// This method and the smooth version share the second half of code. Abstract that out. void StaticPlaneSphereConstraint::computeGeneralizedFrictionDisk( const VectorXs& q, const VectorXs& v, const int start_column, const int num_samples, SparseMatrixsc& D, VectorXs& drel ) const { assert( start_column >= 0 ); assert( start_column < D.cols() ); assert( num_samples > 0 ); assert( start_column + num_samples - 1 < D.cols() ); assert( q.size() % 12 == 0 ); assert( q.size() == 2 * v.size() ); const Vector3s n{ m_plane.n() }; assert( fabs( n.norm() - 1.0 ) <= 1.0e-6 ); std::vector<Vector3s> friction_disk( static_cast<std::vector<Vector3s>::size_type>( num_samples ) ); assert( friction_disk.size() == std::vector<Vector3s>::size_type( num_samples ) ); { // Compute the relative velocity Vector3s tangent_suggestion{ computeRelativeVelocity( q, v ) }; if( tangent_suggestion.cross( n ).squaredNorm() < 1.0e-9 ) { tangent_suggestion = FrictionUtilities::orthogonalVector( n ); } tangent_suggestion *= -1.0; // Sample the friction disk FrictionUtilities::generateOrthogonalVectors( n, friction_disk, tangent_suggestion ); } assert( unsigned( num_samples ) == friction_disk.size() ); // Compute the displacement from the center of mass to the point of contact assert( fabs( n.norm() - 1.0 ) <= 1.0e-10 ); assert( m_r >= 0.0 ); const Vector3s r_world{ - m_r * n }; // Cache the velocity of the collision point on the plane const Vector3s plane_collision_point_vel{ computePlaneCollisionPointVelocity( q ) }; // For each sample of the friction disk const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; for( unsigned friction_sample = 0; friction_sample < unsigned( num_samples ); ++friction_sample ) { const unsigned cur_col{ start_column + friction_sample }; assert( cur_col < unsigned( D.cols() ) ); // Effect on center of mass D.insert( 3 * m_sphere_idx + 0, cur_col ) = friction_disk[friction_sample].x(); D.insert( 3 * m_sphere_idx + 1, cur_col ) = friction_disk[friction_sample].y(); D.insert( 3 * m_sphere_idx + 2, cur_col ) = friction_disk[friction_sample].z(); // Effect on orientation { const Vector3s ntilde{ r_world.cross( friction_disk[friction_sample] ) }; D.insert( 3 * ( nbodies + m_sphere_idx ) + 0, cur_col ) = ntilde.x(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 1, cur_col ) = ntilde.y(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 2, cur_col ) = ntilde.z(); } // Relative velocity contribution from kinematic scripting assert( cur_col < drel.size() ); drel( cur_col ) = - friction_disk[friction_sample].dot( plane_collision_point_vel ); } }
void StaticPlaneSphereConstraint::computeGeneralizedFrictionGivenTangentSample( const VectorXs& q, const VectorXs& t, const unsigned column, SparseMatrixsc& D ) const { assert( t.size() == 3 ); assert( column < unsigned( D.cols() ) ); assert( q.size() % 12 == 0 ); assert( fabs( t.norm() - 1.0 ) <= 1.0e-6 ); assert( fabs( m_plane.n().dot( t ) ) <= 1.0e-6 ); // Effect on center of mass D.insert( 3 * m_sphere_idx + 0, column ) = t.x(); D.insert( 3 * m_sphere_idx + 1, column ) = t.y(); D.insert( 3 * m_sphere_idx + 2, column ) = t.z(); // Effect on orientation { const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; // Compute the displacement from the center of mass to the point of contact assert( fabs( m_plane.n().norm() - 1.0 ) <= 1.0e-10 ); assert( m_r >= 0.0 ); const Vector3s r_world{ - m_r * m_plane.n() }; const Vector3s ntilde{ r_world.cross( Eigen::Map<const Vector3s>( t.data() ) ) }; D.insert( 3 * ( nbodies + m_sphere_idx ) + 0, column ) = ntilde.x(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 1, column ) = ntilde.y(); D.insert( 3 * ( nbodies + m_sphere_idx ) + 2, column ) = ntilde.z(); } }
