IGL_INLINE igl::SolverStatus igl::active_set(
const Eigen::SparseMatrix<AT>& A,
const Eigen::PlainObjectBase<DerivedB> & B,
const Eigen::PlainObjectBase<Derivedknown> & known,
const Eigen::PlainObjectBase<DerivedY> & Y,
const Eigen::SparseMatrix<AeqT>& Aeq,
const Eigen::PlainObjectBase<DerivedBeq> & Beq,
const Eigen::SparseMatrix<AieqT>& Aieq,
const Eigen::PlainObjectBase<DerivedBieq> & Bieq,
const Eigen::PlainObjectBase<Derivedlx> & p_lx,
const Eigen::PlainObjectBase<Derivedux> & p_ux,
const igl::active_set_params & params,
Eigen::PlainObjectBase<DerivedZ> & Z
)
{
//#define ACTIVE_SET_CPP_DEBUG
#if defined(ACTIVE_SET_CPP_DEBUG) && !defined(_MSC_VER)
# warning "ACTIVE_SET_CPP_DEBUG"
#endif
using namespace Eigen;
using namespace std;
SolverStatus ret = SOLVER_STATUS_ERROR;
const int n = A.rows();
assert(n == A.cols() && "A must be square");
// Discard const qualifiers
//if(B.size() == 0)
//{
// B = Eigen::PlainObjectBase<DerivedB>::Zero(n,1);
//}
assert(n == B.rows() && "B.rows() must match A.rows()");
assert(B.cols() == 1 && "B must be a column vector");
assert(Y.cols() == 1 && "Y must be a column vector");
assert((Aeq.size() == 0 && Beq.size() == 0) || Aeq.cols() == n);
assert((Aeq.size() == 0 && Beq.size() == 0) || Aeq.rows() == Beq.rows());
assert((Aeq.size() == 0 && Beq.size() == 0) || Beq.cols() == 1);
assert((Aieq.size() == 0 && Bieq.size() == 0) || Aieq.cols() == n);
assert((Aieq.size() == 0 && Bieq.size() == 0) || Aieq.rows() == Bieq.rows());
assert((Aieq.size() == 0 && Bieq.size() == 0) || Bieq.cols() == 1);
Eigen::Matrix<typename Derivedlx::Scalar,Eigen::Dynamic,1> lx;
Eigen::Matrix<typename Derivedux::Scalar,Eigen::Dynamic,1> ux;
if(p_lx.size() == 0)
{
lx = Eigen::PlainObjectBase<Derivedlx>::Constant(
n,1,-numeric_limits<typename Derivedlx::Scalar>::max());
}else
{
lx = p_lx;
}
if(ux.size() == 0)
{
ux = Eigen::PlainObjectBase<Derivedux>::Constant(
n,1,numeric_limits<typename Derivedux::Scalar>::max());
}else
{
ux = p_ux;
}
assert(lx.rows() == n && "lx must have n rows");
assert(ux.rows() == n && "ux must have n rows");
assert(ux.cols() == 1 && "lx must be a column vector");
assert(lx.cols() == 1 && "ux must be a column vector");
assert((ux.array()-lx.array()).minCoeff() > 0 && "ux(i) must be > lx(i)");
if(Z.size() != 0)
{
// Initial guess should have correct size
assert(Z.rows() == n && "Z must have n rows");
assert(Z.cols() == 1 && "Z must be a column vector");
}
assert(known.cols() == 1 && "known must be a column vector");
// Number of knowns
const int nk = known.size();
// Initialize active sets
typedef int BOOL;
#define TRUE 1
#define FALSE 0
Matrix<BOOL,Dynamic,1> as_lx = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
Matrix<BOOL,Dynamic,1> as_ux = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
Matrix<BOOL,Dynamic,1> as_ieq = Matrix<BOOL,Dynamic,1>::Constant(Aieq.rows(),1,FALSE);
// Keep track of previous Z for comparison
PlainObjectBase<DerivedZ> old_Z;
old_Z = PlainObjectBase<DerivedZ>::Constant(
n,1,numeric_limits<typename DerivedZ::Scalar>::max());
int iter = 0;
while(true)
{
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<"Iteration: "<<iter<<":"<<endl;
cout<<" pre"<<endl;
#endif
// FIND BREACHES OF CONSTRAINTS
int new_as_lx = 0;
int new_as_ux = 0;
int new_as_ieq = 0;
if(Z.size() > 0)
{
for(int z = 0;z < n;z++)
{
if(Z(z) < lx(z))
{
new_as_lx += (as_lx(z)?0:1);
//new_as_lx++;
as_lx(z) = TRUE;
}
if(Z(z) > ux(z))
{
new_as_ux += (as_ux(z)?0:1);
//new_as_ux++;
as_ux(z) = TRUE;
}
}
if(Aieq.rows() > 0)
{
PlainObjectBase<DerivedZ> AieqZ;
AieqZ = Aieq*Z;
for(int a = 0;a<Aieq.rows();a++)
{
if(AieqZ(a) > Bieq(a))
{
new_as_ieq += (as_ieq(a)?0:1);
as_ieq(a) = TRUE;
}
}
}
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<" new_as_lx: "<<new_as_lx<<endl;
cout<<" new_as_ux: "<<new_as_ux<<endl;
#endif
const double diff = (Z-old_Z).squaredNorm();
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<"diff: "<<diff<<endl;
#endif
if(diff < params.solution_diff_threshold)
{
ret = SOLVER_STATUS_CONVERGED;
break;
}
old_Z = Z;
}
const int as_lx_count = count(as_lx.data(),as_lx.data()+n,TRUE);
const int as_ux_count = count(as_ux.data(),as_ux.data()+n,TRUE);
const int as_ieq_count =
count(as_ieq.data(),as_ieq.data()+as_ieq.size(),TRUE);
#ifndef NDEBUG
{
int count = 0;
for(int a = 0;a<as_ieq.size();a++)
{
if(as_ieq(a))
{
assert(as_ieq(a) == TRUE);
count++;
}
}
assert(as_ieq_count == count);
}
#endif
// PREPARE FIXED VALUES
PlainObjectBase<Derivedknown> known_i;
known_i.resize(nk + as_lx_count + as_ux_count,1);
PlainObjectBase<DerivedY> Y_i;
Y_i.resize(nk + as_lx_count + as_ux_count,1);
{
known_i.block(0,0,known.rows(),known.cols()) = known;
Y_i.block(0,0,Y.rows(),Y.cols()) = Y;
int k = nk;
// Then all lx
for(int z = 0;z < n;z++)
{
if(as_lx(z))
{
known_i(k) = z;
Y_i(k) = lx(z);
k++;
}
}
// Finally all ux
for(int z = 0;z < n;z++)
{
if(as_ux(z))
{
known_i(k) = z;
Y_i(k) = ux(z);
k++;
}
}
assert(k==Y_i.size());
assert(k==known_i.size());
}
//cout<<matlab_format((known_i.array()+1).eval(),"known_i")<<endl;
// PREPARE EQUALITY CONSTRAINTS
VectorXi as_ieq_list(as_ieq_count,1);
// Gather active constraints and resp. rhss
PlainObjectBase<DerivedBeq> Beq_i;
Beq_i.resize(Beq.rows()+as_ieq_count,1);
Beq_i.head(Beq.rows()) = Beq;
{
int k =0;
for(int a=0;a<as_ieq.size();a++)
{
if(as_ieq(a))
{
assert(k<as_ieq_list.size());
as_ieq_list(k)=a;
Beq_i(Beq.rows()+k,0) = Bieq(k,0);
k++;
}
}
assert(k == as_ieq_count);
}
// extract active constraint rows
SparseMatrix<AeqT> Aeq_i,Aieq_i;
slice(Aieq,as_ieq_list,1,Aieq_i);
// Append to equality constraints
cat(1,Aeq,Aieq_i,Aeq_i);
min_quad_with_fixed_data<AT> data;
#ifndef NDEBUG
{
// NO DUPES!
Matrix<BOOL,Dynamic,1> fixed = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
for(int k = 0;k<known_i.size();k++)
{
assert(!fixed[known_i(k)]);
fixed[known_i(k)] = TRUE;
}
}
#endif
Eigen::PlainObjectBase<DerivedZ> sol;
if(known_i.size() == A.rows())
{
// Everything's fixed?
