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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 "angle/anglestructure.h"
#include "maths/matrix.h"
#include "triangulation/dim3.h"
#include "utilities/xmlutils.h"
namespace regina {
std::weak_ordering AngleStructure::operator <=> (const AngleStructure& rhs)
const {
if (triangulation_->size() != rhs.triangulation_->size())
return triangulation_->size() <=> rhs.triangulation_->size();
#if defined(LEXCMP_FOUND)
return std::lexicographical_compare_three_way(
vector_.begin(), vector_.end(), rhs.vector_.begin(), rhs.vector_.end());
#else
// The triangulations have the same size, and so both underlying vectors
// should have the same length.
auto i = vector_.begin();
auto j = rhs.vector_.begin();
for ( ; i != vector_.end(); ++i, ++j)
if (auto c = (*i <=> *j); c != 0)
return c;
return std::strong_ordering::equal;
#endif
}
Rational AngleStructure::angle(size_t tetIndex, int edgePair) const {
const Integer& num = vector_[3 * tetIndex + edgePair];
const Integer& den = vector_[3 * triangulation_->size()];
Integer gcd = den.gcd(num); // Guaranteed non-negative
return Rational(num.divExact(gcd), den.divExact(gcd));
}
void AngleStructure::writeTextShort(std::ostream& out) const {
size_t nTets = triangulation_->size();
unsigned j;
for (size_t tet = 0; tet < nTets; tet++) {
if (tet > 0)
out << " ; ";
for (j=0; j<3; j++) {
if (j > 0)
out << ' ';
out << angle(tet, j);
}
}
}
void AngleStructure::writeXMLData(std::ostream& out) const {
// Write the vector length.
size_t vecLen = vector_.size();
out << " <struct len=\"" << vecLen << "\"> ";
// Write the non-zero elements.
Integer entry;
for (size_t i = 0; i < vecLen; i++) {
entry = vector_[i];
if (entry != 0)
out << i << ' ' << entry << ' ';
}
// Write the closing tag.
out << "</struct>\n";
}
void AngleStructure::calculateType() const {
size_t size = vector_.size();
if (size == 1) {
// We have no tetrahedra, which means this angle structure has it all:
// strict, taut and veering.
flags_ |= flagStrict;
flags_ |= flagTaut;
flags_ |= flagVeering;
flags_ |= flagCalculatedType;
return;
}
bool taut = true;
bool strict = true;
// Run through the tetrahedra one by one.
const Integer& scale = vector_[size - 1];
size_t pair;
for (size_t base = 0; base < size - 1; base += 3) {
for (pair = 0; pair < 3; pair++) {
if (vector_[base + pair] == scale) {
// We have a pi; thus all three angles in this
// tetrahedron are pi or zero.
strict = false;
break;
} else if (vector_[base + pair] == 0)
strict = false;
else
taut = false;
}
if ((! strict) && (! taut))
break;
}
// Update the flags as appropriate.
if (strict)
flags_ |= flagStrict;
else
flags_ &= (~flagStrict);
if (taut) {
// This structure is taut.
flags_ |= flagTaut;
// Get a local reference to the triangulation so we do not have
// to repeatedly bounce through the snapshot.
const Triangulation<3>& tri(*triangulation_);
// Is it veering also?
bool veering = true;
if (tri.isOrientable()) {
long nEdges = tri.countEdges();
int* edgeColour = new int[nEdges];
std::fill(edgeColour, edgeColour + nEdges, (int)0);
const Tetrahedron<3>* tet;
int orient;
long e;
for (unsigned i = 0; i < tri.size();
++i) {
tet = tri.tetrahedron(i);
orient = tet->orientation();
if (vector_[3 * i] > 0) {
// Edges 0,5 are marked as pi.
// For a positively oriented tetrahedron:
// Edges 1,4 vs 2,3 are of colour +1 vs -1.
e = tet->edge(1)->index();
if (edgeColour[e] == -orient)
veering = false;
else
edgeColour[e] = orient;
e = tet->edge(4)->index();
if (edgeColour[e] == -orient)
veering = false;
else
edgeColour[e] = orient;
e = tet->edge(2)->index();
if (edgeColour[e] == orient)
veering = false;
else
edgeColour[e] = -orient;
e = tet->edge(3)->index();
if (edgeColour[e] == orient)
veering = false;
else
edgeColour[e] = -orient;
} else if (vector_[3 * i + 1] > 0) {
// Edges 1,4 are marked as pi.
// For a positively oriented tetrahedron:
// Edges 2,3 vs 0,5 are of colour +1 vs -1.
e = tet->edge(2)->index();
if (edgeColour[e] == -orient)
veering = false;
else
edgeColour[e] = orient;
e = tet->edge(3)->index();
if (edgeColour[e] == -orient)
veering = false;
else
edgeColour[e] = orient;
e = tet->edge(0)->index();
if (edgeColour[e] == orient)
veering = false;
else
edgeColour[e] = -orient;
e = tet->edge(5)->index();
if (edgeColour[e] == orient)
veering = false;
else
edgeColour[e] = -orient;
} else if (vector_[3 * i + 2] > 0) {
// Edges 2,3 are marked as pi.
// For a positively oriented tetrahedron:
// Edges 0,5 vs 1,4 are of colour +1 vs -1.
e = tet->edge(0)->index();
if (edgeColour[e] == -orient)
veering = false;
else
edgeColour[e] = orient;
e = tet->edge(5)->index();
if (edgeColour[e] == -orient)
veering = false;
else
edgeColour[e] = orient;
e = tet->edge(1)->index();
if (edgeColour[e] == orient)
veering = false;
else
edgeColour[e] = -orient;
e = tet->edge(4)->index();
if (edgeColour[e] == orient)
veering = false;
else
edgeColour[e] = -orient;
}
if (! veering)
break;
}
delete[] edgeColour;
} else {
// Only orientable triangulations can be veering.
veering = false;
}
if (veering)
flags_ |= flagVeering;
else
flags_ &= (~flagVeering);
} else {
// Not taut, and therefore not veering either.
flags_ &= (~flagTaut);
flags_ &= (~flagVeering);
}
flags_ |= flagCalculatedType;
}
} // namespace regina
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