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;
}
}
}
IGL_INLINE std::vector<bool> igl::is_irregular_vertex(const Eigen::PlainObjectBase<DerivedV> &V, const Eigen::PlainObjectBase<DerivedF> &F)
{
Eigen::VectorXi count = Eigen::VectorXi::Zero(F.maxCoeff());
for(unsigned i=0; i<F.rows();++i)
{
for(unsigned j=0; j<F.cols();++j)
{
if (F(i,j) < F(i,(j+1)%F.cols())) // avoid duplicate edges
{
count(F(i,j )) += 1;
count(F(i,(j+1)%F.cols())) += 1;
}
}
}
std::vector<bool> border = is_border_vertex(V,F);
std::vector<bool> res(count.size());
for (unsigned i=0; i<res.size(); ++i)
res[i] = !border[i] && count[i] != (F.cols() == 3 ? 6 : 4 );
return res;
}
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::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 void igl::directed_edge_parents(
const Eigen::PlainObjectBase<DerivedE> & E,
Eigen::PlainObjectBase<DerivedP> & P)
{
using namespace Eigen;
using namespace std;
VectorXi I = VectorXi::Constant(E.maxCoeff()+1,1,-1);
//I(E.col(1)) = 0:E.rows()-1
slice_into(colon<int>(0,E.rows()-1),E.col(1).eval(),I);
VectorXi roots,_;
setdiff(E.col(0).eval(),E.col(1).eval(),roots,_);
for_each(roots.data(),roots.data()+roots.size(),[&](int r){I(r)=-1;});
slice(I,E.col(0).eval(),P);
}
IGL_INLINE void igl::slice(
const Eigen::PlainObjectBase<DerivedX> & X,
const Eigen::PlainObjectBase<DerivedR> & R,
const Eigen::PlainObjectBase<DerivedC> & C,
Eigen::PlainObjectBase<DerivedY> & Y)
{
#ifndef NDEBUG
int xm = X.rows();
int xn = X.cols();
#endif
int ym = R.size();
int yn = C.size();
// special case when R or C is empty
if(ym == 0 || yn == 0)
{
Y.resize(ym,yn);
return;
}
assert(R.minCoeff() >= 0);
assert(R.maxCoeff() < xm);
assert(C.minCoeff() >= 0);
assert(C.maxCoeff() < xn);
// Resize output
Y.resize(ym,yn);
// loop over output rows, then columns
for(int i = 0;i<ym;i++)
{
for(int j = 0;j<yn;j++)
{
Y(i,j) = X(R(i),C(j));
}
}
}
IGL_INLINE void igl::cut_mesh(
const Eigen::PlainObjectBase<DerivedV> &V,
const Eigen::PlainObjectBase<DerivedF> &F,
const std::vector<std::vector<VFType> >& VF,
const std::vector<std::vector<VFType> >& VFi,
const Eigen::PlainObjectBase<DerivedTT>& TT,
const Eigen::PlainObjectBase<DerivedTT>& TTi,
const std::vector<bool> &V_border,
const Eigen::PlainObjectBase<DerivedC> &cuts,
Eigen::PlainObjectBase<DerivedV> &Vcut,
Eigen::PlainObjectBase<DerivedF> &Fcut)
{
//finding the cuts is done, now we need to actually generate a cut mesh
igl::MeshCutterMini<DerivedV, DerivedF, VFType, DerivedTT, DerivedC> mc(V, F, TT, TTi, VF, VFi, V_border, cuts);
mc.InitMappingSeam();
Fcut = mc.HandleS_Index;
//we have the faces, we need the vertices;
int newNumV = Fcut.maxCoeff()+1;
Vcut.setZero(newNumV,3);
for (int vi=0; vi<V.rows(); ++vi)
for (int i=0; i<mc.HandleV_Integer[vi].size();++i)
Vcut.row(mc.HandleV_Integer[vi][i]) = V.row(vi);
//ugly hack to fix some problematic cases (border vertex that is also on the boundary of the hole
for (int fi =0; fi<Fcut.rows(); ++fi)
for (int k=0; k<3; ++k)
if (Fcut(fi,k)==-1)
{
//we need to add a vertex
Fcut(fi,k) = newNumV;
newNumV ++;
Vcut.conservativeResize(newNumV, Eigen::NoChange);
Vcut.row(newNumV-1) = V.row(F(fi,k));
}
}
IGL_INLINE void igl::gaussian_curvature(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
Eigen::PlainObjectBase<DerivedK> & K)
{
using namespace Eigen;
using namespace std;
// internal corner angles
Matrix<
typename DerivedV::Scalar,
