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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 <queue>
#include "surface/disc.h"
namespace regina {
namespace {
/**
* Stores orientation and sides A/B for a normal disc.
*/
struct OrientData {
int orient { 0 };
/**< Specifies the orientation of the disc.
1 represents with the natural boundary orientation.
-1 represents against the natural boundary orientation.
0 means orientation is not yet determined. */
int sides { 0 };
/**< Specifies which sides of the disc are sides A/B.
If sides is 1, discs are numbered from side A to B.
If sides is -1, discs are numbered from side B to A.
A value of 0 means sides are not yet determined. */
};
}
void NormalSurface::calculateOrientable() const {
// This is going to be ghastly.
// We will create an orientation and side selection for every disc.
orientable_.reset();
twoSided_.reset();
connected_.reset();
// First check that the precondition (compactness) holds, since if
// it doesn't we'll have a rather nasty crash (thanks Nathan).
if (! isCompact())
return;
// All right. Off we go.
DiscSetSurfaceData<OrientData> orients(*this);
// Stores the orientation of each disc.
std::queue<DiscSpec> discQueue;
// A queue of discs whose orientations must be propagated.
DiscSpecIterator it(orients);
// Runs through the discs whose orientations might not have yet
// been determined.
DiscSpec use;
// The disc that currently holds our interest.
int nGluingArcs; // The number of arcs on the current disc to
// which an adjacent disc might may be glued.
Perm<4> arc[8]; // Holds each gluing arc for the current disc.
bool myOrient, yourOrient, sameOrient;
bool mySides, yourSides, sameSides;
int i;
bool noComponents = true;
while (true) {
// If there's no discs to propagate from, choose the next
// unoriented one.
while (discQueue.empty() && (! it.done())) {
if (orients.data(*it).orient == 0) {
orients.data(*it).orient = 1;
orients.data(*it).sides = 1;
discQueue.push(*it);
if (noComponents)
noComponents = false;
else
connected_ = false;
}
++it;
}
if (discQueue.empty())
break;
// At the head of the queue is the next already-oriented disc
// whose orientation must be propagated.
use = discQueue.front();
discQueue.pop();
// Determine along which arcs we may glue other discs.
if (use.type < 4) {
// Current disc is a triangle.
nGluingArcs = 3;
for (i = 0; i < 3; i++)
arc[i] = triDiscArcs[use.type][i];
} else if (use.type < 7) {
// Current disc is a quad.
nGluingArcs = 4;
for (i = 0; i < 4; i++)
arc[i] = quadDiscArcs[use.type - 4][i];
} else {
// Current disc is an octagon.
nGluingArcs = 8;
for (i = 0; i < 8; i++)
arc[i] = octDiscArcs[use.type - 7][i];
}
// Process any discs that might be adjacent to each of these
// gluing arcs.
for (i = 0; i < nGluingArcs; i++) {
// Establish which is the adjacent disc.
auto adjDisc = orients.adjacentDisc(use, arc[i]);
if (! adjDisc)
continue;
// There is actually a disc glued along this arc.
// Determine the desired properties of the adjacent disc.
Perm<4> adjArc = adjDisc->second;
if (! orientable_.has_value()) {
myOrient = discOrientationFollowsEdge(use.type,
arc[i][0], arc[i][1], arc[i][2]);
yourOrient = discOrientationFollowsEdge(adjDisc->first.type,
adjArc[0], adjArc[2], adjArc[1]);
sameOrient = (myOrient && yourOrient) ||
((! myOrient) && (! yourOrient));
} else
sameOrient = true;
if (! twoSided_.has_value()) {
mySides = numberDiscsAwayFromVertex(use.type, arc[i][0]);
yourSides = numberDiscsAwayFromVertex(
adjDisc->first.type, adjArc[0]);
sameSides = (mySides && yourSides) ||
((! mySides) && (! yourSides));
} else
sameSides = true;
// Propagate these properties.
if (orients.data(adjDisc->first).orient == 0) {
orients.data(adjDisc->first).orient = (sameOrient ?
orients.data(use).orient : -orients.data(use).orient);
orients.data(adjDisc->first).sides = (sameSides ?
orients.data(use).sides : -orients.data(use).sides);
discQueue.push(adjDisc->first);
} else {
if (! orientable_.has_value()) {
if (sameOrient) {
if (orients.data(adjDisc->first).orient !=
orients.data(use).orient)
orientable_ = false;
} else {
if (orients.data(adjDisc->first).orient ==
orients.data(use).orient)
orientable_ = false;
}
}
if (! twoSided_.has_value()) {
if (sameSides) {
if (orients.data(adjDisc->first).sides !=
orients.data(use).sides)
twoSided_ = false;
} else {
if (orients.data(adjDisc->first).sides ==
orients.data(use).sides)
twoSided_ = false;
}
}
}
if (orientable_.has_value() && twoSided_.has_value() &&
connected_.has_value())
return;
}
}
// We made it through! Any properties that weren't proven false
// must be true.
if (! orientable_.has_value())
orientable_ = true;
if (! twoSided_.has_value())
twoSided_ = true;
if (! connected_.has_value())
connected_ = true;
}
} // namespace regina
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