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<" everything's fixed."<<endl;
#endif
Z.resize(A.rows(),Y_i.cols());
slice_into(Y_i,known_i,1,Z);
sol.resize(0,Y_i.cols());
assert(Aeq_i.rows() == 0 && "All fixed but linearly constrained");
}else
{
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<" min_quad_with_fixed_precompute"<<endl;
#endif
if(!min_quad_with_fixed_precompute(A,known_i,Aeq_i,params.Auu_pd,data))
{
cerr<<"Error: min_quad_with_fixed precomputation failed."<<endl;
if(iter > 0 && Aeq_i.rows() > Aeq.rows())
{
cerr<<" *Are you sure rows of [Aeq;Aieq] are linearly independent?*"<<
endl;
}
ret = SOLVER_STATUS_ERROR;
break;
}
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<" min_quad_with_fixed_solve"<<endl;
#endif
if(!min_quad_with_fixed_solve(data,B,Y_i,Beq_i,Z,sol))
{
cerr<<"Error: min_quad_with_fixed solve failed."<<endl;
ret = SOLVER_STATUS_ERROR;
break;
}
//cout<<matlab_format((Aeq*Z-Beq).eval(),"cr")<<endl;
//cout<<matlab_format(Z,"Z")<<endl;
#ifdef ACTIVE_SET_CPP_DEBUG
cout<<" post"<<endl;
#endif
// Computing Lagrange multipliers needs to be adjusted slightly if A is not symmetric
assert(data.Auu_sym);
}
// Compute Lagrange multiplier values for known_i
SparseMatrix<AT> Ak;
// Slow
slice(A,known_i,1,Ak);
Eigen::PlainObjectBase<DerivedB> Bk;
slice(B,known_i,Bk);
MatrixXd Lambda_known_i = -(0.5*Ak*Z + 0.5*Bk);
// reverse the lambda values for lx
Lambda_known_i.block(nk,0,as_lx_count,1) =
(-1*Lambda_known_i.block(nk,0,as_lx_count,1)).eval();
// Extract Lagrange multipliers for Aieq_i (always at back of sol)
VectorXd Lambda_Aieq_i(Aieq_i.rows(),1);
for(int l = 0;l<Aieq_i.rows();l++)
{
Lambda_Aieq_i(Aieq_i.rows()-1-l) = sol(sol.rows()-1-l);
}
// Remove from active set
for(int l = 0;l<as_lx_count;l++)
{
if(Lambda_known_i(nk + l) < params.inactive_threshold)
{
as_lx(known_i(nk + l)) = FALSE;
}
}
for(int u = 0;u<as_ux_count;u++)
{
if(Lambda_known_i(nk + as_lx_count + u) <
params.inactive_threshold)
{
as_ux(known_i(nk + as_lx_count + u)) = FALSE;
}
}
for(int a = 0;a<as_ieq_count;a++)
{
if(Lambda_Aieq_i(a) < params.inactive_threshold)
{
as_ieq(as_ieq_list(a)) = FALSE;
}
}
iter++;
//cout<<iter<<endl;
if(params.max_iter>0 && iter>=params.max_iter)
{
ret = SOLVER_STATUS_MAX_ITER;
break;
}
}
return ret;
}
IGL_INLINE void igl::orientable_patches(
const Eigen::PlainObjectBase<DerivedF> & F,
Eigen::PlainObjectBase<DerivedC> & C,
Eigen::SparseMatrix<AScalar> & A)
{
using namespace Eigen;
using namespace std;
// simplex size
assert(F.cols() == 3);
// List of all "half"-edges: 3*#F by 2
Matrix<typename DerivedF::Scalar, Dynamic, 2> allE,sortallE,uE;
allE.resize(F.rows()*3,2);
Matrix<int,Dynamic,2> IX;
VectorXi IA,IC;
allE.block(0*F.rows(),0,F.rows(),1) = F.col(1);
allE.block(0*F.rows(),1,F.rows(),1) = F.col(2);
allE.block(1*F.rows(),0,F.rows(),1) = F.col(2);
allE.block(1*F.rows(),1,F.rows(),1) = F.col(0);
allE.block(2*F.rows(),0,F.rows(),1) = F.col(0);
allE.block(2*F.rows(),1,F.rows(),1) = F.col(1);
// Sort each row
sort(allE,2,true,sortallE,IX);
//IC(i) tells us where to find sortallE(i,:) in uE:
// so that sortallE(i,:) = uE(IC(i),:)
unique_rows(sortallE,uE,IA,IC);
// uE2FT(e,f) = 1 means face f is adjacent to unique edge e
vector<Triplet<AScalar> > uE2FTijv(IC.rows());
for(int e = 0;e<IC.rows();e++)
{
uE2FTijv[e] = Triplet<AScalar>(e%F.rows(),IC(e),1);
}
SparseMatrix<AScalar> uE2FT(F.rows(),uE.rows());
uE2FT.setFromTriplets(uE2FTijv.begin(),uE2FTijv.end());
// kill non-manifold edges
for(int j=0; j<(int)uE2FT.outerSize();j++)
{
int degree = 0;
for(typename SparseMatrix<AScalar>::InnerIterator it (uE2FT,j); it; ++it)
{
degree++;
}
// Iterate over inside
if(degree > 2)
{
for(typename SparseMatrix<AScalar>::InnerIterator it (uE2FT,j); it; ++it)
{
uE2FT.coeffRef(it.row(),it.col()) = 0;
}
}
}
// Face-face Adjacency matrix
SparseMatrix<AScalar> uE2F;
uE2F = uE2FT.transpose().eval();
A = uE2FT*uE2F;
// All ones
for(int j=0; j<A.outerSize();j++)
{
// Iterate over inside
for(typename SparseMatrix<AScalar>::InnerIterator it (A,j); it; ++it)
{
if(it.value() > 1)
{
A.coeffRef(it.row(),it.col()) = 1;
}
}
}
//% Connected components are patches
//%C = components(A); % alternative to graphconncomp from matlab_bgl
//[~,C] = graphconncomp(A);
// graph connected components using boost
components(A,C);
}
IGL_INLINE void igl::upsample(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
Eigen::PlainObjectBase<DerivedNV>& NV,
Eigen::PlainObjectBase<DerivedNF>& NF)
{
// Use "in place" wrapper instead
assert(&V != &NV);
assert(&F != &NF);
using namespace std;
using namespace Eigen;
Eigen::Matrix<
typename DerivedF::Scalar,Eigen::Dynamic,Eigen::Dynamic>
FF,FFi;
triangle_triangle_adjacency(F,FF,FFi);
// TODO: Cache optimization missing from here, it is a mess
// Compute the number and positions of the vertices to insert (on edges)
Eigen::MatrixXi NI = Eigen::MatrixXi::Constant(FF.rows(),FF.cols(),-1);
int counter = 0;
for(int i=0;i<FF.rows();++i)
{
for(int j=0;j<3;++j)
{
if(NI(i,j) == -1)
{
NI(i,j) = counter;
if (FF(i,j) != -1) // If it is not a border
NI(FF(i,j),FFi(i,j)) = counter;
++counter;
}
}
}
int n_odd = V.rows();
int n_even = counter;
// Preallocate NV and NF
NV.resize(V.rows()+n_even,V.cols());
NF.resize(F.rows()*4,3);
// Fill the odd vertices position
NV.block(0,0,V.rows(),V.cols()) = V;
// Fill the even vertices position
for(int i=0;i<FF.rows();++i)
{
for(int j=0;j<3;++j)
{
NV.row(NI(i,j) + n_odd) = 0.5 * V.row(F(i,j)) + 0.5 * V.row(F(i,(j+1)%3));
}
}
// Build the new topology (Every face is replaced by four)
for(int i=0; i<F.rows();++i)
{
VectorXi VI(6);
VI << F(i,0), F(i,1), F(i,2), NI(i,0) + n_odd, NI(i,1) + n_odd, NI(i,2) + n_odd;
VectorXi f0(3), f1(3), f2(3), f3(3);
f0 << VI(0), VI(3), VI(5);
f1 << VI(1), VI(4), VI(3);
f2 << VI(3), VI(4), VI(5);
f3 << VI(4), VI(2), VI(5);
NF.row((i*4)+0) = f0;
NF.row((i*4)+1) = f1;
NF.row((i*4)+2) = f2;
NF.row((i*4)+3) = f3;
}
}
IGL_INLINE bool igl::biharmonic_coordinates(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedT> & T,
const std::vector<std::vector<SType> > & S,
const int k,
Eigen::PlainObjectBase<DerivedW> & W)
{
using namespace Eigen;
using namespace std;
// This is not the most efficient way to build A, but follows "Linear
// Subspace Design for Real-Time Shape Deformation" [Wang et al. 2015].
SparseMatrix<double> A;
{
SparseMatrix<double> N,Z,L,K,M;
normal_derivative(V,T,N);
Array<bool,Dynamic,1> I;
Array<bool,Dynamic,Dynamic> C;
on_boundary(T,I,C);
{
std::vector<Triplet<double> >ZIJV;
for(int t =0;t<T.rows();t++)
{
for(int f =0;f<T.cols();f++)
{
if(C(t,f))
{
const int i = t+f*T.rows();
for(int c = 1;c<T.cols();c++)
{
ZIJV.emplace_back(T(t,(f+c)%T.cols()),i,1);
}
}
}
}
Z.resize(V.rows(),N.rows());
Z.setFromTriplets(ZIJV.begin(),ZIJV.end());
N = (Z*N).eval();
}
cotmatrix(V,T,L);
K = N+L;
massmatrix(V,T,MASSMATRIX_TYPE_DEFAULT,M);
// normalize
M /= ((VectorXd)M.diagonal()).array().abs().maxCoeff();
DiagonalMatrix<double,Dynamic> Minv =
((VectorXd)M.diagonal().array().inverse()).asDiagonal();
switch(k)
{
default:
assert(false && "unsupported");
case 2:
// For C1 smoothness in 2D, one should use bi-harmonic
A = K.transpose() * (Minv * K);
break;
case 3:
// For C1 smoothness in 3D, one should use tri-harmonic
A = K.transpose() * (Minv * (-L * (Minv * K)));
break;
}
}
// Vertices in point handles
const size_t mp =
count_if(S.begin(),S.end(),[](const vector<int> & h){return h.size()==1;});
// number of region handles
const size_t r = S.size()-mp;
// Vertices in region handles
size_t mr = 0;
for(const auto & h : S)
{
if(h.size() > 1)
{
mr += h.size();
}
}
const size_t dim = T.cols()-1;
// Might as well be dense... I think...
