IGL_INLINE void igl::adjacency_matrix(
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::SparseMatrix<T>& A)
{
using namespace std;
using namespace Eigen;
typedef typename DerivedF::Scalar Index;
typedef Triplet<T> IJV;
vector<IJV > ijv;
ijv.reserve(F.size()*2);
// Loop over faces
for(int i = 0;i<F.rows();i++)
{
// Loop over this face
for(int j = 0;j<F.cols();j++)
{
// Get indices of edge: s --> d
Index s = F(i,j);
Index d = F(i,(j+1)%F.cols());
ijv.push_back(IJV(s,d,1));
ijv.push_back(IJV(d,s,1));
}
}
const Index n = F.maxCoeff()+1;
A.resize(n,n);
switch(F.cols())
{
case 3:
A.reserve(6*(F.maxCoeff()+1));
break;
case 4:
A.reserve(26*(F.maxCoeff()+1));
break;
}
A.setFromTriplets(ijv.begin(),ijv.end());
// Force all non-zeros to be one
// Iterate over outside
for(int k=0; k<A.outerSize(); ++k)
{
// Iterate over inside
for(typename Eigen::SparseMatrix<T>::InnerIterator it (A,k); it; ++it)
{
assert(it.value() != 0);
A.coeffRef(it.row(),it.col()) = 1;
}
}
}
void LaplacianOperator::computeLaplacianOperator( Eigen::SparseMatrix<double>& laplacianOperator )
{
laplacianOperator.resize(mMeshVertexCount,mMeshVertexCount);
laplacianOperator.reserve(Eigen::VectorXi::Constant(mMeshVertexCount,10));
for (int i = 0; i < mMeshVertexCount; i++)
{
/* 如果第i个点没有邻接点，即它是一个孤立的点，那么它的laplacian坐标为0 */
if( adjacentMatrix.innerVector(i).nonZeros() == 0)
{
laplacianOperator.insert(i,i) = 0;
continue;
}
laplacianOperator.insert(i,i) = 1;
#ifdef MY_DEBUG
int adjCount = 0;
#endif
for (Eigen::SparseMatrix<double>::InnerIterator it(adjacentMatrix,i); it; it++)
{
if(i != it.row())
{
laplacianOperator.insert(i,it.row()) = -1/degreeMatrix(i);
#ifdef MY_DEBUG
adjCount++;
if(adjCount >= 10)
printf("InnerVector size should expand! CurrentMax:%d.\n",adjCount);
#endif
}
}
}
}
IGL_INLINE void igl::speye(const int m, const int n, Eigen::SparseMatrix<T> & I)
{
// size of diagonal
int d = (m<n?m:n);
I = Eigen::SparseMatrix<T>(m,n);
I.reserve(d);
for(int i = 0;i<d;i++)
{
I.insert(i,i) = 1.0;
}
I.finalize();
}
inline
void
identity_operator(
Eigen::SparseMatrix<double>& result,
int size)
{
result.resize(size, size);
result.reserve(size);
std::vector<double_triplet_t> matrix_coeffs;
matrix_coeffs.reserve(size); // #diag
// diag
for (int i = 0; i < size; ++i) matrix_coeffs.push_back(double_triplet_t(i,i, 1.));
result.setFromTriplets(matrix_coeffs.begin(), matrix_coeffs.end());
}
inline
void
laplace_operator_1d(
Eigen::SparseMatrix<double>& result,
int size)
{
result.resize(size, size);
result.reserve(size*3-2);
std::vector<double_triplet_t> matrix_coeffs;
matrix_coeffs.reserve(size*3-2); // #diag + #diag(-1) + #diag(+1)
// diag
