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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 "algebra/nabeliangroup.h"
#include "manifold/nlensspace.h"
#include "manifold/nsfs.h"
#include "triangulation/nedge.h"
#include "triangulation/ncomponent.h"
#include "triangulation/ntetrahedron.h"
#include "subcomplex/nlayeredloop.h"
namespace regina {
NLayeredLoop* NLayeredLoop::clone() const {
NLayeredLoop* ans = new NLayeredLoop();
ans->length = length;
ans->hinge[0] = hinge[0];
ans->hinge[1] = hinge[1];
return ans;
}
NManifold* NLayeredLoop::getManifold() const {
if (hinge[1]) {
// Not twisted.
return new NLensSpace(length, 1);
} else {
// Twisted.
NSFSpace* ans = new NSFSpace();
ans->insertFibre(2, -1);
ans->insertFibre(2, 1);
ans->insertFibre(length, 1);
ans->reduce();
return ans;
}
}
NLayeredLoop* NLayeredLoop::isLayeredLoop(const NComponent* comp) {
// Basic property check.
if ((! comp->isClosed()) || (! comp->isOrientable()))
return 0;
unsigned long nTet = comp->getNumberOfTetrahedra();
if (nTet == 0)
return 0;
unsigned long nVertices = comp->getNumberOfVertices();
if (nVertices > 2)
return 0;
bool twisted = (nVertices == 1);
// We have at least 1 tetrahedron and precisely 1 or 2 vertices.
// The component is closed and orientable (and connected, since it's
// a component).
// Pick our base tetrahedron.
NTetrahedron* base = comp->getTetrahedron(0);
NTetrahedron* tet = base;
NTetrahedron* next;
int baseTop0, baseTop1, baseBottom0, baseBottom1;
int top0, top1, bottom0, bottom1;
int adjTop0 = 0, adjTop1 = 0, adjBottom0 = 0, adjBottom1 = 0;
int hinge0, hinge1;
NPerm p;
bool ok;
// Declare 0 to be a top face; find its partner.
baseTop0 = 0;
next = base->getAdjacentTetrahedron(0);
for (baseTop1 = 1; baseTop1 < 4; baseTop1++) {
if (base->getAdjacentTetrahedron(baseTop1) != next)
continue;
// Find the vertex joined to baseTop0 by a hinge.
for (baseBottom0 = 1; baseBottom0 < 4; baseBottom0++) {
if (baseBottom0 == baseTop1)
continue;
baseBottom1 = 6 - baseBottom0 - baseTop0 - baseTop1;
// Some basic property checks.
if (base->getAdjacentTetrahedron(baseBottom0) !=
base->getAdjacentTetrahedron(baseBottom1))
continue;
hinge0 = edgeNumber[baseTop0][baseBottom0];
hinge1 = edgeNumber[baseTop1][baseBottom1];
if (twisted) {
if (base->getEdge(hinge0) != base->getEdge(hinge1))
continue;
if (base->getEdge(hinge0)->getNumberOfEmbeddings() != 2 * nTet)
continue;
} else {
if (base->getEdge(hinge0)->getNumberOfEmbeddings() != nTet)
continue;
if (base->getEdge(hinge1)->getNumberOfEmbeddings() != nTet)
continue;
}
top0 = baseTop0; top1 = baseTop1;
bottom0 = baseBottom0; bottom1 = baseBottom1;
// Follow the gluings up.
ok = true;
while (true) {
// Already set: tet, next, topi, bottomi.
// Check that both steps up lead to the same tetrahedron.
// Note that this check has already been done for the first
// iteration of this loop; never mind, no big loss.
if (tet->getAdjacentTetrahedron(top0) !=
tet->getAdjacentTetrahedron(top1)) {
ok = false;
break;
}
// Check that the corresponding gluings are correct.
p = tet->getAdjacentTetrahedronGluing(top0);
adjTop0 = p[bottom0];
adjTop1 = p[top1];
adjBottom0 = p[top0];
adjBottom1 = p[bottom1];
p = tet->getAdjacentTetrahedronGluing(top1);
// Note that only three of the four comparisons are needed.
if (adjTop0 != p[top0] || adjTop1 != p[bottom1] ||
adjBottom0 != p[bottom0]) {
ok = false;
break;
}
// If we've finished the loop, exit at this point so we
// can check that it all glued up correctly.
if (next == base)
break;
// We haven't finished the loop, so the next
// tetrahedron should be different from this one.
if (next == tet) {
ok = false;
break;
}
// Move to the next tetrahedron.
top0 = adjTop0; top1 = adjTop1;
bottom0 = adjBottom0; bottom1 = adjBottom1;
tet = next;
next = tet->getAdjacentTetrahedron(top0);
}
if (ok) {
// Make sure the final gluing wraps everything up
// correctly.
if (twisted) {
if (adjTop0 != baseTop1 || adjTop1 != baseTop0 ||
adjBottom0 != baseBottom1)
continue;
} else {
if (adjTop0 != baseTop0 || adjTop1 != baseTop1 ||
adjBottom0 != baseBottom0)
continue;
}
// We have a solution!
NLayeredLoop* ans = new NLayeredLoop();
ans->length = nTet;
ans->hinge[0] = base->getEdge(hinge0);
ans->hinge[1] = (twisted ? 0 : base->getEdge(hinge1));
return ans;
}
}
}
// Nothing found.
return 0;
}
NAbelianGroup* NLayeredLoop::getHomologyH1() const {
NAbelianGroup* ans = new NAbelianGroup();
if (hinge[1]) {
// Untwisted.
if (length > 1)
ans->addTorsionElement(length);
} else {
// Twisted.
if (length % 2 == 0)
ans->addTorsionElement(2, 2);
else
ans->addTorsionElement(4);
}
return ans;
}
} // namespace regina
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