MatrixXd J = MatrixXd::Zero(mp+mr,mp+r*(dim+1));
VectorXi b(mp+mr);
MatrixXd H(mp+r*(dim+1),dim);
{
int v = 0;
int c = 0;
for(int h = 0;h<S.size();h++)
{
if(S[h].size()==1)
{
H.row(c) = V.block(S[h][0],0,1,dim);
J(v,c++) = 1;
b(v) = S[h][0];
v++;
}else
{
assert(S[h].size() >= dim+1);
for(int p = 0;p<S[h].size();p++)
{
for(int d = 0;d<dim;d++)
{
J(v,c+d) = V(S[h][p],d);
}
J(v,c+dim) = 1;
b(v) = S[h][p];
v++;
}
H.block(c,0,dim+1,dim).setIdentity();
c+=dim+1;
}
}
}
// minimize ½ W' A W'
// subject to W(b,:) = J
return min_quad_with_fixed(
A,VectorXd::Zero(A.rows()).eval(),b,J,{},VectorXd(),true,W);
}
IGL_INLINE bool igl::bbw::bbw(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedEle> & Ele,
const Eigen::PlainObjectBase<Derivedb> & b,
const Eigen::PlainObjectBase<Derivedbc> & bc,
igl::bbw::BBWData & data,
Eigen::PlainObjectBase<DerivedW> & W
)
{
using namespace std;
using namespace Eigen;
// number of domain vertices
int n = V.rows();
// number of handles
int m = bc.cols();
// Build biharmonic operator
SparseMatrix<typename DerivedW::Scalar> L;
cotmatrix(V,Ele,L);
SparseMatrix<typename DerivedW::Scalar> M;
SparseMatrix<typename DerivedW::Scalar> Mi;
massmatrix(V,Ele,MASSMATRIX_TYPE_DEFAULT,M);
invert_diag(M,Mi);
SparseMatrix<typename DerivedW::Scalar> Q = L.transpose() * Mi * L;
assert(!data.partition_unity && "partition_unity not implemented yet");
W.derived().resize(n,m);
{
// No linear terms
VectorXd c = VectorXd::Zero(n);
// No linear constraints
SparseMatrix<typename DerivedW::Scalar> A(0,n),Aeq(0,n),Aieq(0,n);
VectorXd uc(0,1),Beq(0,1),Bieq(0,1),lc(0,1);
// Upper and lower box constraints (Constant bounds)
VectorXd ux = VectorXd::Ones(n);
VectorXd lx = VectorXd::Zero(n);
active_set_params eff_params = data.active_set_params;
switch(data.qp_solver)
{
case QP_SOLVER_IGL_ACTIVE_SET:
{
if(data.verbosity >= 1)
{
cout<<"BBW: max_iter: "<<data.active_set_params.max_iter<<endl;
cout<<"BBW: eff_max_iter: "<<eff_params.max_iter<<endl;
}
if(data.verbosity >= 1)
{
cout<<"BBW: Computing initial weights for "<<m<<" handle"<<
(m!=1?"s":"")<<"."<<endl;
}
min_quad_with_fixed_data<typename DerivedW::Scalar > mqwf;
min_quad_with_fixed_precompute(Q,b,Aeq,true,mqwf);
min_quad_with_fixed_solve(mqwf,c,bc,Beq,W);
// decrement
eff_params.max_iter--;
bool error = false;
// Loop over handles
#pragma omp parallel for
for(int i = 0;i<m;i++)
{
// Quicker exit for openmp
if(error)
{
continue;
}
if(data.verbosity >= 1)
{
#pragma omp critical
cout<<"BBW: Computing weight for handle "<<i+1<<" out of "<<m<<
"."<<endl;
}
VectorXd bci = bc.col(i);
VectorXd Wi;
// use initial guess
Wi = W.col(i);
SolverStatus ret = active_set(
Q,c,b,bci,Aeq,Beq,Aieq,Bieq,lx,ux,eff_params,Wi);
switch(ret)
{
case SOLVER_STATUS_CONVERGED:
break;
case SOLVER_STATUS_MAX_ITER:
cerr<<"active_set: max iter without convergence."<<endl;
break;
case SOLVER_STATUS_ERROR:
default:
cerr<<"active_set error."<<endl;
error = true;
}
W.col(i) = Wi;
}
if(error)
{
return false;
}
break;
}
case QP_SOLVER_MOSEK:
{
#ifdef IGL_NO_MOSEK
assert(false && "Use another QPSolver. Recompile without IGL_NO_MOSEK defined.");
cerr<<"Use another QPSolver. Recompile without IGL_NO_MOSEK defined."<<endl;
return false;
#else
// Loop over handles
for(int i = 0;i<m;i++)
{
if(data.verbosity >= 1)
{
cout<<"BBW: Computing weight for handle "<<i+1<<" out of "<<m<<
"."<<endl;
}
VectorXd bci = bc.col(i);
VectorXd Wi;
// impose boundary conditions via bounds
slice_into(bci,b,ux);
slice_into(bci,b,lx);
bool r = mosek_quadprog(Q,c,0,A,lc,uc,lx,ux,data.mosek_data,Wi);
if(!r)
{
return false;
}
W.col(i) = Wi;
}
#endif
break;
}
default:
{
assert(false && "Unknown qp_solver");
return false;
}
}
#ifndef NDEBUG
const double min_rowsum = W.rowwise().sum().array().abs().minCoeff();
if(min_rowsum < 0.1)
{
cerr<<"bbw.cpp: Warning, minimum row sum is very low. Consider more "
"active set iterations or enforcing partition of unity."<<endl;
}
#endif
}
return true;
}
IGL_INLINE void igl::outer_hull(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
const Eigen::PlainObjectBase<DerivedN> & N,
Eigen::PlainObjectBase<DerivedG> & G,
Eigen::PlainObjectBase<DerivedJ> & J,
Eigen::PlainObjectBase<Derivedflip> & flip)
{
using namespace Eigen;
using namespace std;
using namespace igl;
typedef typename DerivedF::Index Index;
Matrix<Index,DerivedF::RowsAtCompileTime,1> C;
typedef Matrix<typename DerivedV::Scalar,Dynamic,DerivedV::ColsAtCompileTime> MatrixXV;
typedef Matrix<typename DerivedF::Scalar,Dynamic,DerivedF::ColsAtCompileTime> MatrixXF;
typedef Matrix<typename DerivedG::Scalar,Dynamic,DerivedG::ColsAtCompileTime> MatrixXG;
typedef Matrix<typename DerivedJ::Scalar,Dynamic,DerivedJ::ColsAtCompileTime> MatrixXJ;
typedef Matrix<typename DerivedN::Scalar,1,3> RowVector3N;
const Index m = F.rows();
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"outer hull..."<<endl;
#endif
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"edge map..."<<endl;
#endif
typedef Matrix<typename DerivedF::Scalar,Dynamic,2> MatrixX2I;
typedef Matrix<typename DerivedF::Index,Dynamic,1> VectorXI;
MatrixX2I E,uE;
VectorXI EMAP;
vector<vector<typename DerivedF::Index> > uE2E;
unique_edge_map(F,E,uE,EMAP,uE2E);
// TODO:
// uE --> face-edge index, sorted CCW around edge according to normal
// uE --> sorted order index
// uE --> bool, whether needed to flip face to make "consistent" with unique
// edge
// Place order of each half-edge in its corresponding sorted list around edge
VectorXI diIM(3*m);
// Whether face's edge used for sorting is consistent with unique edge
VectorXI dicons(3*m);
// dihedral angles of faces around edge with face of edge in dicons
vector<vector<typename DerivedV::Scalar> > di(uE2E.size());
// For each list of face-edges incide on a unique edge
for(size_t ui = 0;ui<(size_t)uE.rows();ui++)
{
// Base normal vector to orient against
const auto fe0 = uE2E[ui][0];
const RowVector3N & eVp = N.row(fe0%m);
MatrixXd di_I(uE2E[ui].size(),2);
const typename DerivedF::Scalar d = F(fe0%m,((fe0/m)+2)%3);
const typename DerivedF::Scalar s = F(fe0%m,((fe0/m)+1)%3);
// Edge vector
const auto & eV = (V.row(d)-V.row(s)).normalized();
vector<bool> cons(uE2E[ui].size());
// Loop over incident face edges
for(size_t fei = 0;fei<uE2E[ui].size();fei++)
{
const auto & fe = uE2E[ui][fei];
const auto f = fe % m;
const auto c = fe / m;
// source should match destination to be consistent
cons[fei] = (d == F(f,(c+1)%3));
assert( cons[fei] || (d == F(f,(c+2)%3)));
assert(!cons[fei] || (s == F(f,(c+2)%3)));
assert(!cons[fei] || (d == F(f,(c+1)%3)));
// Angle between n and f
const RowVector3N & n = N.row(f);
di_I(fei,0) = M_PI - atan2( eVp.cross(n).dot(eV), eVp.dot(n));
if(!cons[fei])
{
di_I(fei,0) = di_I(fei,0) + M_PI;
if(di_I(fei,0)>=2.*M_PI)
{
di_I(fei,0) = di_I(fei,0) - 2.*M_PI;
}
}
// This signing is very important to make sure different edges sort
// duplicate faces the same way, regardless of their orientations
di_I(fei,1) = (cons[fei]?1.:-1.)*f;
}
VectorXi IM;
//igl::sort(di[ui],true,di[ui],IM);
// Sort, but break ties using index to ensure that duplicates always show
// up in same order.
