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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2016, 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, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
#include "manifold/graphpair.h"
#include "manifold/sfs.h"
#include "subcomplex/blockedsfspair.h"
#include "subcomplex/layering.h"
#include "subcomplex/satblockstarter.h"
#include "subcomplex/satregion.h"
namespace regina {
/**
* A subclass of SatBlockStarterSearcher that, upon finding a starter
* block, attempts to flesh this out to a pair of saturated regions
* joined along their single torus boundaries, as desribed by the
* BlockedSFSPair class.
*/
struct BlockedSFSPairSearcher : public SatBlockStarterSearcher {
SatRegion* region[2];
/**< The two bounded saturated regions that are joined together,
if the entire BlockedSFSPair structure has been successfully
found; otherwise, two null pointers if we are still searching. */
Matrix2 matchingReln;
/**< The matrix describing how the region boundaries are joined
together. This matrix expresses the fibre/base curves on the
second region boundary in terms of the fibre/base curves on
the first, as described by GraphPair::matchingReln(). */
/**
* Creates a new searcher whose \a region pointers are both null.
*/
BlockedSFSPairSearcher() {
region[0] = region[1] = 0;
}
protected:
bool useStarterBlock(SatBlock* starter);
};
BlockedSFSPair::~BlockedSFSPair() {
if (region_[0])
delete region_[0];
if (region_[1])
delete region_[1];
}
Manifold* BlockedSFSPair::manifold() const {
SFSpace* sfs0 = region_[0]->createSFS(false);
if (! sfs0)
return 0;
SFSpace* sfs1 = region_[1]->createSFS(false);
if (! sfs1) {
delete sfs0;
return 0;
}
// Reduce the Seifert fibred space representations and finish up.
sfs0->reduce(false);
sfs1->reduce(false);
if (*sfs1 < *sfs0)
return new GraphPair(sfs1, sfs0, matchingReln_.inverse());
else
return new GraphPair(sfs0, sfs1, matchingReln_);
}
std::ostream& BlockedSFSPair::writeName(std::ostream& out) const {
out << "Blocked SFS Pair [";
region_[0]->writeBlockAbbrs(out, false);
out << " | ";
region_[1]->writeBlockAbbrs(out, false);
return out << ']';
}
std::ostream& BlockedSFSPair::writeTeXName(std::ostream& out) const {
out << "\\mathrm{BSFS\\_Pair}\\left[";
region_[0]->writeBlockAbbrs(out, true);
out << "\\,|\\,";
region_[1]->writeBlockAbbrs(out, true);
return out << "\\right]";
}
void BlockedSFSPair::writeTextLong(std::ostream& out) const {
out << "Blocked SFS pair, matching relation " << matchingReln_ << "\n";
region_[0]->writeDetail(out, "First region");
region_[1]->writeDetail(out, "Second region");
}
BlockedSFSPair* BlockedSFSPair::isBlockedSFSPair(Triangulation<3>* tri) {
// Basic property checks.
if (! tri->isClosed())
return 0;
if (tri->countComponents() > 1)
return 0;
// Watch out for twisted block boundaries that are incompatible with
// neighbouring blocks! Also watch for the boundary between blocks
// being an annulus on one side and a Klein bottle on the other (or
// two incompatible Klein bottles for that matter).
//
// These will result in edges joined to themselves in reverse.
if (! tri->isValid())
return 0;
// Hunt for a starting block.
BlockedSFSPairSearcher searcher;
searcher.findStarterBlocks(tri);
// Any luck?
if (searcher.region[0]) {
// The full expansion worked, and the triangulation is known
// to be closed and connected.
// This means we've got one!
return new BlockedSFSPair(searcher.region[0], searcher.region[1],
searcher.matchingReln);
}
// Nope.
return 0;
}
bool BlockedSFSPairSearcher::useStarterBlock(SatBlock* starter) {
// The region pointers should be null, but just in case...
if (region[0] || region[1]) {
delete starter;
return false;
}
// Flesh out the triangulation as far as we can. We're aiming for
// just one boundary annulus remaining.
// Note that the starter block will now be owned by region[0].
region[0] = new SatRegion(starter);
region[0]->expand(usedTets);
if (region[0]->numberOfBoundaryAnnuli() != 1) {
delete region[0];
region[0] = 0;
return true;
}
// Insist on this boundary being untwisted.