void TeleportedCircleCircleConstraint::evalgradg( const VectorXs& q, const int col, SparseMatrixsc& G, const FlowableSystem& fsys ) const { assert( col >= 0 ); assert( col < G.cols() ); // MUST BE ADDED GOING DOWN THE COLUMN. DO NOT TOUCH ANOTHER COLUMN. assert( m_idx0 < m_idx1 ); assert( 3 * m_idx0 + 1 < unsigned( G.rows() ) ); G.insert( 3 * m_idx0 + 0, col ) = m_n.x(); G.insert( 3 * m_idx0 + 1, col ) = m_n.y(); assert( 3 * m_idx1 + 1 < unsigned( G.rows() ) ); G.insert( 3 * m_idx1 + 0, col ) = - m_n.x(); G.insert( 3 * m_idx1 + 1, col ) = - m_n.y(); }
void StaticPlaneSphereConstraint::evalgradg( const VectorXs& q, const int col, SparseMatrixsc& G, const FlowableSystem& fsys ) const { assert( col >= 0 ); assert( col < G.cols() ); assert( 3 * m_sphere_idx + 2 < unsigned( G.rows() ) ); const Vector3s n{ m_plane.n() }; assert( fabs( n.norm() - 1.0 ) <= 1.0e-6 ); // MUST BE ADDED GOING DOWN THE COLUMN. DO NOT TOUCH ANOTHER COLUMN. G.insert( 3 * m_sphere_idx + 0, col ) = n.x(); G.insert( 3 * m_sphere_idx + 1, col ) = n.y(); G.insert( 3 * m_sphere_idx + 2, col ) = n.z(); }
void BodyBodyConstraint::evalgradg( const VectorXs& q, const int col, SparseMatrixsc& G, const FlowableSystem& fsys ) const { assert( q.size() % 12 == 0 ); assert( col >= 0 ); assert( col < G.cols() ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; // MUST BE ADDED GOING DOWN THE COLUMN. DO NOT TOUCH ANOTHER COLUMN. { assert( 3 * nbodies + 3 * m_idx0 + 2 < unsigned( G.rows() ) ); G.insert( 3 * m_idx0 + 0, col ) = m_n.x(); G.insert( 3 * m_idx0 + 1, col ) = m_n.y(); G.insert( 3 * m_idx0 + 2, col ) = m_n.z(); const Vector3s ntilde_0{ m_r0.cross( m_n ) }; G.insert( 3 * ( m_idx0 + nbodies ) + 0, col ) = ntilde_0.x(); G.insert( 3 * ( m_idx0 + nbodies ) + 1, col ) = ntilde_0.y(); G.insert( 3 * ( m_idx0 + nbodies ) + 2, col ) = ntilde_0.z(); } { assert( 3 * nbodies + 3 * m_idx1 + 2 < unsigned( G.rows() ) ); G.insert( 3 * m_idx1 + 0, col ) = - m_n.x(); G.insert( 3 * m_idx1 + 1, col ) = - m_n.y(); G.insert( 3 * m_idx1 + 2, col ) = - m_n.z(); const Vector3s ntilde_1{ m_r1.cross( m_n ) }; G.insert( 3 * ( m_idx1 + nbodies ) + 0, col ) = - ntilde_1.x(); G.insert( 3 * ( m_idx1 + nbodies ) + 1, col ) = - ntilde_1.y(); G.insert( 3 * ( m_idx1 + nbodies ) + 2, col ) = - ntilde_1.z(); } }
void BodyBodyConstraint::computeGeneralizedFrictionGivenTangentSample( const VectorXs& q, const VectorXs& t, const unsigned column, SparseMatrixsc& D ) const { assert( column < unsigned( D.cols() ) ); assert( q.size() % 12 == 0 ); assert( t.size() == 3 ); assert( fabs( t.norm() - 1.0 ) <= 1.0e-6 ); assert( fabs( m_n.dot( t ) ) <= 1.0e-6 ); assert( m_idx0 < m_idx1 ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; // Effect on center of mass of body i D.insert( 3 * m_idx0 + 0, column ) = t.x(); D.insert( 3 * m_idx0 + 1, column ) = t.y(); D.insert( 3 * m_idx0 + 2, column ) = t.z(); // Effect on orientation of body i { const Vector3s ntilde0{ m_r0.cross( Eigen::Map<const Vector3s>{ t.data() } ) }; D.insert( 3 * ( m_idx0 + nbodies ) + 0, column ) = ntilde0.x(); D.insert( 3 * ( m_idx0 + nbodies ) + 1, column ) = ntilde0.y(); D.insert( 3 * ( m_idx0 + nbodies ) + 2, column ) = ntilde0.z(); } // Effect on center of mass of body j D.insert( 3 * m_idx1 + 0, column ) = - t.x(); D.insert( 3 * m_idx1 + 1, column ) = - t.y(); D.insert( 3 * m_idx1 + 2, column ) = - t.z(); // Effect on orientation of body j { const Vector3s ntilde1{ m_r1.cross( Eigen::Map<const Vector3s>{ t.data() } ) }; D.insert( 3 * ( m_idx1 + nbodies ) + 0, column ) = - ntilde1.x(); D.insert( 3 * ( m_idx1 + nbodies ) + 1, column ) = - ntilde1.y(); D.insert( 3 * ( m_idx1 + nbodies ) + 2, column ) = - ntilde1.z(); } }
