bool MatrixXr_pseudoInverse(const MatrixXr &a, MatrixXr &a_pinv, double epsilon) {
// see : http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#The_general_case_and_the_SVD_method
if ( a.rows()<a.cols() ) return false;
// SVD
Eigen::JacobiSVD<MatrixXr> svdA;
svdA.compute(a,Eigen::ComputeThinU|Eigen::ComputeThinV);
MatrixXr vSingular = svdA.singularValues();
// Build a diagonal matrix with the Inverted Singular values
// The pseudo inverted singular matrix is easy to compute :
// is formed by replacing every nonzero entry by its reciprocal (inversing).
VectorXr vPseudoInvertedSingular(svdA.matrixV().cols(),1);
for (int iRow =0; iRow<vSingular.rows(); iRow++) {
if(fabs(vSingular(iRow))<=epsilon) vPseudoInvertedSingular(iRow,0)=0.;
else vPseudoInvertedSingular(iRow,0)=1./vSingular(iRow);
}
// A little optimization here
MatrixXr mAdjointU = svdA.matrixU().adjoint().block(0,0,vSingular.rows(),svdA.matrixU().adjoint().cols());
// Pseudo-Inversion : V * S * U'
a_pinv = (svdA.matrixV() * vPseudoInvertedSingular.asDiagonal()) * mAdjointU;
return true;
}
void projectorFromSvd(const Eigen::MatrixXd& jac,
Eigen::JacobiSVD<Eigen::MatrixXd>& svd,
Eigen::VectorXd& svdSingular,
Eigen::MatrixXd& preResult,
Eigen::MatrixXd& result,
double epsilon=std::numeric_limits<double>::epsilon(),
double minTol=1e-8)
{
// we are force to compute the Full matrix because of
// the nullspace matrix computation
svd.compute(jac, Eigen::ComputeFullU | Eigen::ComputeFullV);
double tolerance =
epsilon*double(std::max(jac.cols(), jac.rows()))*
std::abs(svd.singularValues()[0]);
tolerance = std::max(tolerance, minTol);
svdSingular.setOnes();
for(int i = 0; i < svd.singularValues().rows(); ++i)
{
svdSingular[i] = svd.singularValues()[i] > tolerance ? 0. : 1.;
}
preResult.noalias() = svd.matrixV()*svdSingular.asDiagonal();
result.noalias() = preResult*svd.matrixV().adjoint();
}
// Assume t = double[3], q = double[4]
void EstimateTfSVD(double* t, double* q)
{
// Assemble the correlation matrix H = target * reference'
Eigen::Matrix3d H = (cloud_tgt_demean * cloud_ref_demean.transpose ()).topLeftCorner<3, 3>();
// Compute the Singular Value Decomposition
Eigen::JacobiSVD<Eigen::Matrix3d> svd (H, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix3d u = svd.matrixU ();
Eigen::Matrix3d v = svd.matrixV ();
// Compute R = V * U'
if (u.determinant () * v.determinant () < 0)
{
for (int i = 0; i < 3; ++i)
v (i, 2) *= -1;
}
// std::cout<< "centroid_src: "<<centroid_src(0) <<" "<< centroid_src(1) <<" "<< centroid_src(2) << " "<< centroid_src(3)<<std::endl;
// std::cout<< "centroid_tgt: "<<centroid_tgt(0) <<" "<< centroid_tgt(1) <<" "<< centroid_tgt(2) << " "<< centroid_tgt(3)<<std::endl;
Eigen::Matrix3d R = v * u.transpose ();
const Eigen::Vector3d Rc (R * centroid_tgt.head<3> ());
Eigen::Vector3d T = centroid_ref.head<3> () - Rc;
// Make sure these memory locations are valid
assert(t != NULL && q!=NULL);
Eigen::Quaterniond Q(R);
t[0] = T(0); t[1] = T(1); t[2] = T(2);
q[0] = Q.w(); q[1] = Q.x(); q[2] = Q.y(); q[3] = Q.z();
}
template <typename PointSource, typename PointTarget, typename Scalar> void
pcl::registration::TransformationEstimationSVD<PointSource, PointTarget, Scalar>::getTransformationFromCorrelation (
const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> &cloud_src_demean,
const Eigen::Matrix<Scalar, 4, 1> ¢roid_src,
const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> &cloud_tgt_demean,
const Eigen::Matrix<Scalar, 4, 1> ¢roid_tgt,
Matrix4 &transformation_matrix) const
{
transformation_matrix.setIdentity ();
// Assemble the correlation matrix H = source * target'
Eigen::Matrix<Scalar, 3, 3> H = (cloud_src_demean * cloud_tgt_demean.transpose ()).topLeftCorner (3, 3);
// Compute the Singular Value Decomposition
Eigen::JacobiSVD<Eigen::Matrix<Scalar, 3, 3> > svd (H, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix<Scalar, 3, 3> u = svd.matrixU ();
Eigen::Matrix<Scalar, 3, 3> v = svd.matrixV ();
// Compute R = V * U'
if (u.determinant () * v.determinant () < 0)
{
for (int x = 0; x < 3; ++x)
v (x, 2) *= -1;
}
Eigen::Matrix<Scalar, 3, 3> R = v * u.transpose ();
// Return the correct transformation
transformation_matrix.topLeftCorner (3, 3) = R;
const Eigen::Matrix<Scalar, 3, 1> Rc (R * centroid_src.head (3));
transformation_matrix.block (0, 3, 3, 1) = centroid_tgt.head (3) - Rc;
}
template <typename PointSource, typename PointTarget> void
pcl::registration::TransformationEstimationSVD<PointSource, PointTarget>::getTransformationFromCorrelation (
const Eigen::MatrixXf &cloud_src_demean,
const Eigen::Vector4f ¢roid_src,
const Eigen::MatrixXf &cloud_tgt_demean,
const Eigen::Vector4f ¢roid_tgt,
Eigen::Matrix4f &transformation_matrix)
{
transformation_matrix.setIdentity ();
// Assemble the correlation matrix H = source * target'
Eigen::Matrix3f H = (cloud_src_demean * cloud_tgt_demean.transpose ()).topLeftCorner<3, 3>();
// Compute the Singular Value Decomposition
Eigen::JacobiSVD<Eigen::Matrix3f> svd (H, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix3f u = svd.matrixU ();
Eigen::Matrix3f v = svd.matrixV ();
// Compute R = V * U'
if (u.determinant () * v.determinant () < 0)
{
for (int x = 0; x < 3; ++x)
v (x, 2) *= -1;
}
Eigen::Matrix3f R = v * u.transpose ();
// Return the correct transformation
transformation_matrix.topLeftCorner<3, 3> () = R;
Eigen::Vector3f Rc = R * centroid_src.head<3> ();
transformation_matrix.block <3, 1> (0, 3) = centroid_tgt.head<3> () - Rc;
}
void pose_estimation_3d3d (
const vector<Point3f>& pts1,
const vector<Point3f>& pts2,
Mat& R, Mat& t
)
{
Point3f p1, p2; // center of mass
int N = pts1.size();
for ( int i=0; i<N; i++ )
{
p1 += pts1[i];
p2 += pts2[i];
}
p1 = Point3f( Vec3f(p1) / N);
p2 = Point3f( Vec3f(p2) / N);
vector<Point3f> q1 ( N ), q2 ( N ); // remove the center
for ( int i=0; i<N; i++ )
{
q1[i] = pts1[i] - p1;
q2[i] = pts2[i] - p2;
}
// compute q1*q2^T
Eigen::Matrix3d W = Eigen::Matrix3d::Zero();
for ( int i=0; i<N; i++ )
{
W += Eigen::Vector3d ( q1[i].x, q1[i].y, q1[i].z ) * Eigen::Vector3d ( q2[i].x, q2[i].y, q2[i].z ).transpose();
}
cout<<"W="<<W<<endl;
// SVD on W
Eigen::JacobiSVD<Eigen::Matrix3d> svd ( W, Eigen::ComputeFullU|Eigen::ComputeFullV );
Eigen::Matrix3d U = svd.matrixU();
Eigen::Matrix3d V = svd.matrixV();
if (U.determinant() * V.determinant() < 0)
{
for (int x = 0; x < 3; ++x)
{
U(x, 2) *= -1;
}
}
cout<<"U="<<U<<endl;
cout<<"V="<<V<<endl;
Eigen::Matrix3d R_ = U* ( V.transpose() );
Eigen::Vector3d t_ = Eigen::Vector3d ( p1.x, p1.y, p1.z ) - R_ * Eigen::Vector3d ( p2.x, p2.y, p2.z );
// convert to cv::Mat
R = ( Mat_<double> ( 3,3 ) <<
R_ ( 0,0 ), R_ ( 0,1 ), R_ ( 0,2 ),
R_ ( 1,0 ), R_ ( 1,1 ), R_ ( 1,2 ),
R_ ( 2,0 ), R_ ( 2,1 ), R_ ( 2,2 )
);
t = ( Mat_<double> ( 3,1 ) << t_ ( 0,0 ), t_ ( 1,0 ), t_ ( 2,0 ) );
}
// Derived from code by Yohann Solaro ( http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2010/01/msg00187.html )
// see : http://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#The_general_case_and_the_SVD_method
Eigen::MatrixXd pinv( const Eigen::MatrixXd &b, double rcond )
{
// TODO: Figure out why it wants fewer rows than columns
// if ( a.rows()<a.cols() )
// return false;
bool flip = false;
Eigen::MatrixXd a;
if( a.rows() < a.cols() )
{
a = b.transpose();
flip = true;
}
else
a = b;
// SVD
Eigen::JacobiSVD<Eigen::MatrixXd> svdA;
svdA.compute( a, Eigen::ComputeFullU | Eigen::ComputeThinV );
Eigen::JacobiSVD<Eigen::MatrixXd>::SingularValuesType vSingular = svdA.singularValues();
// Build a diagonal matrix with the Inverted Singular values
// The pseudo inverted singular matrix is easy to compute :
// is formed by replacing every nonzero entry by its reciprocal (inversing).
