void Mesh::buildBasisCycles()
{
std::vector<BasisCycle> basisCycles;
buildContractibleCycles(basisCycles);
buildNonContractibleCycles(basisCycles);
// build A
Eigen::SparseMatrix<double> A((int)basisCycles.size(), (int)edges.size());
A.setZero();
std::vector<Eigen::Triplet<double>> ATriplet;
for (int i = 0; i < (int)basisCycles.size(); i++) {
for (int j = 0; j < (int)basisCycles[i].size(); j++) {
HalfEdgeIter he = basisCycles[i][j];
int e = he->edge->index;
double coefficient = sqrt((he->cotan() + he->flip->cotan()) * 0.5);
if (coefficient != coefficient) coefficient = 0; // check for negative cotan weights
if (he == he->edge->he) {
ATriplet.push_back(Eigen::Triplet<double>(i, e, coefficient));
} else {
ATriplet.push_back(Eigen::Triplet<double>(i, e, -coefficient));
}
}
}
A.setFromTriplets(ATriplet.begin(), ATriplet.end());
solver.compute(A);
}
void Mesh::buildNonContractibleCycles(std::vector<BasisCycle>& basisCycles)
{
generators.clear();
buildPrimalSpanningTree();
buildDualSpanningTree();
for (EdgeCIter e = edges.begin(); e != edges.end(); e++) {
HalfEdgeIter he = e->he;
if (!he->inPrimalSpanningTree() && !he->inDualSpanningTree()) {
BasisCycle cycle;
cycle.push_back(he);
// trace loop in both directions
BasisCycle temp1;
FaceCIter f = he->flip->face;
while (f != f->parent) {
FaceCIter fp = f->parent;
temp1.push_back(f->sharedEdge(fp));
f = fp;
}
BasisCycle temp2;
f = he->face;
while (f != f->parent) {
FaceCIter fp = f->parent;
temp2.push_back(f->sharedEdge(fp));
f = fp;
}
// remove common edges
int t1 = (int)temp1.size()-1;
int t2 = (int)temp2.size()-1;
while (temp1[t1] == temp2[t2]) {
t1--;
t2--;
}
for (int i = 0; i <= t1; i++) {
cycle.push_back(temp1[i]);
}
for (int i = t2; i >= 0; i--) {
cycle.push_back(temp2[i]->flip);
}
generators.push_back(cycle);
}
}
basisCycles.insert(basisCycles.end(), generators.begin(), generators.end());
}
double Mesh :: connectionOneForm(HalfEdgeIter h) const
{
double angle = 0.0;
// coclosed term
double star1 = 0.5 * ( h->cotan() + h->flip->cotan() );
double u0 = h->flip->vertex->potential;
double u1 = h->vertex->potential;
angle += star1*(u1 - u0);
// harmonic term
for(unsigned k = 0; k < h->harmonicBases.size(); ++k)
angle += this->harmonicCoefs[k] * h->harmonicBases[k];
return angle;
}