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|
/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, 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. *
* *
* 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, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include <algorithm>
#include <utility>
#include "algebra/nabeliangroup.h"
#include "manifold/nsfs.h"
#include "triangulation/ncomponent.h"
#include "triangulation/nedge.h"
#include "triangulation/ntetrahedron.h"
#include "subcomplex/naugtrisolidtorus.h"
#include "subcomplex/nlayeredchain.h"
namespace regina {
const int NAugTriSolidTorus::CHAIN_NONE = 0;
const int NAugTriSolidTorus::CHAIN_MAJOR = 1;
const int NAugTriSolidTorus::CHAIN_AXIS = 2;
NAugTriSolidTorus::~NAugTriSolidTorus() {
if (core)
delete core;
for (int i = 0; i < 3; i++)
if (augTorus[i])
delete augTorus[i];
}
NAugTriSolidTorus* NAugTriSolidTorus::clone() const {
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core->clone();
for (int i = 0; i < 3; i++) {
if (augTorus[i])
ans->augTorus[i] = augTorus[i]->clone();
ans->edgeGroupRoles[i] = edgeGroupRoles[i];
}
ans->chainIndex = chainIndex;
ans->chainType = chainType;
ans->torusAnnulus = torusAnnulus;
return ans;
}
NManifold* NAugTriSolidTorus::getManifold() const {
NSFSpace* ans = new NSFSpace();
if (chainType == CHAIN_MAJOR) {
// Layered solid torus + layered chain.
ans->insertFibre(2, 1);
ans->insertFibre(chainIndex + 1, 1);
long q, r;
if (edgeGroupRoles[torusAnnulus][2] == 2) {
if (augTorus[torusAnnulus]) {
r = augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][0]);
q = augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][1]);
} else {
r = 1;
q = 1;
}
} else {
if (augTorus[torusAnnulus]) {
r = augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][0]);
q = -augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][1]);
} else {
r = (edgeGroupRoles[torusAnnulus][0] == 2 ? 2 : 1);
q = -(edgeGroupRoles[torusAnnulus][1] == 2 ? 2 : 1);
}
}
r = r - q;
if (r < 0) {
r = -r;
q = -q;
}
if (r == 0) {
delete ans;
return 0;
} else
ans->insertFibre(r, q);
} else if (chainType == CHAIN_AXIS) {
// Layered solid torus + layered chain.
ans->insertFibre(2, 1);
ans->insertFibre(2, -1);
long q, r;
if (edgeGroupRoles[torusAnnulus][2] == 2) {
if (augTorus[torusAnnulus]) {
r = augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][0]);
q = augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][1]);
} else {
r = 1;
q = 1;
}
} else {
if (augTorus[torusAnnulus]) {
r = augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][0]);
q = -augTorus[torusAnnulus]->getMeridinalCuts(
edgeGroupRoles[torusAnnulus][1]);
} else {
r = (edgeGroupRoles[torusAnnulus][0] == 2 ? 2 : 1);
q = -(edgeGroupRoles[torusAnnulus][1] == 2 ? 2 : 1);
}
}
long alpha = q - chainIndex * r;
long beta = -r;
if (alpha < 0) {
alpha = -alpha;
beta = -beta;
}
if (alpha == 0) {
delete ans;
return 0;
} else
ans->insertFibre(alpha, beta);
} else {
// Three layered solid tori.
ans->insertFibre(1, 1);
long alpha, beta;
for (int i = 0; i < 3; i++) {
if (edgeGroupRoles[i][2] == 2) {
if (augTorus[i]) {
alpha = augTorus[i]->getMeridinalCuts(edgeGroupRoles[i][0]);
beta = augTorus[i]->getMeridinalCuts(edgeGroupRoles[i][1]);
} else {
alpha = 1;
beta = 1;
}
} else {
if (augTorus[i]) {
alpha = augTorus[i]->getMeridinalCuts(edgeGroupRoles[i][0]);
beta = -augTorus[i]->getMeridinalCuts(edgeGroupRoles[i][1]);
} else {
alpha = (edgeGroupRoles[i][0] == 2 ? 2 : 1);
beta = -(edgeGroupRoles[i][1] == 2 ? 2 : 1);
}
}
if (alpha == 0) {
delete ans;
return 0;
} else
ans->insertFibre(alpha, beta);
}
}
ans->reduce();
return ans;
}
NAugTriSolidTorus* NAugTriSolidTorus::isAugTriSolidTorus(
const NComponent* comp) {
// Basic property checks.
if ((! comp->isClosed()) || (! comp->isOrientable()))
return 0;
if (comp->getNumberOfVertices() > 1)
return 0;
// We have a 1-vertex closed orientable triangulation.
unsigned long nTet = comp->getNumberOfTetrahedra();
if (nTet < 3)
return 0;
// Handle the 3-tetrahedron case separately.
if (nTet == 3) {
// Note that there cannot be a layered chain.
