IGL_INLINE void igl::boundary_loop(
const Eigen::MatrixXd& V,
const Eigen::MatrixXi& F,
Eigen::VectorXi& b)
{
std::vector<int> bnd;
bnd.clear();
std::vector<bool> isVisited(V.rows(),false);
// Actually mesh only needs to be manifold near boundary, so this is
// over zealous (see gptoolbox's outline_loop for a more general
// (and probably faster) implementation)
assert(is_edge_manifold(V,F) && "Mesh must be manifold");
Eigen::MatrixXi TT,TTi;
std::vector<std::vector<int> > VF, VFi;
igl::triangle_triangle_adjacency(V,F,TT,TTi);
igl::vertex_triangle_adjacency(V,F,VF,VFi);
// Extract one boundary edge
bool done = false;
for (int i = 0; i < TT.rows() && !done; i++)
{
for (int j = 0; j < TT.cols(); j++)
{
if (TT(i,j) < 0)
{
int idx1, idx2;
idx1 = F(i,j);
idx2 = F(i,(j+1) % F.cols());
bnd.push_back(idx1);
bnd.push_back(idx2);
isVisited[idx1] = true;
isVisited[idx2] = true;
done = true;
break;
}
}
}
// Traverse boundary
while(1)
{
bool changed = false;
int lastV;
lastV = bnd[bnd.size()-1];
for (int i = 0; i < (int)VF[lastV].size(); i++)
{
int curr_neighbor = VF[lastV][i];
if (TT.row(curr_neighbor).minCoeff() < 0.) // Face contains boundary edge
{
int idx_lastV_in_face;
if (F(curr_neighbor,0) == lastV) idx_lastV_in_face = 0;
if (F(curr_neighbor,1) == lastV) idx_lastV_in_face = 1;
if (F(curr_neighbor,2) == lastV) idx_lastV_in_face = 2;
int idx_prev = (idx_lastV_in_face + F.cols()-1) % F.cols();
int idx_next = (idx_lastV_in_face + 1) % F.cols();
bool isPrevVisited = isVisited[F(curr_neighbor,idx_prev)];
bool isNextVisited = isVisited[F(curr_neighbor,idx_next)];
bool gotBndEdge = false;
int next_bnd_vertex;
if (!isNextVisited && TT(curr_neighbor,idx_lastV_in_face) < 0)
{
next_bnd_vertex = idx_next;
gotBndEdge = true;
}
else if (!isPrevVisited && TT(curr_neighbor,(idx_lastV_in_face+2) % F.cols()) < 0)
{
next_bnd_vertex = idx_prev;
gotBndEdge = true;
}
if (gotBndEdge)
{
changed = true;
bnd.push_back(F(curr_neighbor,next_bnd_vertex));
isVisited[F(curr_neighbor,next_bnd_vertex)] = true;
break;
}
}
}
if (!changed)
break;
}
b.resize(bnd.size());
for(unsigned i=0;i<bnd.size();++i)
b(i) = bnd[i];
}
void igl::crouzeix_raviart_cotmatrix(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedF> & F,
const Eigen::MatrixBase<DerivedE> & E,
const Eigen::MatrixBase<DerivedEMAP> & EMAP,
Eigen::SparseMatrix<LT> & L)
{
// number of rows
const int m = F.rows();
// Element simplex size
const int ss = F.cols();
// Mesh should be edge-manifold
assert(F.cols() != 3 || is_edge_manifold(F));
typedef Eigen::Matrix<LT,Eigen::Dynamic,Eigen::Dynamic> MatrixXS;
MatrixXS C;
cotmatrix_entries(V,F,C);
Eigen::MatrixXi F2E(m,ss);
{
int k =0;
for(int c = 0;c<ss;c++)
{
for(int f = 0;f<m;f++)
{
F2E(f,c) = k++;
}
}
}
// number of entries inserted per facet
const int k = ss*(ss-1)*2;
std::vector<Eigen::Triplet<LT> > LIJV;LIJV.reserve(k*m);
Eigen::VectorXi LI(k),LJ(k),LV(k);
// Compensation factor to match scales in matlab version
double factor = 2.0;
switch(ss)
{
default: assert(false && "unsupported simplex size");
case 3:
factor = 4.0;
LI<<0,1,2,1,2,0,0,1,2,1,2,0;
LJ<<1,2,0,0,1,2,0,1,2,1,2,0;
LV<<2,0,1,2,0,1,2,0,1,2,0,1;
break;
case 4:
factor *= -1.0;
LI<<0,3,3,3,1,2,1,0,1,2,2,0,0,3,3,3,1,2,1,0,1,2,2,0;
LJ<<1,0,1,2,2,0,0,3,3,3,1,2,0,3,3,3,1,2,1,0,1,2,2,0;
LV<<2,3,4,5,0,1,2,3,4,5,0,1,2,3,4,5,0,1,2,3,4,5,0,1;
break;
}
for(int f=0;f<m;f++)
{
for(int c = 0;c<k;c++)
{
LIJV.emplace_back(
EMAP(F2E(f,LI(c))),
EMAP(F2E(f,LJ(c))),
(c<(k/2)?-1.:1.) * factor *C(f,LV(c)));
}
}
L.resize(E.rows(),E.rows());
L.setFromTriplets(LIJV.begin(),LIJV.end());
}