polyfem::utils Namespace Reference

Namespaces
namespace	StringUtils

Classes
class	AxisPlaneSelection
class	BoundarySampler
class	BoxSelection
class	BoxSideSelection
class	CylinderSelection
class	DenseMatrixCache
class	EdgeSampler
struct	EqualUnorderedArray
class	ExpressionValue
class	FileSelection
class	GeogramUtils
struct	HashMatrix
struct	HashPair
struct	HashUnorderedArray
	Hash function for an array where the order does not matter. More...
struct	HashVector
class	InterpolatedFunction2d
class	Interpolation
class	LinearInterpolation
class	LinearRamp
class	MatrixCache
	abstract class used for caching More...
class	NoInterpolation
class	NThread
class	PeriodicBoundary
class	PiecewiseConstantInterpolation
class	PiecewiseCubicInterpolation
class	PiecewiseInterpolation
class	PiecewiseLinearInterpolation
class	PlaneSelection
class	PolygonClipping
class	RBFInterpolation
class	RefElementSampler
class	Selection
class	SparseMatrixCache
class	SpecifiedSelection
class	SphereSelection
class	TetrahedronClipping
class	Timer
struct	Timing
class	TriangleClipping
class	UniformSelection

Functions
double	triangle_area_2D (const Eigen::Vector2d &a, const Eigen::Vector2d &b, const Eigen::Vector2d &c)
	Compute the signed area of a 2D triangle defined by three points.
double	triangle_area_3D (const Eigen::Vector3d &a, const Eigen::Vector3d &b, const Eigen::Vector3d &c)
	Compute the area of a 3D triangle defined by three points.
double	triangle_area (const Eigen::MatrixXd V)
	Compute the signed area of a triangle defined by three points.
double	tetrahedron_volume (const Eigen::Vector3d &a, const Eigen::Vector3d &b, const Eigen::Vector3d &c, const Eigen::Vector3d &d)
	Compute the signed volume of a tetrahedron defined by four points.
double	tetrahedron_volume (const Eigen::MatrixXd V)
	Compute the signed volume of a tetrahedron defined by four points.
Eigen::MatrixXd	triangle_to_clockwise_order (const Eigen::MatrixXd &triangle)
	Reorder the vertices of a triangle so they are in clockwise order.
std::vector< Eigen::MatrixXd >	triangle_fan (const Eigen::MatrixXd &convex_polygon)
	Convert a convex polygon to a list of triangles fanned around the first vertex.
Eigen::VectorXd	barycentric_coordinates (const Eigen::VectorXd &p, const Eigen::MatrixXd &V)
	Compute barycentric coordinates for point p with respect to a simplex.
bool	triangle_intersects_disk (const Eigen::Vector2d &t0, const Eigen::Vector2d &t1, const Eigen::Vector2d &t2, const Eigen::Vector2d &center, const double radius)
	Determine if a 2D triangle intersects a 2D disk.
bool	tetrahedron_intersects_ball (const Eigen::Vector3d &t0, const Eigen::Vector3d &t1, const Eigen::Vector3d &t2, const Eigen::Vector3d &t3, const Eigen::Vector3d &center, const double radius)
	Determine if a 3D tetrahedron intersects a 3D ball.
bool	are_edges_collinear (const VectorNd &ea0, const VectorNd &ea1, const VectorNd &eb0, const VectorNd &eb1, const double tol=1e-10)
	Determine if two edges are collinear.
bool	are_triangles_coplanar (const Eigen::Vector3d &t00, const Eigen::Vector3d &t01, const Eigen::Vector3d &t02, const Eigen::Vector3d &t10, const Eigen::Vector3d &t11, const Eigen::Vector3d &t12, const double tol=1e-10)
	Determine if two triangles are coplanar.
bool	are_aabbs_intersecting (const VectorNd &aabb0_min, const VectorNd &aabb0_max, const VectorNd &aabb1_min, const VectorNd &aabb1_max)
	Determine if two axis-aligned bounding boxes intersect.
void	triangle_area_2D_gradient (double ax, double ay, double bx, double by, double cx, double cy, double g[6])
	Compute the gradient of the signed area of a 2D triangle defined by three points.
void	triangle_area_2D_hessian (double ax, double ay, double bx, double by, double cx, double cy, double H[36])
	Compute the Hessian of the signed area of a 2D triangle defined by three points.
void	tetrahedron_volume_gradient (double ax, double ay, double az, double bx, double by, double bz, double cx, double cy, double cz, double dx, double dy, double dz, double g[12])
	Compute the gradient of the signed volume of a tetrahedron defined by four points.
void	tetrahedron_volume_hessian (double ax, double ay, double az, double bx, double by, double bz, double cx, double cy, double cz, double dx, double dy, double dz, double H[144])
	Compute the gradient of the signed area of a 2D triangle defined by three points.
	NLOHMANN_JSON_SERIALIZE_ENUM (PiecewiseInterpolation::Extend, {{PiecewiseInterpolation::Extend::CONSTANT, "constant"}, {PiecewiseInterpolation::Extend::EXTRAPOLATE, "extrapolate"}, {PiecewiseInterpolation::Extend::REPEAT, "repeat"}, {PiecewiseInterpolation::Extend::REPEAT_OFFSET, "repeat_offset"}})
void	apply_common_params (json &args)
Eigen::Matrix3d	to_rotation_matrix (const json &jr, std::string mode)
bool	is_param_valid (const json &params, const std::string &key)
	Determine if a key exists and is non-null in a json object.
template<typename T >
T	deg2rad (T deg)
template<typename T = json>
std::vector< T >	json_as_array (const json &j)
	Return the value of a json object as an array.
template<typename T >
T	json_value (const json &params, const std::string &key, const T &default_value)
	Get a parameter from a json object or return a default value if the parameter invalid.
void	show_matrix_stats (const Eigen::MatrixXd &M)
template<typename T >
T	determinant (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &mat)
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 >	inverse (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &mat)
Eigen::SparseMatrix< double >	sparse_identity (int rows, int cols)
Eigen::VectorXd	flatten (const Eigen::MatrixXd &X)
	Flatten rowwises.
Eigen::MatrixXd	unflatten (const Eigen::VectorXd &x, int dim)
	Unflatten rowwises, so every dim elements in x become a row.
void	vector2matrix (const Eigen::VectorXd &vec, Eigen::MatrixXd &mat)
Eigen::SparseMatrix< double >	lump_matrix (const Eigen::SparseMatrix< double > &M)
	Lump each row of a matrix into the diagonal.
void	full_to_reduced_matrix (const int full_size, const int reduced_size, const std::vector< int > &removed_vars, const StiffnessMatrix &full, StiffnessMatrix &reduced)
	Map a full size matrix to a reduced one by dropping rows and columns.
Eigen::MatrixXd	reorder_matrix (const Eigen::MatrixXd &in, const Eigen::VectorXi &in_to_out, int out_blocks=-1, const int block_size=1)
	Reorder row blocks in a matrix.
Eigen::MatrixXd	unreorder_matrix (const Eigen::MatrixXd &out, const Eigen::VectorXi &in_to_out, int in_blocks=-1, const int block_size=1)
	Undo the reordering of row blocks in a matrix.
Eigen::MatrixXi	map_index_matrix (const Eigen::MatrixXi &in, const Eigen::VectorXi &index_mapping)
	Map the entrys of an index matrix to new indices.
template<typename DstMat , typename SrcMat >
void	append_rows (DstMat &dst, const SrcMat &src)
template<typename DstMat >
void	append_rows_of_zeros (DstMat &dst, const size_t n_zero_rows)
void	maybe_parallel_for (int size, const std::function< void(int, int, int)> &partial_for)
void	maybe_parallel_for (int size, const std::function< void(int)> &body)
template<typename LocalStorage >
auto	create_thread_storage (const LocalStorage &initial_local_storage)
template<typename Storages >
auto &	get_local_thread_storage (Storages &storage, int thread_id)
void	par_for (const int size, const std::function< void(int, int, int)> &func)
size_t	get_n_threads ()
void	regular_2d_grid (const int n, bool tri, Eigen::MatrixXd &V, Eigen::MatrixXi &F)
	Generate a canonical triangle/quad subdivided from a regular grid.
void	regular_3d_grid (const int nn, bool tet, Eigen::MatrixXd &V, Eigen::MatrixXi &F, Eigen::MatrixXi &T)
	Generate a canonical tet/hex subdivided from a regular grid.
std::string	resolve_path (const std::string &path, const std::string &input_file_path, const bool only_if_exists=false)

