IGL_INLINE void igl::flipped_triangles(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::PlainObjectBase<DerivedX> & X)
{
assert(V.cols() == 2 && "V should contain 2D positions");
std::vector<typename DerivedX::Scalar> flip_idx;
for (int i = 0; i < F.rows(); i++)
{
// https://www.cs.cmu.edu/~quake/robust.html
typedef Eigen::Matrix<typename DerivedV::Scalar,1,2> RowVector2S;
RowVector2S v1_n = V.row(F(i,0));
RowVector2S v2_n = V.row(F(i,1));
RowVector2S v3_n = V.row(F(i,2));
Eigen::Matrix<typename DerivedV::Scalar,3,3> T2_Homo;
T2_Homo.col(0) << v1_n(0),v1_n(1),1.;
T2_Homo.col(1) << v2_n(0),v2_n(1),1.;
T2_Homo.col(2) << v3_n(0),v3_n(1),1.;
double det = T2_Homo.determinant();
assert(det == det && "det should not be NaN");
if (det < 0)
{
flip_idx.push_back(i);
}
}
igl::list_to_matrix(flip_idx,X);
}
IGL_INLINE void igl::cylinder(
const int axis_devisions,
const int height_devisions,
Eigen::PlainObjectBase<DerivedV> & V,
Eigen::PlainObjectBase<DerivedF> & F)
{
V.resize(axis_devisions*height_devisions,3);
F.resize(2*(axis_devisions*(height_devisions-1)),3);
int f = 0;
typedef typename DerivedV::Scalar Scalar;
for(int th = 0;th<axis_devisions;th++)
{
Scalar x = cos(2.*igl::PI*Scalar(th)/Scalar(axis_devisions));
Scalar y = sin(2.*igl::PI*Scalar(th)/Scalar(axis_devisions));
for(int h = 0;h<height_devisions;h++)
{
Scalar z = Scalar(h)/Scalar(height_devisions-1);
V(th+h*axis_devisions,0) = x;
V(th+h*axis_devisions,1) = y;
V(th+h*axis_devisions,2) = z;
if(h > 0)
{
F(f,0) = ((th+0)%axis_devisions)+(h-1)*axis_devisions;
F(f,1) = ((th+1)%axis_devisions)+(h-1)*axis_devisions;
F(f,2) = ((th+0)%axis_devisions)+(h+0)*axis_devisions;
f++;
F(f,0) = ((th+1)%axis_devisions)+(h-1)*axis_devisions;
F(f,1) = ((th+1)%axis_devisions)+(h+0)*axis_devisions;
F(f,2) = ((th+0)%axis_devisions)+(h+0)*axis_devisions;
f++;
}
}
}
assert(f == F.rows());
}
inline void igl::PlanarizerShapeUp<DerivedV, DerivedF>::planarize(Eigen::PlainObjectBase<DerivedV> &Vout)
{
Eigen::Matrix<typename DerivedV::Scalar, Eigen::Dynamic, 1> planarity;
Vout = Vin;
for (int iter =0; iter<maxIter; ++iter)
{
igl::quad_planarity(Vout, Fin, planarity);
typename DerivedV::Scalar nonPlanarity = planarity.cwiseAbs().maxCoeff();
//std::cerr<<"iter #"<<iter<<": max non-planarity: "<<nonPlanarity<<std::endl;
if (nonPlanarity<threshold)
break;
assembleP();
Vv = solver.solve(Q.transpose()*P);
if(solver.info()!=Eigen::Success)
{
std::cerr << "Linear solve failed - PlanarizerShapeUp.cpp" << std::endl;
assert(0);
}
for (int i =0;i<numV;++i)
Vout.row(i) << Vv.segment(3*i,3).transpose();
}
// set the mean of Vout to the mean of Vin
Eigen::Matrix<typename DerivedV::Scalar, 1, 3> oldMean, newMean;
oldMean = Vin.colwise().mean();
newMean = Vout.colwise().mean();
Vout.rowwise() += (oldMean - newMean);
};
IGL_INLINE void igl::sort_vectors_ccw(
const Eigen::PlainObjectBase<DerivedS>& P,
const Eigen::PlainObjectBase<DerivedS>& N,
Eigen::PlainObjectBase<DerivedI> &order)
{
int half_degree = P.cols()/3;
//local frame
Eigen::Matrix<typename DerivedS::Scalar,1,3> e1 = P.head(3).normalized();
Eigen::Matrix<typename DerivedS::Scalar,1,3> e3 = N.normalized();
