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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 <numeric> // for std::gcd()
#include "manifold/lensspace.h"
#include "manifold/sfs.h"
#include "triangulation/dim3.h"
#include "triangulation/example3.h"
namespace regina {
Tetrahedron<3>* Triangulation<3>::layerOn(Edge<3>* edge) {
if (! edge->isBoundary())
throw InvalidArgument("layerOn() requires a boundary edge");
// Locate the two boundary triangles.
// Note that our preconditions ensure they exist and are distinct;
// we won't test this again here.
Tetrahedron<3>* tet1 = edge->front().tetrahedron();
Tetrahedron<3>* tet2 = edge->back().tetrahedron();
Perm<4> roles1 = edge->front().vertices();
Perm<4> roles2 = edge->back().vertices();
// At this stage, roles1 maps (0,1,2) to the tet1 tetrahedron vertices
// for the first boundary triangle, and roles2 maps (0,1,3) to the tet2
// tetrahedron vertices for the second boundary triangle. 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.
if (tet1->triangle(roles1[3]) == tet2->triangle(roles2[2]))
throw InvalidArgument("layerOn() requires an edge between two "
"distinct boundary triangles");
if (tet1->isFacetLocked(roles1[3]) || tet2->isFacetLocked(roles2[2]))
throw LockViolation("An attempt was made to layer on a locked facet");
// Note: we use the "raw" routines (joinRaw, newSimplexRaw), mainly since
// we did all our lock checking beforehand (not during the individual
// joins). This means that the ChangeAndClearSpan here is vital.
ChangeAndClearSpan<ChangeType::PreserveTopology> span(*this);
Tetrahedron<3>* newTet = newSimplexRaw();
newTet->joinRaw(3, tet1, roles1);
newTet->joinRaw(2, tet2, roles2);
return newTet;
}
bool Triangulation<3>::fillTorus(size_t cuts0, size_t cuts1, size_t cuts2,
BoundaryComponent<3>* bc) {
// Check that the cuts arguments are valid.
int maxCuts;
if (cuts2 == cuts0 + cuts1)
maxCuts = 2;
else if (cuts1 == cuts0 + cuts2)
maxCuts = 1;
else if (cuts0 == cuts1 + cuts2)
maxCuts = 0;
else
return false;
if (std::gcd(cuts0, cuts1) != 1)
return false;
// Deduce the boundary component if one was not given.
if (! bc) {
if (countBoundaryComponents() != 1)
return false;
bc = boundaryComponents_.front();
}
// Check that the boundary component is indeed a 2-triangle torus.
if (bc->countTriangles() != 2)
return false;
if (bc->eulerChar() != 0 || ! bc->isOrientable())
return false;
// Identify the two boundary triangles and their relationships to the
// three boundary edges.
//
// For each i = 0,1, we require that vertices (v[i][0], v[i][1], v[i][2])
// of triangle t[i] form a boundary triangle, with v[i][k] opposite edge k
// of the given boundary component.
Tetrahedron<3>* t[2];
Perm<4> v[2];
Edge<3>* e = bc->edge(0);
const EdgeEmbedding<3>& emb0 = e->front();
const EdgeEmbedding<3>& emb1 = e->back();
t[0] = emb0.simplex();
t[1] = emb1.simplex();
// emb0.vertices(): 0,1 -> bc->edge(0); 2 -> other bc vertex.
// emb1.vertices(): 0,1 -> bc->edge(0); 3 -> other bc vertex.
if (t[0]->edge(emb0.vertices()[0], emb0.vertices()[2]) == bc->edge(1)) {
// emb0.vertices(): 0,2 -> bc->edge(1), 1,2 -> bc->edge(2).
// emb1.vertices(): 1,3 -> bc->edge(1), 0,3 -> bc->edge(2).
v[0] = emb0.vertices() * Perm<4>(2, 1, 0, 3);
v[1] = emb1.vertices() * Perm<4>(3, 0, 1, 2);
} else {
// emb0.vertices(): 1,2 -> bc->edge(1), 0,2 -> bc->edge(2).
// emb1.vertices(): 0,3 -> bc->edge(1), 1,3 -> bc->edge(2).
v[0] = emb0.vertices() * Perm<4>(2, 0, 1, 3);
v[1] = emb1.vertices() * Perm<4>(3, 1, 0, 2);
}
// Build and attach the solid torus.