void MathUtilities::createDiagonalMatrix( const scalar& c, SparseMatrixsc& D ) { assert( D.rows() == D.cols() ); D.reserve( VectorXi::Constant( D.cols(), 1 ) ); for( int i = 0; i < D.cols(); ++i ) { D.insert(i,i) = c; } D.makeCompressed(); }
void FrictionOperatorUtilities::formLinearFrictionDiskConstraint( const int num_samples, SparseMatrixsc& E ) { { const VectorXi column_nonzeros{ VectorXi::Constant( E.cols(), num_samples ) }; E.reserve( column_nonzeros ); } // For each column for( int col = 0; col < E.cols(); ++col ) { for( int samplenum = 0; samplenum < num_samples; ++samplenum ) { // Note the negative for QL E.insert( num_samples * col + samplenum, col ) = 1.0; } } E.makeCompressed(); assert( E.nonZeros() == E.cols() * num_samples ); assert( E.sum() == E.nonZeros() ); }
// TODO: Pull the outerIndexPtr arithmetic into a helper function void MathUtilities::extractColumns( const SparseMatrixsc& A0, const std::vector<unsigned>& cols, SparseMatrixsc& A1 ) { const unsigned ncols_to_extract{ static_cast<unsigned>( cols.size() ) }; assert( ncols_to_extract <= static_cast<unsigned>( A0.cols() ) ); #ifndef NDEBUG for( unsigned i = 0; i < ncols_to_extract; ++i ) { assert( cols[i] < unsigned( A0.cols() ) ); } #endif // Compute the number of nonzeros in each column of the new matrix VectorXi column_nonzeros{ ncols_to_extract }; for( unsigned i = 0; i < ncols_to_extract; ++i ) { column_nonzeros( i ) = A0.outerIndexPtr()[cols[i]+1] - A0.outerIndexPtr()[cols[i]]; } // Resize A1 and reserve space A1.resize( A0.rows(), ncols_to_extract ); A1.reserve( column_nonzeros ); // Copy the data over, column by column for( unsigned cur_col = 0; cur_col < ncols_to_extract; ++cur_col ) { for( SparseMatrixsc::InnerIterator it( A0, cols[ cur_col ] ); it; ++it ) { A1.insert( it.row(), cur_col ) = it.value(); } } A1.makeCompressed(); #ifndef NDEBUG for( int i = 0 ; i < A1.cols(); ++i ) { assert( ( A1.outerIndexPtr()[i+1] - A1.outerIndexPtr()[i] ) == column_nonzeros( i ) ); } #endif }
void BodyBodyConstraint::computeGeneralizedFrictionDisk( const VectorXs& q, const VectorXs& v, const int start_column, const int num_samples, SparseMatrixsc& D, VectorXs& drel ) const { assert( start_column >= 0 ); assert( start_column < D.cols() ); assert( num_samples > 0 ); assert( start_column + num_samples - 1 < D.cols() ); assert( q.size() % 12 == 0 ); assert( q.size() == 2 * v.size() ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; assert( fabs( m_n.norm() - 1.0 ) <= 1.0e-6 ); std::vector<Vector3s> friction_disk; { // Compute the relative velocity Vector3s tangent_suggestion{ computeRelativeVelocity( q, v ) }; if( tangent_suggestion.cross( m_n ).squaredNorm() < 1.0e-9 ) { tangent_suggestion = FrictionUtilities::orthogonalVector( m_n ); } tangent_suggestion *= -1.0; // Sample the friction disk friction_disk.resize( num_samples ); FrictionUtilities::generateOrthogonalVectors( m_n, friction_disk, tangent_suggestion ); } assert( unsigned( num_samples ) == friction_disk.size() ); // For each sample of the friction disk assert( m_idx0 < m_idx1 ); for( int i = 0; i < num_samples; ++i ) { const int cur_col{ start_column + i }; assert( cur_col >= 0 ); assert( cur_col < D.cols() ); // Effect on center of mass of body i D.insert( 3 * m_idx0 + 0, cur_col ) = friction_disk[i].x(); D.insert( 