NTetrahedron* base = comp->getTetrahedron(0);
NTriSolidTorus* core;
NPerm annulusMap[3];
// Check every possible choice of vertex roles in tetrahedron 0.
// Note that (a,b,c,d) gives an equivalent core to (d,c,b,a).
int i, j;
for (i = 0; i < 24; i++) {
// Make sure we don't check each possible core twice.
if (allPermsS4[i][0] > allPermsS4[i][3])
continue;
core = NTriSolidTorus::formsTriSolidTorus(base, allPermsS4[i]);
if (core) {
// Check that the annuli are being glued to themselves.
// Since the component is orientable, that's all we need
// to know.
for (j = 0; j < 3; j++) {
if (! core->isAnnulusSelfIdentified(j, annulusMap + j)) {
delete core;
core = 0;
break;
}
}
if (core) {
// We got one!
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core;
// Work out how the mobius strip is glued onto each
// annulus.
for (j = 0; j < 3; j++) {
switch (annulusMap[j][0]) {
case 0:
ans->edgeGroupRoles[j] = NPerm(2, 0, 1, 3);
break;
case 2:
ans->edgeGroupRoles[j] = NPerm(1, 2, 0, 3);
break;
case 3:
ans->edgeGroupRoles[j] = NPerm(0, 1, 2, 3);
break;
}
}
ans->chainIndex = 0;
ans->chainType = CHAIN_NONE;
ans->torusAnnulus = -1;
return ans;
}
}
}
// Didn't find anything.
return 0;
}
// We have strictly more than three tetrahedra.
// There must be bewteen 0 and 3 layered solid tori (note that there
// will be no layered solid tori other than the (0-3) glued to the
// boundary annuli on the core, since no other tetrahedron is glued
// to itself.
int nLayered = 0;
NLayeredSolidTorus* layered[4];
unsigned long usedTets = 0;
for (unsigned long t = 0; t < nTet; t++) {
layered[nLayered] = NLayeredSolidTorus::formsLayeredSolidTorusBase(
comp->getTetrahedron(t));
if (layered[nLayered]) {
usedTets += layered[nLayered]->getNumberOfTetrahedra();
nLayered++;
if (nLayered == 4) {
// Too many layered solid tori.
for (int i = 0; i < nLayered; i++)
delete layered[i];
return 0;
}
}
}
if (nLayered == 0) {
// Our only chance now is a layered chain plus a degenerate
// layered solid torus.
// Start with tetrahedron 0. Either it belongs to the chain or
// it belongs to the core.
NTetrahedron* tet = comp->getTetrahedron(0);
// Run through all possible cores to which it might belong.
int i;
NPerm p, annulusPerm;
NTriSolidTorus* core;
int torusAnnulus;
unsigned long chainLen;
for (i = 0; i < 24; i++) {
p = allPermsS4[i];
if (p[0] > p[3])
continue;
core = NTriSolidTorus::formsTriSolidTorus(tet, p);
if (! core)
continue;
// Let's try this core.
// Look for an identified annulus.
for (torusAnnulus = 0; torusAnnulus < 3; torusAnnulus++)
if (core->isAnnulusSelfIdentified(torusAnnulus, &annulusPerm)) {
// Look now for a layered chain.
// If we don't find it, the entire core must be wrong.
int chainType = CHAIN_NONE;
if ((chainLen = core->areAnnuliLinkedMajor(torusAnnulus)))
chainType = CHAIN_MAJOR;
else if ((chainLen =
core->areAnnuliLinkedAxis(torusAnnulus)))
chainType = CHAIN_AXIS;
if (chainType == CHAIN_NONE || chainLen + 3 != nTet)
break;
// We have the entire structure!
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core;
switch (annulusPerm[0]) {
case 0:
ans->edgeGroupRoles[torusAnnulus] = NPerm(2,0,1,3);
break;
case 2:
ans->edgeGroupRoles[torusAnnulus] = NPerm(1,2,0,3);
break;
case 3:
ans->edgeGroupRoles[torusAnnulus] = NPerm(0,1,2,3);
break;
}
ans->chainIndex = chainLen;
ans->chainType = chainType;
ans->torusAnnulus = torusAnnulus;
return ans;
}
// Didn't find anything.
delete core;
}
// Wasn't the core. Must have been the chain.
