Namespaces
namespace	MeshProcessing3D

namespace	Navigation

namespace	Navigation3D

namespace	Polygons

Classes
class	CMesh2D

class	CMesh3D

struct	Edge

struct	Element

struct	Face

class	LocalBoundary
	Boundary primitive IDs for a single element. More...

class	LocalMesh

class	LocalRelaxationData

class	Mesh
	Abstract mesh class to capture 2d/3d conforming and non-conforming meshes. More...

class	Mesh2D

class	Mesh3D

class	Mesh3DStorage

struct	Mesh_Quality

class	MeshNodes

class	NCMesh2D

class	NCMesh3D

class	Obstacle

class	PhysicsRemesher

class	PhysicsTetRemesher

class	PhysicsTriRemesher

class	Remesher

class	SizingFieldRemesher

class	TetOperationCache

class	TriOperationCache

struct	Vertex

class	WildRemesher

Typedefs
typedef std::function< void(const Eigen::MatrixXd &, Eigen::MatrixXd &, int)>	EvalParametersFunc

typedef std::function< std::tuple< int, int, bool >(int, int)>	GetAdjacentLocalEdge

using	SizingFieldTriRemesher = SizingFieldRemesher< wmtk::TriMesh >

using	SizingFieldTetRemesher = SizingFieldRemesher< wmtk::TetMesh >

using	TriMesh = WildRemesher< wmtk::TriMesh >

using	TetMesh = WildRemesher< wmtk::TetMesh >

using	WildTriRemesher = WildRemesher< wmtk::TriMesh >

using	WildTetRemesher = WildRemesher< wmtk::TetMesh >

using	Tuple = WildTetRemesher::Tuple

Enumerations
enum class	CollisionProxyTessellation { REGULAR , IRREGULAR }

enum class	BoundaryType { TRI_LINE , QUAD_LINE , TRI , QUAD , POLYGON , POLYHEDRON , INVALID }

enum class	ElementType { SIMPLEX = 0 , REGULAR_INTERIOR_CUBE , SIMPLE_SINGULAR_INTERIOR_CUBE , MULTI_SINGULAR_INTERIOR_CUBE , REGULAR_BOUNDARY_CUBE , SIMPLE_SINGULAR_BOUNDARY_CUBE , MULTI_SINGULAR_BOUNDARY_CUBE , INTERFACE_CUBE , INTERIOR_POLYTOPE , BOUNDARY_POLYTOPE , UNDEFINED }
	Type of Element, check [Poly-Spline Finite Element Method] for a complete description. More...

enum class	MeshType { TRI = 0 , QUA , H_SUR , TET , HYB , HEX }

enum class	CollapseEdgeTo { V0 , V1 , MIDPOINT , ILLEGAL }

Functions
void	build_collision_proxy (const std::vector< basis::ElementBases > &bases, const std::vector< basis::ElementBases > &geom_bases, const std::vector< LocalBoundary > &total_local_boundary, const int n_bases, const int dim, const double max_edge_length, Eigen::MatrixXd &proxy_vertices, Eigen::MatrixXi &proxy_faces, std::vector< Eigen::Triplet< double > > &displacement_map_entries, const CollisionProxyTessellation tessellation)

void	build_collision_proxy_displacement_map (const std::vector< basis::ElementBases > &bases, const std::vector< basis::ElementBases > &geom_bases, const std::vector< mesh::LocalBoundary > &total_local_boundary, const int n_bases, const int dim, const Eigen::MatrixXd &proxy_vertices, std::vector< Eigen::Triplet< double > > &displacement_map)
	Build a collision proxy displacement map for a given mesh and proxy mesh.

void	load_collision_proxy (const std::string &mesh_filename, const std::string &weights_filename, const Eigen::VectorXi &in_node_to_node, const json &transformation, Eigen::MatrixXd &vertices, Eigen::VectorXi &codim_vertices, Eigen::MatrixXi &edges, Eigen::MatrixXi &faces, std::vector< Eigen::Triplet< double > > &displacement_map_entries)
	Load a collision proxy mesh and displacement map from files.

void	load_collision_proxy_mesh (const std::string &mesh_filename, const json &transformation, Eigen::MatrixXd &vertices, Eigen::VectorXi &codim_vertices, Eigen::MatrixXi &edges, Eigen::MatrixXi &faces)
	Load a collision proxy mesh from a file.

void	load_collision_proxy_displacement_map (const std::string &weights_filename, const Eigen::VectorXi &in_node_to_node, const size_t num_proxy_vertices, std::vector< Eigen::Triplet< double > > &displacement_map_entries)
	Load a collision proxy displacement map from files.

	NLOHMANN_JSON_SERIALIZE_ENUM (CollisionProxyTessellation, {{CollisionProxyTessellation::REGULAR, "regular"}, {CollisionProxyTessellation::IRREGULAR, "irregular"}})

void	build_collision_proxy (const std::vector< basis::ElementBases > &bases, const std::vector< basis::ElementBases > &geom_bases, const std::vector< mesh::LocalBoundary > &total_local_boundary, const int n_bases, const int dim, const double max_edge_length, Eigen::MatrixXd &proxy_vertices, Eigen::MatrixXi &proxy_faces, std::vector< Eigen::Triplet< double > > &displacement_map, const CollisionProxyTessellation tessellation=CollisionProxyTessellation::REGULAR)
	Build a collision proxy mesh by upsampling a given mesh.

void	stitch_mesh (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, Eigen::MatrixXd &V_out, Eigen::MatrixXi &F_out, const double epsilon=1e-5)
	Stitch a triangle mesh (V, F) together by removing duplicate vertices.

void	stitch_mesh (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const std::vector< Eigen::Triplet< double > > &W, Eigen::MatrixXd &V_out, Eigen::MatrixXi &F_out, std::vector< Eigen::Triplet< double > > &W_out, const double epsilon=1e-5)
	Stitch a triangle mesh (V, F) together by removing duplicate vertices.

double	max_edge_length (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F)
	Compute the maximum edge length of a triangle mesh (V, F)

void	regular_grid_triangle_barycentric_coordinates (const int n, Eigen::MatrixXd &V, Eigen::MatrixXi &F)
	Compute the barycentric coordinates of a regular grid of triangles.

void	regular_grid_tessellation (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const double max_edge_length, Eigen::MatrixXd &V_out, Eigen::MatrixXi &F_out)
	Tessilate a triangle mesh (V, F) with regular grids of triangles of maximum edge length.

