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#include "fast_winding_number.h"
#include "octree.h"
#include "knn.h"
#include "parallel_for.h"
#include "PI.h"
#include <vector>
namespace igl {
template <typename DerivedP, typename DerivedA, typename DerivedN,
typename Index, typename DerivedCH, typename DerivedCM, typename DerivedR,
typename DerivedEC>
IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
const Eigen::MatrixBase<DerivedN>& N,
const Eigen::MatrixBase<DerivedA>& A,
const std::vector<std::vector<Index> > & point_indices,
const Eigen::MatrixBase<DerivedCH>& CH,
const int expansion_order,
Eigen::PlainObjectBase<DerivedCM>& CM,
Eigen::PlainObjectBase<DerivedR>& R,
Eigen::PlainObjectBase<DerivedEC>& EC)
{
typedef typename DerivedP::Scalar real_p;
typedef typename DerivedN::Scalar real_n;
typedef typename DerivedA::Scalar real_a;
typedef typename DerivedCM::Scalar real_cm;
typedef typename DerivedR::Scalar real_r;
typedef typename DerivedEC::Scalar real_ec;
typedef Eigen::Matrix<real_p,1,3> RowVec3p;
int m = CH.size();
int num_terms;
assert(expansion_order < 3 && expansion_order >= 0 && "m must be less than n");
if(expansion_order == 0){
num_terms = 3;
} else if(expansion_order ==1){
num_terms = 3 + 9;
} else if(expansion_order == 2){
num_terms = 3 + 9 + 27;
}
R.resize(m);
CM.resize(m,3);
EC.resize(m,num_terms);
EC.setZero(m,num_terms);
std::function< void(const int) > helper;
helper = [&helper,
&P,&N,&A,&expansion_order,&point_indices,&CH,&EC,&R,&CM]
(const int index)-> void
{
Eigen::Matrix<real_cm,1,3> masscenter;
masscenter << 0,0,0;
Eigen::Matrix<real_ec,1,3> zeroth_expansion;
zeroth_expansion << 0,0,0;
real_p areatotal = 0.0;
for(int j = 0; j < point_indices.at(index).size(); j++){
int curr_point_index = point_indices.at(index).at(j);
areatotal += A(curr_point_index);
masscenter += A(curr_point_index)*P.row(curr_point_index);
zeroth_expansion += A(curr_point_index)*N.row(curr_point_index);
}
masscenter = masscenter/areatotal;
CM.row(index) = masscenter;
EC.block(index,0,1,3) = zeroth_expansion;
real_r max_norm = 0;
real_r curr_norm;
for(int i = 0; i < point_indices.at(index).size(); i++){
//Get max distance from center of mass:
int curr_point_index = point_indices.at(index).at(i);
Eigen::Matrix<real_r,1,3> point =
P.row(curr_point_index)-masscenter;
curr_norm = point.norm();
if(curr_norm > max_norm){
max_norm = curr_norm;
}
//Calculate higher order terms if necessary
Eigen::Matrix<real_ec,3,3> TempCoeffs;
if(EC.cols() >= (3+9)){
TempCoeffs = A(curr_point_index)*point.transpose()*
N.row(curr_point_index);
EC.block(index,3,1,9) +=
Eigen::Map<Eigen::Matrix<real_ec,1,9> >(TempCoeffs.data(),
TempCoeffs.size());
}
if(EC.cols() == (3+9+27)){
for(int k = 0; k < 3; k++){
TempCoeffs = 0.5 * point(k) * (A(curr_point_index)*
point.transpose()*N.row(curr_point_index));
EC.block(index,12+9*k,1,9) += Eigen::Map<
Eigen::Matrix<real_ec,1,9> >(TempCoeffs.data(),
TempCoeffs.size());
}
}
}
R(index) = max_norm;
if(CH(index,0) != -1)
{
for(int i = 0; i < 8; i++){
int child = CH(index,i);
helper(child);
}
}
};
helper(0);
}
template <typename DerivedP, typename DerivedA, typename DerivedN,
typename Index, typename DerivedCH, typename DerivedCM, typename DerivedR,
typename DerivedEC, typename DerivedQ, typename BetaType,
typename DerivedWN>
IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
const Eigen::MatrixBase<DerivedN>& N,
const Eigen::MatrixBase<DerivedA>& A,
const std::vector<std::vector<Index> > & point_indices,
const Eigen::MatrixBase<DerivedCH>& CH,
const Eigen::MatrixBase<DerivedCM>& CM,
const Eigen::MatrixBase<DerivedR>& R,
const Eigen::MatrixBase<DerivedEC>& EC,
const Eigen::MatrixBase<DerivedQ>& Q,
const BetaType beta,
Eigen::PlainObjectBase<DerivedWN>& WN){
typedef typename DerivedP::Scalar real_p;
typedef typename DerivedN::Scalar real_n;
typedef typename DerivedA::Scalar real_a;
typedef typename DerivedCM::Scalar real_cm;
typedef typename DerivedR::Scalar real_r;
typedef typename DerivedEC::Scalar real_ec;
typedef typename DerivedQ::Scalar real_q;
typedef typename DerivedWN::Scalar real_wn;
typedef Eigen::Matrix<real_q,1,3> RowVec;
typedef Eigen::Matrix<real_ec,3,3> EC_3by3;
auto direct_eval = [](const RowVec & loc,
const Eigen::Matrix<real_ec,1,3> & anorm){
real_wn wn = (loc(0)*anorm(0)+loc(1)*anorm(1)+loc(2)*anorm(2))