NTetrahedron* top;
NTetrahedron* bottom;
NPerm topRoles;
NPerm bottomRoles;
int j;
int chainType;
for (i = 0; i < 6; i++) {
p = allPermsS3[i];
NLayeredChain chain(tet, p);
chain.extendMaximal();
// Note that the chain will run into one of the core tetrahedra.
if (chain.getIndex() + 2 == nTet)
chainType = CHAIN_MAJOR;
else if (chain.getIndex() + 3 == nTet)
chainType = CHAIN_AXIS;
else
continue;
// Look for the corresponding core.
// The identified annulus on the core will have to be annulus 0.
// Test the chain at both ends (bottom / top).
for (j = 0; j < 2; j++) {
if (chainType == CHAIN_MAJOR) {
core = NTriSolidTorus::formsTriSolidTorus(chain.getBottom(),
chain.getBottomVertexRoles() * NPerm(2, 3, 0, 1));
if (core) {
// Test that everything is put together properly.
top = chain.getTop();
topRoles = chain.getTopVertexRoles();
if ((top->getAdjacentTetrahedron(topRoles[0]) ==
core->getTetrahedron(1)) &&
(top->getAdjacentTetrahedron(topRoles[3]) ==
core->getTetrahedron(2)) &&
(top->getAdjacentTetrahedronGluing(topRoles[0])
* topRoles * NPerm(1, 0, 2, 3) ==
core->getVertexRoles(1)) &&
(top->getAdjacentTetrahedronGluing(topRoles[3])
* topRoles * NPerm(0, 1, 3, 2) ==
core->getVertexRoles(2)) &&
core->isAnnulusSelfIdentified(
0, &annulusPerm)) {
// We have the entire structure!
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core;
switch (annulusPerm[0]) {
case 0:
ans->edgeGroupRoles[0] = NPerm(2, 0, 1, 3);
break;
case 2:
ans->edgeGroupRoles[0] = NPerm(1, 2, 0, 3);
break;
case 3:
ans->edgeGroupRoles[0] = NPerm(0, 1, 2, 3);
break;
}
ans->chainIndex = chain.getIndex() - 1;
ans->chainType = chainType;
ans->torusAnnulus = 0;
return ans;
}
delete core;
}
} else if (chainType == CHAIN_AXIS) {
bottom = chain.getBottom();
bottomRoles = chain.getBottomVertexRoles();
NTetrahedron* startCore = bottom->getAdjacentTetrahedron(
bottomRoles[2]);
if (startCore)
core = NTriSolidTorus::formsTriSolidTorus(startCore,
bottom->getAdjacentTetrahedronGluing(
bottomRoles[2]) *
bottomRoles * NPerm(0, 3, 2, 1));
else
core = 0;
if (core) {
// Test that everything is put together properly.
top = chain.getTop();
topRoles = chain.getTopVertexRoles();
if ((bottom->getAdjacentTetrahedron(bottomRoles[1]) ==
core->getTetrahedron(1)) &&
(top->getAdjacentTetrahedron(topRoles[0]) ==
core->getTetrahedron(0)) &&
(top->getAdjacentTetrahedron(topRoles[3]) ==
core->getTetrahedron(2)) &&
(bottom->getAdjacentTetrahedronGluing(
bottomRoles[1])
* bottomRoles * NPerm(2, 1, 0, 3) ==
core->getVertexRoles(1)) &&
(top->getAdjacentTetrahedronGluing(topRoles[0])
* topRoles * NPerm(3, 0, 1, 2) ==
core->getVertexRoles(0)) &&
(top->getAdjacentTetrahedronGluing(topRoles[3])
* topRoles * NPerm(1, 2, 3, 0) ==
core->getVertexRoles(2)) &&
core->isAnnulusSelfIdentified(
0, &annulusPerm)) {
// We have the entire structure!
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core;
switch (annulusPerm[0]) {
case 0:
ans->edgeGroupRoles[0] = NPerm(2, 0, 1, 3);
break;
case 2:
ans->edgeGroupRoles[0] = NPerm(1, 2, 0, 3);
break;
case 3:
ans->edgeGroupRoles[0] = NPerm(0, 1, 2, 3);
break;
}
ans->chainIndex = chain.getIndex();
ans->chainType = chainType;
ans->torusAnnulus = 0;
return ans;
}
delete core;
}
}
// If we just tested the bottom, prepare to test the top.
if (j == 0)
chain.reverse();
}
}
// Didn't find anything.
return 0;
}
// We now know nLayered >= 1.