DerivedF::RowsAtCompileTime,
DerivedF::ColsAtCompileTime> A;
internal_angles(V,F,A);
K.resize(V.rows(),1);
K.setConstant(V.rows(),1,2.*PI);
assert(A.rows() == F.rows());
assert(A.cols() == F.cols());
assert(K.rows() == V.rows());
assert(F.maxCoeff() < V.rows());
assert(K.cols() == 1);
const int Frows = F.rows();
//K_G(x_i) = (2π - ∑θj)
//#ifndef IGL_GAUSSIAN_CURVATURE_OMP_MIN_VALUE
//# define IGL_GAUSSIAN_CURVATURE_OMP_MIN_VALUE 1000
//#endif
//#pragma omp parallel for if (Frows>IGL_GAUSSIAN_CURVATURE_OMP_MIN_VALUE)
for(int f = 0;f<Frows;f++)
{
// throw normal at each corner
for(int j = 0; j < 3;j++)
{
// Q: Does this need to be critical?
// H: I think so, sadly. Maybe there's a way to use reduction
//#pragma omp critical
K(F(f,j),0) -= A(f,j);
}
}
}
IGL_INLINE bool igl::arap_precomputation(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
const int dim,
const Eigen::PlainObjectBase<Derivedb> & b,
ARAPData & data)
{
using namespace std;
using namespace Eigen;
typedef typename DerivedV::Scalar Scalar;
// number of vertices
const int n = V.rows();
data.n = n;
assert((b.size() == 0 || b.maxCoeff() < n) && "b out of bounds");
assert((b.size() == 0 || b.minCoeff() >=0) && "b out of bounds");
// remember b
data.b = b;
//assert(F.cols() == 3 && "For now only triangles");
// dimension
//const int dim = V.cols();
assert((dim == 3 || dim ==2) && "dim should be 2 or 3");
data.dim = dim;
//assert(dim == 3 && "Only 3d supported");
// Defaults
data.f_ext = MatrixXd::Zero(n,data.dim);
assert(data.dim <= V.cols() && "solve dim should be <= embedding");
bool flat = (V.cols() - data.dim)==1;
DerivedV plane_V;
DerivedF plane_F;
typedef SparseMatrix<Scalar> SparseMatrixS;
SparseMatrixS ref_map,ref_map_dim;
if(flat)
{
project_isometrically_to_plane(V,F,plane_V,plane_F,ref_map);
repdiag(ref_map,dim,ref_map_dim);
}
const PlainObjectBase<DerivedV>& ref_V = (flat?plane_V:V);
const PlainObjectBase<DerivedF>& ref_F = (flat?plane_F:F);
SparseMatrixS L;
cotmatrix(V,F,L);
ARAPEnergyType eff_energy = data.energy;
if(eff_energy == ARAP_ENERGY_TYPE_DEFAULT)
{
switch(F.cols())
{
case 3:
if(data.dim == 3)
{
eff_energy = ARAP_ENERGY_TYPE_SPOKES_AND_RIMS;
} else
{
eff_energy = ARAP_ENERGY_TYPE_ELEMENTS;
}
break;
case 4:
eff_energy = ARAP_ENERGY_TYPE_ELEMENTS;
break;
default:
assert(false);
}
}
// Get covariance scatter matrix, when applied collects the covariance
// matrices used to fit rotations to during optimization
covariance_scatter_matrix(ref_V,ref_F,eff_energy,data.CSM);
if(flat)
{
data.CSM = (data.CSM * ref_map_dim.transpose()).eval();
}
assert(data.CSM.cols() == V.rows()*data.dim);
// Get group sum scatter matrix, when applied sums all entries of the same
// group according to G
SparseMatrix<double> G_sum;
if(data.G.size() == 0)
{
if(eff_energy == ARAP_ENERGY_TYPE_ELEMENTS)
{
speye(F.rows(),G_sum);
} else
{
speye(n,G_sum);
}
} else
{
// groups are defined per vertex, convert to per face using mode
if(eff_energy == ARAP_ENERGY_TYPE_ELEMENTS)
{
Eigen::Matrix<int,Eigen::Dynamic,1> GG;
MatrixXi GF(F.rows(),F.cols());
for(int j = 0; j<F.cols(); j++)
{
Matrix<int,Eigen::Dynamic,1> GFj;
slice(data.G,F.col(j),GFj);
GF.col(j) = GFj;
}
mode<int>(GF,2,GG);
data.G=GG;
}
//printf("group_sum_matrix()\n");
group_sum_matrix(data.G,G_sum);
}
SparseMatrix<double> G_sum_dim;
repdiag(G_sum,data.dim,G_sum_dim);
assert(G_sum_dim.cols() == data.CSM.rows());