Eigen::MatrixXd	refine_edge (const VectorNd &a, const VectorNd &b, const double max_edge_length)
	Refine an edge (a, b) so each refined edge has length at most max_edge_length.

void	refine_triangle_edges (const VectorNd &a, const VectorNd &b, const VectorNd &c, const double max_edge_len, Eigen::MatrixXd &V, Eigen::MatrixXi &E)
	Refine the edges of a triangle (a, b, c) so each refined edge has length at most max_edge_length.

void	irregular_triangle (const Eigen::Vector3d &a, const Eigen::Vector3d &b, const Eigen::Vector3d &c, const double max_edge_length, Eigen::MatrixXd &V, Eigen::MatrixXi &F)
	Refine a triangle (a, b, c) into a well shaped triangle mesh.

void	irregular_triangle_barycentric_coordinates (const Eigen::Vector3d &a, const Eigen::Vector3d &b, const Eigen::Vector3d &c, const double max_edge_length, Eigen::MatrixXd &UV, Eigen::MatrixXi &F)
	Refine a triangle (a, b, c) into a well shaped triangle mesh.

void	irregular_tessellation (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const double max_edge_length, Eigen::MatrixXd &V_out, Eigen::MatrixXi &F_out)
	Tessilate a triangle mesh (V, F) with well shaped triangles.

std::unique_ptr< Mesh >	read_fem_mesh (const Units &units, const json &j_mesh, const std::string &root_path, const bool non_conforming=false)
	read a FEM mesh from a geometry JSON

std::unique_ptr< Mesh >	read_fem_geometry (const Units &units, const json &geometry, const std::string &root_path, const std::vector< std::string > &names=std::vector< std::string >(), const std::vector< Eigen::MatrixXd > &vertices=std::vector< Eigen::MatrixXd >(), const std::vector< Eigen::MatrixXi > &cells=std::vector< Eigen::MatrixXi >(), const bool non_conforming=false)
	read FEM meshes from a geometry JSON array (or single)

void	read_obstacle_mesh (const Units &units, const json &j_mesh, const std::string &root_path, const int dim, Eigen::MatrixXd &vertices, Eigen::VectorXi &codim_vertices, Eigen::MatrixXi &codim_edges, Eigen::MatrixXi &faces)
	read a obstacle mesh from a geometry JSON

Obstacle	read_obstacle_geometry (const Units &units, const json &geometry, const std::vector< json > &displacements, const std::vector< json > &dirichlets, const std::string &root_path, const int dim, const std::vector< std::string > &names=std::vector< std::string >(), const std::vector< Eigen::MatrixXd > &vertices=std::vector< Eigen::MatrixXd >(), const std::vector< Eigen::MatrixXi > &cells=std::vector< Eigen::MatrixXi >(), const bool non_conforming=false)
	read a FEM mesh from a geometry JSON

void	construct_affine_transformation (const double unit_scale, const json &transform, const VectorNd &mesh_dimensions, MatrixNd &A, VectorNd &b)
	Construct an affine transformation \(Ax+b\).

std::ostream &	operator<< (std::ostream &os, const LocalBoundary &lb)

int	find (const Eigen::VectorXi &vec, int x)

double	line_weight (Eigen::Matrix< double, 2, 2 > &e, Eigen::VectorXd &v)

void	clip_polygon_by_half_plane (const Eigen::MatrixXd &P, const Eigen::RowVector2d &q1, const Eigen::RowVector2d &q2, Eigen::MatrixXd &result)
	Clip a polygon by a half-plane.

void	compute_visibility_kernel (const Eigen::MatrixXd &IV, Eigen::MatrixXd &OV)
	Determine the kernel of the given polygon.

bool	is_star_shaped (const Eigen::MatrixXd &IV, Eigen::RowVector3d &bary)
	Determine whether a polygon is star-shaped or not.

void	offset_polygon (const Eigen::MatrixXd &IV, Eigen::MatrixXd &OV, double eps)
	Compute offset polygon.

int	is_inside (const Eigen::MatrixXd &IV, const Eigen::MatrixXd &Q, std::vector< bool > &inside)
	Compute whether points are inside a polygon.

void	sample_polygon (const Eigen::MatrixXd &IV, int num_samples, Eigen::MatrixXd &S)
	Sample points on a polygon, evenly spaced from each other.

void	edge_adjacency_graph (const Eigen::MatrixXi &Q, Eigen::MatrixXi &edge_index, std::vector< std::vector< int > > &adj, std::vector< std::pair< int, int > > pairs_of_edges=nullptr, std::vector< std::pair< int, int > > pairs_of_quads=nullptr, Eigen::MatrixXi *quad_index=nullptr)

bool	instantiate_pattern (const Eigen::MatrixXd &IV, const Eigen::MatrixXi &IF, const Eigen::MatrixXd &PV, const Eigen::MatrixXi &PF, Eigen::MatrixXd &OV, Eigen::MatrixXi &OF, Eigen::VectorXi *SF=nullptr, EvalParametersFunc evalFunc=nullptr, GetAdjacentLocalEdge getAdjLocalEdge=nullptr)

void	refine_quad_mesh (const Eigen::MatrixXd &IV, const Eigen::MatrixXi &IF, Eigen::MatrixXd &OV, Eigen::MatrixXi &OF)

void	refine_polygonal_mesh (const GEO::Mesh &M_in, GEO::Mesh &M_out, Polygons::SplitFunction split_func)
	Refine a polygonal mesh.

void	refine_triangle_mesh (const GEO::Mesh &M_in, GEO::Mesh &M_out)
	Refine a triangle mesh.

void	refine_polygonal_mesh (const GEO::Mesh &M_in, GEO::Mesh &M_out, bool refine_polygons=false, double t=0.5)

void	singular_vertices (const GEO::Mesh &M, Eigen::VectorXi &V, int regular_degree=4, bool ignore_border=true)

void	singular_edges (const GEO::Mesh &M, const Eigen::VectorXi &V, Eigen::MatrixX2i &E)

void	singularity_graph (const GEO::Mesh &M, Eigen::VectorXi &V, Eigen::MatrixX2i &E, int regular_degree=4, bool ignore_border=true)

void	create_patch_around_singularities (GEO::Mesh &M, const Eigen::VectorXi &V, const Eigen::MatrixX2i &E, double t=0.5)

GEO::vec3	mesh_vertex (const GEO::Mesh &M, GEO::index_t v)
	Retrieve a 3D vector with the position of a given vertex.