Eigen::Matrix<typename DerivedS::Scalar,1,3> e2 = e3.cross(e1);
Eigen::Matrix<typename DerivedS::Scalar,3,3> F; F<<e1.transpose(),e2.transpose(),e3.transpose();
Eigen::Matrix<typename DerivedS::Scalar,Eigen::Dynamic,1> angles(half_degree,1);
for (int i=0; i<half_degree; ++i)
{
Eigen::Matrix<typename DerivedS::Scalar,1,3> Pl = F.colPivHouseholderQr().solve(P.segment(i*3,3).transpose()).transpose();
// assert(fabs(Pl(2))/Pl.cwiseAbs().maxCoeff() <1e-5);
angles[i] = atan2(Pl(1),Pl(0));
}
igl::sort( angles, 1, true, angles, order);
//make sure that the first element is always at the top
while (order[0] != 0)
{
//do a circshift
int temp = order[0];
for (int i =0; i< half_degree-1; ++i)
order[i] = order[i+1];
order(half_degree-1) = temp;
}
}
bool is_orientable(
const Eigen::PlainObjectBase<DerivedF>& F,
const Eigen::PlainObjectBase<DeriveduE>& uE,
const std::vector<std::vector<uE2EType> >& uE2E) {
const size_t num_faces = F.rows();
const size_t num_edges = uE.rows();
auto edge_index_to_face_index = [&](size_t ei) {
return ei % num_faces;
};
auto is_consistent = [&](size_t fid, size_t s, size_t d) {
if ((size_t)F(fid, 0) == s && (size_t)F(fid, 1) == d) return true;
if ((size_t)F(fid, 1) == s && (size_t)F(fid, 2) == d) return true;
if ((size_t)F(fid, 2) == s && (size_t)F(fid, 0) == d) return true;
if ((size_t)F(fid, 0) == d && (size_t)F(fid, 1) == s) return false;
if ((size_t)F(fid, 1) == d && (size_t)F(fid, 2) == s) return false;
if ((size_t)F(fid, 2) == d && (size_t)F(fid, 0) == s) return false;
throw "Invalid face!!";
};
for (size_t i=0; i<num_edges; i++) {
const size_t s = uE(i,0);
const size_t d = uE(i,1);
int count=0;
for (const auto& ei : uE2E[i]) {
const size_t fid = edge_index_to_face_index(ei);
if (is_consistent(fid, s, d)) count++;
else count--;
}
if (count != 0) {
return false;
}
}
return true;
}
IGL_INLINE bool igl::list_to_matrix(const std::vector<std::vector<T > > & V,Eigen::PlainObjectBase<Derived>& M)
{
// number of rows
int m = V.size();
if(m == 0)
{
M.resize(0,0);
return true;
}
// number of columns
int n = igl::min_size(V);
if(n != igl::max_size(V))
{
return false;
}
assert(n != -1);
// Resize output
M.resize(m,n);
// Loop over rows
for(int i = 0;i<m;i++)
{
// Loop over cols
for(int j = 0;j<n;j++)
{
M(i,j) = V[i][j];
}
}
return true;
}
IGL_INLINE void igl::volume(
Eigen::PlainObjectBase<DerivedL>& L,
Eigen::PlainObjectBase<Derivedvol>& vol)
{
using namespace Eigen;
const int m = L.rows();
typedef typename Derivedvol::Scalar ScalarS;
vol.resize(m,1);
for(int t = 0;t<m;t++)
{
const ScalarS u = L(t,0);
const ScalarS v = L(t,1);
const ScalarS w = L(t,2);
const ScalarS U = L(t,3);
const ScalarS V = L(t,4);
const ScalarS W = L(t,5);
const ScalarS X = (w - U + v)*(U + v + w);
const ScalarS x = (U - v + w)*(v - w + U);
const ScalarS Y = (u - V + w)*(V + w + u);
const ScalarS y = (V - w + u)*(w - u + V);
const ScalarS Z = (v - W + u)*(W + u + v);
const ScalarS z = (W - u + v)*(u - v + W);
const ScalarS a = sqrt(x*Y*Z);
const ScalarS b = sqrt(y*Z*X);
const ScalarS c = sqrt(z*X*Y);
const ScalarS d = sqrt(x*y*z);
vol(t) = sqrt(
(-a + b + c + d)*