MatrixXd s_di_I;
igl::sortrows(di_I,true,s_di_I,IM);
di[ui].resize(uE2E[ui].size());
for(size_t i = 0;i<di[ui].size();i++)
{
di[ui][i] = s_di_I(i,0);
}
// copy old list
vector<typename DerivedF::Index> temp = uE2E[ui];
for(size_t fei = 0;fei<uE2E[ui].size();fei++)
{
uE2E[ui][fei] = temp[IM(fei)];
const auto & fe = uE2E[ui][fei];
diIM(fe) = fei;
dicons(fe) = cons[IM(fei)];
}
}
vector<vector<vector<Index > > > TT,_1;
triangle_triangle_adjacency(E,EMAP,uE2E,false,TT,_1);
VectorXI counts;
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"facet components..."<<endl;
#endif
facet_components(TT,C,counts);
assert(C.maxCoeff()+1 == counts.rows());
const size_t ncc = counts.rows();
G.resize(0,F.cols());
J.resize(0,1);
flip.setConstant(m,1,false);
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"reindex..."<<endl;
#endif
// H contains list of faces on outer hull;
vector<bool> FH(m,false);
vector<bool> EH(3*m,false);
vector<MatrixXG> vG(ncc);
vector<MatrixXJ> vJ(ncc);
vector<MatrixXJ> vIM(ncc);
for(size_t id = 0;id<ncc;id++)
{
vIM[id].resize(counts[id],1);
}
// current index into each IM
vector<size_t> g(ncc,0);
// place order of each face in its respective component
for(Index f = 0;f<m;f++)
{
vIM[C(f)](g[C(f)]++) = f;
}
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"barycenters..."<<endl;
#endif
// assumes that "resolve" has handled any coplanar cases correctly and nearly
// coplanar cases can be sorted based on barycenter.
MatrixXV BC;
barycenter(V,F,BC);
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"loop over CCs (="<<ncc<<")..."<<endl;
#endif
for(Index id = 0;id<(Index)ncc;id++)
{
auto & IM = vIM[id];
// starting face that's guaranteed to be on the outer hull and in this
// component
int f;
bool f_flip;
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"outer facet..."<<endl;
#endif
outer_facet(V,F,N,IM,f,f_flip);
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"outer facet: "<<f<<endl;
#endif
int FHcount = 1;
FH[f] = true;
// Q contains list of face edges to continue traversing upong
queue<int> Q;
Q.push(f+0*m);
Q.push(f+1*m);
Q.push(f+2*m);
flip(f) = f_flip;
//cout<<"flip("<<f<<") = "<<(flip(f)?"true":"false")<<endl;
#ifdef IGL_OUTER_HULL_DEBUG
cout<<"BFS..."<<endl;
#endif
while(!Q.empty())
{
// face-edge
const int e = Q.front();
Q.pop();
// face
const int f = e%m;
// corner
const int c = e/m;
// Should never see edge again...
if(EH[e] == true)
{
continue;
}
EH[e] = true;
// source of edge according to f
const int fs = flip(f)?F(f,(c+2)%3):F(f,(c+1)%3);
// destination of edge according to f
const int fd = flip(f)?F(f,(c+1)%3):F(f,(c+2)%3);
// edge valence
const size_t val = uE2E[EMAP(e)].size();
//// find overlapping face-edges
//const auto & neighbors = uE2E[EMAP(e)];
//// normal after possible flipping
//const auto & fN = (flip(f)?-1.:1.)*N.row(f);
//// Edge vector according to f's (flipped) orientation.
////const auto & eV = (V.row(fd)-V.row(fs)).normalized();
//#warning "EXPERIMENTAL, DO NOT USE"
//// THIS IS WRONG! The first face is---after sorting---no longer the face
//// used for orienting the sort.
//const auto ui = EMAP(e);
//const auto fe0 = uE2E[ui][0];
//const auto es = F(fe0%m,((fe0/m)+1)%3);
// is edge consistent with edge of face used for sorting
const int e_cons = (dicons(e) ? 1: -1);
int nfei = -1;
// Loop once around trying to find suitable next face
for(size_t step = 1; step<val+2;step++)
{
const int nfei_new = (diIM(e) + 2*val + e_cons*step*(flip(f)?-1:1))%val;
const int nf = uE2E[EMAP(e)][nfei_new] % m;
// Don't consider faces with identical dihedral angles
if(di[EMAP(e)][diIM(e)] != di[EMAP(e)][nfei_new])
//#warning "THIS IS HACK, FIX ME"
// if( abs(di[EMAP(e)][diIM(e)] - di[EMAP(e)][nfei_new]) < 1e-16 )
{
//#ifdef IGL_OUTER_HULL_DEBUG
// cout<<"Next facet: "<<(f+1)<<" --> "<<(nf+1)<<", |"<<
// di[EMAP(e)][diIM(e)]<<" - "<<di[EMAP(e)][nfei_new]<<"| = "<<
// abs(di[EMAP(e)][diIM(e)] - di[EMAP(e)][nfei_new])
// <<endl;
//#endif
// Only use this face if not already seen
if(!FH[nf])
{
nfei = nfei_new;
}
break;
}
//#ifdef IGL_OUTER_HULL_DEBUG
// cout<<"Skipping co-planar facet: "<<(f+1)<<" --> "<<(nf+1)<<endl;
//#endif
}
int max_ne = -1;
//// Loop over and find max dihedral angle
//typename DerivedV::Scalar max_di = -1;
//for(const auto & ne : neighbors)
//{
// const int nf = ne%m;
// if(nf == f)
// {
// continue;
// }
// // Corner of neighbor
// const int nc = ne/m;
// // Is neighbor oriented consistently with (flipped) f?
// //const int ns = F(nf,(nc+1)%3);
// const int nd = F(nf,(nc+2)%3);
// const bool cons = (flip(f)?fd:fs) == nd;
// // Normal after possibly flipping to match flip or orientation of f
// const auto & nN = (cons? (flip(f)?-1:1.) : (flip(f)?1.:-1.) )*N.row(nf);
// // Angle between n and f
// const auto & ndi = M_PI - atan2( fN.cross(nN).dot(eV), fN.dot(nN));
// if(ndi>=max_di)
// {
// max_ne = ne;
// max_di = ndi;
// }
//}
////cout<<(max_ne != max_ne_2)<<" =?= "<<e_cons<<endl;
//if(max_ne != max_ne_2)
//{
// cout<<(f+1)<<" ---> "<<(max_ne%m)+1<<" != "<<(max_ne_2%m)+1<<" ... "<<e_cons<<" "<<flip(f)<<endl;
// typename DerivedV::Scalar max_di = -1;
// for(size_t nei = 0;nei<neighbors.size();nei++)
// {
// const auto & ne = neighbors[nei];
// const int nf = ne%m;
// if(nf == f)
// {
// cout<<" "<<(ne%m)+1<<":\t"<<0<<"\t"<<di[EMAP[e]][nei]<<" "<<diIM(ne)<<endl;
// continue;
// }
// // Corner of neighbor
// const int nc = ne/m;
// // Is neighbor oriented consistently with (flipped) f?