// Determine whether or not this augmented solid torus must contain a
// layered chain.
bool needChain = (usedTets + 3 != nTet);
if (needChain && nLayered != 1)
return 0;
// Examine each layered solid torus.
NTetrahedron* top[3];
int i, j;
for (i = 0; i < nLayered; i++) {
top[i] = layered[i]->getTopLevel();
if (top[i]->getAdjacentTetrahedron(layered[i]->getTopFace(0)) ==
top[i]->getAdjacentTetrahedron(layered[i]->getTopFace(1))) {
// These two top faces should be glued to different
// tetrahedra.
for (j = 0; j < nLayered; j++)
delete layered[j];
return 0;
}
}
// Run to the top of the first layered solid torus; this should give
// us our core.
int topFace = layered[0]->getTopFace(0);
NTetrahedron* coreTet = top[0]->getAdjacentTetrahedron(topFace);
// We will declare that this face hooks onto vertex roles 0, 1 and 3
// of the first core tetrahedron. Thus the vertex roles permutation
// should map 0, 1 and 3 (in some order) to all vertices except for
// topCoreFace.
int topCoreFace = top[0]->getAdjacentFace(topFace);
NPerm swap3Top(3, topCoreFace);
NPerm swap23(2, 3);
NTriSolidTorus* core;
NTetrahedron* coreTets[3];
NPerm coreVertexRoles[3];
int whichLayered[3];
int usedLayered;
NPerm edgeGroupRoles[3];
int torusAnnulus;
NPerm q;
for (int p = 0; p < 6; p++) {
core = NTriSolidTorus::formsTriSolidTorus(coreTet,
swap3Top * allPermsS3[p] * swap23);
if (core) {
// We have a potential core.
// Now all that remains is to ensure that the layered solid
// tori hang from it accordingly.
for (j = 0; j < 3; j++) {
coreTets[j] = core->getTetrahedron(j);
coreVertexRoles[j] = core->getVertexRoles(j);
}
usedLayered = 0;
torusAnnulus = -1;
for (j = 0; j < 3; j++) {
// Check annulus j.
// Recall that the 3-manifold is orientable so we don't
// have to check for wacky reversed gluings.
if (core->isAnnulusSelfIdentified(j, &q)) {
// We have a degenerate (2,1,1) glued in here.
if (needChain) {
// We already know there is a non-degenerate
// layered solid torus floating about, and the
// other two annuli are reserved for the layered
// chain.
delete core;
core = 0;
break;
}
whichLayered[j] = -1;
switch (q[0]) {
case 0:
edgeGroupRoles[j] = NPerm(2, 0, 1, 3); break;
case 2:
edgeGroupRoles[j] = NPerm(1, 2, 0, 3); break;
case 3:
edgeGroupRoles[j] = NPerm(0, 1, 2, 3); break;
}
} else {
// There should be a layered solid torus glued in here.
for (whichLayered[j] = 0; whichLayered[j] < nLayered;
whichLayered[j]++)
if (coreTets[(j+1)%3]->getAdjacentTetrahedron(
coreVertexRoles[(j+1)%3][2]) ==
top[whichLayered[j]] &&
coreTets[(j+2)%3]->getAdjacentTetrahedron(
coreVertexRoles[(j+2)%3][1]) ==
top[whichLayered[j]]) {
// Annulus j is glued to torus whichLayered[j].
q = coreTets[(j+1)%3]->
getAdjacentTetrahedronGluing(
coreVertexRoles[(j+1)%3][2]) *
coreVertexRoles[(j+1)%3];
// q maps vertex roles in core tetrahedron j+1 to
// vertices of the top tetrahedron in
// layered[whichLayered[j]].
edgeGroupRoles[j] = NPerm(
layered[whichLayered[j]]->getTopEdgeGroup(
edgeNumber[q[0]][q[3]]),
layered[whichLayered[j]]->getTopEdgeGroup(
edgeNumber[q[0]][q[1]]),
layered[whichLayered[j]]->getTopEdgeGroup(
edgeNumber[q[1]][q[3]]),
3);
usedLayered++;
break;
}
if (whichLayered[j] >= nLayered) {
// This annulus was glued neither to itself nor
// to a layered solid torus.
if (needChain)
whichLayered[j] = -1;
else {
delete core;
core = 0;
break;
}
} else {
// This annulus was glued to a layered solid torus.