Eigen::VectorXd vPseudoInvertedSingular( svdA.matrixV().cols() );
for (int iRow=0; iRow<vSingular.rows(); iRow++)
{
if ( fabs(vSingular(iRow)) <= rcond )
{
vPseudoInvertedSingular(iRow)=0.;
}
else
vPseudoInvertedSingular(iRow)=1./vSingular(iRow);
}
// A little optimization here
Eigen::MatrixXd mAdjointU = svdA.matrixU().adjoint().block( 0, 0, vSingular.rows(), svdA.matrixU().adjoint().cols() );
// Pseudo-Inversion : V * S * U'
Eigen::MatrixXd a_pinv = (svdA.matrixV() * vPseudoInvertedSingular.asDiagonal()) * mAdjointU;
if( flip )
{
a = a.transpose();
a_pinv = a_pinv.transpose();
}
return a_pinv;
}
template <typename PointSource, typename PointTarget, typename Scalar> void
pcl::registration::TransformationEstimationSVDScale<PointSource, PointTarget, Scalar>::getTransformationFromCorrelation (
const Eigen::MatrixXf &cloud_src_demean,
const Eigen::Vector4f ¢roid_src,
const Eigen::MatrixXf &cloud_tgt_demean,
const Eigen::Vector4f ¢roid_tgt,
Matrix4 &transformation_matrix) const
{
transformation_matrix.setIdentity ();
// Assemble the correlation matrix H = source * target'
Eigen::Matrix<Scalar, 3, 3> H = (cloud_src_demean.cast<Scalar> () * cloud_tgt_demean.cast<Scalar> ().transpose ()).topLeftCorner (3, 3);
// Compute the Singular Value Decomposition
Eigen::JacobiSVD<Eigen::Matrix<Scalar, 3, 3> > svd (H, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix<Scalar, 3, 3> u = svd.matrixU ();
Eigen::Matrix<Scalar, 3, 3> v = svd.matrixV ();
// Compute R = V * U'
if (u.determinant () * v.determinant () < 0)
{
for (int x = 0; x < 3; ++x)
v (x, 2) *= -1;
}
Eigen::Matrix<Scalar, 3, 3> R = v * u.transpose ();
// rotated cloud
Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> src_ = R * cloud_src_demean.cast<Scalar> ();
float scale1, scale2;
double sum_ss = 0.0f, sum_tt = 0.0f, sum_tt_ = 0.0f;
for (unsigned corrIdx = 0; corrIdx < cloud_src_demean.cols (); ++corrIdx)
{
sum_ss += cloud_src_demean (0, corrIdx) * cloud_src_demean (0, corrIdx);
sum_ss += cloud_src_demean (1, corrIdx) * cloud_src_demean (1, corrIdx);
sum_ss += cloud_src_demean (2, corrIdx) * cloud_src_demean (2, corrIdx);
sum_tt += cloud_tgt_demean (0, corrIdx) * cloud_tgt_demean (0, corrIdx);
sum_tt += cloud_tgt_demean (1, corrIdx) * cloud_tgt_demean (1, corrIdx);
sum_tt += cloud_tgt_demean (2, corrIdx) * cloud_tgt_demean (2, corrIdx);
sum_tt_ += cloud_tgt_demean (0, corrIdx) * src_ (0, corrIdx);
sum_tt_ += cloud_tgt_demean (1, corrIdx) * src_ (1, corrIdx);
sum_tt_ += cloud_tgt_demean (2, corrIdx) * src_ (2, corrIdx);
}
scale1 = sqrt (sum_tt / sum_ss);
scale2 = sum_tt_ / sum_ss;
float scale = scale2;
transformation_matrix.topLeftCorner (3, 3) = scale * R;
const Eigen::Matrix<Scalar, 3, 1> Rc (R * centroid_src.cast<Scalar> ().head (3));
transformation_matrix.block (0, 3, 3, 1) = centroid_tgt.cast<Scalar> (). head (3) - Rc;
}
/**
* estimateRigidTransformationSVD
*/
void RigidTransformationRANSAC::estimateRigidTransformationSVD(
const std::vector<Eigen::Vector3f > &srcPts,
const std::vector<int> &srcIndices,
const std::vector<Eigen::Vector3f > &tgtPts,
const std::vector<int> &tgtIndices,
Eigen::Matrix4f &transform)
{
Eigen::Vector3f srcCentroid, tgtCentroid;
// compute the centroids of source, target
ComputeCentroid (srcPts, srcIndices, srcCentroid);
ComputeCentroid (tgtPts, tgtIndices, tgtCentroid);
// Subtract the centroids from source, target
Eigen::MatrixXf srcPtsDemean;
DemeanPoints(srcPts, srcIndices, srcCentroid, srcPtsDemean);
Eigen::MatrixXf tgtPtsDemean;
DemeanPoints(tgtPts, tgtIndices, tgtCentroid, tgtPtsDemean);
// Assemble the correlation matrix H = source * target'
Eigen::Matrix3f H = (srcPtsDemean * tgtPtsDemean.transpose ()).topLeftCorner<3, 3>();
// Singular Value Decomposition
Eigen::JacobiSVD<Eigen::Matrix3f> svd (H, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix3f u = svd.matrixU ();
Eigen::Matrix3f v = svd.matrixV ();
// Compute R = V * U'
if (u.determinant () * v.determinant () < 0)
{
for (int x = 0; x < 3; ++x)
v (x, 2) *= -1;
}
// Return the transformation
Eigen::Matrix3f R = v * u.transpose ();
Eigen::Vector3f t = tgtCentroid - R * srcCentroid;
// set rotation
transform.block(0,0,3,3) = R;
// set translation
transform.block(0,3,3,1) = t;
transform.block(3, 0, 1, 3).setZero();
transform(3,3) = 1.;
}
template <typename PointT> void
pcl::SampleConsensusModelRegistration<PointT>::estimateRigidTransformationSVD (
const pcl::PointCloud<PointT> &cloud_src,
const std::vector<int> &indices_src,
const pcl::PointCloud<PointT> &cloud_tgt,
const std::vector<int> &indices_tgt,
Eigen::VectorXf &transform)
{
transform.resize (16);
Eigen::Vector4f centroid_src, centroid_tgt;
// Estimate the centroids of source, target
compute3DCentroid (cloud_src, indices_src, centroid_src);
compute3DCentroid (cloud_tgt, indices_tgt, centroid_tgt);
// Subtract the centroids from source, target
Eigen::MatrixXf cloud_src_demean;
demeanPointCloud (cloud_src, indices_src, centroid_src, cloud_src_demean);
Eigen::MatrixXf cloud_tgt_demean;
demeanPointCloud (cloud_tgt, indices_tgt, centroid_tgt, cloud_tgt_demean);
// Assemble the correlation matrix H = source * target'
Eigen::Matrix3f H = (cloud_src_demean * cloud_tgt_demean.transpose ()).topLeftCorner<3, 3>();
// Compute the Singular Value Decomposition
Eigen::JacobiSVD<Eigen::Matrix3f> svd (H, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix3f u = svd.matrixU ();
Eigen::Matrix3f v = svd.matrixV ();
// Compute R = V * U'
if (u.determinant () * v.determinant () < 0)
{
for (int x = 0; x < 3; ++x)
v (x, 2) *= -1;
}
Eigen::Matrix3f R = v * u.transpose ();
// Return the correct transformation
transform.segment<3> (0) = R.row (0); transform[12] = 0;
transform.segment<3> (4) = R.row (1); transform[13] = 0;
transform.segment<3> (8) = R.row (2); transform[14] = 0;
Eigen::Vector3f t = centroid_tgt.head<3> () - R * centroid_src.head<3> ();
transform[3] = t[0]; transform[7] = t[1]; transform[11] = t[2]; transform[15] = 1.0;
}
int main() {
std::ifstream file;
file.open("SVD_benchmark");
if (!file)
{
CGAL_TRACE_STREAM << "Error loading file!\n";
return 0;
}
int ite = 200000;
Eigen::JacobiSVD<Eigen::Matrix3d> svd;
Eigen::Matrix3d u, v, cov, r;
Eigen::Vector3d w;
int matrix_idx = rand()%200;
for (int i = 0; i < matrix_idx; i++)
{
for (int j = 0; j < 3; j++)