// //const int ns = F(nf,(nc+1)%3);
// const int nd = F(nf,(nc+2)%3);
// const bool cons = (flip(f)?fd:fs) == nd;
// // Normal after possibly flipping to match flip or orientation of f
// const auto & nN = (cons? (flip(f)?-1:1.) : (flip(f)?1.:-1.) )*N.row(nf);
// // Angle between n and f
// const auto & ndi = M_PI - atan2( fN.cross(nN).dot(eV), fN.dot(nN));
// cout<<" "<<(ne%m)+1<<":\t"<<ndi<<"\t"<<di[EMAP[e]][nei]<<" "<<diIM(ne)<<endl;
// if(ndi>=max_di)
// {
// max_ne = ne;
// max_di = ndi;
// }
// }
//}
if(nfei >= 0)
{
max_ne = uE2E[EMAP(e)][nfei];
}
if(max_ne>=0)
{
// face of neighbor
const int nf = max_ne%m;
#ifdef IGL_OUTER_HULL_DEBUG
if(!FH[nf])
{
// first time seeing face
cout<<(f+1)<<" --> "<<(nf+1)<<endl;
}
#endif
FH[nf] = true;
FHcount++;
// corner of neighbor
const int nc = max_ne/m;
const int nd = F(nf,(nc+2)%3);
const bool cons = (flip(f)?fd:fs) == nd;
flip(nf) = (cons ? flip(f) : !flip(f));
//cout<<"flip("<<nf<<") = "<<(flip(nf)?"true":"false")<<endl;
const int ne1 = nf+((nc+1)%3)*m;
const int ne2 = nf+((nc+2)%3)*m;
if(!EH[ne1])
{
Q.push(ne1);
}
if(!EH[ne2])
{
Q.push(ne2);
}
}
}
{
vG[id].resize(FHcount,3);
vJ[id].resize(FHcount,1);
//nG += FHcount;
size_t h = 0;
assert(counts(id) == IM.rows());
for(int i = 0;i<counts(id);i++)
{
const size_t f = IM(i);
//if(f_flip)
//{
// flip(f) = !flip(f);
//}
if(FH[f])
{
vG[id].row(h) = (flip(f)?F.row(f).reverse().eval():F.row(f));
vJ[id](h,0) = f;
h++;
}
}
assert((int)h == FHcount);
}
}
// Is A inside B? Assuming A and B are consistently oriented but closed and
// non-intersecting.
const auto & is_component_inside_other = [](
const Eigen::PlainObjectBase<DerivedV> & V,
const MatrixXV & BC,
const MatrixXG & A,
const MatrixXJ & AJ,
const MatrixXG & B)->bool
{
const auto & bounding_box = [](
const Eigen::PlainObjectBase<DerivedV> & V,
const MatrixXG & F)->
MatrixXV
{
MatrixXV BB(2,3);
BB<<
1e26,1e26,1e26,
-1e26,-1e26,-1e26;
const size_t m = F.rows();
for(size_t f = 0;f<m;f++)
{
for(size_t c = 0;c<3;c++)
{
const auto & vfc = V.row(F(f,c));
BB.row(0) = BB.row(0).array().min(vfc.array()).eval();
BB.row(1) = BB.row(1).array().max(vfc.array()).eval();
}
}
return BB;
};
// A lot of the time we're dealing with unrelated, distant components: cull
// them.
MatrixXV ABB = bounding_box(V,A);
MatrixXV BBB = bounding_box(V,B);
if( (BBB.row(0)-ABB.row(1)).maxCoeff()>0 ||
(ABB.row(0)-BBB.row(1)).maxCoeff()>0 )
{
// bounding boxes do not overlap
return false;
}
////////////////////////////////////////////////////////////////////////
// POTENTIAL ROBUSTNESS WEAK AREA
////////////////////////////////////////////////////////////////////////
//
// q could be so close (<~1e-16) to B that the winding number is not a robust way to
// determine inside/outsideness. We could try to find a _better_ q which is
// farther away, but couldn't they all be bad?
MatrixXV q = BC.row(AJ(0));
// In a perfect world, it's enough to test a single point.
double w;
// winding_number_3 expects colmajor
const typename DerivedV::Scalar * Vdata;
Vdata = V.data();
Matrix<
typename DerivedV::Scalar,
DerivedV::RowsAtCompileTime,
DerivedV::ColsAtCompileTime,
ColMajor> Vcol;
if(DerivedV::IsRowMajor)
{
// copy to convert to colmajor
Vcol = V;
Vdata = Vcol.data();
}
winding_number_3(
Vdata,V.rows(),
B.data(),B.rows(),
q.data(),1,&w);
return fabs(w)>0.5;
};
// Reject components which are completely inside other components
vector<bool> keep(ncc,true);
size_t nG = 0;
// This is O( ncc * ncc * m)
for(size_t id = 0;id<ncc;id++)
{
for(size_t oid = 0;oid<ncc;oid++)
{
if(id == oid)
{
continue;
}
const bool inside = is_component_inside_other(V,BC,vG[id],vJ[id],vG[oid]);
#ifdef IGL_OUTER_HULL_DEBUG
cout<<id<<" is inside "<<oid<<" ? "<<inside<<endl;
#endif
keep[id] = keep[id] && !inside;
}
if(keep[id])
{
nG += vJ[id].rows();
}
}
// collect G and J across components
G.resize(nG,3);
J.resize(nG,1);
{
size_t off = 0;
for(Index id = 0;id<(Index)ncc;id++)
{
if(keep[id])
{
assert(vG[id].rows() == vJ[id].rows());
G.block(off,0,vG[id].rows(),vG[id].cols()) = vG[id];
J.block(off,0,vJ[id].rows(),vJ[id].cols()) = vJ[id];
off += vG[id].rows();
}
}
}
}
IGL_INLINE void igl::bounding_box(
const Eigen::PlainObjectBase<DerivedV>& V,
Eigen::PlainObjectBase<DerivedBV>& BV,
Eigen::PlainObjectBase<DerivedBF>& BF)
{
using namespace std;
const int dim = V.cols();
const auto & minV = V.colwise().minCoeff();
const auto & maxV = V.colwise().maxCoeff();
// 2^n vertices
BV.resize((1<<dim),dim);
// Recursive lambda to generate all 2^n combinations
const std::function<void(const int,const int,int*,int)> combos =
[&BV,&minV,&maxV,&combos](
const int dim,
const int i,
int * X,
const int pre_index)
{
for(X[i] = 0;X[i]<2;X[i]++)
{
int index = pre_index*2+X[i];
if((i+1)<dim)
{
combos(dim,i+1,X,index);
}else
{
for(int d = 0;d<dim;d++)
{
BV(index,d) = (X[d]?minV[d]:maxV[d]);
}
}
}
};
Eigen::VectorXi X(dim);
combos(dim,0,X.data(),0);
switch(dim)
{
case 2:
BF.resize(4,2);
BF<<
3,1,
1,0,
0,2,
2,3;
break;
case 3:
BF.resize(12,3);
BF<<
2,0,6,
0,4,6,
5,4,0,
5,0,1,
6,4,5,
5,7,6,
3,0,2,
1,0,3,
3,2,6,
6,7,3,
5,1,3,
3,7,5;
break;
default:
assert(false && "Unsupported dimension.");
break;
}
}
IGL_INLINE bool igl::writeOBJ(
const std::string str,
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
const Eigen::PlainObjectBase<DerivedV>& CN,
const Eigen::PlainObjectBase<DerivedF>& FN,
const Eigen::PlainObjectBase<DerivedT>& TC,
const Eigen::PlainObjectBase<DerivedF>& FTC)
{
FILE * obj_file = fopen(str.c_str(),"w");
if(NULL==obj_file)
{
printf("IOError: %s could not be opened for writing...",str.c_str());
return false;
}
// Loop over V
for(int i = 0;i<(int)V.rows();i++)
{
fprintf(obj_file,"v %0.15g %0.15g %0.15g\n",
V(i,0),
V(i,1),
V(i,2)
);
}
bool write_N = CN.rows() >0;
if(write_N)
{
for(int i = 0;i<(int)CN.rows();i++)
{
fprintf(obj_file,"v %0.15g %0.15g %0.15g\n",
CN(i,0),
CN(i,1),
CN(i,2)
);
}
fprintf(obj_file,"\n");
}
bool write_texture_coords = TC.rows() >0;
if(write_texture_coords)
{
for(int i = 0;i<(int)TC.rows();i++)
{
fprintf(obj_file, "vt %0.15g %0.15g\n",TC(i,0),TC(i,1));
}
fprintf(obj_file,"\n");
}
// loop over F
for(int i = 0;i<(int)F.rows();++i)
{
fprintf(obj_file,"f");
for(int j = 0; j<(int)F.cols();++j)
{
// OBJ is 1-indexed
fprintf(obj_file," %u",F(i,j)+1);
if(write_texture_coords)
fprintf(obj_file,"/%u",FTC(i,j)+1);
if(write_N)
{
if (write_texture_coords)
fprintf(obj_file,"/%u",FN(i,j)+1);
else
fprintf(obj_file,"//%u",FN(i,j)+1);
}
}
fprintf(obj_file,"\n");
}
fclose(obj_file);
return true;
}
IGL_INLINE
void igl::copyleft::cgal::order_facets_around_edge(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
size_t s,
size_t d,
const std::vector<int>& adj_faces,
const Eigen::PlainObjectBase<DerivedV>& pivot_point,
Eigen::PlainObjectBase<DerivedI>& order)
{
assert(V.cols() == 3);
assert(F.cols() == 3);
assert(pivot_point.cols() == 3);
auto signed_index_to_index = [&](int signed_idx)
{
return abs(signed_idx) -1;
};
auto get_opposite_vertex_index = [&](size_t fid) -> typename DerivedF::Scalar
{
typedef typename DerivedF::Scalar Index;
if (F(fid, 0) != (Index)s && F(fid, 0) != (Index)d) return F(fid, 0);
if (F(fid, 1) != (Index)s && F(fid, 1) != (Index)d) return F(fid, 1);
if (F(fid, 2) != (Index)s && F(fid, 2) != (Index)d) return F(fid, 2);
assert(false);
// avoid warning
return -1;
};
{
// Check if s, d and pivot are collinear.