Function Documentation

append_rows()

template<typename DstMat , typename SrcMat >

void polyfem::utils::append_rows	(	DstMat &	dst,
		const SrcMat &	src
	)

Definition at line 143 of file MatrixUtils.hpp.

Referenced by polyfem::mesh::Mesh::append(), polyfem::State::build_collision_mesh(), polyfem::mesh::SizingFieldRemesher< WMTKMesh >::compute_contact_sizing_field(), polyfem::mesh::LocalMesh< M >::LocalMesh(), polyfem::mesh::Remesher::project_quantities(), and polyfem::mesh::Remesher::write_mesh().

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append_rows_of_zeros()

template<typename DstMat >

void polyfem::utils::append_rows_of_zeros	(	DstMat &	dst,
		const size_t	n_zero_rows
	)

Definition at line 155 of file MatrixUtils.hpp.

Referenced by polyfem::io::OutGeometryData::save_volume().

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apply_common_params()

void polyfem::utils::apply_common_params

(

json &

args

)

Definition at line 14 of file JSONUtils.cpp.

References apply_common_params(), polyfem::log_and_throw_error(), and resolve_path().

Referenced by apply_common_params(), and polyfem::State::init().

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are_aabbs_intersecting()

bool polyfem::utils::are_aabbs_intersecting	(	const VectorNd &	aabb0_min,
		const VectorNd &	aabb0_max,
		const VectorNd &	aabb1_min,
		const VectorNd &	aabb1_max
	)

Determine if two axis-aligned bounding boxes intersect.