data.CSM = (G_sum_dim * data.CSM).eval();
arap_rhs(ref_V,ref_F,data.dim,eff_energy,data.K);
if(flat)
{
data.K = (ref_map_dim * data.K).eval();
}
assert(data.K.rows() == data.n*data.dim);
SparseMatrix<double> Q = (-L).eval();
if(data.with_dynamics)
{
const double h = data.h;
assert(h != 0);
SparseMatrix<double> M;
massmatrix(V,F,MASSMATRIX_TYPE_DEFAULT,data.M);
const double dw = (1./data.ym)*(h*h);
SparseMatrix<double> DQ = dw * 1./(h*h)*data.M;
Q += DQ;
// Dummy external forces
data.f_ext = MatrixXd::Zero(n,data.dim);
data.vel = MatrixXd::Zero(n,data.dim);
}
return min_quad_with_fixed_precompute(
Q,b,SparseMatrix<double>(),true,data.solver_data);
}
IGL_INLINE void igl::adjacency_list(
const Eigen::PlainObjectBase<Index> & F,
std::vector<std::vector<IndexVector> >& A,
bool sorted)
{
A.clear();
A.resize(F.maxCoeff()+1);
// 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
int s = F(i,j);
int d = F(i,(j+1)%F.cols());
A.at(s).push_back(d);
A.at(d).push_back(s);
}
}
// Remove duplicates
for(int i=0; i<(int)A.size();++i)
{
std::sort(A[i].begin(), A[i].end());
A[i].erase(std::unique(A[i].begin(), A[i].end()), A[i].end());
}
// If needed, sort every VV
if (sorted)
{
// Loop over faces
// for every vertex v store a set of ordered edges not incident to v that belongs to triangle incident on v.
std::vector<std::vector<std::vector<int> > > SR;
SR.resize(A.size());
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
int s = F(i,j);
int d = F(i,(j+1)%F.cols());
// Get index of opposing vertex v
int v = F(i,(j+2)%F.cols());
std::vector<int> e(2);
e[0] = d;
e[1] = v;
SR[s].push_back(e);
}
}
for(int v=0; v<(int)SR.size();++v)
{
std::vector<IndexVector>& vv = A.at(v);
std::vector<std::vector<int> >& sr = SR[v];
std::vector<std::vector<int> > pn = sr;
// Compute previous/next for every element in sr
for(int i=0;i<(int)sr.size();++i)
{
int a = sr[i][0];
int b = sr[i][1];
// search for previous
int p = -1;
for(int j=0;j<(int)sr.size();++j)
if(sr[j][1] == a)
p = j;
pn[i][0] = p;
// search for next
int n = -1;
for(int j=0;j<(int)sr.size();++j)
if(sr[j][0] == b)
n = j;
pn[i][1] = n;
}
// assume manifoldness (look for beginning of a single chain)
int c = 0;
for(int j=0; j<=(int)sr.size();++j)
if (pn[c][0] != -1)
c = pn[c][0];
if (pn[c][0] == -1) // border case
{
// finally produce the new vv relation
for(int j=0; j<(int)sr.size();++j)
{
vv[j] = sr[c][0];
if (pn[c][1] != -1)
c = pn[c][1];
}
vv.back() = sr[c][1];
}
else
{
// finally produce the new vv relation
for(int j=0; j<(int)sr.size();++j)
{
vv[j] = sr[c][0];
c = pn[c][1];
}
}
}
}
}
void igl::bfs_orient(
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::PlainObjectBase<DerivedFF> & FF,
Eigen::PlainObjectBase<DerivedC> & C)
{
using namespace Eigen;
using namespace igl;
using namespace std;
SparseMatrix<int> A;
manifold_patches(F,C,A);
// number of faces
const int m = F.rows();
// number of patches
const int num_cc = C.maxCoeff()+1;
VectorXi seen = VectorXi::Zero(m);
// Edge sets
const int ES[3][2] = {{1,2},{2,0},{0,1}};
if(&FF != &F)
{
FF = F;
}
// loop over patches
#pragma omp parallel for
for(int c = 0;c<num_cc;c++)
{
queue<int> Q;
// find first member of patch c
for(int f = 0;f<FF.rows();f++)
{
if(C(f) == c)
{
Q.push(f);
break;
}
}
assert(!Q.empty());
while(!Q.empty())
{
const int f = Q.front();
Q.pop();
if(seen(f) > 0)
{
continue;
}
seen(f)++;
// loop over neighbors of f