GEO::vec3	facet_barycenter (const GEO::Mesh &M, GEO::index_t f)

GEO::index_t	mesh_create_vertex (GEO::Mesh &M, const GEO::vec3 &p)

void	compute_element_tags (const GEO::Mesh &M, std::vector< ElementType > &element_tags)
	Compute the type of each facet in a surface mesh.

void	orient_normals_2d (GEO::Mesh &M)
	Orient facets of a 2D mesh so that each connected component has positive volume.

void	reorder_mesh (Eigen::MatrixXd &V, Eigen::MatrixXi &F, const Eigen::VectorXi &C, Eigen::VectorXi &R)
	Reorder vertices of a mesh using color tags, so that vertices are ordered by increasing colors.

void	signed_squared_distances (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::MatrixXd &P, Eigen::VectorXd &D)
	Computes the signed squared distance from a list of points to a triangle mesh.

void	to_geogram_mesh (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, GEO::Mesh &M)
	Converts a triangle mesh to a Geogram mesh.

void	from_geogram_mesh (const GEO::Mesh &M, Eigen::MatrixXd &V, Eigen::MatrixXi &F, Eigen::MatrixXi &T)
	Extract simplices from a Geogram mesh.

void	to_geogram_mesh (const Mesh3D &mesh, GEO::Mesh &M)
	Converts a hex mesh to a Geogram mesh.

double	signed_volume (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F)
	Compute the signed volume of a surface mesh.

void	orient_closed_surface (const Eigen::MatrixXd &V, Eigen::MatrixXi &F, bool positive=true)
	Orient a triangulated surface to have positive volume.

void	extract_polyhedra (const Mesh3D &mesh, std::vector< std::unique_ptr< GEO::Mesh > > &polys, bool triangulated=false)
	Extract polyhedra from a 3D volumetric mesh.

void	tertrahedralize_star_shaped_surface (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::RowVector3d &kernel, Eigen::MatrixXd &OV, Eigen::MatrixXi &OF, Eigen::MatrixXi &OT)
	Tetrahedralize a star-shaped mesh, with a given point in its kernel.

void	sample_surface (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, int num_samples, Eigen::MatrixXd &P, Eigen::MatrixXd *N=nullptr, int num_lloyd=10, int num_newton=10)
	Samples points on a surface.

void	extract_parent_edges (const Eigen::MatrixXd &IV, const Eigen::MatrixXi &IE, const Eigen::MatrixXd &BV, const Eigen::MatrixXi &BE, Eigen::MatrixXi &OE)
	Extract a set of edges that are overlap with a set given set of parent edges, using vertices positions to discriminate.

void	extract_triangle_surface_from_tets (const Eigen::MatrixXd &vertices, const Eigen::MatrixXi &tets, Eigen::MatrixXd &surface_vertices, Eigen::MatrixXi &tris)
	Extract triangular surface from a tetmesh.

bool	read_surface_mesh (const std::string &mesh_path, Eigen::MatrixXd &vertices, Eigen::VectorXi &codim_vertices, Eigen::MatrixXi &codim_edges, Eigen::MatrixXi &faces)
	read a surface mesh

bool	is_planar (const GEO::Mesh &M, const double tol=1e-5)
	Determine if the given mesh is planar (2D or tiny z-range).

int	count_faces (const int dim, const Eigen::MatrixXi &cells)
	Count the number of boundary elements (triangles for tetmesh and edges for triangle mesh)

void	generate_edges (GEO::Mesh &M)
	assing edges to M

Eigen::MatrixXd	unconstrained_L2_projection (const Eigen::SparseMatrix< double > &M, const Eigen::SparseMatrix< double > &A, const Eigen::Ref< const Eigen::MatrixXd > &y)

void	reduced_L2_projection (const Eigen::MatrixXd &M, const Eigen::MatrixXd &A, const Eigen::Ref< const Eigen::MatrixXd > &y, const std::vector< int > &boundary_nodes, Eigen::Ref< Eigen::MatrixXd > x)

Eigen::VectorXd	constrained_L2_projection (std::shared_ptr< polysolve::nonlinear::Solver > nl_solver, const Eigen::SparseMatrix< double > &M, const Eigen::SparseMatrix< double > &A, const Eigen::VectorXd &y, const Eigen::MatrixXd &rest_positions, const Eigen::MatrixXi &elements, const int dim, const ipc::CollisionMesh &collision_mesh, const double dhat, const double barrier_stiffness, const bool use_convergent_formulation, const ipc::BroadPhaseMethod broad_phase_method, const double ccd_tolerance, const int ccd_max_iterations, const std::vector< int > &boundary_nodes, const size_t obstacle_ndof, const Eigen::VectorXd &target_x, const Eigen::VectorXd &x0)

void	unique_facet_tuples (const wmtk::TriMesh &m, std::vector< wmtk::TriMesh::Tuple > &tuples)

void	unique_facet_tuples (const wmtk::TetMesh &m, std::vector< wmtk::TetMesh::Tuple > &tuples)

void	add_solver_timings (decltype(Remesher::timings) &timings, const polyfem::json &solver_info)

template<class WMTKMesh >
double	get_quality (const WildRemesher< WMTKMesh > &m, const typename WMTKMesh::Tuple &t)

template<class WMTKMesh >
void	project_local_quantities (WildRemesher< WMTKMesh > &m, LocalMesh< WildRemesher< WMTKMesh > > &old_local_mesh, LocalMesh< WildRemesher< WMTKMesh > > &new_local_mesh)

double	compute_valence_energy (const WildTriRemesher &m, std::string op, const WildTriRemesher::Tuple &t)

double	compute_area_ratio_energy (const WildTriRemesher &m, std::string op, const WildTriRemesher::Tuple &t)

template<typename WMTKMesh >
Remesher::EdgeMap< typename WildRemesher< WMTKMesh >::EdgeAttributes::EnergyRank >	rank_edges (const Remesher::EdgeMap< double > &edge_energy, const json &args)

bool	apply_slim (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::MatrixXd &V_new, Eigen::MatrixXd &V_smooth, const int max_iters)

Typedef Documentation

◆ EvalParametersFunc

typedef std::function<void(const Eigen::MatrixXd &, Eigen::MatrixXd &, int)> polyfem::mesh::EvalParametersFunc

Definition at line 30 of file Refinement.hpp.

◆ GetAdjacentLocalEdge

typedef std::function<std::tuple<int, int, bool>(int, int)> polyfem::mesh::GetAdjacentLocalEdge

Definition at line 31 of file Refinement.hpp.

◆ SizingFieldTetRemesher

using polyfem::mesh::SizingFieldTetRemesher = typedef SizingFieldRemesher<wmtk::TetMesh>

Definition at line 70 of file SizingFieldRemesher.hpp.