( a - b + c + d)*
( a + b - c + d)*
( a + b + c - d))/
(192.*u*v*w);
}
}
IGL_INLINE void igl::face_areas(
const Eigen::MatrixBase<DerivedL>& L,
const typename DerivedL::Scalar doublearea_nan_replacement,
Eigen::PlainObjectBase<DerivedA>& A)
{
using namespace Eigen;
assert(L.cols() == 6);
const int m = L.rows();
// (unsigned) face Areas (opposite vertices: 1 2 3 4)
Matrix<typename DerivedA::Scalar,Dynamic,1>
A0(m,1), A1(m,1), A2(m,1), A3(m,1);
Matrix<typename DerivedA::Scalar,Dynamic,3>
L0(m,3), L1(m,3), L2(m,3), L3(m,3);
L0<<L.col(1),L.col(2),L.col(3);
L1<<L.col(0),L.col(2),L.col(4);
L2<<L.col(0),L.col(1),L.col(5);
L3<<L.col(3),L.col(4),L.col(5);
doublearea(L0,doublearea_nan_replacement,A0);
doublearea(L1,doublearea_nan_replacement,A1);
doublearea(L2,doublearea_nan_replacement,A2);
doublearea(L3,doublearea_nan_replacement,A3);
A.resize(m,4);
A.col(0) = 0.5*A0;
A.col(1) = 0.5*A1;
A.col(2) = 0.5*A2;
A.col(3) = 0.5*A3;
}
IGL_INLINE void igl::internal_angles(
const Eigen::PlainObjectBase<DerivedL>& L,
Eigen::PlainObjectBase<DerivedK> & K)
{
typedef typename DerivedL::Index Index;
assert(L.cols() == 3 && "Edge-lengths should come from triangles");
const Index m = L.rows();
K.resize(m,3);
//for(int d = 0;d<3;d++)
//{
// const auto & s1 = L.col(d).array();
// const auto & s2 = L.col((d+1)%3).array();
// const auto & s3 = L.col((d+2)%3).array();
// K.col(d) = ((s3.square() + s2.square() - s1.square())/(2.*s3*s2)).acos();
//}
// Minimum number of iterms per openmp thread
#ifndef IGL_OMP_MIN_VALUE
# define IGL_OMP_MIN_VALUE 1000
#endif
#pragma omp parallel for if (m>IGL_OMP_MIN_VALUE)
for(Index f = 0;f<m;f++)
{
for(size_t d = 0;d<3;d++)
{
const auto & s1 = L(f,d);
const auto & s2 = L(f,(d+1)%3);
const auto & s3 = L(f,(d+2)%3);
K(f,d) = acos((s3*s3 + s2*s2 - s1*s1)/(2.*s3*s2));
}
}
}
IGL_INLINE void igl::mat_min(
const Eigen::DenseBase<DerivedX> & X,
const int dim,
Eigen::PlainObjectBase<DerivedY> & Y,
Eigen::PlainObjectBase<DerivedI> & I)
{
assert(dim==1||dim==2);
// output size
int n = (dim==1?X.cols():X.rows());
// resize output
Y.resize(n);
I.resize(n);
// loop over dimension opposite of dim
for(int j = 0;j<n;j++)
{
typename DerivedX::Index PHONY,i;
typename DerivedX::Scalar m;
if(dim==1)
{
m = X.col(j).minCoeff(&i,&PHONY);
}else
{
m = X.row(j).minCoeff(&PHONY,&i);
}
Y(j) = m;
I(j) = i;
}
}
void igl::crouzeix_raviart_massmatrix(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
const Eigen::PlainObjectBase<DerivedE> & E,
const Eigen::PlainObjectBase<DerivedEMAP> & EMAP,
Eigen::SparseMatrix<MT> & M)
{
using namespace Eigen;
using namespace std;
assert(F.cols() == 3);
// Mesh should be edge-manifold
assert(is_edge_manifold(F));
// number of elements (triangles)
int m = F.rows();
// Get triangle areas
VectorXd TA;
doublearea(V,F,TA);
vector<Triplet<MT> > MIJV(3*m);
for(int f = 0;f<m;f++)
{
for(int c = 0;c<3;c++)
{
MIJV[f+m*c] = Triplet<MT>(EMAP(f+m*c),EMAP(f+m*c),TA(f)*0.5);
}
}
M.resize(E.rows(),E.rows());
M.setFromTriplets(MIJV.begin(),MIJV.end());
}
IGL_INLINE void igl::project_to_line_segment(
const Eigen::PlainObjectBase<DerivedP> & P,
const Eigen::PlainObjectBase<DerivedS> & S,