for(typename SparseMatrix<int>::InnerIterator it (A,f); it; ++it)
{
// might be some lingering zeros, and skip self-adjacency
if(it.value() != 0 && it.row() != f)
{
const int n = it.row();
assert(n != f);
// loop over edges of f
for(int efi = 0;efi<3;efi++)
{
// efi'th edge of face f
Vector2i ef(FF(f,ES[efi][0]),FF(f,ES[efi][1]));
// loop over edges of n
for(int eni = 0;eni<3;eni++)
{
// eni'th edge of face n
Vector2i en(FF(n,ES[eni][0]),FF(n,ES[eni][1]));
// Match (half-edges go same direction)
if(ef(0) == en(0) && ef(1) == en(1))
{
// flip face n
FF.row(n) = FF.row(n).reverse().eval();
}
}
}
// add neighbor to queue
Q.push(n);
}
}
}
}
// make sure flip is OK if &FF = &F
}
IGL_INLINE void igl::reorient_facets_raycast(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
int rays_total,
int rays_minimum,
bool facet_wise,
bool use_parity,
bool is_verbose,
Eigen::PlainObjectBase<DerivedI> & I,
Eigen::PlainObjectBase<DerivedC> & C)
{
using namespace Eigen;
using namespace std;
assert(F.cols() == 3);
assert(V.cols() == 3);
// number of faces
const int m = F.rows();
MatrixXi FF = F;
if (facet_wise) {
C.resize(m);
for (int i = 0; i < m; ++i) C(i) = i;
} else {
if (is_verbose) cout << "extracting patches... ";
bfs_orient(F,FF,C);
}
if (is_verbose) cout << (C.maxCoeff() + 1) << " components. ";
// number of patches
const int num_cc = C.maxCoeff()+1;
// Init Embree
EmbreeIntersector ei;
ei.init(V.template cast<float>(),FF);
// face normal
MatrixXd N;
per_face_normals(V,FF,N);
// face area
Matrix<typename DerivedV::Scalar,Dynamic,1> A;
doublearea(V,FF,A);
double area_total = A.sum();
// determine number of rays per component according to its area
VectorXd area_per_component;
area_per_component.setZero(num_cc);
for (int f = 0; f < m; ++f)
{
area_per_component(C(f)) += A(f);
}
VectorXi num_rays_per_component(num_cc);
for (int c = 0; c < num_cc; ++c)
{
num_rays_per_component(c) = max<int>(static_cast<int>(rays_total * area_per_component(c) / area_total), rays_minimum);
}
rays_total = num_rays_per_component.sum();
// generate all the rays
if (is_verbose) cout << "generating rays... ";
uniform_real_distribution<float> rdist;
mt19937 prng;
prng.seed(time(nullptr));
vector<int > ray_face;
vector<Vector3f> ray_ori;
vector<Vector3f> ray_dir;
ray_face.reserve(rays_total);
ray_ori .reserve(rays_total);
ray_dir .reserve(rays_total);
for (int c = 0; c < num_cc; ++c)
{
if (area_per_component[c] == 0)
{
continue;
}
vector<int> CF; // set of faces per component
vector<double> CF_area;
for (int f = 0; f < m; ++f)
{
if (C(f)==c)
{
CF.push_back(f);
CF_area.push_back(A(f));
}
}
// discrete distribution for random selection of faces with probability proportional to their areas
discrete_distribution<int> ddist(CF.size(), 0, CF.size(), [&](double i){ return CF_area[static_cast<int>(i)]; }); // simple ctor of (Iter, Iter) not provided by the stupid VC11/12
for (int i = 0; i < num_rays_per_component[c]; ++i)
{
int f = CF[ddist(prng)]; // select face with probability proportional to face area
float s = rdist(prng); // random barycentric coordinate (reference: Generating Random Points in Triangles [Turk, Graphics Gems I 1990])
float t = rdist(prng);
float sqrt_t = sqrtf(t);
float a = 1 - sqrt_t;
float b = (1 - s) * sqrt_t;
float c = s * sqrt_t;
Vector3f p = a * V.row(FF(f,0)).template cast<float>().eval() // be careful with the index!!!