◆ SizingFieldTriRemesher

using polyfem::mesh::SizingFieldTriRemesher = typedef SizingFieldRemesher<wmtk::TriMesh>

Definition at line 69 of file SizingFieldRemesher.hpp.

◆ TetMesh

using polyfem::mesh::TetMesh = typedef WildRemesher<wmtk::TetMesh>

Definition at line 36 of file LocalMesh.cpp.

◆ TriMesh

using polyfem::mesh::TriMesh = typedef WildRemesher<wmtk::TriMesh>

Definition at line 35 of file LocalMesh.cpp.

◆ Tuple

typedef WildTriRemesher::Tuple polyfem::mesh::Tuple

Definition at line 14 of file WildTetRemesher.cpp.

◆ WildTetRemesher

using polyfem::mesh::WildTetRemesher = typedef WildRemesher<wmtk::TetMesh>

Definition at line 428 of file WildRemesher.hpp.

◆ WildTriRemesher

using polyfem::mesh::WildTriRemesher = typedef WildRemesher<wmtk::TriMesh>

Definition at line 427 of file WildRemesher.hpp.

Enumeration Type Documentation

◆ BoundaryType

enum class polyfem::mesh::BoundaryType

strong

Enumerator
TRI_LINE	Boundary of a triangle in 2D.
QUAD_LINE	Boundary of a quad in 2D.
TRI
QUAD
POLYGON
POLYHEDRON
INVALID

Definition at line 12 of file LocalBoundary.hpp.

◆ CollapseEdgeTo

enum class polyfem::mesh::CollapseEdgeTo

strong

Enumerator
V0
V1
MIDPOINT
ILLEGAL

Definition at line 14 of file WildRemesher.hpp.

◆ CollisionProxyTessellation

enum class polyfem::mesh::CollisionProxyTessellation

strong

Enumerator
REGULAR	Regular tessellation of the mesh.
IRREGULAR	Irregular tessellation of the mesh (requires POLYFEM_WITH_TRIANGLE)

Definition at line 12 of file CollisionProxy.hpp.

◆ ElementType

enum class polyfem::mesh::ElementType

strong

Type of Element, check [Poly-Spline Finite Element Method] for a complete description.

NOTE: For the purpose of the tagging, elements (facets in 2D, cells in 3D) adjacent to a polytope are tagged as boundary, and vertices incident to a polytope are also considered as boundary.

Enumerator
SIMPLEX
REGULAR_INTERIOR_CUBE	Triangle/tet element.
SIMPLE_SINGULAR_INTERIOR_CUBE	Regular quad/hex inside a 3^n patch.
MULTI_SINGULAR_INTERIOR_CUBE	Quad/hex incident to exactly 1 singular vertex (in 2D) or edge (in 3D)
REGULAR_BOUNDARY_CUBE	Quad/Hex incident to more than 1 singular vertices (should not happen in 2D)
SIMPLE_SINGULAR_BOUNDARY_CUBE	Boundary quad/hex, where all boundary vertices/edges are incident to at most 2 quads/hexes.
MULTI_SINGULAR_BOUNDARY_CUBE	Quad incident to exactly 1 singular vertex (in 2D); hex incident to exactly 1 singular interior edge, 0 singular boundary edge, 1 boundary face (in 3D)
INTERFACE_CUBE	Boundary hex that is not regular nor SimpleSingularBoundaryCube.
INTERIOR_POLYTOPE	Quad/hex that is at the interface with a polytope (if a cube has both external boundary and and interface with a polytope, it is marked as interface)
BOUNDARY_POLYTOPE	Interior polytope.
UNDEFINED	Boundary polytope.

Definition at line 22 of file Mesh.hpp.

◆ MeshType

enum class polyfem::mesh::MeshType

strong

Enumerator
TRI
QUA
H_SUR
TET
HYB
HEX

Definition at line 54 of file Mesh3DStorage.hpp.

Function Documentation

◆ add_solver_timings()

void polyfem::mesh::add_solver_timings	(	decltype(Remesher::timings) &	timings,
		const polyfem::json &	solver_info
	)

Definition at line 11 of file LocalRelaxation.cpp.

References polyfem::utils::StringUtils::startswith().

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◆ apply_slim()

bool polyfem::mesh::apply_slim	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const Eigen::MatrixXd &	V_new,
		Eigen::MatrixXd &	V_smooth,
		const int	max_iters
	)

Definition at line 11 of file SlimSmooth.cpp.

References polyfem::adjoint_logger(), polyfem::F, polyfem::solver::AdjointTools::is_flipped(), polyfem::logger(), and V.

Referenced by polyfem::solver::AdjointNLProblem::after_line_search_custom_operation(), and polyfem::solver::AdjointNLProblem::is_step_valid().

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◆ build_collision_proxy() [1/2]

void polyfem::mesh::build_collision_proxy	(	const std::vector< basis::ElementBases > &	bases,
		const std::vector< basis::ElementBases > &	geom_bases,
		const std::vector< LocalBoundary > &	total_local_boundary,
		const int	n_bases,
		const int	dim,
		const double	max_edge_length,
		Eigen::MatrixXd &	proxy_vertices,
		Eigen::MatrixXi &	proxy_faces,
		std::vector< Eigen::Triplet< double > > &	displacement_map_entries,
		const CollisionProxyTessellation	tessellation
	)

Definition at line 73 of file CollisionProxy.cpp.

References polyfem::basis::ElementBases::bases, IRREGULAR, irregular_triangle_barycentric_coordinates(), polyfem::log_and_throw_error(), max_edge_length(), REGULAR, regular_grid_triangle_barycentric_coordinates(), stitch_mesh(), TRI, and x.

Referenced by polyfem::State::build_collision_mesh().

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◆ build_collision_proxy() [2/2]

void polyfem::mesh::build_collision_proxy	(	const std::vector< basis::ElementBases > &	bases,
		const std::vector< basis::ElementBases > &	geom_bases,
		const std::vector< mesh::LocalBoundary > &	total_local_boundary,
		const int	n_bases,
		const int	dim,
		const double	max_edge_length,
		Eigen::MatrixXd &	proxy_vertices,
		Eigen::MatrixXi &	proxy_faces,
		std::vector< Eigen::Triplet< double > > &	displacement_map,
		const CollisionProxyTessellation	tessellation = `CollisionProxyTessellation::REGULAR`
	)

Build a collision proxy mesh by upsampling a given mesh.

