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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 "surface/normalsurface.h"
#include "maths/matrix.h"
#include "maths/rational.h"
#include "triangulation/dim3.h"
namespace regina {
namespace {
/**
* A structure representing one end of an edge.
*/
struct EdgeEnd {
Edge<3>* edge; /**< The edge under consideration. */
int end; /**< Either 0 or 1, indicating which end of the edge. */
};
}
NormalEncoding NormalSurface::reconstructTriangles(
const Triangulation<3>& tri, Vector<LargeInteger>& vector,
NormalEncoding enc) {
// We are offering this function to the public, so do a sanity check on enc.
// For our own code this is redundant but it's just one bit-flag test.
if (enc.storesTriangles())
return enc;
const NormalEncoding newEnc = enc.withTriangles();
const int newBlock = newEnc.block();
const size_t newSize = newBlock * tri.size();
Vector<LargeInteger> ans(newSize);
// Set every triangular coordinate in the answer to infinity.
// For coordinates about vertices not enjoying infinitely many discs,
// infinity will mean "unknown".
for (size_t row = 0; row < newSize; row += newBlock)
for (int i = 0; i < 4; ++i)
ans[row + i].makeInfinite();
// Copy across the other (non-triangular) coordinates.
for (size_t row = 0; newBlock * row < newSize; ++row)
for (int i = 0; i < enc.block(); ++i)
ans[newBlock * row + 4 + i] = vector[enc.block() * row + i];
// Record which edge ends we have already examined.
bool* used = new bool[2 * tri.countEdges()];
std::fill(used, used + 2 * tri.countEdges(), false);
// Prepare a stack of edge ends that we are ready to examine.
auto* examine = new EdgeEnd[2 * tri.countEdges()];
size_t nExamine = 0;
// Run through the vertices and fix the triangular coordinates
// about each vertex in turn.
for (Vertex<3>* v : tri.vertices()) {
nExamine = 0;
bool broken = false; // Are the equations broken around this vertex?
// Pick some triangular disc and set it to zero.
const VertexEmbedding<3>& vemb = v->front();
ans[newBlock * vemb.tetrahedron()->index() + vemb.vertex()] = 0;
LargeInteger min; // The minimum triangle coordinate around this vertex.
// Mark the three surrounding edge ends for examination.
for (int i=0; i<4; i++) {
if (i == vemb.vertex())
continue;
EdgeEnd e {
vemb.tetrahedron()->edge(Edge<3>::edgeNumber[vemb.vertex()][i]),
vemb.tetrahedron()->edgeMapping(
Edge<3>::edgeNumber[vemb.vertex()][i])[0] == i ? 1 : 0
};
size_t usedIndex = 2 * e.edge->index() + e.end;
if (! used[usedIndex]) {
used[usedIndex] = true;
examine[nExamine++] = e;
}
}
// Run a depth-first search through the edge ends that meet this
// vertex link.
while ((! broken) && nExamine) {
EdgeEnd current = examine[--nExamine];
// Run around this edge end.
// We know there is a pre-chosen coordinate somewhere; run
// forwards and find this.
const auto beginit = current.edge->begin();
const auto endit = current.edge->end();
auto eembit = beginit;
for ( ; eembit != endit; ++eembit)
if (! ans[newBlock * eembit->tetrahedron()->index() +
eembit->vertices()[current.end]].isInfinite())
break;
// We are now at the first pre-chosen coordinate about this
// vertex. Run backwards from here and fill in all the holes.
Perm<4> adjPerm = eembit->vertices();
size_t adjPos = newBlock * eembit->tetrahedron()->index();
auto backupit = eembit;
while (eembit != beginit) {
--eembit;
// Work out the coordinate for the disc type at eembit.