3 * m_idx0 + 1, cur_col ) = friction_disk[i].y(); D.insert( 3 * m_idx0 + 2, cur_col ) = friction_disk[i].z(); // Effect on orientation of body i { const Vector3s ttilde0{ m_r0.cross( friction_disk[i] ) }; D.insert( 3 * ( m_idx0 + nbodies ) + 0, cur_col ) = ttilde0.x(); D.insert( 3 * ( m_idx0 + nbodies ) + 1, cur_col ) = ttilde0.y(); D.insert( 3 * ( m_idx0 + nbodies ) + 2, cur_col ) = ttilde0.z(); } // Effect on center of mass of body j D.insert( 3 * m_idx1 + 0, cur_col ) = - friction_disk[i].x(); D.insert( 3 * m_idx1 + 1, cur_col ) = - friction_disk[i].y(); D.insert( 3 * m_idx1 + 2, cur_col ) = - friction_disk[i].z(); // Effect on orientation of body j { const Vector3s ttilde1{ m_r1.cross( friction_disk[i] ) }; D.insert( 3 * ( m_idx1 + nbodies ) + 0, cur_col ) = - ttilde1.x(); D.insert( 3 * ( m_idx1 + nbodies ) + 1, cur_col ) = - ttilde1.y(); D.insert( 3 * ( m_idx1 + nbodies ) + 2, cur_col ) = - ttilde1.z(); } // Relative velocity contribution from kinematic scripting assert( cur_col < drel.size() ); // Zero for now drel( cur_col ) = 0.0; } }
void BodyBodyConstraint::computeSmoothGeneralizedFrictionDisk( const VectorXs& q, const VectorXs& v, const int start_column, SparseMatrixsc& D ) const { assert( start_column >= 0 ); assert( start_column < D.cols() ); assert( start_column+1 < D.cols() ); assert( q.size() % 12 == 0 ); assert( q.size() == 2 * v.size() ); std::vector<Vector3s> friction_disk{ 2 }; // Compute the relative velocity to use as a direction for the tangent sample friction_disk[0] = computeRelativeVelocity( q, v ); // If the relative velocity is zero, any vector will do if( friction_disk[0].cross( m_n ).squaredNorm() < 1.0e-9 ) { friction_disk[0] = FrictionUtilities::orthogonalVector( m_n ); } // Otherwise project out the component along the normal and normalize the relative velocity else { friction_disk[0] = ( friction_disk[0] - friction_disk[0].dot( m_n ) * m_n ).normalized(); } // Invert the tangent vector in order to oppose friction_disk[0] *= -1.0; // Create a second orthogonal sample in the tangent plane friction_disk[1] = m_n.cross( friction_disk[0] ).normalized(); // Don't need to normalize but it won't hurt assert( MathUtilities::isRightHandedOrthoNormal( m_n, friction_disk[0], friction_disk[1], 1.0e-6 ) ); // For each sample of the friction disk assert( m_idx0 < m_idx1 ); const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) }; for( int i = 0; i < 2; ++i ) { const int cur_col = start_column + i; assert( cur_col >= 0 ); assert( cur_col < D.cols() ); // Effect on center of mass of body i D.insert( 3 * m_idx0 + 0, cur_col ) = friction_disk[i].x(); D.insert( 3 * m_idx0 + 1, cur_col ) = friction_disk[i].y(); D.insert( 3 * m_idx0 + 2, cur_col ) = friction_disk[i].z(); // Effect on orientation of body i { const Vector3s ntilde0{ m_r0.cross( friction_disk[i] ) }; D.insert( 3 * ( m_idx0 + nbodies ) + 0, cur_col ) = ntilde0.x(); D.insert( 3 * ( m_idx0 + nbodies ) + 1, cur_col ) = ntilde0.y(); D.insert( 3 * ( m_idx0 + nbodies ) + 2, cur_col ) = ntilde0.z(); } // Effect on center of mass of body j D.insert( 3 * m_idx1 + 0, cur_col ) = - friction_disk[i].x(); D.insert( 3 * m_idx1 + 1, cur_col ) = - friction_disk[i].y(); D.insert( 3 * m_idx1 + 2, cur_col ) = - friction_disk[i].z(); // Effect on orientation of body j { const Vector3s ntilde1{ m_r1.cross( friction_disk[i] ) }; D.insert( 3 * ( m_idx1 + nbodies ) + 0, cur_col ) = - ntilde1.x(); D.insert( 3 * ( m_idx1 + nbodies ) + 1, cur_col ) = - ntilde1.y(); D.insert( 3 * ( m_idx1 + nbodies ) + 2, cur_col ) = - ntilde1.z(); } } }