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);
}
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;
}