{
for (int k = 0; k < 3; k++)
{
file >> cov(j, k);
}
}
}
CGAL::Timer task_timer;
CGAL_TRACE_STREAM << "Start SVD decomposition...";
task_timer.start();
for (int i = 0; i < ite; i++)
{
svd.compute( cov, Eigen::ComputeFullU | Eigen::ComputeFullV );
u = svd.matrixU(); v = svd.matrixV(); w = svd.singularValues();
r = v*u.transpose();
}
task_timer.stop();
file.close();
CGAL_TRACE_STREAM << "done: " << task_timer.time() << "s\n";
return 0;
}
const CPoint3DCAMERA CMiniVisionToolbox::getPointStereoLinearTriangulationSVDDLT( const cv::Point2d& p_ptPointLEFT, const cv::Point2d& p_ptPointRIGHT, const Eigen::Matrix< double, 3, 4 >& p_matProjectionLEFT, const Eigen::Matrix< double, 3, 4 >& p_matProjectionRIGHT )
{
//ds A matrix for system: A*X=0
Eigen::Matrix4d matAHomogeneous;
matAHomogeneous.row(0) = p_ptPointLEFT.x*p_matProjectionLEFT.row(2)-p_matProjectionLEFT.row(0);
matAHomogeneous.row(1) = p_ptPointLEFT.y*p_matProjectionLEFT.row(2)-p_matProjectionLEFT.row(1);
matAHomogeneous.row(2) = p_ptPointRIGHT.x*p_matProjectionRIGHT.row(2)-p_matProjectionRIGHT.row(0);
matAHomogeneous.row(3) = p_ptPointRIGHT.y*p_matProjectionRIGHT.row(2)-p_matProjectionRIGHT.row(1);
//ds solve system subject to ||A*x||=0 ||x||=1
const Eigen::JacobiSVD< Eigen::Matrix4d > matSVD( matAHomogeneous, Eigen::ComputeFullU | Eigen::ComputeFullV );
//ds solution x is the last column of V
const Eigen::Vector4d vecX( matSVD.matrixV( ).col( 3 ) );
return vecX.head( 3 )/vecX(3);
}
bool pseudoInverse(
const _Matrix_Type_ &a, _Matrix_Type_ &result,
double epsilon =
std::numeric_limits<typename _Matrix_Type_::Scalar>::epsilon()) {
if (a.rows() < a.cols())
return false;
Eigen::JacobiSVD<_Matrix_Type_> svd = a.jacobiSvd();
typename _Matrix_Type_::Scalar tolerance =
epsilon * std::max(a.cols(), a.rows()) *
svd.singularValues().array().abs().maxCoeff();
result = svd.matrixV() *
_Matrix_Type_(
_Matrix_Type_((svd.singularValues().array().abs() > tolerance)
.select(svd.singularValues().array().inverse(),
0)).diagonal()) *
svd.matrixU().adjoint();
}
template<typename PointInT, typename PointNT, typename PointOutT> void
pcl::BOARDLocalReferenceFrameEstimation<PointInT, PointNT, PointOutT>::planeFitting (
Eigen::Matrix<float,
Eigen::Dynamic, 3> const &points,
Eigen::Vector3f ¢er,
Eigen::Vector3f &norm)
{
// -----------------------------------------------------
// Plane Fitting using Singular Value Decomposition (SVD)
// -----------------------------------------------------
int n_points = static_cast<int> (points.rows ());
if (n_points == 0)
{
return;
}
//find the center by averaging the points positions
center.setZero ();
for (int i = 0; i < n_points; ++i)
{
center += points.row (i);
}
center /= static_cast<float> (n_points);
//copy points - average (center)
Eigen::Matrix<float, Eigen::Dynamic, 3> A (n_points, 3); //PointData
for (int i = 0; i < n_points; ++i)
{
A (i, 0) = points (i, 0) - center.x ();
A (i, 1) = points (i, 1) - center.y ();
A (i, 2) = points (i, 2) - center.z ();
}
Eigen::JacobiSVD<Eigen::MatrixXf> svd (A, Eigen::ComputeFullV);
norm = svd.matrixV ().col (2);
}
inline Eigen::Affine3f
pcl::TransformationFromCorrespondences::getTransformation ()
{
//Eigen::JacobiSVD<Eigen::Matrix<float, 3, 3> > svd (covariance_, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::JacobiSVD<Eigen::Matrix<float, 3, 3> > svd (covariance_, Eigen::ComputeFullU | Eigen::ComputeFullV);
const Eigen::Matrix<float, 3, 3>& u = svd.matrixU(),
& v = svd.matrixV();
Eigen::Matrix<float, 3, 3> s;
s.setIdentity();
if (u.determinant()*v.determinant() < 0.0f)
s(2,2) = -1.0f;
Eigen::Matrix<float, 3, 3> r = u * s * v.transpose();
Eigen::Vector3f t = mean2_ - r*mean1_;
Eigen::Affine3f ret;
ret(0,0)=r(0,0); ret(0,1)=r(0,1); ret(0,2)=r(0,2); ret(0,3)=t(0);
ret(1,0)=r(1,0); ret(1,1)=r(1,1); ret(1,2)=r(1,2); ret(1,3)=t(1);
ret(2,0)=r(2,0); ret(2,1)=r(2,1); ret(2,2)=r(2,2); ret(2,3)=t(2);
ret(3,0)=0.0f; ret(3,1)=0.0f; ret(3,2)=0.0f; ret(3,3)=1.0f;
return (ret);
}
void pseudoInverse(const Eigen::MatrixXd& jac,
Eigen::JacobiSVD<Eigen::MatrixXd>& svd,
Eigen::VectorXd& svdSingular,
Eigen::MatrixXd& prePseudoInv,
Eigen::MatrixXd& result,
double epsilon=std::numeric_limits<double>::epsilon(),
double minTol=1e-8)
{
svd.compute(jac, Eigen::ComputeThinU | Eigen::ComputeThinV);
// singular values are sorted in decreasing order
// so the first one is the max one
double tolerance =
epsilon*double(std::max(jac.cols(), jac.rows()))*
std::abs(svd.singularValues()[0]);
tolerance = std::max(tolerance, minTol);
svdSingular = ((svd.singularValues().array().abs() > tolerance).
select(svd.singularValues().array().inverse(), 0.));
prePseudoInv.noalias() = svd.matrixV()*svdSingular.asDiagonal();
result.noalias() = prePseudoInv*svd.matrixU().adjoint();
}
// typename DerivedA::Scalar
void pseudo_inverse_svd(const Eigen::MatrixBase<DerivedA>& M,
Eigen::MatrixBase<OutputMatrixType>& Minv,
typename DerivedA::Scalar epsilon = 1e-6)//std::numeric_limits<typename DerivedA::Scalar>::epsilon())
{
// CONTROLIT_INFO << "Method called!\n epsilon = " << epsilon << ", M = \n" << M;
// Ensure matrix Minv has the correct size. Its size should be equal to M.transpose().
assert_msg(M.rows() == Minv.cols(), "Minv has invalid number of columns. Expected " << M.rows() << " got " << Minv.cols());
assert_msg(M.cols() == Minv.rows(), "Minv has invalid number of rows. Expected " << M.cols() << " got " << Minv.rows());
// According to Eigen documentation, "If the input matrix has inf or nan coefficients, the result of the
// computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time."
Eigen::JacobiSVD<DerivedA> svd = M.jacobiSvd(Eigen::ComputeFullU | Eigen::ComputeFullV);
// Get the max singular value
typename DerivedA::Scalar maxSingularValue = svd.singularValues().array().abs().maxCoeff();
// Use Minv to temporarily hold sigma
Minv.setZero();
typename DerivedA::Scalar tolerance = 0;
// Only compute sigma if the max singular value is greater than zero.
if (maxSingularValue > epsilon)
{
tolerance = epsilon * std::max(M.cols(), M.rows()) * maxSingularValue;
// For each singular value of matrix M's SVD decomposition, check if it is greater than
// the tolerance value. If it is, save 1/(singular value) in the sigma vector.
// Otherwise save zero in the sigma vector.