for (int i = 0; i < size; ++i) matrix_coeffs.push_back(double_triplet_t(i,i, -2.));
// diag(-1)
for (int i = 1; i < size; ++i) matrix_coeffs.push_back(double_triplet_t(i,i-1, 1.));
// diag(+1)
for (int i = 0; i < size-1; ++i) matrix_coeffs.push_back(double_triplet_t(i,i+1, 1.));
result.setFromTriplets(matrix_coeffs.begin(), matrix_coeffs.end());
}
IGL_INLINE void igl::cotmatrix(
const Eigen::MatrixBase<DerivedV> & V,
const Eigen::MatrixBase<DerivedF> & F,
Eigen::SparseMatrix<Scalar>& L)
{
using namespace Eigen;
using namespace std;
L.resize(V.rows(),V.rows());
Matrix<int,Dynamic,2> edges;
int simplex_size = F.cols();
// 3 for triangles, 4 for tets
assert(simplex_size == 3 || simplex_size == 4);
if(simplex_size == 3)
{
// This is important! it could decrease the comptuation time by a factor of 2
// Laplacian for a closed 2d manifold mesh will have on average 7 entries per
// row
L.reserve(10*V.rows());
edges.resize(3,2);
edges <<
1,2,
2,0,
0,1;
}else if(simplex_size == 4)
{
L.reserve(17*V.rows());
edges.resize(6,2);
edges <<
1,2,
2,0,
0,1,
3,0,
3,1,
3,2;
}else
{
return;
}
// Gather cotangents
Matrix<Scalar,Dynamic,Dynamic> C;
cotmatrix_entries(V,F,C);
vector<Triplet<Scalar> > IJV;
IJV.reserve(F.rows()*edges.rows()*4);
// Loop over triangles
for(int i = 0; i < F.rows(); i++)
{
// loop over edges of element
for(int e = 0;e<edges.rows();e++)
{
int source = F(i,edges(e,0));
int dest = F(i,edges(e,1));
IJV.push_back(Triplet<Scalar>(source,dest,C(i,e)));
IJV.push_back(Triplet<Scalar>(dest,source,C(i,e)));
IJV.push_back(Triplet<Scalar>(source,source,-C(i,e)));
IJV.push_back(Triplet<Scalar>(dest,dest,-C(i,e)));
}
}
L.setFromTriplets(IJV.begin(),IJV.end());
}
IGL_INLINE void igl::arap_linear_block_spokes(
const MatV & V,
const MatF & F,
const int d,
Eigen::SparseMatrix<Scalar> & Kd)
{
using namespace std;
using namespace Eigen;
// simplex size (3: triangles, 4: tetrahedra)
int simplex_size = F.cols();
// Number of elements
int m = F.rows();
// Temporary output
Matrix<int,Dynamic,2> edges;
Kd.resize(V.rows(), V.rows());
vector<Triplet<Scalar> > Kd_IJV;
if(simplex_size == 3)
{
// triangles
Kd.reserve(7*V.rows());
Kd_IJV.reserve(7*V.rows());
edges.resize(3,2);
edges <<
1,2,
2,0,
0,1;
}else if(simplex_size == 4)
{
// tets
Kd.reserve(17*V.rows());
Kd_IJV.reserve(17*V.rows());
edges.resize(6,2);
edges <<
1,2,
2,0,
0,1,
3,0,
3,1,
3,2;
}
// gather cotangent weights
Matrix<Scalar,Dynamic,Dynamic> C;
cotmatrix_entries(V,F,C);
// should have weights for each edge
assert(C.cols() == edges.rows());
// loop over elements
for(int i = 0;i<m;i++)
{
// loop over edges of element
for(int e = 0;e<edges.rows();e++)
{