Tetrahedron<3>* filling;
switch (maxCuts) {
case 0:
if (cuts1 <= cuts2) {
filling = insertLayeredSolidTorus(cuts1, cuts2);
if (cuts0 <= 2) {
// filling:12,03 -> bc->edge(2)
// filling:02,13 -> bc->edge(0)
// filling:01 -> bc->edge(1)
filling->join(3, t[0],
Perm<4>(v[0][2], v[0][0], v[0][1], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][0], v[1][2], v[1][3], v[1][1]));
} else {
// filling:12,03 -> bc->edge(1)
// filling:02,13 -> bc->edge(2)
// filling:01 -> bc->edge(0)
filling->join(3, t[0],
Perm<4>(v[0][1], v[0][2], v[0][0], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][2], v[1][1], v[1][3], v[1][0]));
}
} else {
filling = insertLayeredSolidTorus(cuts2, cuts1);
if (cuts0 <= 2) {
// filling:12,03 -> bc->edge(1)
// filling:02,13 -> bc->edge(0)
// filling:01 -> bc->edge(2)
filling->join(3, t[0],
Perm<4>(v[0][1], v[0][0], v[0][2], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][0], v[1][1], v[1][3], v[1][2]));
} else {
// filling:12,03 -> bc->edge(2)
// filling:02,13 -> bc->edge(1)
// filling:01 -> bc->edge(0)
filling->join(3, t[0],
Perm<4>(v[0][2], v[0][1], v[0][0], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][1], v[1][2], v[1][3], v[1][0]));
}
}
break;
case 1:
if (cuts0 <= cuts2) {
filling = insertLayeredSolidTorus(cuts0, cuts2);
if (cuts1 <= 2) {
// filling:12,03 -> bc->edge(2)
// filling:02,13 -> bc->edge(1)
// filling:01 -> bc->edge(0)
filling->join(3, t[0],
Perm<4>(v[0][2], v[0][1], v[0][0], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][1], v[1][2], v[1][3], v[1][0]));
} else {
// filling:12,03 -> bc->edge(0)
// filling:02,13 -> bc->edge(2)
// filling:01 -> bc->edge(1)
filling->join(3, t[0],
Perm<4>(v[0][0], v[0][2], v[0][1], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][2], v[1][0], v[1][3], v[1][1]));
}
} else {
filling = insertLayeredSolidTorus(cuts2, cuts0);
if (cuts1 <= 2) {
// filling:12,03 -> bc->edge(0)
// filling:02,13 -> bc->edge(1)
// filling:01 -> bc->edge(2)
filling->join(3, t[0],
Perm<4>(v[0][0], v[0][1], v[0][2], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][1], v[1][0], v[1][3], v[1][2]));
} else {
// filling:12,03 -> bc->edge(2)
// filling:02,13 -> bc->edge(0)
// filling:01 -> bc->edge(1)
filling->join(3, t[0],
Perm<4>(v[0][2], v[0][0], v[0][1], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][0], v[1][2], v[1][3], v[1][1]));
}
}
break;
case 2:
if (cuts0 <= cuts1) {
filling = insertLayeredSolidTorus(cuts0, cuts1);
if (cuts2 <= 2) {
// filling:12,03 -> bc->edge(1)
// filling:02,13 -> bc->edge(2)
// filling:01 -> bc->edge(0)
filling->join(3, t[0],
Perm<4>(v[0][1], v[0][2], v[0][0], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][2], v[1][1], v[1][3], v[1][0]));
} else {
// filling:12,03 -> bc->edge(0)
// filling:02,13 -> bc->edge(1)
// filling:01 -> bc->edge(2)
filling->join(3, t[0],
Perm<4>(v[0][0], v[0][1], v[0][2], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][1], v[1][0], v[1][3], v[1][2]));
}
} else {
filling = insertLayeredSolidTorus(cuts1, cuts0);
if (cuts2 <= 2) {
// filling:12,03 -> bc->edge(0)
// filling:02,13 -> bc->edge(2)
// filling:01 -> bc->edge(1)
filling->join(3, t[0],
Perm<4>(v[0][0], v[0][2], v[0][1], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][2], v[1][0], v[1][3], v[1][1]));
} else {
// filling:12,03 -> bc->edge(1)
// filling:02,13 -> bc->edge(0)
// filling:01 -> bc->edge(2)
filling->join(3, t[0],
Perm<4>(v[0][1], v[0][0], v[0][2], v[0][3]));
filling->join(2, t[1],
Perm<4>(v[1][0], v[1][1], v[1][3], v[1][2]));
}
}
break;
}
simplify();
return true;
}
bool Triangulation<3>::fillTorus(Edge<3>* e0, Edge<3>* e1, Edge<3>* e2,
size_t cuts0, size_t cuts1, size_t cuts2) {
if (e0 == e1 || e0 == e2 || e1 == e2)
return false;
BoundaryComponent<3>* bc = e0->boundaryComponent();
if ((! bc) || bc != e1->boundaryComponent() ||
bc != e2->boundaryComponent())
return false;
if (bc->countEdges() != 3)
return false;
// e0, e1 and e2 are now known to be the three distinct edges of bc.