DerivedA sigmaVector = DerivedA( (svd.singularValues().array().abs() > tolerance).select(svd.singularValues().array().inverse(), 0) );
// DerivedA zeroSVs = DerivedA( (svd.singularValues().array().abs() <= tolerance).select(svd.singularValues().array().inverse(), 0) );
// CONTROLIT_INFO << "epsilon: " << epsilon << ", std::max(M.cols(), M.rows()): " << std::max(M.cols(), M.rows()) << ", maxSingularValue: " << maxSingularValue << ", tolerance: " << tolerance;
// CONTROLIT_INFO << "sigmaVector = " << sigmaVector.transpose();
// CONTROLIT_INFO << "zeroSigmaVector : "<< zeroSVs.transpose();
Minv.block(0, 0, sigmaVector.rows(), sigmaVector.rows()) = sigmaVector.asDiagonal();
}
// Double check to make sure the matrices have the correct dimensions
assert_msg(svd.matrixV().cols() == Minv.rows(),
"Matrix dimension mismatch, svd.matrixV().cols() = " << svd.matrixV().cols() << ", Minv.rows() = " << Minv.rows() << ".");
assert_msg(Minv.cols() == svd.matrixU().adjoint().rows(),
"Matrix dimension mismatch, Minv.cols() = " << Minv.cols() << ", svd.matrixU().adjoint().rows() = " << svd.matrixU().adjoint().rows() << ".");
Minv = svd.matrixV() *
Minv *
svd.matrixU().adjoint(); // take the transpose of matrix U
// CONTROLIT_INFO << "Done method call! Minv = " << Minv;
// typename DerivedA::Scalar errorNorm = std::abs((M * Minv - DerivedA::Identity(M.rows(), Minv.cols())).norm());
// if (tolerance != 0 && errorNorm > tolerance * 10)
// {
// CONTROLIT_WARN << "Problems computing pseudoinverse. Perhaps the tolerance is too high?\n"
// << " - epsilon: " << epsilon << "\n"
// << " - tolerance: " << tolerance << "\n"
// << " - maxSingularValue: " << maxSingularValue << "\n"
// << " - errorNorm: " << errorNorm << "\n"
// << " - M:\n" << M << "\n"
// << " - Minv:\n" << Minv;
// }
// return errorNorm;
}
IGL_INLINE void igl::min_quad_dense_precompute(
const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& A,
const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& Aeq,
const bool use_lu_decomposition,
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& S)
{
typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> Mat;
// This threshold seems to matter a lot but I'm not sure how to
// set it
const T treshold = igl::FLOAT_EPS;
//const T treshold = igl::DOUBLE_EPS;
const int n = A.rows();
assert(A.cols() == n);
const int m = Aeq.rows();
assert(Aeq.cols() == n);
// Lagrange multipliers method:
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> LM(n + m, n + m);
LM.block(0, 0, n, n) = A;
LM.block(0, n, n, m) = Aeq.transpose();
LM.block(n, 0, m, n) = Aeq;
LM.block(n, n, m, m).setZero();
Mat LMpinv;
if(use_lu_decomposition)
{
// if LM is close to singular, use at your own risk :)
LMpinv = LM.inverse();
}else
{
// use SVD
typedef Eigen::Matrix<T, Eigen::Dynamic, 1> Vec;
Vec singValues;
Eigen::JacobiSVD<Mat> svd;
svd.compute(LM, Eigen::ComputeFullU | Eigen::ComputeFullV );
const Mat& u = svd.matrixU();
const Mat& v = svd.matrixV();
const Vec& singVals = svd.singularValues();
Vec pi_singVals(n + m);
int zeroed = 0;
for (int i=0; i<n + m; i++)
{
T sv = singVals(i, 0);
assert(sv >= 0);
// printf("sv: %lg ? %lg\n",(double) sv,(double)treshold);
if (sv > treshold) pi_singVals(i, 0) = T(1) / sv;
else
{
pi_singVals(i, 0) = T(0);
zeroed++;
}
}
printf("min_quad_dense_precompute: %i singular values zeroed (threshold = %e)\n", zeroed, treshold);
Eigen::DiagonalMatrix<T, Eigen::Dynamic> pi_diag(pi_singVals);
LMpinv = v * pi_diag * u.transpose();
}
S = LMpinv.block(0, 0, n, n + m);
//// debug:
//mlinit(&g_pEngine);
//
//mlsetmatrix(&g_pEngine, "A", A);
//mlsetmatrix(&g_pEngine, "Aeq", Aeq);
//mlsetmatrix(&g_pEngine, "LM", LM);
//mlsetmatrix(&g_pEngine, "u", u);
//mlsetmatrix(&g_pEngine, "v", v);
//MatrixXd svMat = singVals;
//mlsetmatrix(&g_pEngine, "singVals", svMat);
//mlsetmatrix(&g_pEngine, "LMpinv", LMpinv);
//mlsetmatrix(&g_pEngine, "S", S);
//int hu = 1;
}
template<typename PointInT, typename PointNT, typename PointOutT> bool
pcl::OURCVFHEstimation<PointInT, PointNT, PointOutT>::sgurf (Eigen::Vector3f & centroid, Eigen::Vector3f & normal_centroid,
PointInTPtr & processed, std::vector<Eigen::Matrix4f, Eigen::aligned_allocator<Eigen::Matrix4f> > & transformations,
PointInTPtr & grid, pcl::PointIndices & indices)
{
Eigen::Vector3f plane_normal;
plane_normal[0] = -centroid[0];
plane_normal[1] = -centroid[1];
plane_normal[2] = -centroid[2];
Eigen::Vector3f z_vector = Eigen::Vector3f::UnitZ ();
plane_normal.normalize ();
Eigen::Vector3f axis = plane_normal.cross (z_vector);
double rotation = -asin (axis.norm ());
axis.normalize ();
Eigen::Affine3f transformPC (Eigen::AngleAxisf (static_cast<float> (rotation), axis));
grid->points.resize (processed->points.size ());
for (size_t k = 0; k < processed->points.size (); k++)
grid->points[k].getVector4fMap () = processed->points[k].getVector4fMap ();
pcl::transformPointCloud (*grid, *grid, transformPC);
Eigen::Vector4f centroid4f (centroid[0], centroid[1], centroid[2], 0);
Eigen::Vector4f normal_centroid4f (normal_centroid[0], normal_centroid[1], normal_centroid[2], 0);
centroid4f = transformPC * centroid4f;
normal_centroid4f = transformPC * normal_centroid4f;
Eigen::Vector3f centroid3f (centroid4f[0], centroid4f[1], centroid4f[2]);
Eigen::Vector4f farthest_away;
pcl::getMaxDistance (*grid, indices.indices, centroid4f, farthest_away);
farthest_away[3] = 0;
float max_dist = (farthest_away - centroid4f).norm ();
pcl::demeanPointCloud (*grid, centroid4f, *grid);
Eigen::Matrix4f center_mat;
center_mat.setIdentity (4, 4);
center_mat (0, 3) = -centroid4f[0];
center_mat (1, 3) = -centroid4f[1];
center_mat (2, 3) = -centroid4f[2];
Eigen::Matrix3f scatter;
scatter.setZero ();
float sum_w = 0.f;
//for (int k = 0; k < static_cast<intgrid->points[k].getVector3fMap ();> (grid->points.size ()); k++)
for (int k = 0; k < static_cast<int> (indices.indices.size ()); k++)
{
Eigen::Vector3f pvector = grid->points[indices.indices[k]].getVector3fMap ();
float d_k = (pvector).norm ();
float w = (max_dist - d_k);
Eigen::Vector3f diff = (pvector);
Eigen::Matrix3f mat = diff * diff.transpose ();
scatter = scatter + mat * w;
sum_w += w;
}
scatter /= sum_w;
Eigen::JacobiSVD <Eigen::MatrixXf> svd (scatter, Eigen::ComputeFullV);
Eigen::Vector3f evx = svd.matrixV ().col (0);
Eigen::Vector3f evy = svd.matrixV ().col (1);
Eigen::Vector3f evz = svd.matrixV ().col (2);
Eigen::Vector3f evxminus = evx * -1;
Eigen::Vector3f evyminus = evy * -1;
Eigen::Vector3f evzminus = evz * -1;
float s_xplus, s_xminus, s_yplus, s_yminus;
s_xplus = s_xminus = s_yplus = s_yminus = 0.f;
//disambiguate rf using all points
for (int k = 0; k < static_cast<int> (grid->points.size ()); k++)
{
Eigen::Vector3f pvector = grid->points[k].getVector3fMap ();
float dist_x, dist_y;