Tetrahedron<3>* tet = eembit->tetrahedron();
Perm<4> tetPerm = eembit->vertices();
size_t tetPos = newBlock * tet->index();
LargeInteger expect =
ans[adjPos + adjPerm[current.end]]
+ ans[adjPos + 4 +
quadSeparating[adjPerm[3]][adjPerm[current.end]]]
- ans[tetPos + 4 +
quadSeparating[tetPerm[2]][tetPerm[current.end]]];
if (enc.storesOctagons()) {
expect = expect
+ ans[adjPos + 7 + quadMeeting
[adjPerm[3]][adjPerm[current.end]][0]]
+ ans[adjPos + 7 + quadMeeting
[adjPerm[3]][adjPerm[current.end]][1]]
- ans[tetPos + 7 + quadMeeting
[tetPerm[2]][tetPerm[current.end]][0]]
- ans[tetPos + 7 + quadMeeting
[tetPerm[2]][tetPerm[current.end]][1]];
}
ans[tetPos + tetPerm[current.end]] = expect;
if (expect < min)
min = expect;
// Remember to examine the new edge end if appropriate.
EdgeEnd e {
tet->edge(Edge<3>::edgeNumber[tetPerm[2]]
[tetPerm[current.end]]),
tet->edgeMapping(Edge<3>::edgeNumber[tetPerm[2]]
[tetPerm[current.end]])[0] == tetPerm[2] ? 1 : 0
};
size_t usedIndex = 2 * e.edge->index() + e.end;
if (! used[usedIndex]) {
used[usedIndex] = true;
examine[nExamine++] = e;
}
adjPerm = tetPerm;
adjPos = tetPos;
}
// Now move forwards from the original first pre-chosen
// coordinate, again filling in the holes.
eembit = backupit;
adjPerm = eembit->vertices();
adjPos = newBlock * eembit->tetrahedron()->index();
for (++eembit; eembit != endit; ++eembit) {
// Work out the coordinate for the disc type at eembit.
Tetrahedron<3>* tet = eembit->tetrahedron();
Perm<4> tetPerm = eembit->vertices();
size_t tetPos = newBlock * tet->index();
LargeInteger expect =
ans[adjPos + adjPerm[current.end]]
+ ans[adjPos + 4 +
quadSeparating[adjPerm[2]][adjPerm[current.end]]]
- ans[tetPos + 4 +
quadSeparating[tetPerm[3]][tetPerm[current.end]]];
if (enc.storesOctagons()) {
expect = expect
+ ans[adjPos + 7 + quadMeeting
[adjPerm[2]][adjPerm[current.end]][0]]
+ ans[adjPos + 7 + quadMeeting
[adjPerm[2]][adjPerm[current.end]][1]]
- ans[tetPos + 7 + quadMeeting
[tetPerm[3]][tetPerm[current.end]][0]]
- ans[tetPos + 7 + quadMeeting
[tetPerm[3]][tetPerm[current.end]][1]];
}
size_t row = tetPos + tetPerm[current.end];
if (ans[row].isInfinite()) {
ans[row] = expect;
if (expect < min)
min = expect;
// Remember to examine the new edge end if appropriate.
EdgeEnd e {
tet->edge(Edge<3>::edgeNumber[tetPerm[3]]
[tetPerm[current.end]]),
tet->edgeMapping(Edge<3>::edgeNumber[tetPerm[3]]
[tetPerm[current.end]])[0] == tetPerm[3] ? 1 : 0
};
size_t usedIndex = 2 * e.edge->index() + e.end;
if (! used[usedIndex]) {
used[usedIndex] = true;
examine[nExamine++] = e;
}
} else {
// This coordinate has already been set.
// Make sure it's the same value!
if (ans[row] != expect) {
broken = true;
break;
}
}
adjPerm = tetPerm;
adjPos = tetPos;
}
}
// If the matching equations were broken, set every coordinate
// to infinity. Otherwise subtract min from every coordinate to
// make the values as small as possible.
for (const auto& emb : *v) {
size_t row = newBlock * emb.tetrahedron()->index() + emb.vertex();
if (broken)
ans[row].makeInfinite();
else
ans[row] -= min;
}
}
delete[] used;
// Note that there should be no need to remove common factors since
// the quad coordinates have not changed and in theory they already
// had gcd=1.
vector = std::move(ans);
return newEnc;
}
} // namespace regina
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