const Eigen::PlainObjectBase<DerivedD> & D,
Eigen::PlainObjectBase<Derivedt> & t,
Eigen::PlainObjectBase<DerivedsqrD> & sqrD)
{
project_to_line(P,S,D,t,sqrD);
const int np = P.rows();
// loop over points and fix those that projected beyond endpoints
#pragma omp parallel for if (np>10000)
for(int p = 0;p<np;p++)
{
const Eigen::PlainObjectBase<DerivedS> Pp = P.row(p);
if(t(p)<0)
{
sqrD(p) = (Pp-S).squaredNorm();
t(p) = 0;
}else if(t(p)>1)
{
sqrD(p) = (Pp-D).squaredNorm();
t(p) = 1;
}
}
}
IGL_INLINE void igl::slice_into(
const Eigen::PlainObjectBase<DerivedX> & X,
const Eigen::Matrix<int,Eigen::Dynamic,1> & R,
const Eigen::Matrix<int,Eigen::Dynamic,1> & C,
Eigen::PlainObjectBase<DerivedX> & Y)
{
int xm = X.rows();
int xn = X.cols();
assert(R.size() == xm);
assert(C.size() == xn);
#ifndef NDEBUG
int ym = Y.size();
int yn = Y.size();
assert(R.minCoeff() >= 0);
assert(R.maxCoeff() < ym);
assert(C.minCoeff() >= 0);
assert(C.maxCoeff() < yn);
#endif
// Build reindexing maps for columns and rows, -1 means not in map
Eigen::Matrix<int,Eigen::Dynamic,1> RI;
RI.resize(xm);
for(int i = 0;i<xm;i++)
{
for(int j = 0;j<xn;j++)
{
Y(R(i),C(j)) = X(i,j);
}
}
}
IGL_INLINE void igl::slice(
const MatX& X,
const Eigen::PlainObjectBase<DerivedR> & R,
const int dim,
MatY& Y)
{
Eigen::Matrix<typename DerivedR::Scalar,Eigen::Dynamic,1> C;
switch(dim)
{
case 1:
// boring base case
if(X.cols() == 0)
{
Y.resize(R.size(),0);
return;
}
igl::colon(0,X.cols()-1,C);
return slice(X,R,C,Y);
case 2:
// boring base case
if(X.rows() == 0)
{
Y.resize(0,R.size());
return;
}
igl::colon(0,X.rows()-1,C);
return slice(X,C,R,Y);
default:
assert(false && "Unsupported dimension");
return;
}
}
IGL_INLINE bool igl::writeOBJ(
const std::string str,
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F)
{
std::ofstream s(str.c_str());
if(!s.is_open())
{
fprintf(stderr,"IOError: writeOBJ() could not open %s\n",str.c_str());
return false;
}
for(int i=0;i<(int)V.rows();++i)
{
s << "v " << V(i,0) << " " << V(i,1) << " " << V(i,2) << std::endl;
}
for(int i=0;i<(int)F.rows();++i)
{
s << "f " << F(i,0)+1 << " " << F(i,1)+1 << " " << F(i,2)+1 << std::endl;
}
s.close();
return true;
}
IGL_INLINE void igl::polyvector_field_singularities_from_matchings(
const Eigen::PlainObjectBase<DerivedV> &V,
const Eigen::PlainObjectBase<DerivedF> &F,
const std::vector<bool> &V_border,
const std::vector<std::vector<VFType> > &VF,
const Eigen::MatrixXi &TT,
const Eigen::MatrixXi &E2F,
const Eigen::MatrixXi &F2E,
const Eigen::PlainObjectBase<DerivedM> &match_ab,
const Eigen::PlainObjectBase<DerivedM> &match_ba,
Eigen::PlainObjectBase<DerivedS> &singularities,
Eigen::PlainObjectBase<DerivedS> &singularity_indices)
{
igl::polyvector_field_singularities_from_matchings(V, F, V_border, VF, TT, E2F, F2E, match_ab, match_ba, singularities);
singularity_indices.setZero(singularities.size(), 1);
//get index from first vector only
int vector_to_match = 0;
for (int i =0; i<singularities.size(); ++i)
{
int vi = singularities[i];
// Eigen::VectorXi mvi,fi;
// igl::polyvector_field_one_ring_matchings(V, F, VF, E2F, F2E, TT, match_ab, match_ba, vi, vector_to_match, mvi, fi);
