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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2009, 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 "algebra/nabeliangroup.h"
#include "manifold/nhandlebody.h"
#include "manifold/nlensspace.h"
#include "manifold/nsimplesurfacebundle.h"
#include "triangulation/nboundarycomponent.h"
#include "triangulation/ncomponent.h"
#include "triangulation/nedge.h"
#include "triangulation/nface.h"
#include "subcomplex/ntrivialtri.h"
namespace regina {
const int NTrivialTri::N2 = 200;
const int NTrivialTri::N3_1 = 301;
const int NTrivialTri::N3_2 = 302;
const int NTrivialTri::SPHERE_4_VERTEX = 5000;
const int NTrivialTri::BALL_3_VERTEX = 5100;
const int NTrivialTri::BALL_4_VERTEX = 5101;
NTrivialTri* NTrivialTri::isTrivialTriangulation(const NComponent* comp) {
// Since the triangulations are so small we can use census results
// to recognise the triangulations by properties alone.
// Are there any boundary components?
if (! comp->isClosed()) {
if (comp->getNumberOfBoundaryComponents() == 1) {
// We have precisely one boundary component.
NBoundaryComponent* bc = comp->getBoundaryComponent(0);
if (! bc->isIdeal()) {
// The boundary component includes boundary faces.
// Look for a one-tetrahedron ball.
if (comp->getNumberOfTetrahedra() == 1) {
if (bc->getNumberOfFaces() == 4)
return new NTrivialTri(BALL_4_VERTEX);
if (bc->getNumberOfFaces() == 2 &&
comp->getNumberOfVertices() == 3)
return new NTrivialTri(BALL_3_VERTEX);
}
}
}
// Not recognised.
return 0;
}
// Otherwise we are dealing with a closed component.
// Before we do our validity check, make sure the number of
// tetrahedra is in the supported range.
if (comp->getNumberOfTetrahedra() > 3)
return 0;
// Is the triangulation valid?
// Since the triangulations is closed we know that the vertices are
// valid; all that remains is to check the edges.
unsigned long nEdges = comp->getNumberOfEdges();
unsigned long i;
for (i = 0; i < nEdges; i++)
if (! comp->getEdge(i)->isValid())
return 0;
// Test for the specific triangulations that we know about.
if (comp->getNumberOfTetrahedra() == 2) {
if (comp->isOrientable()) {
if (comp->getNumberOfVertices() == 4) {
// There's only one closed valid two-tetrahedron
// four-vertex orientable triangulation.
return new NTrivialTri(SPHERE_4_VERTEX);
}
} else {
// There's only one closed valid two-tetrahedron non-orientable
// triangulation.
return new NTrivialTri(N2);
}
return 0;
}
if (comp->getNumberOfTetrahedra() == 3) {
if (! comp->isOrientable()) {
// If the triangulation is valid and the edge degrees
// are 2,4,4,6 then we have N(3,1) or N(3,2).
// All of the vertices are valid since there are no boundary
// faces; we thus only need to check the edges.
if (comp->getNumberOfEdges() != 4)
return 0;
int degree[4];
for (i = 0; i < 4; i++)
degree[i] = comp->getEdge(i)->getDegree();
std::sort(degree, degree + 4);
if (degree[0] == 2 && degree[1] == 4 && degree[2] == 6 &&
degree[3] == 6) {
// We have N(3,1) or N(3,2)!
// Search for Mobius band faces.
unsigned long nFaces = comp->getNumberOfFaces();
for (i = 0; i < nFaces; i++)
if (comp->getFace(i)->isMobiusBand())
return new NTrivialTri(N3_2);
return new NTrivialTri(N3_1);
}
}
}
return 0;
}
NManifold* NTrivialTri::getManifold() const {
if (type == SPHERE_4_VERTEX)
return new NLensSpace(1, 0);
else if (type == BALL_3_VERTEX || type == BALL_4_VERTEX)
return new NHandlebody(0, true);
else if (type == N2)
return new NSimpleSurfaceBundle(NSimpleSurfaceBundle::S2xS1_TWISTED);
else if (type == N3_1 || type == N3_2)
return new NSimpleSurfaceBundle(NSimpleSurfaceBundle::RP2xS1);
return 0;
}
NAbelianGroup* NTrivialTri::getHomologyH1() const {
NAbelianGroup* ans = new NAbelianGroup();
if (type == N2)
ans->addRank();
else if (type == N3_1 || type == N3_2) {
ans->addRank();
ans->addTorsionElement(2);
}
return ans;
}
std::ostream& NTrivialTri::writeName(std::ostream& out) const {
if (type == SPHERE_4_VERTEX)
out << "S3 (4-vtx)";
else if (type == BALL_3_VERTEX)
out << "B3 (3-vtx)";
else if (type == BALL_4_VERTEX)
out << "B3 (4-vtx)";
else if (type == N2)
out << "N(2)";
else if (type == N3_1)
out << "N(3,1)";
else if (type == N3_2)
out << "N(3,2)";
return out;
}
std::ostream& NTrivialTri::writeTeXName(std::ostream& out) const {
if (type == SPHERE_4_VERTEX)
out << "S^3_{v=4}";
else if (type == BALL_3_VERTEX)
out << "B^3_{v=3}";
else if (type == BALL_4_VERTEX)
out << "B^3_{v=4}";
else if (type == N2)
out << "N_{2}";
else if (type == N3_1)
out << "N_{3,1}";
else if (type == N3_2)
out << "N_{3,2}";
return out;
}
void NTrivialTri::writeTextLong(std::ostream& out) const {
if (type == SPHERE_4_VERTEX)
out << "Two-tetrahedron four-vertex 3-sphere";
else if (type == BALL_3_VERTEX)
out << "One-tetrahedron three-vertex ball";
else if (type == BALL_4_VERTEX)
out << "One-tetrahedron four-vertex ball";
else if (type == N2)
out << "Non-orientable triangulation N(2)";
else if (type == N3_1)
out << "Non-orientable triangulation N(3,1)";
else if (type == N3_2)
out << "Non-orientable triangulation N(3,2)";
}
} // namespace regina
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