Parameters

[in]	bases	Bases for elements
[in]	geom_bases	Geometry bases for elements
[in]	total_local_boundary	Local boundaries for elements
[in]	n_bases	Number of bases (nodes)
[in]	dim	Dimension of the mesh
[in]	max_edge_length	Maximum edge length of the proxy mesh
[out]	proxy_vertices	Output vertices of the proxy mesh
[out]	proxy_faces	Output faces of the proxy mesh
[out]	displacement_map	Output displacement map from proxy mesh to original mesh
[in]	tessellation	Type of tessellation to use

◆ build_collision_proxy_displacement_map()

void polyfem::mesh::build_collision_proxy_displacement_map	(	const std::vector< basis::ElementBases > &	bases,
		const std::vector< basis::ElementBases > &	geom_bases,
		const std::vector< mesh::LocalBoundary > &	total_local_boundary,
		const int	n_bases,
		const int	dim,
		const Eigen::MatrixXd &	proxy_vertices,
		std::vector< Eigen::Triplet< double > > &	displacement_map
	)

Build a collision proxy displacement map for a given mesh and proxy mesh.

Parameters

[in]	bases	Bases for elements
[in]	geom_bases	Geometry bases for elements
[in]	total_local_boundary	Local boundaries for elements
[in]	n_bases	Number of bases (nodes)
[in]	dim	Dimension of the mesh
[in]	proxy_vertices	Vertices of the proxy mesh
[out]	displacement_map	Output displacement map from proxy mesh to original mesh

Definition at line 168 of file CollisionProxy.cpp.

References polyfem::log_and_throw_error().

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◆ clip_polygon_by_half_plane()

void polyfem::mesh::clip_polygon_by_half_plane	(	const Eigen::MatrixXd &	P,
		const Eigen::RowVector2d &	q1,
		const Eigen::RowVector2d &	q2,
		Eigen::MatrixXd &	result
	)

Clip a polygon by a half-plane.

https://github.com/alicevision/geogram/blob/cfbc0a5827d71d59f8bcf0369cc1731ef12f82ef/src/examples/graphics/demo_Delaunay2d/main.cpp#L677

Parameters

[in]	P	Input polygon
[in]	q1	First endpoint of the clipping line
[in]	q2	Second endpoint of the clipping line
[out]	result	Clipped polygon

Definition at line 51 of file PolygonUtils.cpp.

Referenced by compute_visibility_kernel().

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◆ compute_area_ratio_energy()

double polyfem::mesh::compute_area_ratio_energy	(	const WildTriRemesher &	m,
		std::string	op,
		const WildTriRemesher::Tuple &	t
	)

Definition at line 207 of file Swap.cpp.

References compute_area_ratio_energy(), and polyfem::mesh::WildRemesher< WMTKMesh >::element_volume().

Referenced by compute_area_ratio_energy().

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◆ compute_element_tags()

void polyfem::mesh::compute_element_tags	(	const GEO::Mesh &	M,
		std::vector< ElementType > &	element_tags
	)

Compute the type of each facet in a surface mesh.

Parameters

[in]	M	Input surface mesh
[out]	element_tags	Types of each facet element

Definition at line 97 of file MeshUtils.cpp.

Referenced by polyfem::mesh::CMesh2D::compute_elements_tag(), and polyfem::mesh::CMesh2D::update_elements_tag().

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◆ compute_valence_energy()

double polyfem::mesh::compute_valence_energy	(	const WildTriRemesher &	m,
		std::string	op,
		const WildTriRemesher::Tuple &	t
	)

Definition at line 182 of file Swap.cpp.

References compute_valence_energy(), and polyfem::mesh::WildRemesher< WMTKMesh >::is_boundary_vertex().

Referenced by compute_valence_energy(), and polyfem::mesh::PhysicsTriRemesher::swap_edges().

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◆ compute_visibility_kernel()

void polyfem::mesh::compute_visibility_kernel	(	const Eigen::MatrixXd &	IV,
		Eigen::MatrixXd &	OV
	)

Determine the kernel of the given polygon.

Parameters

[in]	IV	#IV x (2\|3) vertex positions around the input polygon
[out]	OV	#OV x (2\|3) vertex positions around the output polygon

Definition at line 121 of file PolygonUtils.cpp.

References clip_polygon_by_half_plane().

Referenced by is_star_shaped().

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◆ constrained_L2_projection()

Eigen::VectorXd polyfem::mesh::constrained_L2_projection	(	std::shared_ptr< polysolve::nonlinear::Solver >	nl_solver,
		const Eigen::SparseMatrix< double > &	M,
		const Eigen::SparseMatrix< double > &	A,
		const Eigen::VectorXd &	y,
		const Eigen::MatrixXd &	rest_positions,
		const Eigen::MatrixXi &	elements,
		const int	dim,
		const ipc::CollisionMesh &	collision_mesh,
		const double	dhat,
		const double	barrier_stiffness,
		const bool	use_convergent_formulation,
		const ipc::BroadPhaseMethod	broad_phase_method,
		const double	ccd_tolerance,
		const int	ccd_max_iterations,
		const std::vector< int > &	boundary_nodes,
		const size_t	obstacle_ndof,
		const Eigen::VectorXd &	target_x,
		const Eigen::VectorXd &	x0
	)

Definition at line 70 of file L2Projection.cpp.

References polyfem::solver::ALSolver::solve_al(), polyfem::utils::unflatten(), x, and y.

Referenced by polyfem::mesh::Remesher::project_quantities(), and polyfem::mesh::WildRemesher< wmtk::TetMesh >::smooth_vertices().

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◆ construct_affine_transformation()

void polyfem::mesh::construct_affine_transformation	(	const double	unit_scale,
		const json &	transform,
		const VectorNd &	mesh_dimensions,
		MatrixNd &	A,
		VectorNd &	b
	)

Construct an affine transformation \(Ax+b\).

Parameters

[in]	transform	JSON object with the mesh data
[in]	mesh_dimensions	Dimensions of the mesh (i.e., width, height, depth)
[out]	A	Multiplicative matrix component of transformation
[out]	b	Additive translation component of transformation

Definition at line 688 of file GeometryReader.cpp.

References polyfem::utils::deg2rad(), polyfem::log_and_throw_error(), and polyfem::utils::to_rotation_matrix().

Referenced by load_collision_proxy_mesh(), read_fem_mesh(), and read_obstacle_mesh().

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◆ count_faces()

int polyfem::mesh::count_faces	(	const int	dim,
		const Eigen::MatrixXi &	cells
	)

Count the number of boundary elements (triangles for tetmesh and edges for triangle mesh)

Definition at line 1194 of file MeshUtils.cpp.