Parameters

aabb0_min	Minimum corner of the first AABB.
aabb0_max	Maximum corner of the first AABB.
aabb1_min	Minimum corner of the second AABB.
aabb1_max	Maximum corner of the second AABB.

Returns

True if the AABBs intersect, false otherwise.

Definition at line 196 of file GeometryUtils.cpp.

Referenced by polyfem::mesh::LocalMesh< M >::ball_selection().

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are_edges_collinear()

bool polyfem::utils::are_edges_collinear	(	const VectorNd &	ea0,
		const VectorNd &	ea1,
		const VectorNd &	eb0,
		const VectorNd &	eb1,
		const double	tol = 1e-10
	)

Determine if two edges are collinear.

Parameters

ea0	First vertex of the first edge.
ea1	Second vertex of the first edge.
eb0	First vertex of the second edge.
eb1	Second vertex of the second edge.
tol	Tolerance for collinearity.

Returns

True if the edges are collinear, false otherwise.

Definition at line 169 of file GeometryUtils.cpp.

are_triangles_coplanar()

bool polyfem::utils::are_triangles_coplanar	(	const Eigen::Vector3d &	t00,
		const Eigen::Vector3d &	t01,
		const Eigen::Vector3d &	t02,
		const Eigen::Vector3d &	t10,
		const Eigen::Vector3d &	t11,
		const Eigen::Vector3d &	t12,
		const double	tol = 1e-10
	)

Determine if two triangles are coplanar.

Parameters

t00	First vertex of the first triangle.
t01	Second vertex of the first triangle.
t02	Third vertex of the first triangle.
t10	First vertex of the second triangle.
t11	Second vertex of the second triangle.
t12	Third vertex of the second triangle.
tol	Tolerance for coplanarity.

Returns

True if the triangles are coplanar, false otherwise.

Definition at line 182 of file GeometryUtils.cpp.

References polyfem::assembler::cross().

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barycentric_coordinates()

Eigen::VectorXd polyfem::utils::barycentric_coordinates	(	const Eigen::VectorXd &	p,
		const Eigen::MatrixXd &	V
	)

Compute barycentric coordinates for point p with respect to a simplex.

Parameters

p	Query point.
V	Verties of the simplex as rows of a matrix.

Returns

The barycentric coordinates for point p with respect to the simplex.

Definition at line 88 of file GeometryUtils.cpp.

References V.

Referenced by polyfem::assembler::MassMatrixAssembler::assemble_cross().

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create_thread_storage()

template<typename LocalStorage >

auto polyfem::utils::create_thread_storage ( const LocalStorage &  initial_local_storage )

inline

Referenced by polyfem::assembler::MassMatrixAssembler::assemble(), polyfem::assembler::NLAssembler::assemble_energy(), polyfem::assembler::NLAssembler::assemble_energy_per_element(), polyfem::solver::TransientForm::compute_adjoint_rhs(), polyfem::assembler::RhsAssembler::compute_energy(), polyfem::assembler::PressureAssembler::compute_grad_volume(), polyfem::assembler::PressureAssembler::compute_hess_volume_2d(), polyfem::assembler::PressureAssembler::compute_hess_volume_3d(), polyfem::solver::TransientForm::compute_partial_gradient(), polyfem::assembler::PressureAssembler::compute_volume(), polyfem::solver::ElasticForm::force_material_derivative(), polyfem::solver::InertiaForm::force_shape_derivative(), polyfem::solver::ElasticForm::force_shape_derivative(), polyfem::solver::BodyForm::force_shape_derivative(), polyfem::solver::AdjointTools::integrate_objective(), polyfem::assembler::PressureAssembler::is_closed_or_boundary_fixed(), polyfem::solver::InversionBarrierForm::second_derivative_unweighted(), and polyfem::solver::TransientForm::value_unweighted().

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deg2rad()

template<typename T >

T polyfem::utils::deg2rad ( T  deg )

inline

Definition at line 18 of file JSONUtils.hpp.

References deg2rad().

Referenced by polyfem::mesh::construct_affine_transformation(), deg2rad(), and to_rotation_matrix().

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determinant()

template<typename T >

T polyfem::utils::determinant

(

const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &

mat

)

Definition at line 16 of file MatrixUtils.hpp.

References mat.

Referenced by polyfem::assembler::NeoHookeanElasticity::compute_energy_aux(), polyfem::assembler::AMIPSEnergy::elastic_energy(), polyfem::assembler::MooneyRivlin3ParamElasticity::elastic_energy(), polyfem::assembler::MooneyRivlinElasticity::elastic_energy(), polyfem::assembler::NeoHookeanAutodiff::elastic_energy(), polyfem::assembler::MooneyRivlin3ParamSymbolic::elastic_energy(), inverse(), and polyfem::third_invariant().

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flatten()

Eigen::VectorXd polyfem::utils::flatten

(

const Eigen::MatrixXd &

X

)

Flatten rowwises.

Definition at line 34 of file MatrixUtils.cpp.

References x.