dist_x = std::abs (evx.dot (pvector));
dist_y = std::abs (evy.dot (pvector));
if ((pvector).dot (evx) >= 0)
s_xplus += dist_x;
else
s_xminus += dist_x;
if ((pvector).dot (evy) >= 0)
s_yplus += dist_y;
else
s_yminus += dist_y;
}
if (s_xplus < s_xminus)
evx = evxminus;
if (s_yplus < s_yminus)
evy = evyminus;
//select the axis that could be disambiguated more easily
float fx, fy;
float max_x = static_cast<float> (std::max (s_xplus, s_xminus));
float min_x = static_cast<float> (std::min (s_xplus, s_xminus));
float max_y = static_cast<float> (std::max (s_yplus, s_yminus));
float min_y = static_cast<float> (std::min (s_yplus, s_yminus));
fx = (min_x / max_x);
fy = (min_y / max_y);
Eigen::Vector3f normal3f = Eigen::Vector3f (normal_centroid4f[0], normal_centroid4f[1], normal_centroid4f[2]);
if (normal3f.dot (evz) < 0)
evz = evzminus;
//if fx/y close to 1, it was hard to disambiguate
//what if both are equally easy or difficult to disambiguate, namely fy == fx or very close
float max_axis = std::max (fx, fy);
float min_axis = std::min (fx, fy);
if ((min_axis / max_axis) > axis_ratio_)
{
PCL_WARN("Both axis are equally easy/difficult to disambiguate\n");
Eigen::Vector3f evy_copy = evy;
Eigen::Vector3f evxminus = evx * -1;
Eigen::Vector3f evyminus = evy * -1;
if (min_axis > min_axis_value_)
{
//combination of all possibilities
evy = evx.cross (evz);
Eigen::Matrix4f trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
evx = evxminus;
evy = evx.cross (evz);
trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
evx = evy_copy;
evy = evx.cross (evz);
trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
evx = evyminus;
evy = evx.cross (evz);
trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
}
else
{
//1-st case (evx selected)
evy = evx.cross (evz);
Eigen::Matrix4f trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
//2-nd case (evy selected)
evx = evy_copy;
evy = evx.cross (evz);
trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
}
}
else
{
if (fy < fx)
{
evx = evy;
fx = fy;
}
evy = evx.cross (evz);
Eigen::Matrix4f trans = createTransFromAxes (evx, evy, evz, transformPC, center_mat);
transformations.push_back (trans);
}
return true;
}
//Do the interpolation calculations
bool SIM_SnowSolver::solveGasSubclass(SIM_Engine &engine, SIM_Object *obj, SIM_Time time, SIM_Time framerate){
/// STEP #0: Retrieve all data objects from Houdini
//Scalar params
freal particle_mass = getPMass();
freal YOUNGS_MODULUS = getYoungsModulus();
freal POISSONS_RATIO = getPoissonsRatio();
freal CRIT_COMPRESS = getCritComp();
freal CRIT_STRETCH = getCritStretch();
freal FLIP_PERCENT = getFlipPercent();
freal HARDENING = getHardening();
freal CFL = getCfl();
freal COF = getCof();
freal division_size = getDivSize();
freal max_vel = getMaxVel();
//Vector params
vector3 GRAVITY = getGravity();
vector3 bbox_min_limit = getBboxMin();
vector3 bbox_max_limit = getBboxMax();
//Particle params
UT_String s_p, s_vol, s_den, s_vel, s_fe, s_fp;
getParticles(s_p);
getPVol(s_vol);
getPD(s_den);
getPVel(s_vel);
getPFe(s_fe);
getPFp(s_fp);
SIM_Geometry* geometry = (SIM_Geometry*) obj->getNamedSubData(s_p);
if (!geometry) return true;
//Get particle data
//Do we use the attribute name???
// GU_DetailHandle gdh = geometry->getGeometry().getWriteableCopy();
GU_DetailHandle gdh = geometry->getOwnGeometry();
const GU_Detail* gdp_in = gdh.readLock(); // Must unlock later
GU_Detail* gdp_out = gdh.writeLock();
GA_RWAttributeRef p_ref_position = gdp_out->findPointAttribute("P");
GA_RWHandleT<vector3> p_position(p_ref_position.getAttribute());
GA_RWAttributeRef p_ref_volume = gdp_out->findPointAttribute(s_vol);
GA_RWHandleT<freal> p_volume(p_ref_volume.getAttribute());
GA_RWAttributeRef p_ref_density = gdp_out->findPointAttribute(s_den);
GA_RWHandleT<freal> p_density(p_ref_density.getAttribute());
GA_RWAttributeRef p_ref_vel = gdp_out->findPointAttribute(s_vel);
GA_RWHandleT<vector3> p_vel(p_ref_vel.getAttribute());
GA_RWAttributeRef p_ref_Fe = gdp_out->findPointAttribute(s_fe);
GA_RWHandleT<matrix3> p_Fe(p_ref_Fe.getAttribute());
GA_RWAttributeRef p_ref_Fp = gdp_out->findPointAttribute(s_fp);
GA_RWHandleT<matrix3> p_Fp(p_ref_Fp.getAttribute());
//EVALUATE PARAMETERS
freal mu = YOUNGS_MODULUS/(2+2*POISSONS_RATIO);
freal lambda = YOUNGS_MODULUS*POISSONS_RATIO/((1+POISSONS_RATIO)*(1-2*POISSONS_RATIO));
//Get grid data
SIM_ScalarField *g_mass_field;
SIM_DataArray g_mass_data;
getMatchingData(g_mass_data, obj, MPM_G_MASS);
g_mass_field = SIM_DATA_CAST(g_mass_data(0), SIM_ScalarField);
SIM_VectorField *g_nvel_field;
SIM_DataArray g_nvel_data;
getMatchingData(g_nvel_data, obj, MPM_G_NVEL);
g_nvel_field = SIM_DATA_CAST(g_nvel_data(0), SIM_VectorField);
SIM_VectorField *g_ovel_field;
SIM_DataArray g_ovel_data;
getMatchingData(g_ovel_data, obj, MPM_G_OVEL);
g_ovel_field = SIM_DATA_CAST(g_ovel_data(0), SIM_VectorField);
SIM_ScalarField *g_active_field;
SIM_DataArray g_active_data;
getMatchingData(g_active_data, obj, MPM_G_ACTIVE);
g_active_field = SIM_DATA_CAST(g_active_data(0), SIM_ScalarField);
SIM_ScalarField *g_density_field;
SIM_DataArray g_density_data;
getMatchingData(g_density_data, obj, MPM_G_DENSITY);
g_density_field = SIM_DATA_CAST(g_density_data(0), SIM_ScalarField);
SIM_ScalarField *g_col_field;
SIM_DataArray g_col_data;
getMatchingData(g_col_data, obj, MPM_G_COL);
g_col_field = SIM_DATA_CAST(g_col_data(0), SIM_ScalarField);
SIM_VectorField *g_colVel_field;
SIM_DataArray g_colVel_data;
getMatchingData(g_colVel_data, obj, MPM_G_COLVEL);
g_colVel_field = SIM_DATA_CAST(g_colVel_data(0), SIM_VectorField);
SIM_VectorField *g_extForce_field;
SIM_DataArray g_extForce_data;
getMatchingData(g_extForce_data, obj, MPM_G_EXTFORCE);
g_extForce_field = SIM_DATA_CAST(g_extForce_data(0), SIM_VectorField);
UT_VoxelArrayF
*g_mass = g_mass_field->getField()->fieldNC(),
*g_nvelX = g_nvel_field->getField(0)->fieldNC(),
*g_nvelY = g_nvel_field->getField(1)->fieldNC(),
*g_nvelZ = g_nvel_field->getField(2)->fieldNC(),
*g_ovelX = g_ovel_field->getField(0)->fieldNC(),
*g_ovelY = g_ovel_field->getField(1)->fieldNC(),
*g_ovelZ = g_ovel_field->getField(2)->fieldNC(),
*g_colVelX = g_colVel_field->getField(0)->fieldNC(),
*g_colVelY = g_colVel_field->getField(1)->fieldNC(),
*g_colVelZ = g_colVel_field->getField(2)->fieldNC(),
*g_extForceX = g_extForce_field->getField(0)->fieldNC(),
*g_extForceY = g_extForce_field->getField(1)->fieldNC(),
*g_extForceZ = g_extForce_field->getField(2)->fieldNC(),
*g_col = g_col_field->getField()->fieldNC(),
*g_active = g_active_field->getField()->fieldNC();
int point_count = gdp_out->getPointRange().getEntries();
std::vector<boost::array<freal,64> > p_w(point_count);
std::vector<boost::array<vector3,64> > p_wgh(point_count);
//Get world-to-grid conversion ratios