◆ create_patch_around_singularities()

void polyfem::mesh::create_patch_around_singularities	(	GEO::Mesh &	M,
		const Eigen::VectorXi &	V,
		const Eigen::MatrixX2i &	E,
		double	t = `0.5`
	)

Definition at line 84 of file Singularities.cpp.

References facet_barycenter(), mesh_create_vertex(), mesh_vertex(), and V.

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◆ edge_adjacency_graph()

void polyfem::mesh::edge_adjacency_graph	(	const Eigen::MatrixXi &	Q,
		Eigen::MatrixXi &	edge_index,
		std::vector< std::vector< int > > &	adj,
		std::vector< std::pair< int, int > > *	pairs_of_edges = `nullptr`,
		std::vector< std::pair< int, int > > *	pairs_of_quads = `nullptr`,
		Eigen::MatrixXi *	quad_index = `nullptr`
	)

Definition at line 16 of file Refinement.cpp.

References adj, x, and y.

Referenced by instantiate_pattern().

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◆ extract_parent_edges()

void polyfem::mesh::extract_parent_edges	(	const Eigen::MatrixXd &	IV,
		const Eigen::MatrixXi &	IE,
		const Eigen::MatrixXd &	BV,
		const Eigen::MatrixXi &	BE,
		Eigen::MatrixXi &	OE
	)

Extract a set of edges that are overlap with a set given set of parent edges, using vertices positions to discriminate.

Parameters

[in]	IV	#IV x 3 input vertices positions
[in]	IE	#IE x 2 input edge indices
[in]	BV	#BV x 3 base vertices positions to test against
[in]	BE	#BE x 2 base edge indices to test against
[out]	OE	#OE x 2 output extracted edges

Definition at line 946 of file MeshUtils.cpp.

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

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◆ extract_polyhedra()

void polyfem::mesh::extract_polyhedra	(	const Mesh3D &	mesh,
		std::vector< std::unique_ptr< GEO::Mesh > > &	polys,
		bool	triangulated = `false`
	)

Extract polyhedra from a 3D volumetric mesh.

Parameters

[in]	mesh	Input volume mesh
[out]	polys	Extracted polyhedral surfaces

Definition at line 715 of file MeshUtils.cpp.

References polyfem::mesh::Mesh3D::get_index_from_element(), polyfem::mesh::Mesh::is_polytope(), polyfem::mesh::Mesh3D::kernel(), polyfem::mesh::Mesh3D::n_cell_faces(), polyfem::mesh::Mesh::n_cell_vertices(), polyfem::mesh::Mesh::n_cells(), polyfem::mesh::Mesh::n_face_vertices(), polyfem::mesh::Mesh::n_faces(), polyfem::mesh::Mesh::n_vertices(), polyfem::mesh::Mesh3D::next_around_face(), and polyfem::mesh::Mesh::point().

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◆ extract_triangle_surface_from_tets()

void polyfem::mesh::extract_triangle_surface_from_tets	(	const Eigen::MatrixXd &	vertices,
		const Eigen::MatrixXi &	tets,
		Eigen::MatrixXd &	surface_vertices,
		Eigen::MatrixXi &	tris
	)

Extract triangular surface from a tetmesh.

Parameters

[in]	v,tets	tet mesh
[out]	s_v,tris	{ surface mesh }

Definition at line 1052 of file MeshUtils.cpp.

References find_triangle_surface_from_tets().

Referenced by read_surface_mesh().

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◆ facet_barycenter()

GEO::vec3 polyfem::mesh::facet_barycenter	(	const GEO::Mesh &	M,
		GEO::index_t	f
	)

Definition at line 64 of file MeshUtils.cpp.

References mesh_vertex().

Referenced by create_patch_around_singularities(), and refine_polygonal_mesh().

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◆ find()

int polyfem::mesh::find	(	const Eigen::VectorXi &	vec,
		int	x
	)

Definition at line 289 of file NCMesh2D.cpp.

References vec, and x.

Referenced by polyfem::mesh::MeshProcessing3D::build_connectivity(), polyfem::mesh::NCMesh2D::build_element_vertex_adjacency(), polyfem::mesh::Navigation3D::get_index_from_element_face(), polyfem::mesh::CMesh3D::load(), polyfem::mesh::MeshProcessing3D::refine_catmul_clark_polar(), and polyfem::mesh::NCMesh2D::switch_edge().

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◆ from_geogram_mesh()

void polyfem::mesh::from_geogram_mesh	(	const GEO::Mesh &	M,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F,
		Eigen::MatrixXi &	T
	)

Extract simplices from a Geogram mesh.

Parameters

[in]	M	Input Geogram mesh
[out]	V	V x 3 output mesh vertices
[out]	F	F x 3 output mesh faces
[out]	T	#T x 4 output mesh tets

Definition at line 639 of file MeshUtils.cpp.

References V.

◆ generate_edges()

void polyfem::mesh::generate_edges ( GEO::Mesh & M )

assing edges to M

Parameters

[in/out] M geogram mesh to appen edges to

Definition at line 1244 of file MeshUtils.cpp.

Referenced by polyfem::mesh::Mesh::create(), and polyfem::mesh::CMesh2D::refine().

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◆ get_quality()

template<class WMTKMesh >

double polyfem::mesh::get_quality	(	const WildRemesher< WMTKMesh > &	m,
		const typename WMTKMesh::Tuple &	t
	)

Definition at line 17 of file Smooth.cpp.

References polyfem::mesh::WildRemesher< WMTKMesh >::element_vids(), and polyfem::mesh::WildRemesher< WMTKMesh >::vertex_attrs.

Referenced by polyfem::mesh::WildRemesher< WMTKMesh >::smooth_after(), and polyfem::mesh::WildRemesher< WMTKMesh >::smooth_vertices().

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◆ instantiate_pattern()

bool polyfem::mesh::instantiate_pattern	(	const Eigen::MatrixXd &	IV,
		const Eigen::MatrixXi &	IF,
		const Eigen::MatrixXd &	PV,
		const Eigen::MatrixXi &	PF,
		Eigen::MatrixXd &	OV,
		Eigen::MatrixXi &	OF,
		Eigen::VectorXi *	SF = `nullptr`,
		EvalParametersFunc	evalFunc = `nullptr`,
		GetAdjacentLocalEdge	getAdjLocalEdge = `nullptr`
	)

Definition at line 278 of file Refinement.cpp.

References adj, edge_adjacency_graph(), polyfem::F, polyfem::logger(), V, x, and y.

Referenced by refine_quad_mesh().

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◆ irregular_tessellation()

void polyfem::mesh::irregular_tessellation	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const double	max_edge_length,
		Eigen::MatrixXd &	V_out,
		Eigen::MatrixXi &	F_out
	)

Tessilate a triangle mesh (V, F) with well shaped triangles.

