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();
}
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;
}
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();
}
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();
}
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;
}
// 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;
}
// 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;
}
//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;
}