Referenced by polyfem::solver::AMIPSForm::AMIPSForm(), polyfem::solver::CollisionBarrierForm::CollisionBarrierForm(), polyfem::solver::BoundarySmoothingForm::compute_partial_gradient(), polyfem::assembler::NeoHookeanElasticity::compute_stiffness_value(), polyfem::solver::DeformedCollisionBarrierForm::DeformedCollisionBarrierForm(), polyfem::solver::NLHomoProblem::full_to_reduced(), polyfem::io::Evaluator::generate_linear_field(), polyfem::solver::ElasticEnergyForm::get_integral_functional(), polyfem::solver::StressNormForm::get_integral_functional(), polyfem::solver::ComplianceForm::get_integral_functional(), polyfem::solver::StressForm::get_integral_functional(), polyfem::solver::ShapeVariableToSimulation::inverse_eval(), polyfem::solver::NLHomoProblem::macro_reduced_to_full(), polyfem::mesh::LocalRelaxationData< M >::sol(), polyfem::State::solve_homogenization_step(), polyfem::solver::MacroStrainALForm::update_quantities(), and polyfem::solver::MacroStrainLagrangianForm::update_quantities().

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full_to_reduced_matrix()

void polyfem::utils::full_to_reduced_matrix	(	const int	full_size,
		const int	reduced_size,
		const std::vector< int > &	removed_vars,
		const StiffnessMatrix &	full,
		StiffnessMatrix &	reduced
	)

Map a full size matrix to a reduced one by dropping rows and columns.

Parameters

[in]	full_size	Number of variables in the full system.
[in]	reduced_size	Number of variables in the reduced system.
[in]	removed_vars	Indices of the variables (rows and columns of full) to remove.
[in]	full	Full size matrix.
[out]	reduced	Output reduced size matrix.

Definition at line 103 of file MatrixUtils.cpp.

References entries, and POLYFEM_SCOPED_TIMER.

Referenced by polyfem::solver::NLProblem::full_hessian_to_reduced_hessian().

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get_local_thread_storage()

template<typename Storages >

auto & polyfem::utils::get_local_thread_storage ( Storages &  storage, int  thread_id  )

inline

Referenced by polyfem::assembler::MassMatrixAssembler::assemble(), polyfem::assembler::NLAssembler::assemble_energy(), polyfem::assembler::NLAssembler::assemble_energy_per_element(), polyfem::solver::TransientForm::compute_adjoint_rhs(), polyfem::assembler::RhsAssembler::compute_energy(), polyfem::solver::TransientForm::compute_partial_gradient(), polyfem::solver::ElasticForm::force_material_derivative(), polyfem::solver::InertiaForm::force_shape_derivative(), polyfem::solver::ElasticForm::force_shape_derivative(), polyfem::solver::BodyForm::force_shape_derivative(), polyfem::solver::AdjointTools::integrate_objective(), and polyfem::solver::TransientForm::value_unweighted().

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get_n_threads()

size_t polyfem::utils::get_n_threads ( )

inline

Definition at line 51 of file par_for.hpp.

References polyfem::utils::NThread::get(), and polyfem::utils::NThread::num_threads().

Referenced by par_for(), and polyfem::io::OutStatsData::save_json().

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inverse()

template<typename T >

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > polyfem::utils::inverse

(

const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, 0, 3, 3 > &

mat

)

Definition at line 32 of file MatrixUtils.hpp.

References determinant(), and mat.

Referenced by polyfem::mesh::stitch_mesh().

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is_param_valid()

bool polyfem::utils::is_param_valid	(	const json &	params,
		const std::string &	key
	)

Determine if a key exists and is non-null in a json object.

Parameters

params	JSON of parameters
key	Key to check

Returns

True if the key exists and is non-null, false otherwise.

Definition at line 131 of file JSONUtils.cpp.

Referenced by polyfem::assembler::MacroStrainValue::init(), polyfem::mesh::LocalRelaxationData< M >::init_assembler(), polyfem::State::init_time(), json_value(), polyfem::State::load_mesh(), polyfem::mesh::read_fem_mesh(), polyfem::mesh::read_obstacle_geometry(), polyfem::mesh::read_obstacle_mesh(), polyfem::OptState::root_path(), polyfem::State::root_path(), polyfem::State::set_materials(), polyfem::State::set_materials(), polyfem::assembler::GenericTensorProblem::set_parameters(), polyfem::assembler::GenericScalarProblem::set_parameters(), and polyfem::State::solve_homogenization().

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json_as_array()

template<typename T = json>

std::vector< T > polyfem::utils::json_as_array

(

const json &

j

)

Return the value of a json object as an array.

If the value is an array return it directly otherwise return a vector with the value.

Parameters

j	JSON object

Returns

Array of values

Definition at line 38 of file JSONUtils.hpp.

Referenced by polyfem::assembler::GenericMatParams::add_multimaterial(), polyfem::State::boundary_conditions_ids(), polyfem::State::build_collision_mesh(), polyfem::solver::SolveData::init_forms(), polyfem::State::load_mesh(), polyfem::State::load_mesh(), and polyfem::problem::NodeProblem::set_parameters().

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json_value()

template<typename T >

T polyfem::utils::json_value	(	const json &	params,
		const std::string &	key,
		const T &	default_value
	)

Get a parameter from a json object or return a default value if the parameter invalid.