int source = F(i,edges(e,0));
int dest = F(i,edges(e,1));
double v = 0.5*C(i,e)*(V(source,d)-V(dest,d));
Kd_IJV.push_back(Triplet<Scalar>(source,dest,v));
Kd_IJV.push_back(Triplet<Scalar>(dest,source,-v));
Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
}
}
Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
Kd.makeCompressed();
}
IGL_INLINE void igl::slice_tets(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedT>& T,
const Eigen::PlainObjectBase<Derivedplane> & plane,
Eigen::PlainObjectBase<DerivedU>& U,
Eigen::PlainObjectBase<DerivedG>& G,
Eigen::PlainObjectBase<DerivedJ>& J,
Eigen::SparseMatrix<BCType> & BC)
{
using namespace Eigen;
using namespace std;
assert(V.cols() == 3 && "V should be #V by 3");
assert(T.cols() == 4 && "T should be #T by 4");
assert(plane.size() == 4 && "Plane equation should be 4 coefficients");
// number of tets
const size_t m = T.rows();
typedef typename DerivedV::Scalar Scalar;
typedef typename DerivedT::Scalar Index;
typedef Matrix<Scalar,Dynamic,1> VectorXS;
typedef Matrix<Scalar,Dynamic,4> MatrixX4S;
typedef Matrix<Scalar,Dynamic,3> MatrixX3S;
typedef Matrix<Scalar,Dynamic,2> MatrixX2S;
typedef Matrix<Index,Dynamic,4> MatrixX4I;
typedef Matrix<Index,Dynamic,3> MatrixX3I;
typedef Matrix<Index,Dynamic,1> VectorXI;
typedef Matrix<bool,Dynamic,1> VectorXb;
// Value of plane's implicit function at all vertices
VectorXS IV =
(V.col(0)*plane(0) +
V.col(1)*plane(1) +
V.col(2)*plane(2)).array()
+ plane(3);
MatrixX4S IT(m,4);
for(size_t t = 0;t<m;t++)
{
for(size_t c = 0;c<4;c++)
{
IT(t,c) = IV(T(t,c));
}
}
const auto & extract_rows = [](
const PlainObjectBase<DerivedT> & T,
const MatrixX4S & IT,
const VectorXb & I,
MatrixX4I & TI,
MatrixX4S & ITI,
VectorXI & JI)
{
const Index num_I = std::count(I.data(),I.data()+I.size(),true);
TI.resize(num_I,4);
ITI.resize(num_I,4);
JI.resize(num_I,1);
{
size_t k = 0;
for(size_t t = 0;t<(size_t)T.rows();t++)
{
if(I(t))
{
TI.row(k) = T.row(t);
ITI.row(k) = IT.row(t);
JI(k) = t;
k++;
}
}
assert(k == num_I);
}
};
VectorXb I13 = (IT.array()<0).rowwise().count()==1;
VectorXb I31 = (IT.array()>0).rowwise().count()==1;
VectorXb I22 = (IT.array()<0).rowwise().count()==2;
MatrixX4I T13,T31,T22;
MatrixX4S IT13,IT31,IT22;
VectorXI J13,J31,J22;
extract_rows(T,IT,I13,T13,IT13,J13);
extract_rows(T,IT,I31,T31,IT31,J31);
extract_rows(T,IT,I22,T22,IT22,J22);
const auto & apply_sort = [] (
const MatrixX4I & T,
const MatrixX4I & sJ,
MatrixX4I & sT)
{
sT.resize(T.rows(),4);
for(size_t t = 0;t<(size_t)T.rows();t++)
{
for(size_t c = 0;c<4;c++)
{
sT(t,c) = T(t,sJ(t,c));
}
}
};
const auto & one_below = [&V,&apply_sort](
const MatrixX4I & T,