Eigen::VectorXi fi;
Eigen::MatrixXi mvi;
igl::polyvector_field_one_ring_matchings(V, F, VF, E2F, F2E, TT, match_ab, match_ba, vi, mvi, fi);
singularity_indices[i] = (mvi(mvi.rows()-1,vector_to_match) - vector_to_match);
}
}
void igl::sort_triangles(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::PlainObjectBase<DerivedFF> & FF,
Eigen::PlainObjectBase<DerivedI> & I)
{
using namespace Eigen;
using namespace igl;
using namespace std;
// Put model, projection, and viewport matrices into double arrays
Matrix4d MV;
Matrix4d P;
glGetDoublev(GL_MODELVIEW_MATRIX, MV.data());
glGetDoublev(GL_PROJECTION_MATRIX, P.data());
if(V.cols() == 3)
{
Matrix<typename DerivedV::Scalar, DerivedV::RowsAtCompileTime,4> hV;
hV.resize(V.rows(),4);
hV.block(0,0,V.rows(),V.cols()) = V;
hV.col(3).setConstant(1);
return sort_triangles(hV,F,MV,P,FF,I);
}else
{
return sort_triangles(V,F,MV,P,FF,I);
}
}
IGL_INLINE void igl::min(
const Eigen::SparseMatrix<AType> & A,
const int dim,
Eigen::PlainObjectBase<DerivedB> & B,
Eigen::PlainObjectBase<DerivedI> & I)
{
const int n = A.cols();
const int m = A.rows();
B.resize(dim==1?n:m);
B.setConstant(std::numeric_limits<typename DerivedB::Scalar>::max());
I.resize(dim==1?n:m);
for_each(A,[&B,&I,&dim](int i, int j,const typename DerivedB::Scalar v)
{
if(dim == 2)
{
std::swap(i,j);
}
// Coded as if dim == 1, assuming swap for dim == 2
if(v < B(j))
{
B(j) = v;
I(j) = i;
}
});
Eigen::VectorXi Z;
find_zero(A,dim,Z);
for(int j = 0;j<I.size();j++)
{
if(Z(j) != (dim==1?m:n) && 0 < B(j))
{
B(j) = 0;
I(j) = Z(j);
}
}
}
IGL_INLINE void igl::per_face_normals(
const Eigen::MatrixBase<DerivedV>& V,
const Eigen::MatrixBase<DerivedF>& F,
const Eigen::MatrixBase<DerivedZ> & Z,
Eigen::PlainObjectBase<DerivedN> & N)
{
N.resize(F.rows(),3);
// loop over faces
int Frows = F.rows();
#pragma omp parallel for if (Frows>10000)
for(int i = 0; i < Frows;i++)
{
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> v1 = V.row(F(i,1)) - V.row(F(i,0));
const Eigen::Matrix<typename DerivedV::Scalar, 1, 3> v2 = V.row(F(i,2)) - V.row(F(i,0));
N.row(i) = v1.cross(v2);//.normalized();
typename DerivedV::Scalar r = N.row(i).norm();
if(r == 0)
{
N.row(i) = Z;
}else
{
N.row(i) /= r;
}
}
}
IGL_INLINE void igl::in_element(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::MatrixXi & Ele,
const Eigen::PlainObjectBase<DerivedQ> & Q,
const AABB<DerivedV,DIM> & aabb,
Eigen::SparseMatrix<Scalar> & I)
{
using namespace std;
using namespace Eigen;
using namespace igl;
const int Qr = Q.rows();
std::vector<Triplet<Scalar> > IJV;
IJV.reserve(Qr);
#pragma omp parallel for if (Qr>10000)
for(int e = 0;e<Qr;e++)
{
// find all
const auto R = aabb.find(V,Ele,Q.row(e),false);
for(const auto r : R)
{
#pragma omp critical
IJV.push_back(Triplet<Scalar>(e,r,1));
}
}
I.resize(Qr,Ele.rows());
I.setFromTriplets(IJV.begin(),IJV.end());
}
IGL_INLINE void igl::find(
const Eigen::DenseBase<DerivedX>& X,
Eigen::PlainObjectBase<DerivedI> & I,
Eigen::PlainObjectBase<DerivedJ> & J,
Eigen::PlainObjectBase<DerivedV> & V)
{
const int nnz = X.count();
I.resize(nnz,1);
J.resize(nnz,1);