Similar to json::value() but return default value if the parameter is null.

Definition at line 56 of file JSONUtils.hpp.

References is_param_valid().

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lump_matrix()

Eigen::SparseMatrix< double > polyfem::utils::lump_matrix

(

const Eigen::SparseMatrix< double > &

M

)

Lump each row of a matrix into the diagonal.

Parameters

M	Matrix to lump.

Returns

Lumped matrix.

Definition at line 84 of file MatrixUtils.cpp.

Referenced by polyfem::State::assemble_mass_mat(), polyfem::solver::BCLagrangianForm::init_masked_lumped_mass(), and polyfem::solver::BCPenaltyForm::init_masked_lumped_mass().

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map_index_matrix()

Eigen::MatrixXi polyfem::utils::map_index_matrix	(	const Eigen::MatrixXi &	in,
		const Eigen::VectorXi &	index_mapping
	)

Map the entrys of an index matrix to new indices.

Parameters

in	Input index matrix.
index_mapping	Mapping from old to new indices.

Returns

Mapped index matrix.

Definition at line 223 of file MatrixUtils.cpp.

Referenced by polyfem::mesh::Remesher::project_quantities(), and polyfem::mesh::LocalMesh< M >::reorder_vertices().

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maybe_parallel_for() [1/2]

void polyfem::utils::maybe_parallel_for ( int  size, const std::function< void(int)> &  body  )

inline

maybe_parallel_for() [2/2]

void polyfem::utils::maybe_parallel_for ( int  size, const std::function< void(int, int, int)> &  partial_for  )

inline

Referenced by polyfem::assembler::MassMatrixAssembler::assemble(), polyfem::assembler::NLAssembler::assemble_energy(), polyfem::assembler::NLAssembler::assemble_energy_per_element(), polyfem::solver::TransientForm::compute_adjoint_rhs(), polyfem::assembler::RhsAssembler::compute_energy(), polyfem::assembler::PressureAssembler::compute_grad_volume(), polyfem::assembler::PressureAssembler::compute_hess_volume_2d(), polyfem::assembler::PressureAssembler::compute_hess_volume_3d(), polyfem::solver::TransientForm::compute_partial_gradient(), polyfem::assembler::PressureAssembler::compute_volume(), polyfem::solver::InversionBarrierForm::first_derivative_unweighted(), polyfem::solver::ElasticForm::force_material_derivative(), polyfem::solver::InertiaForm::force_shape_derivative(), polyfem::solver::ElasticForm::force_shape_derivative(), polyfem::solver::BodyForm::force_shape_derivative(), polyfem::assembler::AssemblyValsCache::init(), polyfem::solver::AdjointTools::integrate_objective(), polyfem::assembler::PressureAssembler::is_closed_or_boundary_fixed(), polyfem::utils::SparseMatrixCache::operator+(), polyfem::utils::SparseMatrixCache::operator+=(), polyfem::solver::InversionBarrierForm::second_derivative_unweighted(), polyfem::solver::AdjointNLProblem::solve_pde(), polyfem::solver::ContactForm::value_per_element_unweighted(), polyfem::solver::TransientForm::value_unweighted(), polyfem::solver::InversionBarrierForm::value_unweighted(), and polyfem::solver::MaxStressForm::value_unweighted_step().

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NLOHMANN_JSON_SERIALIZE_ENUM()

polyfem::utils::NLOHMANN_JSON_SERIALIZE_ENUM	(	PiecewiseInterpolation::Extend	,
		{{PiecewiseInterpolation::Extend::CONSTANT, "constant"}, {PiecewiseInterpolation::Extend::EXTRAPOLATE, "extrapolate"}, {PiecewiseInterpolation::Extend::REPEAT, "repeat"}, {PiecewiseInterpolation::Extend::REPEAT_OFFSET, "repeat_offset"}}
	)

References polyfem::utils::PiecewiseInterpolation::CONSTANT, polyfem::utils::PiecewiseInterpolation::EXTRAPOLATE, polyfem::utils::PiecewiseInterpolation::REPEAT, and polyfem::utils::PiecewiseInterpolation::REPEAT_OFFSET.

par_for()

void polyfem::utils::par_for	(	const int	size,
		const std::function< void(int, int, int)> &	func
	)

Definition at line 10 of file par_for.cpp.

References get_n_threads(), and x.

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regular_2d_grid()

void polyfem::utils::regular_2d_grid	(	const int	n,
		bool	tri,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F
	)

Generate a canonical triangle/quad subdivided from a regular grid.

Parameters

[in]	n	n grid quads
[in]	tri	is a tri or a quad
[out]	V	V x 2 output vertices positions
[out]	F	F x 3 output triangle indices

Definition at line 31 of file RefElementSampler.cpp.

References polyfem::F, and V.

Referenced by polyfem::utils::RefElementSampler::build().

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regular_3d_grid()

void polyfem::utils::regular_3d_grid	(	const int	nn,
		bool	tet,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F,
		Eigen::MatrixXi &	T
	)

Generate a canonical tet/hex subdivided from a regular grid.