//Particle's grid position can be found via (pos - grid_origin)/voxel_dims
vector3
voxel_dims = g_mass_field->getVoxelSize(),
grid_origin = g_mass_field->getOrig(),
grid_divs = g_mass_field->getDivisions();
//Houdini uses voxel centers for grid nodes, rather than grid corners
grid_origin += voxel_dims/2.0;
freal voxelArea = voxel_dims[0]*voxel_dims[1]*voxel_dims[2];
/*
//Reset grid
for(int iX=0; iX < grid_divs[0]; iX++){
for(int iY=0; iY < grid_divs[1]; iY++){
for(int iZ=0; iZ < grid_divs[2]; iZ++){
g_mass->setValue(iX,iY,iZ,0);
g_active->setValue(iX,iY,iZ,0);
g_ovelX->setValue(iX,iY,iZ,0);
g_ovelY->setValue(iX,iY,iZ,0);
g_ovelZ->setValue(iX,iY,iZ,0);
g_nvelX->setValue(iX,iY,iZ,0);
g_nvelY->setValue(iX,iY,iZ,0);
g_nvelZ->setValue(iX,iY,iZ,0);
}
}
}
*/
/// STEP #1: Transfer mass to grid
if (p_position.isValid()){
//Iterate through particles
for (GA_Iterator it(gdp_out->getPointRange()); !it.atEnd(); it.advance()){
int pid = it.getOffset();
//Get grid position
vector3 gpos = (p_position.get(pid) - grid_origin)/voxel_dims;
int p_gridx = (int) gpos[0], p_gridy = (int) gpos[1], p_gridz = (int) gpos[2];
//g_mass_field->posToIndex(p_position.get(pid),p_gridx,p_gridy,p_gridz);
freal particle_density = p_density.get(pid);
//Compute weights and transfer mass
for (int idx=0, z=p_gridz-1, z_end=z+3; z<=z_end; z++){
//Z-dimension interpolation
freal z_pos = gpos[2]-z,
wz = SIM_SnowSolver::bspline(z_pos),
dz = SIM_SnowSolver::bsplineSlope(z_pos);
for (int y=p_gridy-1, y_end=y+3; y<=y_end; y++){
//Y-dimension interpolation
freal y_pos = gpos[1]-y,
wy = SIM_SnowSolver::bspline(y_pos),
dy = SIM_SnowSolver::bsplineSlope(y_pos);
for (int x=p_gridx-1, x_end=x+3; x<=x_end; x++, idx++){
//X-dimension interpolation
freal x_pos = gpos[0]-x,
wx = SIM_SnowSolver::bspline(x_pos),
dx = SIM_SnowSolver::bsplineSlope(x_pos);
//Final weight is dyadic product of weights in each dimension
freal weight = wx*wy*wz;
p_w[pid-1][idx] = weight;
//Weight gradient is a vector of partial derivatives
p_wgh[pid-1][idx] = vector3(dx*wy*wz, wx*dy*wz, wx*wy*dz)/voxel_dims;
//Interpolate mass
freal node_mass = g_mass->getValue(x,y,z);
node_mass += weight*particle_mass;
g_mass->setValue(x,y,z,node_mass);
}
}
}
}
}
/// STEP #2: First timestep only - Estimate particle volumes using grid mass
/*
if (time == 0.0){
//Iterate through particles
for (GA_Iterator it(gdp_out->getPointRange()); !it.atEnd(); it.advance()){
int pid = it.getOffset();
freal density = 0;
//Get grid position
int p_gridx = 0, p_gridy = 0, p_gridz = 0;
vector3 gpos = (p_position.get(pid) - grid_origin)/voxel_dims;
int p_gridx = (int) gpos[0], p_gridy = (int) gpos[1], p_gridz = (int) gpos[2];
//g_nvel_field->posToIndex(0,p_position.get(pid),p_gridx,p_gridy,p_gridz);
//Transfer grid density (within radius) to particles
for (int idx=0, z=p_gridz-1, z_end=z+3; z<=z_end; z++){
for (int y=p_gridy-1, y_end=y+3; y<=y_end; y++){
for (int x=p_gridx-1, x_end=x+3; x<=x_end; x++, idx++){
freal w = p_w[pid-1][idx];
if (w > EPSILON){
//Transfer density
density += w * g_mass->getValue(x,y,z);
}
}
}
}
density /= voxelArea;
p_density.set(pid,density);
p_volume.set(pid, particle_mass/density);
}
}
//*/
/// STEP #3: Transfer velocity to grid
//This must happen after transferring mass, to conserve momentum
//Iterate through particles and transfer
for (GA_Iterator it(gdp_in->getPointRange()); !it.atEnd(); it.advance()){
int pid = it.getOffset();
vector3 vel_fac = p_vel.get(pid)*particle_mass;
//Get grid position
vector3 gpos = (p_position.get(pid) - grid_origin)/voxel_dims;
int p_gridx = (int) gpos[0], p_gridy = (int) gpos[1], p_gridz = (int) gpos[2];
//g_nvel_field->posToIndex(0,p_position.get(pid),p_gridx,p_gridy,p_gridz);
//Transfer to grid nodes within radius
for (int idx=0, z=p_gridz-1, z_end=z+3; z<=z_end; z++){
for (int y=p_gridy-1, y_end=y+3; y<=y_end; y++){
for (int x=p_gridx-1, x_end=x+3; x<=x_end; x++, idx++){
freal w = p_w[pid-1][idx];
if (w > EPSILON){
freal nodex_vel = g_ovelX->getValue(x,y,z) + vel_fac[0]*w;
freal nodey_vel = g_ovelY->getValue(x,y,z) + vel_fac[1]*w;
freal nodez_vel = g_ovelZ->getValue(x,y,z) + vel_fac[2]*w;
g_ovelX->setValue(x,y,z,nodex_vel);
g_ovelY->setValue(x,y,z,nodey_vel);
g_ovelZ->setValue(x,y,z,nodez_vel);
g_active->setValue(x,y,z,1.0);
}
}
}
}
}
//Division is slow (maybe?); we only want to do divide by mass once, for each active node
for(int iX=0; iX < grid_divs[0]; iX++){
for(int iY=0; iY < grid_divs[1]; iY++){
for(int iZ=0; iZ < grid_divs[2]; iZ++){
//Only check nodes that have mass
if (g_active->getValue(iX,iY,iZ)){
freal node_mass = 1/(g_mass->getValue(iX,iY,iZ));
g_ovelX->setValue(iX,iY,iZ,(g_ovelX->getValue(iX,iY,iZ)*node_mass));
g_ovelY->setValue(iX,iY,iZ,(g_ovelY->getValue(iX,iY,iZ)*node_mass));
g_ovelZ->setValue(iX,iY,iZ,(g_ovelZ->getValue(iX,iY,iZ)*node_mass));
}
}
}
}
/// STEP #4: Compute new grid velocities
//Temporary variables for plasticity and force calculation
//We need one set of variables for each thread that will be running
eigen_matrix3 def_elastic, def_plastic, energy, svd_u, svd_v;
Eigen::JacobiSVD<eigen_matrix3, Eigen::NoQRPreconditioner> svd;
eigen_vector3 svd_e;
matrix3 HDK_def_plastic, HDK_def_elastic, HDK_energy;
freal* data_dp = HDK_def_plastic.data();
freal* data_de = HDK_def_elastic.data();
freal* data_energy = HDK_energy.data();
//Map Eigen matrices to HDK matrices
Eigen::Map<eigen_matrix3> data_dp_map(data_dp);
Eigen::Map<eigen_matrix3> data_de_map(data_de);
Eigen::Map<eigen_matrix3> data_energy_map(data_energy);
//Compute force at each particle and transfer to Eulerian grid
//We use "nvel" to hold the grid force, since that variable is not in use
for (GA_Iterator it(gdp_in->getPointRange()); !it.atEnd(); it.advance()){
int pid = it.getOffset();
//Apply plasticity to deformation gradient, before computing forces
//We need to use the Eigen lib to do the SVD; transfer houdini matrices to Eigen matrices
HDK_def_plastic = p_Fp.get(pid);
HDK_def_elastic = p_Fe.get(pid);
def_plastic = Eigen::Map<eigen_matrix3>(data_dp);
def_elastic = Eigen::Map<eigen_matrix3>(data_de);
//Compute singular value decomposition (uev*)
svd.compute(def_elastic, Eigen::ComputeFullV | Eigen::ComputeFullU);
svd_e = svd.singularValues();
svd_u = svd.matrixU();
svd_v = svd.matrixV();
//Clamp singular values
for (int i=0; i<3; i++){
if (svd_e[i] < CRIT_COMPRESS)
svd_e[i] = CRIT_COMPRESS;
else if (svd_e[i] > CRIT_STRETCH)
svd_e[i] = CRIT_STRETCH;
}
//Put SVD back together for new elastic and plastic gradients
def_plastic = svd_v * svd_e.asDiagonal().inverse() * svd_u.transpose() * def_elastic * def_plastic;
svd_v.transposeInPlace();
def_elastic = svd_u * svd_e.asDiagonal() * svd_v;
//Now compute the energy partial derivative (which we use to get force at each grid node)
