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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 "manifold/nlensspace.h"
#include "manifold/nsfs.h"
#include "triangulation/ntriangulation.h"
namespace regina {
NTetrahedron* NTriangulation::layerOn(NEdge* edge) {
// Locate the two boundary faces.
// Note that our preconditions ensure they exist and are distinct;
// we won't test this again here.
const std::deque<NEdgeEmbedding>& embs(edge->getEmbeddings());
NTetrahedron* tet1 = embs.front().getTetrahedron();
NTetrahedron* tet2 = embs.back().getTetrahedron();
NPerm roles1 = embs.front().getVertices();
NPerm roles2 = embs.back().getVertices();
// At this stage, roles1 maps (0,1,2) to the tet1 tetrahedron vertices
// for the first boundary face, and roles2 maps (0,1,3) to the tet2
// tetrahedron vertices for the second boundary face. In each case,
// (0,1) maps to the endpoints of the given edge.
//
// The simplest thing to do is let (0,1,2,3) in the preimages for
// roles1 and roles2 match up with vertices (0,1,2,3) of the new
// tetrahedron.
ChangeEventBlock block(this);
NTetrahedron* newTet = new NTetrahedron();
addTetrahedron(newTet);
newTet->joinTo(3, tet1, roles1);
newTet->joinTo(2, tet2, roles2);
gluingsHaveChanged();
return newTet;
}
NTetrahedron* NTriangulation::insertLayeredSolidTorus(
unsigned long cuts0, unsigned long cuts1) {
ChangeEventBlock block(this);
unsigned long cuts2 = cuts0 + cuts1;
NTetrahedron* newTet = new NTetrahedron();
addTetrahedron(newTet);
// Take care of the case that can be done with a single
// tetrahedron.
if (cuts2 == 3) {
// Must be a 1-2-3 arrangement that can be done with a single
// tetrahedron.
newTet->joinTo(0, newTet, NPerm(1,2,3,0));
gluingsHaveChanged();
return newTet;
}
// Take care of the special small cases.
if (cuts2 == 2) {
// Make a 1-2-1 arrangement.
NTetrahedron* base = insertLayeredSolidTorus(1, 2);
base->joinTo(2, newTet, NPerm(2,3,0,1));
base->joinTo(3, newTet, NPerm(2,3,0,1));
gluingsHaveChanged();
return newTet;
}
if (cuts2 == 1) {
// Make a 1-1-0 arrangement.
NTetrahedron* base = insertLayeredSolidTorus(1, 1);
base->joinTo(2, newTet, NPerm(0,2,1,3));
base->joinTo(3, newTet, NPerm(3,1,2,0));
gluingsHaveChanged();
return newTet;
}
// At this point we know cuts2 > 3. Recursively build the layered
// triangulation.
if (cuts1 - cuts0 > cuts0) {
NTetrahedron* base = insertLayeredSolidTorus(cuts0, cuts1 - cuts0);
base->joinTo(2, newTet, NPerm(0,2,1,3));
base->joinTo(3, newTet, NPerm(3,1,2,0));
} else {
NTetrahedron* base = insertLayeredSolidTorus(cuts1 - cuts0, cuts0);
base->joinTo(2, newTet, NPerm(3,1,0,2));
base->joinTo(3, newTet, NPerm(0,2,3,1));
}
gluingsHaveChanged();
return newTet;
}
void NTriangulation::insertLayeredLensSpace(unsigned long p, unsigned long q) {
ChangeEventBlock block(this);
NTetrahedron* chain;
if (p == 0) {
chain = insertLayeredSolidTorus(1, 1);
chain->joinTo(3, chain, NPerm(3, 0, 1, 2));
} else if (p == 1) {
chain = insertLayeredSolidTorus(1, 2);
chain->joinTo(3, chain, NPerm(0, 1, 3, 2));
} else if (p == 2) {
chain = insertLayeredSolidTorus(1, 3);
chain->joinTo(3, chain, NPerm(0, 1, 3, 2));
} else if (p == 3) {
chain = insertLayeredSolidTorus(1, 1);
// Either of the following gluings will work.
chain->joinTo(3, chain, NPerm(1, 3, 0, 2));
// chain->joinTo(3, chain, NPerm(0, 1, 3, 2));
} else {
if (2 * q > p)
q = p - q;
if (3 * q > p) {
chain = insertLayeredSolidTorus(p - 2 * q, q);
chain->joinTo(3, chain, NPerm(1, 3, 0, 2));
} else {
chain = insertLayeredSolidTorus(q, p - 2 * q);
chain->joinTo(3, chain, NPerm(3, 0, 1, 2));
}
}
gluingsHaveChanged();
}
void NTriangulation::insertLayeredLoop(unsigned long length, bool twisted) {
if (length == 0)
return;
ChangeEventBlock block(this);
// Insert a layered chain of the given length.
// We should probably split this out into a separate routine.