Parameters

[in]	n	n grid quads
[in]	tet	is a tet or a hex
[out]	V	V x 3 output vertices positions
[out]	F	F x 3 output triangle indices
[out]	T	F x 4 output tet indices

Definition at line 116 of file RefElementSampler.cpp.

References polyfem::F, and V.

Referenced by polyfem::utils::RefElementSampler::build().

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reorder_matrix()

Eigen::MatrixXd polyfem::utils::reorder_matrix	(	const Eigen::MatrixXd &	in,
		const Eigen::VectorXi &	in_to_out,
		int	out_blocks = -1,
		const int	block_size = 1
	)

Reorder row blocks in a matrix.

Parameters

in	Input matrix.
in_to_out	Mapping from input blocks to output blocks.
out_blocks	Number of blocks in the output matrix.
block_size	Size of each block.

Returns

Reordered matrix.

Definition at line 162 of file MatrixUtils.cpp.

Referenced by polyfem::mesh::Remesher::project_quantities(), and polyfem::mesh::LocalMesh< M >::reorder_vertices().

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resolve_path()

std::string polyfem::utils::resolve_path	(	const std::string &	path,
		const std::string &	input_file_path,
		const bool	only_if_exists = false
	)

Definition at line 103 of file StringUtils.cpp.

Referenced by apply_common_params(), polyfem::utils::Selection::build(), polyfem::State::build_collision_mesh(), polyfem::utils::Selection::build_selections(), polyfem::OptState::init(), polyfem::mesh::read_fem_mesh(), polyfem::mesh::read_obstacle_geometry(), polyfem::mesh::read_obstacle_mesh(), polyfem::State::resolve_input_path(), polyfem::assembler::GenericTensorProblem::set_parameters(), and polyfem::assembler::GenericScalarProblem::set_parameters().

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show_matrix_stats()

void polyfem::utils::show_matrix_stats

(

const Eigen::MatrixXd &

M

)

Definition at line 8 of file MatrixUtils.cpp.

References polyfem::logger().

Referenced by polyfem::basis::RBFWithQuadraticLagrange::compute_constraints_matrix_2d_old(), and polyfem::basis::RBFWithQuadraticLagrange::compute_constraints_matrix_3d().

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sparse_identity()

Eigen::SparseMatrix< double > polyfem::utils::sparse_identity ( int  rows, int  cols  )

inline

Definition at line 77 of file MatrixUtils.hpp.

Referenced by polyfem::solver::BCLagrangianForm::init_masked_lumped_mass(), and polyfem::solver::BCPenaltyForm::init_masked_lumped_mass().

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tetrahedron_intersects_ball()

bool polyfem::utils::tetrahedron_intersects_ball	(	const Eigen::Vector3d &	t0,
		const Eigen::Vector3d &	t1,
		const Eigen::Vector3d &	t2,
		const Eigen::Vector3d &	t3,
		const Eigen::Vector3d &	center,
		const double	radius
	)

Determine if a 3D tetrahedron intersects a 3D ball.

Parameters

t0	Tetrahedron first vertex.
t1	Tetrahedron second vertex.
t2	Tetrahedron third vertex.
t3	Tetrahedron fourth vertex.
center	Center of the ball.
radius	Radius of the ball.

Returns

True if the tetrahedron intersects the ball, false otherwise.

Definition at line 137 of file GeometryUtils.cpp.

Referenced by polyfem::mesh::LocalMesh< M >::ball_selection().

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tetrahedron_volume() [1/2]

double polyfem::utils::tetrahedron_volume

(

const Eigen::MatrixXd

V

)

Compute the signed volume of a tetrahedron defined by four points.

Parameters

V	The vertices of the terahedron as rows of a matrix.

Returns

The signed volume of the tetrahedron.

Definition at line 52 of file GeometryUtils.cpp.

References tetrahedron_volume(), and V.

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tetrahedron_volume() [2/2]

double polyfem::utils::tetrahedron_volume	(	const Eigen::Vector3d &	a,
		const Eigen::Vector3d &	b,
		const Eigen::Vector3d &	c,
		const Eigen::Vector3d &	d
	)

Compute the signed volume of a tetrahedron defined by four points.

Parameters

a	First point of the tetrahedron.
b	Second point of the tetrahedron.
c	Third point of the tetrahedron.
d	Fourth point of the tetrahedron.

Returns

The signed volume of the tetrahedron.

Definition at line 43 of file GeometryUtils.cpp.

Referenced by polyfem::assembler::MassMatrixAssembler::assemble_cross(), polyfem::utils::TetrahedronClipping::clip(), polyfem::solver::InversionBarrierForm::element_volume(), and tetrahedron_volume().

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tetrahedron_volume_gradient()

void polyfem::utils::tetrahedron_volume_gradient	(	double	ax,
		double	ay,
		double	az,
		double	bx,
		double	by,
		double	bz,
		double	cx,
		double	cy,
		double	cz,
		double	dx,
		double	dy,
		double	dz,
		double	g[12]
	)

Compute the gradient of the signed volume of a tetrahedron defined by four points.

