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 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 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();
}
scalar HertzianPenaltyForce::computePotential( const VectorXs& q, const SparseMatrixsc& M, const VectorXs& r ) const
{
assert( q.size() % 2 == 0 ); assert( q.size() == M.rows() ); assert( q.size() == M.cols() ); assert( r.size() == q.size() / 2 );
scalar U{ 0.0 };
// For each ball
for( unsigned ball0 = 0; ball0 < r.size(); ++ball0 )
{
// For each subsequent ball
for( unsigned ball1 = ball0 + 1; ball1 < r.size(); ++ball1 )
{
// Compute the total radius
const scalar total_radius{ r(ball0) + r(ball1) };
// Compute a vector pointing from ball0 to ball1
const Vector2s n{ q.segment<2>( 2 * ball1 ) - q.segment<2>( 2 * ball0 ) };
// If the squared distance is greater or equal to the sum of the radii squared, no force
if( n.squaredNorm() > total_radius * total_radius )
{
continue;
}
// Compute the penetration depth
const scalar delta{ n.norm() - total_radius };
assert( delta < 0.0 );
// U = 0.5 * k * pen_depth^(5/2)
U += 0.5 * m_k * std::pow( -delta, scalar( 2.5 ) );
}
}
return U;
}
void Ball2DGravityForce::computeForce( const VectorXs& q, const VectorXs& v, const SparseMatrixsc& M, const VectorXs& r, VectorXs& result ) const
{
assert( q.size() % 2 == 0 ); assert( q.size() == v.size() ); assert( q.size() == M.rows() );
assert( q.size() == M.cols() ); assert( q.size() == result.size() );
for( int i = 0; i < q.size(); i += 2 )
{
assert( M.valuePtr()[ i ] == M.valuePtr()[ i + 1 ] ); assert( M.valuePtr()[ i ] > 0.0 );
result.segment<2>( i ) += M.valuePtr()[ i ] * m_g;
}
}
scalar Ball2DGravityForce::computePotential( const VectorXs& q, const SparseMatrixsc& M, const VectorXs& r ) const
{
assert( q.size() % 2 == 0 ); assert( q.size() == M.rows() ); assert( q.size() == M.cols() );
scalar U{ 0.0 };
for( int i = 0; i < q.size(); i += 2 )
{
assert( M.valuePtr()[ i ] == M.valuePtr()[ i + 1 ] ); assert( M.valuePtr()[ i ] > 0.0 );
U += - M.valuePtr()[ i ] * m_g.dot( q.segment<2>( i ) );
}
return U;
}
void FrictionOperatorUtilities::formGeneralizedFrictionBasis( const VectorXs& q0, const VectorXs& v0, const std::vector<std::unique_ptr<Constraint>>& K, const int num_samples, SparseMatrixsc& D, VectorXs& drel )
{
assert( num_samples > 0 );
assert( D.rows() == v0.size() );
assert( num_samples * int( K.size() ) == D.cols() );
// Reserve space for entries
reserveSpaceInBasisMatrix( num_samples, K, D );
// Build the matrix
buildLinearFrictionBasis( q0, v0, num_samples, K, D, drel );
D.makeCompressed();
}
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 MathUtilities::extractLowerTriangularMatrix( const SparseMatrixsc& A, SparseMatrixsc& B )
{
std::vector< Eigen::Triplet<scalar> > triplets;
for( int col = 0; col < A.outerSize(); ++col )
{
for( SparseMatrixsc::InnerIterator it( A, col ); it; ++it )
{
if( col > it.row() ) { continue; }
triplets.push_back( Eigen::Triplet<scalar>( it.row(), col, it.value() ) );
}
}
B.resize( A.rows(), A.cols() );
B.setFromTriplets( triplets.begin(), triplets.end() );
B.makeCompressed();
}
void NearEarthGravityForce::computeForce( const VectorXs& q, const VectorXs& v, const SparseMatrixsc& M, VectorXs& result ) const
{
assert( q.size() % 12 == 0 );
assert( v.size() == q.size() / 2 );
assert( M.rows() == M.cols() );
assert( M.nonZeros() == q.size() );
const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) };
const Eigen::Map<const VectorXs> masses{ M.valuePtr(), 3 * nbodies };
for( unsigned i = 0; i < nbodies; ++i )
{
assert( masses( 3 * i + 0 ) == masses( 3 * i + 1 ) );
assert( masses( 3 * i + 1 ) == masses( 3 * i + 2 ) );
result.segment<3>( 3 * i ) += masses( 3 * i ) * m_g;
}
}
void MathUtilities::serialize( const SparseMatrixsc& A, std::ostream& stm )
{
assert( stm.good() );
VectorXi col_ptr;
VectorXi row_ind;
VectorXs val;
MathUtilities::extractDataCCS( A, col_ptr, row_ind, val );
assert( col_ptr.size() == A.cols() + 1 ); assert( row_ind.size() == A.nonZeros() ); assert( val.size() == A.nonZeros() );
// Size of col_ptr == A.cols() + 1
Utilities::serializeBuiltInType( A.rows(), stm );