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
K::Point_3 ps(V(s,0), V(s,1), V(s,2));
K::Point_3 pd(V(d,0), V(d,1), V(d,2));
K::Point_3 pp(pivot_point(0,0), pivot_point(0,1), pivot_point(0,2));
if (CGAL::collinear(ps, pd, pp)) {
throw std::runtime_error(
"Pivot point is collinear with the outer edge!");
}
}
const size_t N = adj_faces.size();
const size_t num_faces = N + 1; // N adj faces + 1 pivot face
// Because face indices are used for tie breaking, the original face indices
// in the new faces array must be ascending.
auto comp = [&](int i, int j)
{
return signed_index_to_index(adj_faces[i]) <
signed_index_to_index(adj_faces[j]);
};
std::vector<size_t> adj_order(N);
for (size_t i=0; i<N; i++) adj_order[i] = i;
std::sort(adj_order.begin(), adj_order.end(), comp);
DerivedV vertices(num_faces + 2, 3);
for (size_t i=0; i<N; i++)
{
const size_t fid = signed_index_to_index(adj_faces[adj_order[i]]);
vertices.row(i) = V.row(get_opposite_vertex_index(fid));
}
vertices.row(N ) = pivot_point;
vertices.row(N+1) = V.row(s);
vertices.row(N+2) = V.row(d);
DerivedF faces(num_faces, 3);
for (size_t i=0; i<N; i++)
{
if (adj_faces[adj_order[i]] < 0)
{
faces(i,0) = N+1; // s
faces(i,1) = N+2; // d
faces(i,2) = i ;
} else
{
faces(i,0) = N+2; // d
faces(i,1) = N+1; // s
faces(i,2) = i ;
}
}
// Last face is the pivot face.
faces(N, 0) = N+1;
faces(N, 1) = N+2;
faces(N, 2) = N;
std::vector<int> adj_faces_with_pivot(num_faces);
for (size_t i=0; i<num_faces; i++)
{
if ((size_t)faces(i,0) == N+1 && (size_t)faces(i,1) == N+2)
{
adj_faces_with_pivot[i] = int(i+1) * -1;
} else
{
adj_faces_with_pivot[i] = int(i+1);
}
}
DerivedI order_with_pivot;
order_facets_around_edge(
vertices, faces, N+1, N+2, adj_faces_with_pivot, order_with_pivot);
assert((size_t)order_with_pivot.size() == num_faces);
order.resize(N);
size_t pivot_index = num_faces + 1;
for (size_t i=0; i<num_faces; i++)
{
if ((size_t)order_with_pivot[i] == N)
{
pivot_index = i;
break;
}
}
assert(pivot_index < num_faces);
for (size_t i=0; i<N; i++)
{
order[i] = adj_order[order_with_pivot[(pivot_index+i+1)%num_faces]];
}
}
IGL_INLINE void igl::ismember_rows(
const Eigen::PlainObjectBase<DerivedA> & A,
const Eigen::PlainObjectBase<DerivedB> & B,
Eigen::PlainObjectBase<DerivedIA> & IA,
Eigen::PlainObjectBase<DerivedLOCB> & LOCB)
{
using namespace Eigen;
using namespace std;
assert(A.cols() == B.cols() && "number of columns must match");
IA.resize(A.rows(),1);
IA.setConstant(false);
LOCB.resize(A.rows(),1);
LOCB.setConstant(-1);
// boring base cases
if(A.size() == 0)
{
return;
}
if(B.size() == 0)
{
return;
}
// Get rid of any duplicates
DerivedA uA;
DerivedB uB;
Eigen::Matrix<typename DerivedA::Index,Dynamic,1> uIA,uIuA,uIB,uIuB;
unique_rows(A,uA,uIA,uIuA);
unique_rows(B,uB,uIB,uIuB);
// Sort both
DerivedA sA;
DerivedB sB;
Eigen::Matrix<typename DerivedA::Index,Dynamic,1> sIA,sIB;
sortrows(uA,true,sA,sIA);
sortrows(uB,true,sB,sIB);
Eigen::Matrix<bool,Eigen::Dynamic,1> uF =
Eigen::Matrix<bool,Eigen::Dynamic,1>::Zero(sA.size(),1);
Eigen::Matrix<typename DerivedLOCB::Scalar, Eigen::Dynamic,1> uLOCB =
Eigen::Matrix<typename DerivedLOCB::Scalar,Eigen::Dynamic,1>::
Constant(sA.size(),1,-1);
const auto & row_greater_than = [&sA,&sB](const int a, const int b)
{
for(int c = 0;c<sA.cols();c++)
{
if(sA(a,c) > sB(b,c)) return true;
if(sA(a,c) < sB(b,c)) return false;
}
return false;
};
{
int bi = 0;
// loop over sA
bool past = false;
for(int a = 0;a<sA.rows();a++)
{
while(!past && row_greater_than(a,bi))
{
bi++;
past = bi>=sB.size();
}
if(!past && (sA.row(a).array()==sB.row(bi).array()).all() )
{
uF(sIA(a)) = true;
uLOCB(sIA(a)) = uIB(sIB(bi));
}
}
}
for(int a = 0;a<A.rows();a++)
{
IA(a) = uF(uIuA(a));
LOCB(a) = uLOCB(uIuA(a));
}
}
IGL_INLINE void igl::ismember(
const Eigen::MatrixBase<DerivedA> & A,
const Eigen::MatrixBase<DerivedB> & B,
Eigen::PlainObjectBase<DerivedIA> & IA,
Eigen::PlainObjectBase<DerivedLOCB> & LOCB)
{
using namespace Eigen;
using namespace std;
IA.resizeLike(A);
IA.setConstant(false);
LOCB.resizeLike(A);
LOCB.setConstant(-1);
// boring base cases
if(A.size() == 0)
{
return;
}
if(B.size() == 0)
{
return;
}
// Get rid of any duplicates
typedef Matrix<typename DerivedA::Scalar,Dynamic,1> VectorA;
typedef Matrix<typename DerivedB::Scalar,Dynamic,1> VectorB;
const VectorA vA(Eigen::Map<const VectorA>(DerivedA(A).data(), A.cols()*A.rows(),1));
const VectorB vB(Eigen::Map<const VectorB>(DerivedB(B).data(), B.cols()*B.rows(),1));
VectorA uA;
VectorB uB;
Eigen::Matrix<typename DerivedA::Index,Dynamic,1> uIA,uIuA,uIB,uIuB;
unique(vA,uA,uIA,uIuA);
unique(vB,uB,uIB,uIuB);
// Sort both
VectorA sA;
VectorB sB;
Eigen::Matrix<typename DerivedA::Index,Dynamic,1> sIA,sIB;
sort(uA,1,true,sA,sIA);
sort(uB,1,true,sB,sIB);
Eigen::Matrix<bool,Eigen::Dynamic,1> uF =
Eigen::Matrix<bool,Eigen::Dynamic,1>::Zero(sA.size(),1);
Eigen::Matrix<typename DerivedLOCB::Scalar, Eigen::Dynamic,1> uLOCB =
Eigen::Matrix<typename DerivedLOCB::Scalar,Eigen::Dynamic,1>::
Constant(sA.size(),1,-1);
{
int bi = 0;
// loop over sA
bool past = false;
for(int a = 0;a<sA.size();a++)
{
while(!past && sA(a)>sB(bi))
{
bi++;
past = bi>=sB.size();
}
if(!past && sA(a)==sB(bi))
{
uF(sIA(a)) = true;
uLOCB(sIA(a)) = uIB(sIB(bi));
}
}
}
Map< Matrix<typename DerivedIA::Scalar,Dynamic,1> >
vIA(IA.data(),IA.cols()*IA.rows(),1);
Map< Matrix<typename DerivedLOCB::Scalar,Dynamic,1> >
vLOCB(LOCB.data(),LOCB.cols()*LOCB.rows(),1);
for(int a = 0;a<A.size();a++)
{
vIA(a) = uF(uIuA(a));
vLOCB(a) = uLOCB(uIuA(a));
}
}
IGL_INLINE void igl::boolean::mesh_boolean(
const Eigen::PlainObjectBase<DerivedVA > & VA,
const Eigen::PlainObjectBase<DerivedFA > & FA,
const Eigen::PlainObjectBase<DerivedVB > & VB,
const Eigen::PlainObjectBase<DerivedFB > & FB,
const MeshBooleanType & type,
const std::function<void(
const Eigen::Matrix<typename DerivedVC::Scalar,Eigen::Dynamic,3>&,
const Eigen::Matrix<typename DerivedFC::Scalar, Eigen::Dynamic,3>&,
Eigen::Matrix<typename DerivedVC::Scalar,Eigen::Dynamic,3>&,
Eigen::Matrix<typename DerivedFC::Scalar, Eigen::Dynamic,3>&,
Eigen::Matrix<typename DerivedJ::Scalar, Eigen::Dynamic,1>&)>
& resolve_fun,
Eigen::PlainObjectBase<DerivedVC > & VC,
Eigen::PlainObjectBase<DerivedFC > & FC,
Eigen::PlainObjectBase<DerivedJ > & J)
{
using namespace Eigen;
using namespace std;
using namespace igl;
using namespace igl::cgal;
MeshBooleanType eff_type = type;
// Concatenate A and B into a single mesh
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::FT ExactScalar;
typedef typename DerivedVC::Scalar Scalar;
typedef typename DerivedFC::Scalar Index;
typedef Matrix<Scalar,Dynamic,3> MatrixX3S;
typedef Matrix<ExactScalar,Dynamic,3> MatrixX3ES;
typedef Matrix<Index,Dynamic,3> MatrixX3I;
typedef Matrix<Index,Dynamic,2> MatrixX2I;