Note: Uses Triangle to perform the refinement (requires POLYFEM_WITH_TRIANGLE).

Parameters

V	vertices
F	triangular faces
max_edge_length	maximum edge length
V_out	tessilated vertices
F_out	tessilated faces

Definition at line 288 of file UpsampleMesh.cpp.

References polyfem::F, irregular_triangle(), max_edge_length(), stitch_mesh(), and V.

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◆ irregular_triangle()

void polyfem::mesh::irregular_triangle	(	const Eigen::Vector3d &	a,
		const Eigen::Vector3d &	b,
		const Eigen::Vector3d &	c,
		const double	max_edge_length,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F
	)

Refine a triangle (a, b, c) into a well shaped triangle mesh.

Note: Uses Triangle to perform the refinement (requires POLYFEM_WITH_TRIANGLE).

Parameters

a	first vertex of the triangle
b	second vertex of the triangle
c	third vertex of the triangle
max_edge_len	maximum edge length of the refined triangle mesh
V	vertices of the refined triangle
F	faces of the refined triangle

Definition at line 217 of file UpsampleMesh.cpp.

References polyfem::assembler::cross(), polyfem::F, polyfem::log_and_throw_error(), max_edge_length(), refine_triangle_edges(), polyfem::utils::triangle_area(), V, and z.

Referenced by irregular_tessellation(), and irregular_triangle_barycentric_coordinates().

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◆ irregular_triangle_barycentric_coordinates()

void polyfem::mesh::irregular_triangle_barycentric_coordinates	(	const Eigen::Vector3d &	a,
		const Eigen::Vector3d &	b,
		const Eigen::Vector3d &	c,
		const double	max_edge_length,
		Eigen::MatrixXd &	UV,
		Eigen::MatrixXi &	F
	)

Refine a triangle (a, b, c) into a well shaped triangle mesh.

Note: Uses Triangle to perform the refinement (requires POLYFEM_WITH_TRIANGLE).

Parameters

a	first vertex of the triangle
b	second vertex of the triangle
c	third vertex of the triangle
max_edge_len	maximum edge length of the refined triangle mesh
UV	barycentric coordinates of the refined triangle
F	faces of the refined triangle

Definition at line 266 of file UpsampleMesh.cpp.

References polyfem::F, irregular_triangle(), max_edge_length(), and V.

Referenced by build_collision_proxy().

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◆ is_inside()

int polyfem::mesh::is_inside	(	const Eigen::MatrixXd &	IV,
		const Eigen::MatrixXd &	Q,
		std::vector< bool > &	inside
	)

Compute whether points are inside a polygon.

Parameters

[in]	IV	#IV x 2 of vertex positions for the input polygon
[in]	Q	#Q x 2 of query point positions
[out]	inside	Whether the i-th query point is inside or not

Returns: Number of points inside

Definition at line 243 of file PolygonUtils.cpp.

◆ is_planar()

bool polyfem::mesh::is_planar	(	const GEO::Mesh &	M,
		const double	tol = `1e-5`
	)

Determine if the given mesh is planar (2D or tiny z-range).

Definition at line 31 of file MeshUtils.cpp.

Referenced by polyfem::mesh::Mesh::create(), and read_surface_mesh().

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◆ is_star_shaped()

bool polyfem::mesh::is_star_shaped	(	const Eigen::MatrixXd &	IV,
		Eigen::RowVector3d &	bary
	)

Determine whether a polygon is star-shaped or not.

Parameters

[in]	IV	#IV x (2\|3) of vertex positions around the polygon
[out]	bary	The barycenter of the kernel

Returns: True if star shaped, False otherwise.

Definition at line 151 of file PolygonUtils.cpp.

References compute_visibility_kernel().

Referenced by polyfem::mesh::Polygons::catmul_clark_split(), and polyfem::mesh::Polygons::polar_split().

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◆ line_weight()

double polyfem::mesh::line_weight	(	Eigen::Matrix< double, 2, 2 > &	e,
		Eigen::VectorXd &	v
	)

Definition at line 364 of file NCMesh2D.cpp.

Referenced by polyfem::mesh::NCMesh2D::build_element_vertex_adjacency().

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◆ load_collision_proxy()

void polyfem::mesh::load_collision_proxy	(	const std::string &	mesh_filename,
		const std::string &	weights_filename,
		const Eigen::VectorXi &	in_node_to_node,
		const json &	transformation,
		Eigen::MatrixXd &	vertices,
		Eigen::VectorXi &	codim_vertices,
		Eigen::MatrixXi &	edges,
		Eigen::MatrixXi &	faces,
		std::vector< Eigen::Triplet< double > > &	displacement_map_entries
	)

Load a collision proxy mesh and displacement map from files.

Parameters

[in]	mesh_filename	Mesh filename
[in]	weights_filename	Weights filename
[in]	in_node_to_node	Map from input node IDs to node IDs
[in]	transformation	Transformation to apply to the mesh
[out]	vertices	Output vertices of the proxy mesh
[out]	codim_vertices	Output codimension vertices of the proxy mesh
[out]	edges	Output edges of the proxy mesh
[out]	faces	Output faces of the proxy mesh
[out]	displacement_map_entries	Output displacement map entries

Definition at line 315 of file CollisionProxy.cpp.

References faces, load_collision_proxy(), load_collision_proxy_displacement_map(), and load_collision_proxy_mesh().

Referenced by polyfem::State::build_collision_mesh(), and load_collision_proxy().

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◆ load_collision_proxy_displacement_map()

void polyfem::mesh::load_collision_proxy_displacement_map	(	const std::string &	weights_filename,
		const Eigen::VectorXi &	in_node_to_node,
		const size_t	num_proxy_vertices,
		std::vector< Eigen::Triplet< double > > &	displacement_map_entries
	)

Load a collision proxy displacement map from files.

Parameters

[in]	weights_filename	Weights filename
[in]	in_node_to_node	Map from input node IDs to node IDs
[out]	displacement_map_entries	Output displacement map entries

Definition at line 368 of file CollisionProxy.cpp.

References load_collision_proxy_displacement_map().

Referenced by load_collision_proxy(), and load_collision_proxy_displacement_map().

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◆ load_collision_proxy_mesh()

void polyfem::mesh::load_collision_proxy_mesh	(	const std::string &	mesh_filename,
		const json &	transformation,
		Eigen::MatrixXd &	vertices,
		Eigen::VectorXi &	codim_vertices,
		Eigen::MatrixXi &	edges,
		Eigen::MatrixXi &	faces
	)

Load a collision proxy mesh from a file.

