IGL_INLINE void igl::PolyVectorFieldFinder<DerivedV, DerivedF>::computeCoefficientLaplacian(int n, Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &D)
{
std::vector<Eigen::Triplet<std::complex<typename DerivedV::Scalar> > > tripletList;
// For every non-border edge
for (unsigned eid=0; eid<numE; ++eid)
{
if (!isBorderEdge[eid])
{
int fid0 = E2F(eid,0);
int fid1 = E2F(eid,1);
tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid0,
fid0,
std::complex<typename DerivedV::Scalar>(1.)));
tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid1,
fid1,
std::complex<typename DerivedV::Scalar>(1.)));
tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid0,
fid1,
-1.*std::polar(1.,-1.*n*K[eid])));
tripletList.push_back(Eigen::Triplet<std::complex<typename DerivedV::Scalar> >(fid1,
fid0,
-1.*std::polar(1.,1.*n*K[eid])));
}
}
D.resize(numF,numF);
D.setFromTriplets(tripletList.begin(), tripletList.end());
}
IGL_INLINE void igl::GeneralPolyVectorFieldFinder<DerivedV, DerivedF>::
precomputeInteriorEdges()
{
// Flag border edges
numInteriorEdges = 0;
isBorderEdge.setZero(numE,1);
indFullToInterior = -1*Eigen::VectorXi::Ones(numE,1);
for(unsigned i=0; i<numE; ++i)
{
if ((E2F(i,0) == -1) || ((E2F(i,1) == -1)))
isBorderEdge[i] = 1;
else
{
indFullToInterior[i] = numInteriorEdges;
numInteriorEdges++;
}
}
E2F_int.resize(numInteriorEdges, 2);
indInteriorToFull.setZero(numInteriorEdges,1);
int ii = 0;
for (int k=0; k<numE; ++k)
{
if (isBorderEdge[k])
continue;
E2F_int.row(ii) = E2F.row(k);
indInteriorToFull[ii] = k;
ii++;
}
}
IGL_INLINE void igl::PolyVectorFieldFinder<DerivedV, DerivedF>::computek()
{
K.setZero(numE);
// For every non-border edge
for (unsigned eid=0; eid<numE; ++eid)
{
if (!isBorderEdge[eid])
{
int fid0 = E2F(eid,0);
int fid1 = E2F(eid,1);
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> N0 = FN.row(fid0);
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> N1 = FN.row(fid1);
// find common edge on triangle 0 and 1
int fid0_vc = -1;
int fid1_vc = -1;
for (unsigned i=0;i<3;++i)
{
if (F2E(fid0,i) == eid)
fid0_vc = i;
if (F2E(fid1,i) == eid)
fid1_vc = i;
}
assert(fid0_vc != -1);
assert(fid1_vc != -1);
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> common_edge = V.row(F(fid0,(fid0_vc+1)%3)) - V.row(F(fid0,fid0_vc));
common_edge.normalize();
// Map the two triangles in a new space where the common edge is the x axis and the N0 the z axis
Eigen::Matrix<typename DerivedV::Scalar, 3, 3> P;
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> o = V.row(F(fid0,fid0_vc));
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> tmp = -N0.cross(common_edge);
P << common_edge, tmp, N0;
// P.transposeInPlace();
Eigen::Matrix<typename DerivedV::Scalar, 3, 3> V0;
V0.row(0) = V.row(F(fid0,0)) -o;
V0.row(1) = V.row(F(fid0,1)) -o;
V0.row(2) = V.row(F(fid0,2)) -o;
V0 = (P*V0.transpose()).transpose();
// assert(V0(0,2) < 1e-10);
// assert(V0(1,2) < 1e-10);
// assert(V0(2,2) < 1e-10);
Eigen::Matrix<typename DerivedV::Scalar, 3, 3> V1;
V1.row(0) = V.row(F(fid1,0)) -o;
V1.row(1) = V.row(F(fid1,1)) -o;
V1.row(2) = V.row(F(fid1,2)) -o;
V1 = (P*V1.transpose()).transpose();
// assert(V1(fid1_vc,2) < 10e-10);
// assert(V1((fid1_vc+1)%3,2) < 10e-10);
// compute rotation R such that R * N1 = N0
// i.e. map both triangles to the same plane
double alpha = -atan2(V1((fid1_vc+2)%3,2),V1((fid1_vc+2)%3,1));
Eigen::Matrix<typename DerivedV::Scalar, 3, 3> R;
R << 1, 0, 0,
0, cos(alpha), -sin(alpha) ,
0, sin(alpha), cos(alpha);
V1 = (R*V1.transpose()).transpose();
// assert(V1(0,2) < 1e-10);
// assert(V1(1,2) < 1e-10);
// assert(V1(2,2) < 1e-10);
// measure the angle between the reference frames
// k_ij is the angle between the triangle on the left and the one on the right
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> ref0 = V0.row(1) - V0.row(0);
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> ref1 = V1.row(1) - V1.row(0);
ref0.normalize();
ref1.normalize();
double ktemp = atan2(ref1(1),ref1(0)) - atan2(ref0(1),ref0(0));
// just to be sure, rotate ref0 using angle ktemp...
Eigen::Matrix<typename DerivedV::Scalar, 2, 2> R2;
R2 << cos(ktemp), -sin(ktemp), sin(ktemp), cos(ktemp);
Eigen::Matrix<typename DerivedV::Scalar, 1, 2> tmp1 = R2*(ref0.head(2)).transpose();
// assert(tmp1(0) - ref1(0) < 1e-10);
// assert(tmp1(1) - ref1(1) < 1e-10);
K[eid] = ktemp;
}
}
}