Parameters

ax	First point's x coordinate.
ay	First point's y coordinate.
ay	First point's z coordinate.
bx	Second point's x coordinate.
by	Second point's y coordinate.
by	Second point's z coordinate.
cx	Third point's x coordinate.
cy	Third point's y coordinate.
cy	Third point's z coordinate.
dx	Fourth point's x coordinate.
dy	Fourth point's y coordinate.
dy	Fourth point's z coordinate.
g	Output gradient with respect to the four points.

Definition at line 261 of file GeometryUtils.cpp.

Referenced by polyfem::solver::InversionBarrierForm::element_volume_gradient().

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tetrahedron_volume_hessian()

void polyfem::utils::tetrahedron_volume_hessian	(	double	ax,
		double	ay,
		double	az,
		double	bx,
		double	by,
		double	bz,
		double	cx,
		double	cy,
		double	cz,
		double	dx,
		double	dy,
		double	dz,
		double	H[144]
	)

Compute the gradient of the signed area of a 2D triangle defined by three points.

Parameters

ax	First point's x coordinate.
ay	First point's y coordinate.
ay	First point's z coordinate.
bx	Second point's x coordinate.
by	Second point's y coordinate.
by	Second point's z coordinate.
cx	Third point's x coordinate.
cy	Third point's y coordinate.
cy	Third point's z coordinate.
dx	Fourth point's x coordinate.
dy	Fourth point's y coordinate.
dy	Fourth point's z coordinate.
g	Output flattened Hessian with respect to the four points.

Definition at line 295 of file GeometryUtils.cpp.

Referenced by polyfem::solver::InversionBarrierForm::element_volume_hessian().

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to_rotation_matrix()

Eigen::Matrix3d polyfem::utils::to_rotation_matrix	(	const json &	jr,
		std::string	mode
	)

Definition at line 61 of file JSONUtils.cpp.

References deg2rad().

Referenced by polyfem::mesh::construct_affine_transformation().

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triangle_area()

double polyfem::utils::triangle_area

(

const Eigen::MatrixXd

V

)

Compute the signed area of a triangle defined by three points.

Parameters

V	The vertices of the triangle as rows of a matrix.

Returns

The signed area of the triangle.

Definition at line 30 of file GeometryUtils.cpp.

References triangle_area_2D(), triangle_area_3D(), and V.

Referenced by polyfem::assembler::MassMatrixAssembler::assemble_cross(), polyfem::solver::InversionBarrierForm::element_volume(), polyfem::mesh::irregular_triangle(), and triangle_to_clockwise_order().

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triangle_area_2D()

double polyfem::utils::triangle_area_2D	(	const Eigen::Vector2d &	a,
		const Eigen::Vector2d &	b,
		const Eigen::Vector2d &	c
	)

Compute the signed area of a 2D triangle defined by three points.

Parameters

a	First point of the triangle.
b	Second point of the triangle.
c	Third point of the triangle.

Returns

The signed area of the triangle.

Definition at line 14 of file GeometryUtils.cpp.

Referenced by polyfem::mesh::WildRemesher< WMTKMesh >::swap_edge_before(), and triangle_area().

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triangle_area_2D_gradient()

void polyfem::utils::triangle_area_2D_gradient	(	double	ax,
		double	ay,
		double	bx,
		double	by,
		double	cx,
		double	cy,
		double	g[6]
	)

Compute the gradient of the signed area of a 2D triangle defined by three points.

Parameters

ax	First point's x coordinate.
ay	First point's y coordinate.
bx	Second point's x coordinate.
by	Second point's y coordinate.
cx	Third point's x coordinate.
cy	Third point's y coordinate.
g	Output gradient with respect to the three points.

Definition at line 209 of file GeometryUtils.cpp.

Referenced by polyfem::solver::InversionBarrierForm::element_volume_gradient().

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triangle_area_2D_hessian()

void polyfem::utils::triangle_area_2D_hessian	(	double	ax,
		double	ay,
		double	bx,
		double	by,
		double	cx,
		double	cy,
		double	H[36]
	)

Compute the Hessian of the signed area of a 2D triangle defined by three points.

Parameters

ax	First point's x coordinate.
ay	First point's y coordinate.
bx	Second point's x coordinate.
by	Second point's y coordinate.
cx	Third point's x coordinate.
cy	Third point's y coordinate.
g	Output flattened Hessian with respect to the three points.

Definition at line 221 of file GeometryUtils.cpp.

Referenced by polyfem::solver::InversionBarrierForm::element_volume_hessian().

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triangle_area_3D()

double polyfem::utils::triangle_area_3D	(	const Eigen::Vector3d &	a,
		const Eigen::Vector3d &	b,
		const Eigen::Vector3d &	c
	)

Compute the area of a 3D triangle defined by three points.

Parameters

a	First point of the triangle.
b	Second point of the triangle.
c	Third point of the triangle.

Returns

The signed area of the triangle.

Definition at line 22 of file GeometryUtils.cpp.

Referenced by triangle_area().

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triangle_fan()

std::vector< Eigen::MatrixXd > polyfem::utils::triangle_fan

(

const Eigen::MatrixXd &

convex_polygon

)

Convert a convex polygon to a list of triangles fanned around the first vertex.