Utilities::serializeBuiltInType( A.cols(), stm );
stm.write( reinterpret_cast<char*>( col_ptr.data() ), col_ptr.size() * sizeof(int) );
// Size of row_ind == size of val == A.nonZeros()
Utilities::serializeBuiltInType( A.nonZeros(), stm );
stm.write( reinterpret_cast<char*>( row_ind.data() ), row_ind.size() * sizeof(int) );
stm.write( reinterpret_cast<char*>( val.data() ), val.size() * sizeof(scalar) );
}
scalar NearEarthGravityForce::computePotential( const VectorXs& q, const SparseMatrixsc& M ) const
{
assert( q.size() % 12 == 0 );
assert( M.rows() == M.cols() );
assert( M.nonZeros() == q.size() );
const unsigned nbodies{ static_cast<unsigned>( q.size() / 12 ) };
const Eigen::Map<const VectorXs> masses{ M.valuePtr(), 3 * nbodies };
scalar U = 0.0;
for( unsigned i = 0; i < nbodies; ++i )
{
assert( masses( 3 * i + 0 ) == masses( 3 * i + 1 ) );
assert( masses( 3 * i + 1 ) == masses( 3 * i + 2 ) );
U += - masses( 3 * i ) * m_g.dot( q.segment<3>( 3 * i ) );
}
return U;
}
void StaticPlaneSphereConstraint::resolveImpact( const scalar& CoR, const SparseMatrixsc& M, const scalar& ndotv, VectorXs& vout, scalar& alpha ) const
{
assert( CoR >= 0.0 );
assert( CoR <= 1.0 );
assert( ndotv < 0.0 );
assert( vout.size() % 3 == 0 );
assert( M.rows() == M.cols() );
assert( M.nonZeros() == 2 * vout.size() );
assert( 3 * m_sphere_idx + 2 < vout.size() );
const Eigen::Map<const VectorXs> m{ M.valuePtr(), vout.size() };
assert( m( 3 * m_sphere_idx ) == m( 3 * m_sphere_idx + 1 ) );
assert( m( 3 * m_sphere_idx ) == m( 3 * m_sphere_idx + 2 ) );
const scalar msphere{ m( 3 * m_sphere_idx ) };
// Compute the impulse
alpha = - ( 1.0 + CoR ) * ndotv * msphere;
assert( alpha >= 0.0 );
vout.segment<3>( 3 * m_sphere_idx ) += - ( 1.0 + CoR ) * ndotv * m_plane.n();
}
// 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 LCPOperatorQL::flow( const std::vector<std::unique_ptr<Constraint>>& cons, const SparseMatrixsc& M, const SparseMatrixsc& Minv, const VectorXs& q0, const VectorXs& v0, const VectorXs& v0F, const SparseMatrixsc& N, const SparseMatrixsc& Q, const VectorXs& nrel, const VectorXs& CoR, VectorXs& alpha )
{
// Q in 1/2 \alpha^T Q \alpha
assert( Q.rows() == Q.cols() );
MatrixXXsc Qdense = Q;
// Linear term in the objective
VectorXs Adense;
ImpactOperatorUtilities::computeLCPQPLinearTerm( N, nrel, CoR, v0, v0F, Adense );
// Solve the QP
assert( Qdense.rows() == Adense.size() ); assert( Adense.size() == alpha.size() );
const int status = solveQP( m_tol, Qdense, Adense, alpha );
// Check for problems
if( 0 != status )
{
std::cerr << "Warning, failed to solve QP in LCPOperatorQL::flow: " << QLUtilities::QLReturnStatusToString(status) << std::endl;
}
// TODO: Sanity check the solution here
}
void HertzianPenaltyForce::computeForce( const VectorXs& q, const VectorXs& v, const SparseMatrixsc& M, const VectorXs& r, VectorXs& result ) const
{
assert( q.size() % 2 == 0 ); assert( q.size() == v.size() ); assert( q.size() == M.rows() );
assert( q.size() == M.cols() ); assert( r.size() == q.size() / 2 ); assert( q.size() == result.size() );
// For each ball
for( unsigned ball0 = 0; ball0 < r.size(); ++ball0 )
{
// For each subsequent ball
for( unsigned ball1 = ball0 + 1; ball1 < r.size(); ++ball1 )
{
// Compute the total radius
const scalar total_radius{ r(ball0) + r(ball1) };
// Compute a vector pointing from ball0 to ball1
Vector2s n{ q.segment<2>( 2 * ball1 ) - q.segment<2>( 2 * ball0 ) };
// Compute the squared length of the vector
scalar d{ n.squaredNorm() };
// If the squared distance is greater or equal to the sum of the radii squared, no force
if( d > total_radius * total_radius )
{
continue;
}
// Normalize the vector between the balls
d = sqrt( d );
assert( d != 0.0 );
n /= d;
assert( fabs( n.norm() - 1.0 ) <= 1.0e-6 );
// Compute the penetration depth
d -= total_radius;
assert( d < 0.0 );
// F = 5 * k * pen_depth^(3/2) * n
const Vector2s F{ ( 5.0 / 4.0 ) * m_k * std::pow( -d, scalar( 1.5 ) ) * n };
result.segment<2>( 2 * ball1 ) += F;
result.segment<2>( 2 * ball0 ) -= F;
}
}
}
bool MathUtilities::isSquare( const SparseMatrixsc& matrix )
{
return matrix.rows() == matrix.cols();
}