NTetrahedron* base;
NTetrahedron* curr;
NTetrahedron* next;
base = new NTetrahedron();
addTetrahedron(base);
curr = base;
for (unsigned long i = 1; i < length; i++) {
next = new NTetrahedron();
curr->joinTo(0, next, NPerm(1, 0, 2, 3));
curr->joinTo(3, next, NPerm(0, 1, 3, 2));
addTetrahedron(next);
curr = next;
}
// Join the two ends of the layered chain.
if (twisted) {
curr->joinTo(0, base, NPerm(2, 3, 1, 0));
curr->joinTo(3, base, NPerm(3, 2, 0, 1));
} else {
curr->joinTo(0, base, NPerm(1, 0, 2, 3));
curr->joinTo(3, base, NPerm(0, 1, 3, 2));
}
gluingsHaveChanged();
}
void NTriangulation::insertAugTriSolidTorus(long a1, long b1,
long a2, long b2, long a3, long b3) {
ChangeEventBlock block(this);
int i;
// Construct the core triangular solid torus.
NTetrahedron* core[3];
for (i = 0; i < 3; i++) {
core[i] = new NTetrahedron();
addTetrahedron(core[i]);
}
for (i = 0; i < 3; i++)
core[i]->joinTo(0, core[(i + 1) % 3], NPerm(3, 0, 1, 2));
// Attach the external layered solid tori.
long axis, major, minor;
unsigned long absAxis, absMajor, absMinor;
NTetrahedron* lstTop;
for (i = 0; i < 3; i++) {
if (i == 0) axis = a1; else if (i == 1) axis = a2; else axis = a3;
if (i == 0) major = b1; else if (i == 1) major = b2; else major = b3;
minor = -(axis + major);
absAxis = (axis < 0 ? -axis : axis);
absMajor = (major < 0 ? -major : major);
absMinor = (minor < 0 ? -minor : minor);
// Are we simply attaching a mobius band?
if (absAxis <= 2 && absMajor <= 2 && absMinor <= 2) {
// We have either (2,1,1) or (1,1,0).
if (absAxis == 2) {
core[i]->joinTo(2, core[(i + 1) % 3], NPerm(0, 2, 1, 3));
continue;
} else if (absMajor == 2) {
core[i]->joinTo(2, core[(i + 1) % 3], NPerm(2, 3, 1, 0));
continue;
} else if (absMinor == 2) {
core[i]->joinTo(2, core[(i + 1) % 3], NPerm(3, 0, 1, 2));
continue;
}
// It's (1,1,0). But this needs to be handled specially anyway.
lstTop = insertLayeredSolidTorus(0, 1);
if (absAxis == 0) {
core[i]->joinTo(2, lstTop, NPerm(0, 2, 3, 1));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(0, 2, 3, 1));
} else if (absMajor == 0) {
core[i]->joinTo(2, lstTop, NPerm(1, 0, 3, 2));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(3, 2, 1, 0));
} else {
core[i]->joinTo(2, lstTop, NPerm(3, 0, 2, 1));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(0, 3, 1, 2));
}
continue;
}
if (absAxis >= absMajor && absAxis >= absMinor) {
// Most cuts on the axis edges.
if (absMinor <= absMajor) {
// (minor, major, axis)
lstTop = insertLayeredSolidTorus(absMinor, absMajor);
core[i]->joinTo(2, lstTop, NPerm(0, 2, 3, 1));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(0, 2, 3, 1));
} else {
// (major, minor, axis)
lstTop = insertLayeredSolidTorus(absMajor, absMinor);
core[i]->joinTo(2, lstTop, NPerm(1, 2, 3, 0));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(1, 2, 3, 0));
}
} else if (absMajor >= absMinor) {
// Most cuts on the major edges.
if (absMinor <= absAxis) {
// (minor, axis, major)
lstTop = insertLayeredSolidTorus(absMinor, absAxis);
core[i]->joinTo(2, lstTop, NPerm(0, 1, 3, 2));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(3, 2, 0, 1));
} else {
// (axis, minor, major)
lstTop = insertLayeredSolidTorus(absAxis, absMinor);
core[i]->joinTo(2, lstTop, NPerm(1, 0, 3, 2));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(3, 2, 1, 0));
}
} else {
// Most cuts on the minor edges.
if (absAxis <= absMajor) {
// (axis, major, minor)
lstTop = insertLayeredSolidTorus(absAxis, absMajor);
core[i]->joinTo(2, lstTop, NPerm(3, 1, 2, 0));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(1, 3, 0, 2));
} else {
// (major, axis, minor)
lstTop = insertLayeredSolidTorus(absMajor, absAxis);
core[i]->joinTo(2, lstTop, NPerm(3, 0, 2, 1));
core[(i + 1) % 3]->joinTo(1, lstTop, NPerm(0, 3, 1, 2));
}
}
}
gluingsHaveChanged();
}
void NTriangulation::insertSFSOverSphere(long a1, long b1, long a2, long b2,
long a3, long b3) {
// Construct the SFS that we seek.
NSFSpace sfs;
if (a1 < 0)
sfs.insertFibre(-a1, -b1);
else
sfs.insertFibre(a1, b1);
if (a2 < 0)
sfs.insertFibre(-a2, -b2);
else
sfs.insertFibre(a2, b2);
if (a3 < 0)
sfs.insertFibre(-a3, -b3);
else
sfs.insertFibre(a3, b3);
sfs.reduce();
// Use the SFS construction routine, which can handle this type of SFS.
NTriangulation* ans = sfs.construct();
insertTriangulation(*ans);
delete ans;
}
} // namespace regina
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