if (needChain)
torusAnnulus = j;
}
}
}
if (! core)
continue;
if (usedLayered < nLayered) {
// We didn't use all our layered solid tori.
delete core;
continue;
}
if (needChain) {
// We found our one layered solid torus. The other two
// boundary annuli *must* be linked via a layered chain.
int chainType = CHAIN_NONE;
unsigned long chainLen;
if ((chainLen = core->areAnnuliLinkedMajor(torusAnnulus)))
chainType = CHAIN_MAJOR;
else if ((chainLen = core->areAnnuliLinkedAxis(torusAnnulus)))
chainType = CHAIN_AXIS;
if (chainType == CHAIN_NONE ||
usedTets + chainLen + 3 != nTet) {
delete core;
continue;
}
// We've got one!
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core;
for (j = 0; j < 3; j++) {
if (whichLayered[j] >= 0) {
ans->augTorus[j] = layered[whichLayered[j]];
ans->edgeGroupRoles[j] = edgeGroupRoles[j];
}
}
ans->chainIndex = chainLen;
ans->chainType = chainType;
ans->torusAnnulus = torusAnnulus;
return ans;
} else {
// We're not looking for a layered chain.
// This means we have found the entire structure!
NAugTriSolidTorus* ans = new NAugTriSolidTorus();
ans->core = core;
for (j = 0; j < 3; j++) {
ans->edgeGroupRoles[j] = edgeGroupRoles[j];
if (whichLayered[j] >= 0)
ans->augTorus[j] = layered[whichLayered[j]];
}
ans->chainIndex = 0;
ans->chainType = CHAIN_NONE;
ans->torusAnnulus = -1;
return ans;
}
}
}
// Nothing was found.
for (i = 0; i < nLayered; i++)
delete layered[i];
return 0;
}
std::ostream& NAugTriSolidTorus::writeCommonName(std::ostream& out,
bool tex) const {
if (chainIndex) {
// We have a layered solid torus and a layered chain.
NPerm roles = edgeGroupRoles[torusAnnulus];
const NLayeredSolidTorus* torus = augTorus[torusAnnulus];
long params[3];
if (torus) {
params[0] = torus->getMeridinalCuts(0);
params[1] = torus->getMeridinalCuts(1);
params[2] = - torus->getMeridinalCuts(2);
} else {
params[0] = 1;
params[1] = 1;
params[2] = -2;
}
if (params[roles[0]] < 0) {
params[0] = - params[0];
params[1] = - params[1];
params[2] = - params[2];
}
if (chainType == CHAIN_MAJOR)
out << (tex ? "J_{" : "J(");
else
out << (tex ? "X_{" : "X(");
return out << chainIndex << " | " << params[roles[0]] << ','
<< params[roles[1]] << (tex ? '}' : ')');
} else {
// We have three layered solid tori.
std::pair<long, long> allParams[3];
int nAllParams = 0;
NPerm roles;
const NLayeredSolidTorus* torus;
long params[3];
std::pair<long, long> lstParams;
int i;
for (i = 0; i < 3; i++) {
roles = edgeGroupRoles[i];
torus = augTorus[i];
if (torus) {
params[0] = torus->getMeridinalCuts(0);
params[1] = torus->getMeridinalCuts(1);
params[2] = - torus->getMeridinalCuts(2);
} else {
params[0] = 1;
params[1] = 1;
params[2] = -2;
}
lstParams = std::make_pair(params[roles[0]], params[roles[1]]);
if (lstParams.first < 0) {
lstParams.first = - lstParams.first;
lstParams.second = - lstParams.second;
}
if (! (lstParams.first == 2 && lstParams.second == -1))
allParams[nAllParams++] = lstParams;
}
sort(allParams, allParams + nAllParams);
out << (tex ? "A_{" : "A(");
for (i = 0; i < nAllParams; i++) {
if (i > 0)
out << " | ";
out << allParams[i].first << ',' << allParams[i].second;
}
return out << (tex ? '}' : ')');
}
}
std::ostream& NAugTriSolidTorus::writeName(std::ostream& out) const {
return writeCommonName(out, false);
}
std::ostream& NAugTriSolidTorus::writeTeXName(std::ostream& out) const {
return writeCommonName(out, true);
}
void NAugTriSolidTorus::writeTextLong(std::ostream& out) const {
out << (chainIndex ? "Chained " : "Augmented ")
<< "triangular solid torus "
<< (torusAnnulus == -1 ? "(three tori): " : "(torus + chain): ");
writeName(out);
}
} // namespace regina
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