SatBlock* bdryBlock;
unsigned bdryAnnulus;
bool bdryVert, bdryHoriz;
region[0]->boundaryAnnulus(0, bdryBlock, bdryAnnulus,
bdryVert, bdryHoriz);
bool firstRegionReflected =
((bdryVert && ! bdryHoriz) || (bdryHoriz && ! bdryVert));
SatBlock* tmpBlock;
unsigned tmpAnnulus;
bool tmpVert, tmpHoriz;
bdryBlock->nextBoundaryAnnulus(bdryAnnulus, tmpBlock, tmpAnnulus,
tmpVert, tmpHoriz, false);
if (tmpVert) {
delete region[0];
region[0] = 0;
return true;
}
SatAnnulus bdry = bdryBlock->annulus(bdryAnnulus);
// We have a boundary annulus for the first region.
// Hunt for a layering.
Layering layering(bdry.tet[0], bdry.roles[0], bdry.tet[1], bdry.roles[1]);
layering.extend();
// Relation from fibre/orbifold to layering first triangle markings 01/02:
Matrix2 curves0ToLayering = layering.boundaryReln() *
Matrix2(-1, 0, 0, firstRegionReflected ? -1 : 1);
// We make the shell of an other-side boundary annulus; we will fill
// in the precise vertex role permutations later on.
SatAnnulus otherSide(layering.newBoundaryTet(0), Perm<4>(),
layering.newBoundaryTet(1), Perm<4>());
if (otherSide.meetsBoundary()) {
delete region[0];
region[0] = 0;
return true;
}
// Mapping from (layering first triangle markings 01/02) to
// (other side annulus first triangle markings 01/02). Like the other
// side vertex roles, this mapping will be filled in later.
Matrix2 layeringToAnnulus1;
// Try the three possible orientations for fibres on the other side.
SatBlock* otherStarter;
for (int plugPos = 0; plugPos < 3; plugPos++) {
// Construct the boundary annulus for the second region.
// Refresh the tetrahedra as well as the vertex roles, since
// it may have switched sides since our last run through the loop.
otherSide.tet[0] = layering.newBoundaryTet(0);
otherSide.tet[1] = layering.newBoundaryTet(1);
if (plugPos == 0) {
otherSide.roles[0] = layering.newBoundaryRoles(0);
otherSide.roles[1] = layering.newBoundaryRoles(1);
layeringToAnnulus1 = Matrix2(1, 0, 0, 1);
} else if (plugPos == 1) {
otherSide.roles[0] = layering.newBoundaryRoles(0) *
Perm<4>(1, 2, 0, 3);
otherSide.roles[1] = layering.newBoundaryRoles(1) *
Perm<4>(1, 2, 0, 3);
layeringToAnnulus1 = Matrix2(-1, 1, -1, 0);
} else {
otherSide.roles[0] = layering.newBoundaryRoles(0) *
Perm<4>(2, 0, 1, 3);
otherSide.roles[1] = layering.newBoundaryRoles(1) *
Perm<4>(2, 0, 1, 3);
layeringToAnnulus1 = Matrix2(0, -1, 1, -1);
}
// Clear out the used tetrahedron list. Everything before the new
// layering boundary is self-contained, so we won't run into it
// again on the other side. We'll just re-insert the layering
// boundary tetrahedra.
usedTets.clear();
usedTets.insert(layering.newBoundaryTet(0));
usedTets.insert(layering.newBoundaryTet(1));
// See if we can flesh the other side out to an entire region.
otherSide.switchSides();
if ((otherStarter = SatBlock::isBlock(otherSide, usedTets))) {
region[1] = new SatRegion(otherStarter);
region[1]->expand(usedTets);
if (region[1]->numberOfBoundaryAnnuli() == 1) {
// This is it! Stop searching.
// Do a final conversion from annulus first triangle markings
// 01/02 and exit.
matchingReln = Matrix2(-1, 0, 0, 1) * layeringToAnnulus1 *
curves0ToLayering;
return false;
}
// Nup, this one didn't work.
delete region[1];
region[1] = 0;
}
}
// Sigh, nothing works.
delete region[0];
region[0] = 0;
return true;
}
} // namespace regina
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