typedef Matrix<Index,Dynamic,1> VectorXI;
typedef Matrix<typename DerivedJ::Scalar,Dynamic,1> VectorXJ;
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"mesh boolean..."<<endl;
#endif
MatrixX3S V(VA.rows()+VB.rows(),3);
MatrixX3I F(FA.rows()+FB.rows(),3);
V.block(0,0,VA.rows(),VA.cols()) = VA;
V.block(VA.rows(),0,VB.rows(),VB.cols()) = VB;
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"prepare selfintersect input..."<<endl;
#endif
switch(type)
{
// Minus is implemented by flipping B and computing union
case MESH_BOOLEAN_TYPE_MINUS:
F.block(0,0,FA.rows(),FA.cols()) = FA.rowwise().reverse();
F.block(FA.rows(),0,FB.rows(),FB.cols()) = FB.array()+VA.rows();
//F.block(0,0,FA.rows(),3) = FA;
//F.block(FA.rows(),0,FB.rows(),3) =
// FB.rowwise().reverse().array()+VA.rows();
eff_type = MESH_BOOLEAN_TYPE_INTERSECT;
break;
default:
F.block(0,0,FA.rows(),FA.cols()) = FA;
F.block(FA.rows(),0,FB.rows(),FB.cols()) = FB.array()+VA.rows();
break;
}
// Resolve intersections (assumes A and B are solid)
const auto & libigl_resolve = [](
const MatrixX3S & V,
const MatrixX3I & F,
MatrixX3ES & CV,
MatrixX3I & CF,
VectorXJ & J)
{
MatrixX3ES SV;
MatrixX3I SF;
MatrixX2I SIF;
VectorXI SIM,UIM;
igl::cgal::RemeshSelfIntersectionsParam params;
remesh_self_intersections(V,F,params,SV,SF,SIF,J,SIM);
for_each(SF.data(),SF.data()+SF.size(),[&SIM](int & a){a=SIM(a);});
{
remove_unreferenced(SV,SF,CV,CF,UIM);
}
};
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"resolve..."<<endl;
#endif
MatrixX3S CV;
MatrixX3ES EV;
MatrixX3I CF;
VectorXJ CJ;
if(resolve_fun)
{
resolve_fun(V,F,CV,CF,CJ);
}else
{
libigl_resolve(V,F,EV,CF,CJ);
CV.resize(EV.rows(), EV.cols());
std::transform(EV.data(), EV.data() + EV.rows()*EV.cols(),
CV.data(), [&](ExactScalar val) {
return CGAL::to_double(val);
});
}
if(type == MESH_BOOLEAN_TYPE_RESOLVE)
{
FC = CF;
VC = CV;
J = CJ;
return;
}
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"peel..."<<endl;
#endif
Matrix<bool,Dynamic,1> from_A(CF.rows());
// peel layers keeping track of odd and even flips
VectorXi I;
Matrix<bool,Dynamic,1> flip;
peel_outer_hull_layers(EV,CF,I,flip);
// 0 is "first" iteration, so it's odd
Array<bool,Dynamic,1> odd = igl::mod(I,2).array()==0;
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"categorize..."<<endl;
#endif
const Index m = CF.rows();
// Faces of output vG[i] = j means ith face of output should be jth face in F
std::vector<Index> vG;
// Whether faces of output should be flipped, Gflip[i] = true means ith face
// of output should be F.row(vG[i]).reverse() rather than F.row(vG[i])
std::vector<bool> Gflip;
for(Index f = 0;f<m;f++)
{
switch(eff_type)
{
case MESH_BOOLEAN_TYPE_XOR:
case MESH_BOOLEAN_TYPE_UNION:
if((odd(f)&&!flip(f))||(!odd(f)&&flip(f)))
{
vG.push_back(f);
Gflip.push_back(false);
}else if(eff_type == MESH_BOOLEAN_TYPE_XOR)
{
vG.push_back(f);
Gflip.push_back(true);
}
break;
case MESH_BOOLEAN_TYPE_INTERSECT:
if((!odd(f) && !flip(f)) || (odd(f) && flip(f)))
{
vG.push_back(f);
Gflip.push_back(type == MESH_BOOLEAN_TYPE_MINUS);
}
break;
default:
assert(false && "Unknown type");
return;
}
}
const Index gm = vG.size();
MatrixX3I G(gm,3);
VectorXi GJ(gm,1);
for(Index g = 0;g<gm;g++)
{
G.row(g) = Gflip[g] ? CF.row(vG[g]).reverse().eval() : CF.row(vG[g]);
GJ(g) = CJ(vG[g]);
}
#ifdef IGL_MESH_BOOLEAN_DEBUG
{
MatrixXd O;
boundary_facets(FC,O);
cout<<"# boundary: "<<O.rows()<<endl;
}
cout<<"# exterior: "<<exterior_edges(FC).rows()<<endl;
#endif
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"clean..."<<endl;
#endif
// Deal with duplicate faces
{
VectorXi IA,IC;
MatrixX3I uG;
unique_simplices(G,uG,IA,IC);
assert(IA.rows() == uG.rows());
// faces ontop of each unique face
vector<vector<Index> > uG2G(uG.rows());
// signed counts
VectorXi counts = VectorXi::Zero(uG.rows());
VectorXi ucounts = VectorXi::Zero(uG.rows());
// loop over all faces
for(Index g = 0;g<gm;g++)
{
const int ug = IC(g);
assert(ug < uG2G.size());
uG2G[ug].push_back(g);
// is uG(g,:) just a rotated version of G(g,:) ?
const bool consistent =
(G(g,0) == uG(ug,0) && G(g,1) == uG(ug,1) && G(g,2) == uG(ug,2)) ||
(G(g,0) == uG(ug,1) && G(g,1) == uG(ug,2) && G(g,2) == uG(ug,0)) ||
(G(g,0) == uG(ug,2) && G(g,1) == uG(ug,0) && G(g,2) == uG(ug,1));
counts(ug) += consistent ? 1 : -1;
ucounts(ug)++;
}
MatrixX3I oldG = G;
// Faces of output vG[i] = j means ith face of output should be jth face in
// oldG
vG.clear();
for(size_t ug = 0;ug < uG2G.size();ug++)
{
// if signed occurrences is zero or ±two then keep none
// else if signed occurrences is ±one then keep just one facet
switch(abs(counts(ug)))
{
case 1:
assert(uG2G[ug].size() > 0);
vG.push_back(uG2G[ug][0]);
#ifdef IGL_MESH_BOOLEAN_DEBUG
if(abs(ucounts(ug)) != 1)
{
cout<<"count,ucount of "<<counts(ug)<<","<<ucounts(ug)<<endl;
}
#endif
break;
case 0:
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"Skipping "<<uG2G[ug].size()<<" facets..."<<endl;
if(abs(ucounts(ug)) != 0)
{
cout<<"count,ucount of "<<counts(ug)<<","<<ucounts(ug)<<endl;
}
#endif
break;
default:
#ifdef IGL_MESH_BOOLEAN_DEBUG
cout<<"Didn't expect to be here."<<endl;
#endif
assert(false && "Shouldn't count be -1/0/1 ?");
}
}
G.resize(vG.size(),3);
J.resize(vG.size());
for(size_t g = 0;g<vG.size();g++)
{
G.row(g) = oldG.row(vG[g]);
J(g) = GJ(vG[g]);
}
}
// remove unreferenced vertices
VectorXi newIM;
remove_unreferenced(CV,G,VC,FC,newIM);
//cerr<<"warning not removing unref"<<endl;
//VC = CV;
//FC = G;
#ifdef IGL_MESH_BOOLEAN_DEBUG
{
MatrixXd O;
boundary_facets(FC,O);
cout<<"# boundary: "<<O.rows()<<endl;
}
cout<<"# exterior: "<<exterior_edges(FC).rows()<<endl;
#endif
}
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();
}
}
}
IGL_INLINE void igl::cotangent(
const Eigen::PlainObjectBase<DerivedV>& V,
const Eigen::PlainObjectBase<DerivedF>& F,
Eigen::PlainObjectBase<DerivedC>& C)
{
using namespace igl;
using namespace std;
using namespace Eigen;
// simplex size (3: triangles, 4: tetrahedra)
int simplex_size = F.cols();
// Number of elements
int m = F.rows();
// Law of cosines + law of sines
switch(simplex_size)
{
case 3:
{
// Triangles
//Matrix<typename DerivedC::Scalar,Dynamic,3> l;
//edge_lengths(V,F,l);
// edge lengths numbered same as opposite vertices
Matrix<typename DerivedC::Scalar,Dynamic,3> l;
igl::edge_lengths(V,F,l);
// double area
Matrix<typename DerivedC::Scalar,Dynamic,1> dblA;
doublearea(l,dblA);
// cotangents and diagonal entries for element matrices
// correctly divided by 4 (alec 2010)
C.resize(m,3);
for(int i = 0;i<m;i++)
{
C(i,0) = (l(i,1)*l(i,1) + l(i,2)*l(i,2) - l(i,0)*l(i,0))/dblA(i)/4.0;
C(i,1) = (l(i,2)*l(i,2) + l(i,0)*l(i,0) - l(i,1)*l(i,1))/dblA(i)/4.0;
C(i,2) = (l(i,0)*l(i,0) + l(i,1)*l(i,1) - l(i,2)*l(i,2))/dblA(i)/4.0;
}
break;
}