+ b * V.row(FF(f,1)).template cast<float>().eval()
+ c * V.row(FF(f,2)).template cast<float>().eval();
Vector3f n = N.row(f).cast<float>();
if (n.isZero()) continue;
// random direction in hemisphere around n (avoid too grazing angle)
Vector3f d;
while (true) {
d = random_dir().cast<float>();
float ndotd = n.dot(d);
if (fabsf(ndotd) < 0.1f)
{
continue;
}
if (ndotd < 0)
{
d *= -1.0f;
}
break;
}
ray_face.push_back(f);
ray_ori .push_back(p);
ray_dir .push_back(d);
if (is_verbose && ray_face.size() % (rays_total / 10) == 0) cout << ".";
}
}
if (is_verbose) cout << ray_face.size() << " rays. ";
// per component voting: first=front, second=back
vector<pair<float, float>> C_vote_distance(num_cc, make_pair(0, 0)); // sum of distance between ray origin and intersection
vector<pair<int , int >> C_vote_infinity(num_cc, make_pair(0, 0)); // number of rays reaching infinity
vector<pair<int , int >> C_vote_parity(num_cc, make_pair(0, 0)); // sum of parity count for each ray
if (is_verbose) cout << "shooting rays... ";
#pragma omp parallel for
for (int i = 0; i < (int)ray_face.size(); ++i)
{
int f = ray_face[i];
Vector3f o = ray_ori [i];
Vector3f d = ray_dir [i];
int c = C(f);
// shoot ray toward front & back
vector<Hit> hits_front;
vector<Hit> hits_back;
int num_rays_front;
int num_rays_back;
ei.intersectRay(o, d, hits_front, num_rays_front);
ei.intersectRay(o, -d, hits_back , num_rays_back );
if (!hits_front.empty() && hits_front[0].id == f) hits_front.erase(hits_front.begin());
if (!hits_back .empty() && hits_back [0].id == f) hits_back .erase(hits_back .begin());
if (use_parity) {
#pragma omp atomic
C_vote_parity[c].first += hits_front.size() % 2;
#pragma omp atomic
C_vote_parity[c].second += hits_back .size() % 2;
} else {
if (hits_front.empty())
{
#pragma omp atomic
C_vote_infinity[c].first++;
} else {
#pragma omp atomic
C_vote_distance[c].first += hits_front[0].t;
}
if (hits_back.empty())
{
#pragma omp atomic
C_vote_infinity[c].second++;
} else {
#pragma omp atomic
C_vote_distance[c].second += hits_back[0].t;
}
}
}
I.resize(m);
for(int f = 0; f < m; ++f)
{
int c = C(f);
if (use_parity) {
I(f) = C_vote_parity[c].first > C_vote_parity[c].second ? 1 : 0; // Ideally, parity for the front/back side should be 1/0 (i.e., parity sum for all rays should be smaller on the front side)
} else {
I(f) = (C_vote_infinity[c].first == C_vote_infinity[c].second && C_vote_distance[c].first < C_vote_distance[c].second) ||
C_vote_infinity[c].first < C_vote_infinity[c].second
? 1 : 0;
}
// To account for the effect of bfs_orient
if (F.row(f) != FF.row(f))
I(f) = 1 - I(f);
}
if (is_verbose) cout << "done!" << endl;
}
IGL_INLINE void igl::boundary_loop(
const Eigen::PlainObjectBase<DerivedF> & F,
std::vector<std::vector<Index> >& L)
{
using namespace std;