energy = 2*mu*(def_elastic - svd_u*svd_v)*def_elastic.transpose();
//Je is the determinant of def_elastic (equivalent to svd_e.prod())
freal Je = svd_e.prod(),
contour = lambda*Je*(Je-1),
jp = def_plastic.determinant(),
particle_vol = p_volume.get(pid);
for (int i=0; i<3; i++)
energy(i,i) += contour;
energy *= particle_vol * exp(HARDENING*(1-jp));
//Transfer Eigen matrices back to HDK
data_dp_map = def_plastic;
data_de_map = def_elastic;
data_energy_map = energy;
p_Fp.set(pid,HDK_def_plastic);
p_Fe.set(pid,HDK_def_elastic);
//Transfer energy to surrounding grid nodes
vector3 gpos = (p_position.get(pid) - grid_origin)/voxel_dims;
int p_gridx = (int) gpos[0], p_gridy = (int) gpos[1], p_gridz = (int) gpos[2];
for (int idx=0, z=p_gridz-1, z_end=z+3; z<=z_end; z++){
for (int y=p_gridy-1, y_end=y+3; y<=y_end; y++){
for (int x=p_gridx-1, x_end=x+3; x<=x_end; x++, idx++){
freal w = p_w[pid-1][idx];
if (w > EPSILON){
vector3 ngrad = p_wgh[pid-1][idx];
g_nvelX->setValue(x,y,z,g_nvelX->getValue(x,y,z) + ngrad.dot(HDK_energy[0]));
g_nvelY->setValue(x,y,z,g_nvelY->getValue(x,y,z) + ngrad.dot(HDK_energy[1]));
g_nvelZ->setValue(x,y,z,g_nvelZ->getValue(x,y,z) + ngrad.dot(HDK_energy[2]));
}
}
}
}
}
//Use new forces to solve for new velocities
for(int iX=0; iX < grid_divs[0]; iX++){
for(int iY=0; iY < grid_divs[1]; iY++){
for(int iZ=0; iZ < grid_divs[2]; iZ++){
//Only compute for active nodes
if (g_active->getValue(iX,iY,iZ)){
freal nodex_ovel = g_ovelX->getValue(iX,iY,iZ);
freal nodey_ovel = g_ovelY->getValue(iX,iY,iZ);
freal nodez_ovel = g_ovelZ->getValue(iX,iY,iZ);
freal forcex = g_nvelX->getValue(iX,iY,iZ);
freal forcey = g_nvelY->getValue(iX,iY,iZ);
freal forcez = g_nvelZ->getValue(iX,iY,iZ);
freal node_mass = 1/(g_mass->getValue(iX,iY,iZ));
freal ext_forceX = GRAVITY[0] + g_extForceX->getValue(iX,iY,iZ);
freal ext_forceY = GRAVITY[1] + g_extForceY->getValue(iX,iY,iZ);
freal ext_forceZ = GRAVITY[2] + g_extForceZ->getValue(iX,iY,iZ);
nodex_ovel += framerate*(ext_forceX - forcex*node_mass);
nodey_ovel += framerate*(ext_forceY - forcey*node_mass);
nodez_ovel += framerate*(ext_forceZ - forcez*node_mass);
//Limit velocity to max_vel
vector3 g_nvel(nodex_ovel, nodey_ovel, nodez_ovel);
freal nvelNorm = g_nvel.length();
if(nvelNorm > max_vel){
freal velRatio = max_vel/nvelNorm;
g_nvel*= velRatio;
}
g_nvelX->setValue(iX,iY,iZ,g_nvel[0]);
g_nvelY->setValue(iX,iY,iZ,g_nvel[1]);
g_nvelZ->setValue(iX,iY,iZ,g_nvel[2]);
}
}
}
}
/// STEP #5: Grid collision resolution
vector3 sdf_normal;
//*
for(int iX=1; iX < grid_divs[0]-1; iX++){
for(int iY=1; iY < grid_divs[1]-1; iY++){
for(int iZ=1; iZ < grid_divs[2]-1; iZ++){
if (g_active->getValue(iX,iY,iZ)){
if (!computeSDFNormal(g_col, iX, iY, iZ, sdf_normal))
continue;
//Collider velocity
vector3 vco(
g_colVelX->getValue(iX,iY,iZ),
g_colVelY->getValue(iX,iY,iZ),
g_colVelZ->getValue(iX,iY,iZ)
);
//Grid velocity
vector3 v(
g_nvelX->getValue(iX,iY,iZ),
g_nvelY->getValue(iX,iY,iZ),
g_nvelZ->getValue(iX,iY,iZ)
);
//Skip if bodies are separating
vector3 vrel = v - vco;
freal vn = vrel.dot(sdf_normal);
if (vn >= 0) continue;
//Resolve collisions; also add velocity of collision object to snow velocity
//Sticks to surface (too slow to overcome static friction)
vector3 vt = vrel - (sdf_normal*vn);
freal stick = vn*COF, vt_norm = vt.length();
if (vt_norm <= -stick)
vt = vco;
//Dynamic friction
else vt += stick*vt/vt_norm + vco;
g_nvelX->setValue(iX,iY,iZ,vt[0]);
g_nvelY->setValue(iX,iY,iZ,vt[1]);
g_nvelZ->setValue(iX,iY,iZ,vt[2]);
}
}
}
}
//*/
/// STEP #6: Transfer grid velocities to particles and integrate
/// STEP #7: Particle collision resolution
vector3 pic, flip, col_vel;
matrix3 vel_grad;
//Iterate through particles
for (GA_Iterator it(gdp_in->getPointRange()); !it.atEnd(); it.advance()){
int pid = it.getOffset();
//Particle position
vector3 pos(p_position.get(pid));
//Reset velocity
pic[0] = 0.0;
pic[1] = 0.0;
pic[2] = 0.0;
flip = p_vel.get(pid);
vel_grad.zero();
freal density = 0;
//Get grid position
vector3 gpos = (pos - grid_origin)/voxel_dims;
int p_gridx = (int) gpos[0], p_gridy = (int) gpos[1], p_gridz = (int) gpos[2];
for (int idx=0, z=p_gridz-1, z_end=z+3; z<=z_end; z++){
for (int y=p_gridy-1, y_end=y+3; y<=y_end; y++){
for (int x=p_gridx-1, x_end=x+3; x<=x_end; x++, idx++){
freal w = p_w[pid-1][idx];
if (w > EPSILON){
const vector3 node_wg = p_wgh[pid-1][idx];
const vector3 node_nvel(
g_nvelX->getValue(x,y,z),
g_nvelY->getValue(x,y,z),
g_nvelZ->getValue(x,y,z)
);
//Transfer velocities
pic += node_nvel*w;
flip[0] += (node_nvel[0] - g_ovelX->getValue(x,y,z))*w;
flip[1] += (node_nvel[1]- g_ovelY->getValue(x,y,z))*w;
flip[2] += (node_nvel[2] - g_ovelZ->getValue(x,y,z))*w;
//Transfer density
density += w * g_mass->getValue(x,y,z);
//Transfer veloctiy gradient
vel_grad.outerproductUpdate(1.0, node_nvel, node_wg);
}
}
}
}
//Finalize velocity update
vector3 vel = flip*FLIP_PERCENT + pic*(1-FLIP_PERCENT);
//Reset collision data
freal col_sdf = 0;
sdf_normal[0] = 0;
sdf_normal[1] = 0;
sdf_normal[2] = 0;
col_vel[0] = 0;
col_vel[1] = 0;
col_vel[2] = 0;
//Interpolate surrounding nodes' SDF info to the particle (trilinear interpolation)
for (int idx=0, z=p_gridz, z_end=z+1; z<=z_end; z++){
freal w_z = gpos[2]-z;
for (int y=p_gridy, y_end=y+1; y<=y_end; y++){
freal w_zy = w_z*(gpos[1]-y);
for (int x=p_gridx, x_end=x+1; x<=x_end; x++, idx++){
freal weight = fabs(w_zy*(gpos[0]-x));
//cout << w_zy << "," << (gpos[0]-x) << "," << weight << endl;
vector3 temp_normal;
computeSDFNormal(g_col, x, y, z, temp_normal);
//goto SKIP_PCOLLIDE;
//cout << g_col->getValue(x, y, z) << endl;
//Interpolate
sdf_normal += temp_normal*weight;
col_sdf += g_col->getValue(x, y, z)*weight;
col_vel[0] += g_colVelX->getValue(x, y, z)*weight;
col_vel[1] += g_colVelY->getValue(x, y, z)*weight;
col_vel[2] += g_colVelZ->getValue(x, y, z)*weight;
}
}
}
//Resolve particle collisions
//cout << col_sdf << endl;
if (col_sdf > 0){
vector3 vrel = vel - col_vel;
freal vn = vrel.dot(sdf_normal);
//Skip if bodies are separating
if (vn < 0){
//Resolve and add velocity of collision object to snow velocity
//Sticks to surface (too slow to overcome static friction)
vel = vrel - (sdf_normal*vn);
freal stick = vn*COF, vel_norm = vel.length();
if (vel_norm <= -stick)
vel = col_vel;
//Dynamic friction
else vel += stick*vel/vel_norm + col_vel;
}
}
SKIP_PCOLLIDE:
//Finalize density update
density /= voxelArea;
p_density.set(pid,density);
//Update particle position
pos += framerate*vel;
//Limit particle position
int mask = 0;
/*
for (int i=0; i<3; i++){
if (pos[i] > bbox_max_limit[i]){
pos[i] = bbox_max_limit[i];
vel[i] = 0.0;
mask |= 1 << i;
}
else if (pos[i] < bbox_min_limit[i]){
pos[i] = bbox_min_limit[i];
vel[i] = 0.0;
mask |= 1 << i;
}
}
//Slow particle down at bounds (not really necessary...)