Parameters

convex_polygon

The vertices of the convex polygon as rows of a matrix.

Returns

The list of triangles as matrices of rows.

Definition at line 74 of file GeometryUtils.cpp.

Referenced by polyfem::utils::TriangleClipping::clip().

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triangle_intersects_disk()

bool polyfem::utils::triangle_intersects_disk	(	const Eigen::Vector2d &	t0,
		const Eigen::Vector2d &	t1,
		const Eigen::Vector2d &	t2,
		const Eigen::Vector2d &	center,
		const double	radius
	)

Determine if a 2D triangle intersects a 2D disk.

Parameters

t0	Triangle first vertex.
t1	Triangle second vertex.
t2	Triangle third vertex.
center	Center of the disk.
radius	Radius of the disk.

Returns

True if the triangle intersects the disk, false otherwise.

Definition at line 107 of file GeometryUtils.cpp.

Referenced by polyfem::mesh::LocalMesh< M >::ball_selection().

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triangle_to_clockwise_order()

Eigen::MatrixXd polyfem::utils::triangle_to_clockwise_order

(

const Eigen::MatrixXd &

triangle

)

Reorder the vertices of a triangle so they are in clockwise order.

Parameters

triangle

The vertices of the triangle as rows of a matrix.

Returns

The vertices of the triangle in clockwise order as rows of a matrix.

Definition at line 58 of file GeometryUtils.cpp.

References triangle_area().

Referenced by polyfem::utils::TriangleClipping::clip().

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unflatten()

Eigen::MatrixXd polyfem::utils::unflatten	(	const Eigen::VectorXd &	x,
		int	dim
	)

Unflatten rowwises, so every dim elements in x become a row.

Definition at line 53 of file MatrixUtils.cpp.

References x.

Referenced by polyfem::solver::ContactForm::compute_displaced_surface(), polyfem::State::compute_force_jacobian_prev(), polyfem::solver::CollisionBarrierForm::compute_partial_gradient(), polyfem::solver::DeformedCollisionBarrierForm::compute_partial_gradient(), polyfem::solver::FrictionForm::compute_surface_velocities(), polyfem::mesh::constrained_L2_projection(), polyfem::io::OutGeometryData::export_data(), polyfem::solver::InversionBarrierForm::first_derivative_unweighted(), polyfem::solver::FrictionForm::force_shape_derivative(), polyfem::solver::ElasticEnergyForm::get_integral_functional(), polyfem::utils::PiecewiseCubicInterpolation::init(), polyfem::State::init_nonlinear_tensor_solve(), polyfem::solver::CollisionBarrierForm::is_step_collision_free(), polyfem::solver::AMIPSForm::is_step_valid(), polyfem::solver::InversionBarrierForm::is_step_valid(), polyfem::solver::CollisionBarrierForm::max_step_size(), polyfem::solver::NLHomoProblem::reduced_to_full(), polyfem::io::OutGeometryData::save_contact_surface(), polyfem::io::OutGeometryData::save_volume(), polyfem::io::OutGeometryData::save_volume_vector_field(), polyfem::solver::InversionBarrierForm::second_derivative_unweighted(), polyfem::solver::CollisionBarrierForm::solution_changed(), polyfem::solver::DeformedCollisionBarrierForm::solution_changed(), polyfem::State::solve_homogenization(), polyfem::State::solve_homogenization_step(), polyfem::solver::CollisionBarrierForm::value_unweighted(), polyfem::solver::DeformedCollisionBarrierForm::value_unweighted(), polyfem::solver::InversionBarrierForm::value_unweighted(), vector2matrix(), polyfem::mesh::Remesher::write_mesh(), and polyfem::mesh::LocalMesh< M >::write_mesh().

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unreorder_matrix()

Eigen::MatrixXd polyfem::utils::unreorder_matrix	(	const Eigen::MatrixXd &	out,
		const Eigen::VectorXi &	in_to_out,
		int	in_blocks = -1,
		const int	block_size = 1
	)

Undo the reordering of row blocks in a matrix.

Parameters

out	Reordered matrix.
in_to_out	Mapping from input blocks to output blocks.
in_blocks	Number of blocks in the input matrix.
block_size	Size of each block.

Returns

Unreordered matrix.

Definition at line 193 of file MatrixUtils.cpp.

Referenced by polyfem::mesh::Remesher::project_quantities().

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vector2matrix()

void polyfem::utils::vector2matrix	(	const Eigen::VectorXd &	vec,
		Eigen::MatrixXd &	mat
	)

Definition at line 69 of file MatrixUtils.cpp.

References mat, unflatten(), and vec.

Referenced by polyfem::solver::ComplianceForm::compute_partial_gradient_step(), polyfem::solver::AdjointTools::compute_shape_derivative_functional_term(), polyfem::solver::ElasticForm::force_material_derivative(), polyfem::solver::ElasticForm::force_shape_derivative(), polyfem::solver::StressNormForm::get_integral_functional(), polyfem::solver::ComplianceForm::get_integral_functional(), and polyfem::solver::StressForm::get_integral_functional().

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