const MatrixX4S & IT,
MatrixX3I & G,
SparseMatrix<BCType> & BC)
{
// Number of tets
const size_t m = T.rows();
MatrixX4S sIT;
MatrixX4I sJ;
sort(IT,2,true,sIT,sJ);
MatrixX4I sT;
apply_sort(T,sJ,sT);
MatrixX3S lambda =
sIT.rightCols(3).array() /
(sIT.rightCols(3).colwise()-sIT.col(0)).array();
vector<Triplet<BCType> > IJV;
IJV.reserve(m*3*2);
for(size_t c = 0;c<3;c++)
{
for(size_t t = 0;t<(size_t)m;t++)
{
IJV.push_back(Triplet<BCType>(c*m+t, sT(t,0), lambda(t,c)));
IJV.push_back(Triplet<BCType>(c*m+t,sT(t,c+1),1-lambda(t,c)));
}
}
BC.resize(m*3,V.rows());
BC.reserve(m*3*2);
BC.setFromTriplets(IJV.begin(),IJV.end());
G.resize(m,3);
for(size_t c = 0;c<3;c++)
{
G.col(c).setLinSpaced(m,0+c*m,(m-1)+c*m);
}
};
const auto & two_below = [&V,&apply_sort](
const MatrixX4I & T,
const MatrixX4S & IT,
MatrixX3I & G,
SparseMatrix<BCType> & BC)
{
// Number of tets
const size_t m = T.rows();
MatrixX4S sIT;
MatrixX4I sJ;
sort(IT,2,true,sIT,sJ);
MatrixX4I sT;
apply_sort(T,sJ,sT);
MatrixX2S lambda =
sIT.rightCols(2).array() /
(sIT.rightCols(2).colwise()-sIT.col(0)).array();
MatrixX2S gamma =
sIT.rightCols(2).array() /
(sIT.rightCols(2).colwise()-sIT.col(1)).array();
vector<Triplet<BCType> > IJV;
IJV.reserve(m*4*2);
for(size_t c = 0;c<2;c++)
{
for(size_t t = 0;t<(size_t)m;t++)
{
IJV.push_back(Triplet<BCType>(0*2*m+c*m+t, sT(t,0), lambda(t,c)));
IJV.push_back(Triplet<BCType>(0*2*m+c*m+t,sT(t,c+2),1-lambda(t,c)));
IJV.push_back(Triplet<BCType>(1*2*m+c*m+t, sT(t,1), gamma(t,c)));
IJV.push_back(Triplet<BCType>(1*2*m+c*m+t,sT(t,c+2),1- gamma(t,c)));
}
}
BC.resize(m*4,V.rows());
BC.reserve(m*4*2);
BC.setFromTriplets(IJV.begin(),IJV.end());
G.resize(2*m,3);
G.block(0,0,m,1) = VectorXI::LinSpaced(m,0+0*m,(m-1)+0*m);
G.block(0,1,m,1) = VectorXI::LinSpaced(m,0+1*m,(m-1)+1*m);
G.block(0,2,m,1) = VectorXI::LinSpaced(m,0+3*m,(m-1)+3*m);
G.block(m,0,m,1) = VectorXI::LinSpaced(m,0+0*m,(m-1)+0*m);
G.block(m,1,m,1) = VectorXI::LinSpaced(m,0+3*m,(m-1)+3*m);
G.block(m,2,m,1) = VectorXI::LinSpaced(m,0+2*m,(m-1)+2*m);
};
MatrixX3I G13,G31,G22;
SparseMatrix<BCType> BC13,BC31,BC22;
one_below(T13,IT13,G13,BC13);
one_below(T31,-IT31,G31,BC31);
two_below(T22,IT22,G22,BC22);
BC = cat(1,cat(1,BC13,BC31),BC22);
U = BC*V;
G.resize(G13.rows()+G31.rows()+G22.rows(),3);
G<<G13,(G31.array()+BC13.rows()),(G22.array()+BC13.rows()+BC31.rows());
MatrixX3S N;
per_face_normals(U,G,N);
Matrix<Scalar,1,3> planeN(plane(0),plane(1),plane(2));
VectorXb flip = (N.array().rowwise() * planeN.array()).rowwise().sum()<0;
for(size_t g = 0;g<(size_t)G.rows();g++)
{
if(flip(g))
{
G.row(g) = G.row(g).reverse().eval();
}
}
J.resize(G.rows());
J<<J13,J31,J22,J22;
}