using namespace Eigen;
using namespace igl;
MatrixXd Vdummy(F.maxCoeff(),1);
MatrixXi TT,TTi;
vector<std::vector<int> > VF, VFi;
triangle_triangle_adjacency(Vdummy,F,TT,TTi);
vertex_triangle_adjacency(Vdummy,F,VF,VFi);
vector<bool> unvisited = is_border_vertex(Vdummy,F);
set<int> unseen;
for (int i = 0; i < unvisited.size(); ++i)
{
if (unvisited[i])
unseen.insert(unseen.end(),i);
}
while (!unseen.empty())
{
vector<Index> l;
// Get first vertex of loop
int start = *unseen.begin();
unseen.erase(unseen.begin());
unvisited[start] = false;
l.push_back(start);
bool done = false;
while (!done)
{
// Find next vertex
bool newBndEdge = false;
int v = l[l.size()-1];
int next;
for (int i = 0; i < (int)VF[v].size() && !newBndEdge; i++)
{
int fid = VF[v][i];
if (TT.row(fid).minCoeff() < 0.) // Face contains boundary edge
{
int vLoc;
if (F(fid,0) == v) vLoc = 0;
if (F(fid,1) == v) vLoc = 1;
if (F(fid,2) == v) vLoc = 2;
int vPrev = F(fid,(vLoc + F.cols()-1) % F.cols());
int vNext = F(fid,(vLoc + 1) % F.cols());
bool newBndEdge = false;
if (unvisited[vPrev] && TT(fid,(vLoc+2) % F.cols()) < 0)
{
next = vPrev;
newBndEdge = true;
}
else if (unvisited[vNext] && TT(fid,vLoc) < 0)
{
next = vNext;
newBndEdge = true;
}
}
}
if (newBndEdge)
{
l.push_back(next);
unseen.erase(next);
unvisited[next] = false;
}
else
done = true;
}
L.push_back(l);
}
}
IGL_INLINE void igl::orient_outward(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
const Eigen::PlainObjectBase<DerivedC> & C,
Eigen::PlainObjectBase<DerivedFF> & FF,
Eigen::PlainObjectBase<DerivedI> & I)
{
using namespace Eigen;
using namespace std;
assert(C.rows() == F.rows());
assert(F.cols() == 3);
assert(V.cols() == 3);
// number of faces
const int m = F.rows();
// number of patches
const int num_cc = C.maxCoeff()+1;
I.resize(num_cc);
if(&FF != &F)
{
FF = F;
}
PlainObjectBase<DerivedV> N,BC,BCmean;
Matrix<typename DerivedV::Scalar,Dynamic,1> A;
VectorXd totA(num_cc), dot(num_cc);
Matrix<typename DerivedV::Scalar,3,1> Z(1,1,1);
per_face_normals(V,F,Z.normalized(),N);
barycenter(V,F,BC);
doublearea(V,F,A);
BCmean.setConstant(num_cc,3,0);
dot.setConstant(num_cc,1,0);
totA.setConstant(num_cc,1,0);
// loop over faces
for(int f = 0;f<m;f++)
{
BCmean.row(C(f)) += A(f)*BC.row(f);
totA(C(f))+=A(f);
}
// take area weighted average
for(int c = 0;c<num_cc;c++)
{
BCmean.row(c) /= (typename DerivedV::Scalar) totA(c);
}
// subtract bcmean
for(int f = 0;f<m;f++)
{
BC.row(f) -= BCmean.row(C(f));
dot(C(f)) += A(f)*N.row(f).dot(BC.row(f));
}
// take area weighted average
for(int c = 0;c<num_cc;c++)
{
dot(c) /= (typename DerivedV::Scalar) totA(c);
if(dot(c) < 0)
{
I(c) = true;
}else
{
I(c) = false;
}
}
// flip according to I
for(int f = 0;f<m;f++)
{
if(I(C(f)))
{
FF.row(f) = FF.row(f).reverse().eval();
}
}
}