t) {
for (int side = 0; side < 2; ++side) {
if (side == 1) {
if (! bothSides)
continue; // side 0 is enough
// We do both sides for this embedding (which is
// the first in the list), but *only* this
// embedding.
bothSides = false;
}
const Tetrahedron<4>* tet = emb.pentachoron()->
tetrahedron(emb.vertices()[side == 0 ? 3 : 4]);
if (use3[tet->index()])
continue;
int found = 0;
for (int j = 0; j < 4; ++j)
if (use2[tet->triangle(j)->index()]) {
++found;
if (found == 2)
break;
}
if (found == 2) {
// Absorb the entire tetrahedron.
thin = false;
use3[tet->index()] = true;
process3.push(tet);
for (int j = 0; j < 4; ++j) {
const Triangle<4>* next = tet->triangle(j);
if (! use2[next->index()]) {
use2[next->index()] = true;
process2.push(next);
}
}
for (int j = 0; j < 6; ++j) {
const Edge<4>* next = tet->edge(j);
if (! use1[next->index()]) {
use1[next->index()] = true;
process1.push(next);
}
}
}
}
}
continue;
}
if (! process1.empty()) {
const Edge<4>* e = process1.top();
process1.pop();
// We need to check all *triangles* that contain e.
// The code below is quite inefficient, in that it checks far
// too many triangles, and moreover checks the same triangles
// multiple times. It should probably be improved.
for (const auto& emb : *e) {
const Pentachoron<4>* pent = emb.pentachoron();
// For now, just check *all* triangles of pent.
for (int i = 0; i < 10; ++i) {
const Triangle<4>* triangle = pent->triangle(i);
if (use2[triangle->index()])
continue;
int found = 0;
for (int j = 0; j < 3; ++j)
if (use1[triangle->edge(j)->index()]) {
++found;
if (found == 2)
break;
}
if (found == 2) {
// Absorb the entire triangle.
thin = false;
use2[triangle->index()] = true;
process2.push(triangle);
for (int j = 0; j < 3; ++j) {
const Edge<4>* next = triangle->edge(j);
if (! use1[next->index()]) {
use1[next->index()] = true;
process1.push(next);
}
}
}
}
}
continue;
}
break;
}
size_t pentIndex = 0;
for (const Pentachoron<4>* pent : pentachora()) {
if (use4[pentIndex])
goto donePent;
for (int j = 0; j < 5; ++j)
if (use3[pent->tetrahedron(j)->index()]) {
if (use0[pent->vertex(j)->index()])
coords[15 * pentIndex + j] = 2;
else
coords[15 * pentIndex + j] = 1;
goto donePent;
}
for (int j = 0; j < 10; ++j)
if (use2[pent->triangle(j)->index()]) {
if (use1[pent->edge(j)->index()])
coords[15 * pentIndex + 5 + j] = 2;
else {
coords[15 * pentIndex + 5 + j] = 1;
for (int end = 0; end < 2; ++end) {
int v = Edge<4>::edgeVertex[j][end];
if (use0[pent->vertex(v)->index()])
coords[15 * pentIndex + v] = 1;
}
}
goto donePent;
}
// We are down to just edges and/or vertices.
// There could be multiple disjoint edges, or multiple vertices.
{
bool skipVertex[5] = { false, false, false, false, false };
for (int j = 0; j < 10; ++j)
if (use1[pent->edge(j)->index()]) {
coords[15 * pentIndex + 5 + j] = 1;
skipVertex[Edge<4>::edgeVertex[j][0]] = true;
skipVertex[Edge<4>::edgeVertex[j][1]] = true;
}
for (int j = 0; j < 5; ++j)
if ((! skipVertex[j]) && use0[pent->vertex(j)->index()])
coords[15 * pentIndex + j] = 1;
}
donePent:
++pentIndex;
}
delete[] use0;
delete[] use1;
delete[] use2;
delete[] use3;
delete[] use4;
}
return { NormalHypersurface(*this, HyperCoords::Standard,
std::move(coords)), thin };
}
// Instantiate linkingSurface() for all possible template arguments,
// so that the implementation can stay out of the headers.
template std::pair<NormalHypersurface, bool>
Triangulation<4>::linkingSurface<0>(const Face<4, 0>&) const;
template std::pair<NormalHypersurface, bool>
Triangulation<4>::linkingSurface<1>(const Face<4, 1>&) const;
template std::pair<NormalHypersurface, bool>
Triangulation<4>::linkingSurface<2>(const Face<4, 2>&) const;
template std::pair<NormalHypersurface, bool>
Triangulation<4>::linkingSurface<3>(const Face<4, 3>&) const;
} // namespace regina
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