if (e0 == bc->edge(0)) {
if (e1 == bc->edge(1))
return fillTorus(cuts0, cuts1, cuts2, bc);
else
return fillTorus(cuts0, cuts2, cuts1, bc);
} else if (e0 == bc->edge(1)) {
if (e1 == bc->edge(0))
return fillTorus(cuts1, cuts0, cuts2, bc);
else
return fillTorus(cuts2, cuts0, cuts1, bc);
} else if (e0 == bc->edge(2)) {
if (e1 == bc->edge(0))
return fillTorus(cuts1, cuts2, cuts0, bc);
else
return fillTorus(cuts2, cuts1, cuts0, bc);
}
return false;
}
Tetrahedron<3>* Triangulation<3>::insertLayeredSolidTorus(
size_t cuts0, size_t cuts1) {
if (cuts0 > cuts1)
throw InvalidArgument("insertLayeredSolidTorus() requires "
"cuts0 ≤ cuts1");
// Note: we use the "raw" routines (joinRaw, newSimplexRaw, etc.),
// mainly so that deleting tetrahedra is easy in the case where
// the arguments were not coprime and we have to unwind the operation.
// This means that the ChangeAndClearSpan here is vital.
ChangeAndClearSpan<> span(*this);
size_t cuts2 = cuts0 + cuts1;
if (cuts2 < 3) {
// These are the degenerate cases.
// Valid options: 0-1-1, 1-1-2
// Invalid options: 0-0-0, 0-2-2
if (cuts1 != 1)
throw InvalidArgument("insertLayeredSolidTorus() requires "
"cuts0 and cuts1 to be coprime");
if (cuts2 == 2) {
auto [top, base] = newSimplicesRaw<2>();
base->joinRaw(0, base, {1,2,3,0});
base->joinRaw(2, top, {2,3,0,1});
base->joinRaw(3, top, {2,3,0,1});
return top;
} else {
auto [top, middle, base] = newSimplicesRaw<3>();
base->joinRaw(0, base, {1,2,3,0});
base->joinRaw(2, middle, {2,3,0,1});
base->joinRaw(3, middle, {2,3,0,1});
middle->joinRaw(2, top, {0,2,1,3});
middle->joinRaw(3, top, {3,1,2,0});
return top;
}
}
// This is a standard case that begins with a 1-2-3 LST and works up.
Tetrahedron<3>* top = newSimplexRaw();
Tetrahedron<3>* curr = top;
while (cuts0 > 0 && cuts2 > 3) {
// Work our way down to the 1-2-3 case.
Tetrahedron<3>* next = newSimplexRaw();
if (cuts1 - cuts0 > cuts0) {
next->joinRaw(2, curr, Perm<4>(0,2,1,3));
next->joinRaw(3, curr, Perm<4>(3,1,2,0));
// Remaining to build: (cuts0, cuts1 - cuts0, cuts1)
cuts2 = cuts1;
cuts1 = cuts1 - cuts0;
} else {
next->joinRaw(2, curr, Perm<4>(3,1,0,2));
next->joinRaw(3, curr, Perm<4>(0,2,3,1));
// Remaining to build: (cuts1 - cuts0, cuts0, cuts1)
cuts2 = cuts1;
cuts1 = cuts0;
cuts0 = cuts2 - cuts1;
}
curr = next;
}
// One of two things happens at this point:
// - we successfully worked our way down to 1-2-3; or
// - we worked our way down to 0-k-k for some k > 1, which means that
// the arguments were not coprime.
// Note that the (valid) 0-1-1 case was already handled earlier, in the
// section for degenerate cases.
if (cuts0 == 0) {
// The arguments were not coprime.
// Unwind the operation that we performed thus far, and throw.
// We don't bother with isolating the tetrahedra before removal,
// since we are deleting an entire connected component.
auto deleteFrom = simplices_.begin() + top->markedIndex();
for (auto it = deleteFrom; it != simplices_.end(); ++it)
delete *it;
simplices_.erase(deleteFrom, simplices_.end());
throw InvalidArgument("insertLayeredSolidTorus() requires "
"cuts0 and cuts1 to be coprime");
}
// Finalise the 1-2-3 LST at the base, and return.
curr->joinRaw(0, curr, {1,2,3,0});
return top;
}
} // namespace regina
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