static tetrahedra read_tetrahedra (boost::tokenizer<>::iterator & p,
const boost::tokenizer<>::iterator & end,
std::list<vertex_id> & finalized_vertices,
const dias::vertex_db & vertices,
int v_count)
{
vertex_id v_ids[4];
int j = 0;
while (p != end)
{
std::string v_str = *p++;
int v = boost::lexical_cast<int> (v_str);
if (v >= 0)
v_ids[j] = v;
else
{
v_ids[j] = v_count + v;
finalized_vertices.push_back (v_ids[j]);
}
j++;
}
assert (j == 4);
return tetrahedra (v_ids, vertices);
}
/// Returns the number of tetrahedra in the alpha shape.
int AlphaShape::tetrahedronCount() const
{
return tetrahedra().size();
}
const NGroupPresentation& Dim4Triangulation::fundamentalGroup() const {
if (fundGroup_.known())
return *fundGroup_.value();
NGroupPresentation* ans = new NGroupPresentation();
if (isEmpty())
return *(fundGroup_ = ans);
ensureSkeleton();
// Each non-boundary not-in-forest tetrahedron is a generator.
// Each non-boundary triangle is a relation.
long nBdryTets = 0;
for (BoundaryComponentIterator bit = boundaryComponents_.begin();
bit != boundaryComponents_.end(); ++bit)
nBdryTets += (*bit)->countTetrahedra();
// Cast away all unsignedness in case we run into problems subtracting.
long nGens = static_cast<long>(countTetrahedra()) - nBdryTets
- static_cast<long>(size())
+ static_cast<long>(countComponents());
// Insert the generators.
ans->addGenerator(nGens);
// Find out which tetrahedron corresponds to which generator.
long* genIndex = new long[countTetrahedra()];
long i = 0;
for (Dim4Tetrahedron* tet : tetrahedra())
if (! (tet->isBoundary() || tet->inMaximalForest()))
genIndex[tet->index()] = i++;
// Run through each triangle and insert the corresponding relations.
Dim4Pentachoron* pent;
int facet;
Dim4Tetrahedron* tet;
NGroupExpression* rel;
for (Dim4Triangle* f : triangles()) {
if (f->isBoundary())
continue;
// Put in the relation corresponding to this triangle.
rel = new NGroupExpression();
for (auto& emb : *f) {
pent = emb.pentachoron();
facet = emb.vertices()[3];
tet = pent->tetrahedron(facet);
if (tet->inMaximalForest())
continue;
// We define the "direction" for this dual edge to point
// from embedding tet->front() to embedding tet->back().
//
// Test whether we are traversing this dual edge forwards or
// backwards as we walk around the triangle (*fit).
if ((tet->front().pentachoron() == pent) &&
(tet->front().tetrahedron() == facet))
rel->addTermLast(genIndex[tet->index()], 1);
else
rel->addTermLast(genIndex[tet->index()], -1);
}
ans->addRelation(rel);
}
// Tidy up.
delete[] genIndex;
ans->intelligentSimplify();
return *(fundGroup_ = ans);
}