/(4.0*igl::PI*std::pow(loc.norm(),3));
if(std::isnan(wn)){
return 0.5;
}else{
return wn;
}
};
auto expansion_eval = [&direct_eval](const RowVec & loc,
const Eigen::RowVectorXd & EC){
real_wn wn = direct_eval(loc,EC.head<3>());
double r = loc.norm();
if(EC.size()>3){
Eigen::Matrix<real_ec,3,3> SecondDerivative =
Eigen::Matrix<real_ec,3,3>::Identity()/(4.0*igl::PI*std::pow(r,3));
SecondDerivative += -3.0*loc.transpose()*loc/(4.0*igl::PI*std::pow(r,5));
Eigen::Matrix<real_ec,1,9> derivative_vector =
Eigen::Map<Eigen::Matrix<real_ec,1,9> >(SecondDerivative.data(),
SecondDerivative.size());
wn += derivative_vector.cwiseProduct(EC.segment<9>(3)).sum();
}
if(EC.size()>3+9){
Eigen::Matrix<real_ec,3,3> ThirdDerivative;
for(int i = 0; i < 3; i++){
ThirdDerivative =
15.0*loc(i)*loc.transpose()*loc/(4.0*igl::PI*std::pow(r,7));
Eigen::Matrix<real_ec,3,3> Diagonal;
Diagonal << loc(i), 0, 0,
0, loc(i), 0,
0, 0, loc(i);
Eigen::Matrix<real_ec,3,3> RowCol;
RowCol.setZero(3,3);
RowCol.row(i) = loc;
Eigen::Matrix<real_ec,3,3> RowColT = RowCol.transpose();
RowCol = RowCol + RowColT;
ThirdDerivative +=
-3.0/(4.0*igl::PI*std::pow(r,5))*(RowCol+Diagonal);
Eigen::Matrix<real_ec,1,9> derivative_vector =
Eigen::Map<Eigen::Matrix<real_ec,1,9> >(ThirdDerivative.data(),
ThirdDerivative.size());
wn += derivative_vector.cwiseProduct(
EC.segment<9>(12 + i*9)).sum();
}
}
return wn;
};
int m = Q.rows();
WN.resize(m,1);
std::function< real_wn(const RowVec, const std::vector<int>) > helper;
helper = [&helper,
&P,&N,&A,
&point_indices,&CH,
&CM,&R,&EC,&beta,
&direct_eval,&expansion_eval]
(const RowVec query, const std::vector<int> near_indices)-> real_wn
{
std::vector<int> new_near_indices;
real_wn wn = 0;
for(int i = 0; i < near_indices.size(); i++){
int index = near_indices.at(i);
//Leaf Case, Brute force
if(CH(index,0) == -1){
for(int j = 0; j < point_indices.at(index).size(); j++){
int curr_row = point_indices.at(index).at(j);
wn += direct_eval(P.row(curr_row)-query,
N.row(curr_row)*A(curr_row));
}
}
//Non-Leaf Case
else {
for(int child = 0; child < 8; child++){
int child_index = CH(index,child);
if(point_indices.at(child_index).size() > 0){
if((CM.row(child_index)-query).norm() > beta*R(child_index)){
if(CH(child_index,0) == -1){
for(int j=0;j<point_indices.at(child_index).size();j++){
int curr_row = point_indices.at(child_index).at(j);
wn += direct_eval(P.row(curr_row)-query,
N.row(curr_row)*A(curr_row));
}
}else{
wn += expansion_eval(CM.row(child_index)-query,
EC.row(child_index));
}
}else {
new_near_indices.emplace_back(child_index);
}
}
}
}
}
if(new_near_indices.size() > 0){
wn += helper(query,new_near_indices);
}
return wn;
};
if(beta > 0){
std::vector<int> near_indices_start = {0};
igl::parallel_for(m,[&](int iter){
WN(iter) = helper(Q.row(iter),near_indices_start);
},1000);
} else {
igl::parallel_for(m,[&](int iter){
double wn = 0;
for(int j = 0; j <P.rows(); j++){
wn += direct_eval(P.row(j)-Q.row(iter),N.row(j)*A(j));
}
WN(iter) = wn;
},1000);
}
}
template <typename DerivedP, typename DerivedA, typename DerivedN,
typename DerivedQ, typename BetaType, typename DerivedWN>
IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
const Eigen::MatrixBase<DerivedN>& N,
const Eigen::MatrixBase<DerivedA>& A,
const Eigen::MatrixBase<DerivedQ>& Q,
const int expansion_order,
const BetaType beta,
Eigen::PlainObjectBase<DerivedWN>& WN
){
typedef typename DerivedWN::Scalar real;
std::vector<std::vector<int> > point_indices;
Eigen::Matrix<int,Eigen::Dynamic,8> CH;
Eigen::Matrix<real,Eigen::Dynamic,3> CN;
Eigen::Matrix<real,Eigen::Dynamic,1> W;
octree(P,point_indices,CH,CN,W);
Eigen::Matrix<real,Eigen::Dynamic,Eigen::Dynamic> EC;
Eigen::Matrix<real,Eigen::Dynamic,3> CM;
Eigen::Matrix<real,Eigen::Dynamic,1> R;
fast_winding_number(P,N,A,point_indices,CH,expansion_order,CM,R,EC);
fast_winding_number(P,N,A,point_indices,CH,CM,R,EC,Q,beta,WN);
}
template <typename DerivedP, typename DerivedA, typename DerivedN,
typename DerivedQ, typename DerivedWN>
IGL_INLINE void fast_winding_number(const Eigen::MatrixBase<DerivedP>& P,
const Eigen::MatrixBase<DerivedN>& N,
const Eigen::MatrixBase<DerivedA>& A,
const Eigen::MatrixBase<DerivedQ>& Q,
Eigen::PlainObjectBase<DerivedWN>& WN
){
fast_winding_number(P,N,A,Q,2,2.0,WN);
}
}
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