V.resize(nnz,1);
{
int k = 0;
for(int j = 0;j<X.cols();j++)
{
for(int i = 0;i<X.rows();i++)
{
if(X(i,j))
{
I(k) = i;
J(k) = j;
V(k) = X(i,j);
k++;
}
}
}
}
}
IGL_INLINE void igl::matlab::parse_rhs_double(
const mxArray *prhs[],
Eigen::PlainObjectBase<DerivedV> & V)
{
using namespace std;
using namespace Eigen;
// set number of mesh vertices
const int n = mxGetM(prhs[0]);
// set vertex position pointers
double * Vp = mxGetPr(prhs[0]);
const int dim = mxGetN(prhs[0]);
typedef typename DerivedV::Scalar Scalar;
Matrix<Scalar, DerivedV::ColsAtCompileTime, DerivedV::RowsAtCompileTime, RowMajor> VT;
Scalar * V_data;
if(DerivedV::IsRowMajor)
{
VT.resize(dim,n);
V_data = VT.data();
}else
{
V.resize(n,dim);
V_data = V.data();
}
copy(Vp,Vp+n*dim,V_data);
if(DerivedV::IsRowMajor)
{
V = VT.transpose();
}
}
IGL_INLINE void igl::unique_edge_map(
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::PlainObjectBase<DerivedE> & E,
Eigen::PlainObjectBase<DeriveduE> & uE,
Eigen::PlainObjectBase<DerivedEMAP> & EMAP,
std::vector<std::vector<uE2EType> > & uE2E)
{
using namespace Eigen;
using namespace std;
// All occurances of directed edges
all_edges(F,E);
const size_t ne = E.rows();
// This is 2x faster to create than a map from pairs to lists of edges and 5x
// faster to access (actually access is probably assympotically faster O(1)
// vs. O(log m)
Matrix<typename DerivedEMAP::Scalar,Dynamic,1> IA;
unique_simplices(E,uE,IA,EMAP);
uE2E.resize(uE.rows());
// This does help a little
for_each(uE2E.begin(),uE2E.end(),[](vector<uE2EType > & v){v.reserve(2);});
assert((size_t)EMAP.size() == ne);
for(uE2EType e = 0;e<(uE2EType)ne;e++)
{
uE2E[EMAP(e)].push_back(e);
}
}
IGL_INLINE void igl::randperm(
const int n,
Eigen::PlainObjectBase<DerivedI> & I)
{
Eigen::VectorXi II;
igl::colon(0,1,n-1,II);
I = II;
std::random_shuffle(I.data(),I.data()+n);
}
IGL_INLINE int igl::unproject_to_zero_plane(
const Eigen::PlainObjectBase<Derivedwin> & win,
Eigen::PlainObjectBase<Derivedobj> & obj)
{
return unproject_to_zero_plane(win(0),win(1),
&obj.data()[0],
&obj.data()[1],
&obj.data()[2]);
}
IGL_INLINE void igl::jet(
const Eigen::PlainObjectBase<DerivedZ> & Z,
const bool normalize,
Eigen::PlainObjectBase<DerivedC> & C)
{
const double min_z = (normalize?Z.minCoeff():0);
const double max_z = (normalize?Z.maxCoeff():-1);
return jet(Z,min_z,max_z,C);
}
IGL_INLINE void igl::sort(
const Eigen::PlainObjectBase<DerivedX>& X,
const int dim,
const bool ascending,
Eigen::PlainObjectBase<DerivedY>& Y,
Eigen::PlainObjectBase<DerivedIX>& IX)
{
// get number of rows (or columns)
int num_inner = (dim == 1 ? X.rows() : X.cols() );
// Special case for swapping
if(num_inner == 2)
{
return igl::sort2(X,dim,ascending,Y,IX);
}
using namespace Eigen;
// get number of columns (or rows)
int num_outer = (dim == 1 ? X.cols() : X.rows() );
// dim must be 2 or 1
assert(dim == 1 || dim == 2);
// Resize output
Y.resize(X.rows(),X.cols());
IX.resize(X.rows(),X.cols());
// idea is to process each column (or row) as a std vector
// loop over columns (or rows)
for(int i = 0; i<num_outer;i++)
{
// Unsorted index map for this column (or row)