case 4:
{
// edge lengths numbered same as opposite vertices
Matrix<typename DerivedC::Scalar,Dynamic,6> l;
edge_lengths(V,F,l);
Matrix<typename DerivedC::Scalar,Dynamic,4> s;
face_areas(l,s);
Matrix<typename DerivedC::Scalar,Dynamic,6> cos_theta,theta;
dihedral_angles_intrinsic(l,s,theta,cos_theta);
// volume
Matrix<typename DerivedC::Scalar,Dynamic,1> vol;
volume(l,vol);
// Law of sines
// http://mathworld.wolfram.com/Tetrahedron.html
Matrix<typename DerivedC::Scalar,Dynamic,6> sin_theta(m,6);
sin_theta.col(0) = vol.array() / ((2./(3.*l.col(0).array())).array() * s.col(1).array() * s.col(2).array());
sin_theta.col(1) = vol.array() / ((2./(3.*l.col(1).array())).array() * s.col(2).array() * s.col(0).array());
sin_theta.col(2) = vol.array() / ((2./(3.*l.col(2).array())).array() * s.col(0).array() * s.col(1).array());
sin_theta.col(3) = vol.array() / ((2./(3.*l.col(3).array())).array() * s.col(3).array() * s.col(0).array());
sin_theta.col(4) = vol.array() / ((2./(3.*l.col(4).array())).array() * s.col(3).array() * s.col(1).array());
sin_theta.col(5) = vol.array() / ((2./(3.*l.col(5).array())).array() * s.col(3).array() * s.col(2).array());
// http://arxiv.org/pdf/1208.0354.pdf Page 18
C = (1./6.) * l.array() * cos_theta.array() / sin_theta.array();
break;
}
default:
{
fprintf(stderr,
"cotangent.h: Error: Simplex size (%d) not supported\n", simplex_size);
assert(false);
}
}
}
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::embree::bone_visible(
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
const EmbreeIntersector & ei,
const Eigen::PlainObjectBase<DerivedSD> & s,
const Eigen::PlainObjectBase<DerivedSD> & d,
Eigen::PlainObjectBase<Derivedflag> & flag)
{
using namespace std;
using namespace Eigen;
flag.resize(V.rows());
const double sd_norm = (s-d).norm();
// Embree seems to be parallel when constructing but not when tracing rays
#pragma omp parallel for
// loop over mesh vertices
for(int v = 0;v<V.rows();v++)
{
const Vector3d Vv = V.row(v);
// Project vertex v onto line segment sd
//embree.intersectSegment
double t,sqrd;
Vector3d projv;
// degenerate bone, just snap to s
if(sd_norm < DOUBLE_EPS)
{
t = 0;
sqrd = (Vv-s).array().pow(2).sum();
projv = s;
}else
{
// project onto (infinite) line
project_to_line(
Vv(0),Vv(1),Vv(2),s(0),s(1),s(2),d(0),d(1),d(2),
projv(0),projv(1),projv(2),t,sqrd);
// handle projections past endpoints
if(t<0)
{
t = 0;
sqrd = (Vv-s).array().pow(2).sum();
projv = s;
} else if(t>1)
{
t = 1;
sqrd = (Vv-d).array().pow(2).sum();
projv = d;
}
}
igl::Hit hit;
// perhaps 1.0 should be 1.0-epsilon, or actually since we checking the
// incident face, perhaps 1.0 should be 1.0+eps
const Vector3d dir = (Vv-projv)*1.0;
if(ei.intersectSegment(
projv.template cast<float>(),
dir.template cast<float>(),
hit))
{
// mod for double sided lighting
const int fi = hit.id % F.rows();
//if(v == 1228-1)
//{
// Vector3d bc,P;
// bc << 1 - hit.u - hit.v, hit.u, hit.v; // barycentric
// P = V.row(F(fi,0))*bc(0) +
// V.row(F(fi,1))*bc(1) +
// V.row(F(fi,2))*bc(2);
// cout<<(fi+1)<<endl;
// cout<<bc.transpose()<<endl;
// cout<<P.transpose()<<endl;
// cout<<hit.t<<endl;
// cout<<(projv + dir*hit.t).transpose()<<endl;
// cout<<Vv.transpose()<<endl;
//}
// Assume hit is valid, so not visible
flag(v) = false;
// loop around corners of triangle
for(int c = 0;c<F.cols();c++)
{
if(F(fi,c) == v)
{
// hit self, so no hits before, so vertex v is visible
flag(v) = true;
break;
}
}
// Hit is actually past v
if(!flag(v) && (hit.t*hit.t*dir.squaredNorm())>sqrd)
{
flag(v) = true;
}
}else
{
// no hit so vectex v is visible
flag(v) = true;
}
}
}
IGL_INLINE bool igl::writePLY(
const std::string & filename,
const Eigen::PlainObjectBase<DerivedV> & V,
const Eigen::PlainObjectBase<DerivedF> & F,
const Eigen::PlainObjectBase<DerivedN> & N,
const Eigen::PlainObjectBase<DerivedUV> & UV,
const bool ascii)
{
// Largely based on obj2ply.c
typedef struct Vertex
{
double x,y,z,w; /* position */
double nx,ny,nz; /* surface normal */
double s,t; /* texture coordinates */
} Vertex;
typedef struct Face
{
unsigned char nverts; /* number of vertex indices in list */
int *verts; /* vertex index list */
} Face;
PlyProperty vert_props[] =
{ /* list of property information for a vertex */
{"x", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,x), 0, 0, 0, 0},
{"y", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,y), 0, 0, 0, 0},
{"z", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,z), 0, 0, 0, 0},
{"nx", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,nx), 0, 0, 0, 0},
{"ny", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,ny), 0, 0, 0, 0},
{"nz", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,nz), 0, 0, 0, 0},
{"s", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,s), 0, 0, 0, 0},
{"t", PLY_DOUBLE, PLY_DOUBLE, offsetof(Vertex,t), 0, 0, 0, 0},
};
PlyProperty face_props[] =
{ /* list of property information for a face */
{"vertex_indices", PLY_INT, PLY_INT, offsetof(Face,verts),
1, PLY_UCHAR, PLY_UCHAR, offsetof(Face,nverts)},
};
const bool has_normals = N.rows() > 0;
const bool has_texture_coords = UV.rows() > 0;
std::vector<Vertex> vlist(V.rows());
std::vector<Face> flist(F.rows());
for(size_t i = 0;i<(size_t)V.rows();i++)
{
vlist[i].x = V(i,0);
vlist[i].y = V(i,1);
vlist[i].z = V(i,2);
if(has_normals)
{
vlist[i].nx = N(i,0);
vlist[i].ny = N(i,1);
vlist[i].nz = N(i,2);
}
if(has_texture_coords)
{
vlist[i].s = UV(i,0);
vlist[i].t = UV(i,1);
}
}
for(size_t i = 0;i<(size_t)F.rows();i++)
{
flist[i].nverts = F.cols();
flist[i].verts = new int[F.cols()];
for(size_t c = 0;c<(size_t)F.cols();c++)
{
flist[i].verts[c] = F(i,c);
}
}
const char * elem_names[] = {"vertex","face"};
FILE * fp = fopen(filename.c_str(),"w");
if(fp==NULL)
{
return false;
}
PlyFile * ply = ply_write(fp, 2,elem_names,
(ascii ? PLY_ASCII : PLY_BINARY_LE));
if(ply==NULL)
{
return false;
}
std::vector<PlyProperty> plist;
plist.push_back(vert_props[0]);
plist.push_back(vert_props[1]);
plist.push_back(vert_props[2]);
if (has_normals)
{
plist.push_back(vert_props[3]);
plist.push_back(vert_props[4]);
plist.push_back(vert_props[5]);
}
if (has_texture_coords)
{
plist.push_back(vert_props[6]);
plist.push_back(vert_props[7]);
}
ply_describe_element(ply, "vertex", V.rows(),plist.size(),
&plist[0]);
ply_describe_element(ply, "face", F.rows(),1,&face_props[0]);
ply_header_complete(ply);
ply_put_element_setup(ply, "vertex");
for(const auto v : vlist)
{
ply_put_element(ply, (void *) &v);
}
ply_put_element_setup(ply, "face");
for(const auto f : flist)
{
ply_put_element(ply, (void *) &f);
}
ply_close(ply);
for(size_t i = 0;i<(size_t)F.rows();i++)
{
delete[] flist[i].verts;
}
return true;
}
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];
}
}
}
}
}