if (mask){
for (int i=0; i<3; i++){
if (mask & 0x1)
vel[i] *= .05;
mask >>= 1;
}
}//*/
p_vel.set(pid,vel);
p_position.set(pid,pos);
//Update particle deformation gradient
//Note: plasticity is computed on the next timestep...
vel_grad *= framerate;
vel_grad(0,0) += 1;
vel_grad(1,1) += 1;
vel_grad(2,2) += 1;
p_Fe.set(pid, vel_grad*p_Fe.get(pid));
}
gdh.unlock(gdp_out);
gdh.unlock(gdp_in);
return true;
}
Types::Transform PlaneToPlaneCalibration::estimateTransform(const std::vector<PlanePair> & plane_pair_vector)
{
const int size = plane_pair_vector.size();
Eigen::MatrixXd normals_1(3, size);
Eigen::MatrixXd normals_2(3, size);
Eigen::VectorXd distances_1(size);
Eigen::VectorXd distances_2(size);
for (int i = 0; i < size; ++i)
{
const Types::Plane &plane_1 = plane_pair_vector[i].plane_1_;
const Types::Plane &plane_2 = plane_pair_vector[i].plane_2_;
if (plane_1.offset() > 0)
{
normals_1.col(i) = -plane_1.normal();
distances_1(i) = plane_1.offset();
}
else
{
normals_1.col(i) = plane_1.normal();
distances_1(i) = -plane_1.offset();
}
if (plane_2.offset() > 0)
{
normals_2.col(i) = -plane_2.normal();
distances_2(i) = plane_2.offset();
}
else
{
normals_2.col(i) = plane_2.normal();
distances_2(i) = -plane_2.offset();
}
}
// std::cout << normals_1 << std::endl;
// std::cout << distances_1.transpose() << std::endl;
// std::cout << normals_2 << std::endl;
// std::cout << distances_2.transpose() << std::endl;
Eigen::Matrix3d USV = normals_2 * normals_1.transpose();
Eigen::JacobiSVD<Eigen::Matrix3d> svd;
svd.compute(USV, Eigen::ComputeFullU | Eigen::ComputeFullV);
Types::Pose pose;
pose.translation() = (normals_1 * normals_1.transpose()).inverse() * normals_1 * (distances_1 - distances_2);
pose.linear() = svd.matrixV() * svd.matrixU().transpose();
// // Point-Plane Constraints
//
// // Initial system (Eq. 10)
//
// Eigen::MatrixXd system(size * 3, 13);
// for (int i = 0; i < size; ++i)
// {
// const double d = plane_pair_vector[i].plane_1_.offset();
// const Eigen::Vector3d n = plane_pair_vector[i].plane_1_.normal();
//
// const Point3d x = -plane_pair_vector[i].plane_2_.normal() * plane_pair_vector[i].plane_2_.offset();
//
// Eigen::Matrix3d X(Eigen::Matrix3d::Random());
// while (X.determinant() < 1e-5)
// X = Eigen::Matrix3d::Random();
//
// const Eigen::Vector3d & n2 = plane_pair_vector[i].plane_2_.normal();
//// X.col(1)[2] = -n2.head<2>().dot(X.col(1).head<2>()) / n2[2];
//// X.col(2)[2] = -n2.head<2>().dot(X.col(2).head<2>()) / n2[2];
// X.col(1) -= n2 * n2.dot(X.col(1));
// X.col(2) -= n2 * n2.dot(X.col(2));
//
// X.col(0) = x;
// X.col(1) += x;
// X.col(2) += x;
//
// for (int j = 0; j < 3; ++j)
// {
// const Point3d & x = X.col(j);
//
// system.row(i + size * j) << d + n[0] * x[0] + n[1] * x[1] + n[2] * x[2], // q_0^2
// 2 * n[2] * x[1] - 2 * n[1] * x[2], // q_0 * q_1
// 2 * n[0] * x[2] - 2 * n[2] * x[0], // q_0 * q_2
// 2 * n[1] * x[0] - 2 * n[0] * x[1], // q_0 * q_3
// d + n[0] * x[0] - n[1] * x[1] - n[2] * x[2], // q_1^2
// 2 * n[0] * x[1] + 2 * n[1] * x[0], // q_1 * q_2
// 2 * n[0] * x[2] + 2 * n[2] * x[0], // q_1 * q_3
// d - n[0] * x[0] + n[1] * x[1] - n[2] * x[2], // q_2^2
// 2 * n[1] * x[2] + 2 * n[2] * x[1], // q_2 * q_3
// d - n[0] * x[0] - n[1] * x[1] + n[2] * x[2], // q_3^2
// n[0], n[1], n[2]; // q'*q*t
// }
// }
//
// //std::cout << system << std::endl;
//
// // Gaussian reduction
// for (int k = 0; k < 3; ++k)
// for (int i = k + 1; i < size * 3; ++i)
// system.row(i) = system.row(i) - system.row(k) * system.row(i)[10 + k] / system.row(k)[10 + k];
//
// //std::cout << system << std::endl;
//
// // Quaternion q
// Eigen::Vector4d q;
//
// // Transform to inhomogeneous (Eq. 13)
// bool P_is_ok(false);
// while (not P_is_ok)
// {
// Eigen::Matrix4d P(Eigen::Matrix4d::Random().normalized());
// while (P.determinant() < 1e-5)
// P = Eigen::Matrix4d::Random().normalized();
//
// Eigen::MatrixXd reduced_system(size * 3 - 3, 10);
// for (int i = 3; i < size * 3; ++i)
// {
// const Eigen::VectorXd & row = system.row(i);
// Eigen::Matrix4d Mi_tilde;
//
// Mi_tilde << row[0] , row[1] / 2, row[2] / 2, row[3] / 2,
// row[1] / 2, row[4] , row[5] / 2, row[6] / 2,
// row[2] / 2, row[5] / 2, row[7] , row[8] / 2,
// row[3] / 2, row[6] / 2, row[8] / 2, row[9] ;
//
// Eigen::Matrix4d Mi_bar(P.transpose() * Mi_tilde * P);
//
// reduced_system.row(i - 3) << Mi_bar(0, 0),
// Mi_bar(0, 1) + Mi_bar(1, 0),
// Mi_bar(0, 2) + Mi_bar(2, 0),
// Mi_bar(0, 3) + Mi_bar(3, 0),
// Mi_bar(1, 1),
// Mi_bar(1, 2) + Mi_bar(2, 1),
// Mi_bar(1, 3) + Mi_bar(3, 1),
// Mi_bar(2, 2),
// Mi_bar(2, 3) + Mi_bar(3, 2),
// Mi_bar(3, 3);
// }
//
// // Solve A m* = b
// Eigen::MatrixXd A = reduced_system.rightCols<9>();
//
// Eigen::VectorXd b = - reduced_system.leftCols<1>();
// Eigen::VectorXd m_star = A.jacobiSvd(Eigen::ComputeFullU | Eigen::ComputeFullV).solve(b);
//
// Eigen::Vector4d q_bar(1, m_star[0], m_star[1], m_star[2]);
//
// Eigen::VectorXd err(6);
// err << q_bar[1] * q_bar[1],
// q_bar[1] * q_bar[2],
// q_bar[1] * q_bar[3],
// q_bar[2] * q_bar[2],
// q_bar[2] * q_bar[3],
// q_bar[3] * q_bar[3];
// err -= m_star.tail<6>();
//
// if (err.norm() < 0.1) // P is ok?
// P_is_ok = true;
//
// q = P * q_bar;
// }
//
// // We want q.w > 0 (Why?)
// if (q[0] < 0)
// q = -q;
// Eigen::Quaterniond rotation(q[0], q[1], q[2], q[3]);
// rotation.normalize();
//
// Eigen::VectorXd m(10);
// m << q[0] * q[0],
// q[0] * q[1],
// q[0] * q[2],
// q[0] * q[3],
// q[1] * q[1],
// q[1] * q[2],
// q[1] * q[3],
// q[2] * q[2],
// q[2] * q[3],
// q[3] * q[3];
//
// // Solve A (q^T q t) = b
//
// Eigen::Matrix3d A = system.topRightCorner<3, 3>();
// Eigen::Vector3d b = - system.topLeftCorner<3, 10>() * m;
//
// std::cout << A << " " << b.transpose() << std::endl;
// Eigen::Translation3d translation(A.colPivHouseholderQr().solve(b) / q.squaredNorm());
//
// Eigen::Quaterniond tmp(pose.linear());
// Eigen::Translation3d tmp2(pose.translation());
// std::cout << "Prev: " << tmp.normalized().coeffs().transpose() << " " << tmp2.vector().transpose() << std::endl;
// std::cout << "New : " << rotation.coeffs().transpose() << " " << translation.vector().transpose() << std::endl;
//
// pose = translation * rotation;
return pose;
}