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growthpairs.cc
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growthpairs.cc
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/*
This file is part of a program to fill borders of patches.
Copyright (C) 2006-2007 Bart Coppens <kde@bartcoppens.be>
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 3 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, see <http://www.gnu.org/licenses/>.
*/
#include <iostream>
#include <cassert>
#include "growthpairs.h"
using namespace std;
static bool d = false;
bool isFaceRemovableFromPatch(const Patch& patch, Vertex start, Vertex direction) {
Vertex current = start;
Vertex prev = InVertex;
Vertex next = direction;
const VertexVector& list = patch.list;
Neighbours nb;
bool prevOnEdge = false;
int differentOutsides = 0;
begin_neighbour_iteration(prev, current, next, nb, list, nextIndex) {
// It lies on the border if the start and stop vertices lie on the
// border _and_ the difference between start->direction is 1 (mod size):
// otherwise we count edges having a single edge from one side of the patch
// to the other
if (current < patch.borderLength && next < patch.borderLength
&& ((patch.borderLength + next - current) % patch.borderLength) == 1) { // Does not connect 2 different regions of the border?
// This edge lies on the border
if (!prevOnEdge) {
prevOnEdge = true;
differentOutsides++;
}
} else {
prevOnEdge = false;
}
} end_neighbour_iteration(start, current, next, nb, nextIndex);
if (differentOutsides > 2)
return false;
else if (differentOutsides <= 1)
return true;
// There is the possibility that we saw 2 outsides, but it was only one!
// For example if we started halfway the only outside, then cross
// the internal part, and then come out of it, we will count the first part
// again.
// This only happens when the edge given as start is on the outside, as
// is the next: the edge we recieve as start is actually the _last_ we visit,
// so if differentOutsides == 2, and that vertex, and the next, are on the outside,
// we maybe counted too much.
if (start < patch.borderLength && direction < patch.borderLength
&& ((patch.borderLength + direction - start) % patch.borderLength) == 1) { // Prev on border
nb = list.at(direction);
int nextIndex = indexOfNextVertex(start, nb);
next = nb.nb[nextIndex];
// Next on border (startpos == direction, already there)
if (next < patch.borderLength && ((patch.borderLength + next - direction) % patch.borderLength) == 1) {
return true;
}
}
return false;
}
// the mapping is the mapping from p1 to p2 (gets changed, even if return false, but if returns true, the mapping is 'complete')
bool isBorderIsomorphism(const Patch& p1, const Patch& p2, Vertex p1Start, Vertex p2Start, int p2Direction, vector<Vertex>& mapping) {
// What we check, is that if we walk around p1's border from p1Start, in the direction of p1Direction (0 and 1 are
// arbitrary indicators for left or right) and simultaneously we walk on p2 with the same parameters, we check if
// each '2' bordervertex on p1 corresponds with a '2' vertex on p2, and the same for the '3' ones.
Neighbours nb1, nb2;
// We abuse the fact here that the vertices of the border are the first vertices of a patch
for (unsigned int i = 0; i < p1.borderLength; i++) {
bool hasOutEdge1 = false;
bool hasOutEdge2 = false;
Vertex v2;
nb1 = p1.list.at( (p1Start + i) % p1.borderLength );
if (p2Direction == 0) {
v2 = (p2Start + i) % p2.borderLength;
} else {
v2 = (p2.borderLength + p2Start - i) % p2.borderLength;
}
nb2 = p2.list.at(v2);
for (int j = 0; j < 3; j++) {
if (nb1.nb[j] == OutVertex)
hasOutEdge1 = true;
if (nb2.nb[j] == OutVertex)
hasOutEdge2 = true;
}
if (hasOutEdge1 != hasOutEdge2)
return false;
assert(v2 < p2.borderLength);
mapping.at(i) = v2;
}
return true;
}
bool isIrreducibleGrowthPair(const Patch& p1, const Patch& p2) {
Neighbours nb;
// What we choose for p1 is not really important ###
Vertex p1Start = 0;
vector<Vertex> mapping(p1.borderLength);
vector<bool> visited(p1.borderLength);
assert(p1.borderLength == p2.borderLength);
// We choose one ordered edge in p1, and then
// try mapping it to any possible ordered edge so that we get an
// isomorphism of the border.
for (unsigned int i = 0; i < p2.borderLength; i++) {
nb = p2.list.at(i);
for (int j = 0; j <= 1; j++) {
// We have a border edge, see if it is indeed isomorph
if (!isBorderIsomorphism(p1, p2, p1Start, i, j, mapping)) {
continue;
}
// Now we iterate over each face on the boundary of p1, see
// if it is removable. If it is, then we see what its image is
// under the isomorphism. If that is also removable, we
// see if they both are 5- or 6-gons. If they are,
// the pair is reducible.
// The border in the patch is 0->1->2->...->0, use that
for (unsigned int k = 0; k < p1.borderLength; k++)
visited.at(k) = false;
bool allRemovableFacesMappedToDifferents = true;
for (unsigned int k = 0; k < p1.borderLength; k++) {
//if (visited.at(k))
// continue;
// We get the edge k -> k+1 (mod length):
Vertex p1To = (k + 1) % p1.borderLength;
// Is the k->k+1 edge-bounded face removable?
if (!isFaceRemovableFromPatch(p1, k, p1To))
continue;
// Is the face bounded by the isomorph-edge on p2 removable?
if (j == 0) {
// Direction not switched, regular direction
if (!isFaceRemovableFromPatch(p2, mapping.at(k), mapping.at(p1To)))
continue;
} else {
// Direction switched, reverse direction ### isn't it a hack?
if (!isFaceRemovableFromPatch(p2, mapping.at(p1To), mapping.at(k)))
continue;
}
// Are the number of edges on both sides the same?
int face1Edges = nGon(p1.list, k, p1To, 0);
int face2Edges;
if (j == 0) {
// Direction not switched, regular direction
face2Edges = nGon(p2.list, mapping.at(k), mapping.at(p1To), 0);
} else {
// Direction switched, reverse direction ### isn't it a hack?
face2Edges = nGon(p2.list, mapping.at(p1To), mapping.at(k), 0);
}
// We have an isomorphism of the boundaries that maps a non
if (face1Edges == face2Edges) {
allRemovableFacesMappedToDifferents = false;
}
}
if (allRemovableFacesMappedToDifferents) {
return true;
}
}
}
// Since we assume the patches of the pair have the same boundaries,
// there is certainly an isomorphism. So, if we arrive here, we conclude
// that an isomorphism of the boundaries exists, that does not map any
// removable face of p1 to a removable face of p2 of the same size (or
// we'd have return'ed already). And so this pair is irreducible.
return false;
}
bool borderEncodingIsEmbeddableInFullerene(CanonicalBorder b, int length) {
// Will block '(33333) (Will not detect HIDDEN stuff, or somesuch!)
static const unsigned int mask = (1) | (1<<1) | (1<<2) | (1<<3) | (1<<4);
if (length < 5)
return true; // 'Safe' assumption
for (int i = 0; i <= length - 5; i++) {
if ((b & CanonicalBorder(mask << i)) == CanonicalBorder(mask << i))
return false;
}
return true;
}