std::vector<size_t> index_map(num_inner);
std::vector<double> data(num_inner);
for(int j = 0;j<num_inner;j++)
{
if(dim == 1)
{
data[j] = (double) X(j,i);
}else
{
data[j] = (double) X(i,j);
}
}
// sort this column (or row)
igl::sort( data, ascending, data, index_map);
// Copy into Y and IX
for(int j = 0;j<num_inner;j++)
{
if(dim == 1)
{
Y(j,i) = data[j];
IX(j,i) = index_map[j];
}else
{
Y(i,j) = data[j];
IX(i,j) = index_map[j];
}
}
}
}
IGL_INLINE void igl::reorient_facets_raycast(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::PlainObjectBase<DerivedFF> & FF,
Eigen::PlainObjectBase<DerivedI> & I)
{
const int rays_total = F.rows()*100;
const int rays_minimum = 10;
const bool facet_wise = false;
const bool use_parity = false;
const bool is_verbose = false;
Eigen::VectorXi C;
reorient_facets_raycast(
V,F,rays_total,rays_minimum,facet_wise,use_parity,is_verbose,I,C);
// Conservative in case FF = F
FF.conservativeResize(F.rows(),F.cols());
for(int i = 0;i<I.rows();i++)
{
if(I(i))
{
FF.row(i) = (F.row(i).reverse()).eval();
}else
{
FF.row(i) = F.row(i);
}
}
}
IGL_INLINE void igl::components(
const Eigen::SparseMatrix<AScalar> & A,
Eigen::PlainObjectBase<DerivedC> & C,
Eigen::PlainObjectBase<Derivedcounts> & counts)
{
using namespace Eigen;
using namespace std;
assert(A.rows() == A.cols() && "A should be square.");
const size_t n = A.rows();
Array<bool,Dynamic,1> seen = Array<bool,Dynamic,1>::Zero(n,1);
C.resize(n,1);
typename DerivedC::Scalar id = 0;
vector<typename Derivedcounts::Scalar> vcounts;
// breadth first search
for(int k=0; k<A.outerSize(); ++k)
{
if(seen(k))
{
continue;
}
queue<int> Q;
Q.push(k);
vcounts.push_back(0);
while(!Q.empty())
{
const int f = Q.front();
Q.pop();
if(seen(f))
{
continue;
}
seen(f) = true;
C(f,0) = id;
vcounts[id]++;
// Iterate over inside
for(typename SparseMatrix<AScalar>::InnerIterator it (A,f); it; ++it)
{
const int g = it.index();
if(!seen(g) && it.value())
{
Q.push(g);
}
}
}
id++;
}
assert((size_t) id == vcounts.size());
const size_t ncc = vcounts.size();
assert((size_t)C.maxCoeff()+1 == ncc);
counts.resize(ncc,1);
for(size_t i = 0;i<ncc;i++)
{
counts(i) = vcounts[i];
}
}
IGL_INLINE int igl::ray_sphere_intersect(
const Eigen::PlainObjectBase<Derivedo> & ao,
const Eigen::PlainObjectBase<Derivedd> & d,
const Eigen::PlainObjectBase<Derivedc> & ac,
r_type r,
t_type & t0,
t_type & t1)
{
Eigen::Vector3d o = ao-ac;
// http://wiki.cgsociety.org/index.php/Ray_Sphere_Intersection
//Compute A, B and C coefficients
double a = d.dot(d);
double b = 2 * d.dot(o);
double c = o.dot(o) - (r * r);
//Find discriminant
double disc = b * b - 4 * a * c;
// if discriminant is negative there are no real roots, so return
// false as ray misses sphere
if (disc < 0)
{
return 0;
}
// compute q as described above
double distSqrt = sqrt(disc);
double q;
if (b < 0)
{
q = (-b - distSqrt)/2.0;
} else
{
q = (-b + distSqrt)/2.0;
}
// compute t0 and t1
t0 = q / a;
double _t1 = c/q;
if(_t1 == t0)
{
return 1;
}
t1 = _t1;
// make sure t0 is smaller than t1
if (t0 > t1)
{
// if t0 is bigger than t1 swap them around
double temp = t0;
t0 = t1;
t1 = temp;
}
return 2;
}