Parameters

[in]	mesh_filename	Mesh filename
[in]	transformation	Transformation to apply to the mesh
[out]	vertices	Output vertices of the proxy mesh
[out]	codim_vertices	Output codimension vertices of the proxy mesh
[out]	edges	Output edges of the proxy mesh
[out]	faces	Output faces of the proxy mesh

Definition at line 330 of file CollisionProxy.cpp.

References construct_affine_transformation(), faces, load_collision_proxy_mesh(), and read_surface_mesh().

Referenced by load_collision_proxy(), and load_collision_proxy_mesh().

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◆ max_edge_length()

double polyfem::mesh::max_edge_length	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F
	)

Compute the maximum edge length of a triangle mesh (V, F)

Parameters

V	vertices
F	triangular faces

Definition at line 87 of file UpsampleMesh.cpp.

References polyfem::F, max_edge_length(), and V.

Referenced by build_collision_proxy(), polyfem::mesh::WildRemesher< WMTKMesh >::collapse_edge_before(), irregular_tessellation(), irregular_triangle(), irregular_triangle_barycentric_coordinates(), max_edge_length(), refine_edge(), and regular_grid_tessellation().

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◆ mesh_create_vertex()

GEO::index_t polyfem::mesh::mesh_create_vertex	(	GEO::Mesh &	M,
		const GEO::vec3 &	p
	)

Definition at line 77 of file MeshUtils.cpp.

Referenced by create_patch_around_singularities(), refine_polygonal_mesh(), and refine_triangle_mesh().

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◆ mesh_vertex()

GEO::vec3 polyfem::mesh::mesh_vertex	(	const GEO::Mesh &	M,
		GEO::index_t	v
	)

Retrieve a 3D vector with the position of a given vertex.

Contrary to geogram's version, this function works with both single and double precision meshes, as well as 2D meshes too.

Parameters

[in]	M	Input mesh
[in]	v	Vertex index whose position to retrieve

Returns: Position of the given vertex in 3D

Definition at line 44 of file MeshUtils.cpp.

Referenced by create_patch_around_singularities(), facet_barycenter(), refine_polygonal_mesh(), and refine_triangle_mesh().

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◆ NLOHMANN_JSON_SERIALIZE_ENUM()

polyfem::mesh::NLOHMANN_JSON_SERIALIZE_ENUM	(	CollisionProxyTessellation	,
		{{CollisionProxyTessellation::REGULAR, "regular"}, {CollisionProxyTessellation::IRREGULAR, "irregular"}}
	)

References IRREGULAR, and REGULAR.

◆ offset_polygon()

void polyfem::mesh::offset_polygon	(	const Eigen::MatrixXd &	IV,
		Eigen::MatrixXd &	OV,
		double	eps
	)

Compute offset polygon.

Parameters

[in]	IV	#IV x 2 of vertex positions for the input polygon
[out]	OV	#OV x 2 of vertex positions for the offset polygon
[in]	eps	Offset distance

Definition at line 179 of file PolygonUtils.cpp.

◆ operator<<()

std::ostream & polyfem::mesh::operator<<	(	std::ostream &	os,
		const LocalBoundary &	lb
	)

Parameters

os	Output stream
lb	LocalBoundary to print

Returns: Output stream

Definition at line 49 of file LocalBoundary.cpp.

◆ orient_closed_surface()

void polyfem::mesh::orient_closed_surface	(	const Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F,
		bool	positive = `true`
	)

Orient a triangulated surface to have positive volume.

Parameters

[in]	V	V x 3 input mesh vertices
[in]	F	F x 3 input mesh facets
[in]	positive	Orient for positive volume, or negative volume

Definition at line 702 of file MeshUtils.cpp.

References signed_volume(), and V.

Referenced by polyfem::basis::PolygonalBasis3d::build_bases().

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◆ orient_normals_2d()

void polyfem::mesh::orient_normals_2d ( GEO::Mesh & M )

Orient facets of a 2D mesh so that each connected component has positive volume.

Parameters

[in,out] M Surface mesh to reorient

Definition at line 304 of file MeshUtils.cpp.

Referenced by polyfem::mesh::CMesh2D::build_from_matrices(), polyfem::mesh::NCMesh2D::build_from_matrices(), polyfem::mesh::CMesh2D::load(), and polyfem::mesh::NCMesh2D::load().

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◆ project_local_quantities()

template<class WMTKMesh >

void polyfem::mesh::project_local_quantities	(	WildRemesher< WMTKMesh > &	m,
		LocalMesh< WildRemesher< WMTKMesh > > &	old_local_mesh,
		LocalMesh< WildRemesher< WMTKMesh > > &	new_local_mesh
	)

Definition at line 45 of file Smooth.cpp.

References POLYFEM_REMESHER_SCOPED_TIMER.

Referenced by polyfem::mesh::WildRemesher< WMTKMesh >::smooth_after().

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◆ rank_edges()

template<typename WMTKMesh >

Remesher::EdgeMap< typename WildRemesher< WMTKMesh >::EdgeAttributes::EnergyRank > polyfem::mesh::rank_edges	(	const Remesher::EdgeMap< double > &	edge_energy,
		const json &	args
	)

Definition at line 47 of file WildRemesher.cpp.

◆ read_fem_geometry()

std::unique_ptr< Mesh > polyfem::mesh::read_fem_geometry	(	const Units &	units,
		const json &	geometry,
		const std::string &	root_path,
		const std::vector< std::string > &	names = `std::vector< std::string >()`,
		const std::vector< Eigen::MatrixXd > &	vertices = `std::vector< Eigen::MatrixXd >()`,
		const std::vector< Eigen::MatrixXi > &	cells = `std::vector< Eigen::MatrixXi >()`,
		const bool	non_conforming = `false`
	)

read FEM meshes from a geometry JSON array (or single)

Parameters

[in]	geometry	geometry JSON object(s)
[in]	root_path	root path of JSON

Returns: created Mesh object

Definition at line 230 of file GeometryReader.cpp.

References polyfem::utils::json_as_array(), polyfem::log_and_throw_error(), and read_fem_mesh().

Referenced by polyfem::State::load_mesh().

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◆ read_fem_mesh()

std::unique_ptr< Mesh > polyfem::mesh::read_fem_mesh	(	const Units &	units,
		const json &	j_mesh,
		const std::string &	root_path,
		const bool	non_conforming = `false`
	)

read a FEM mesh from a geometry JSON

Parameters

[in]	j_mesh	geometry JSON
[in]	root_path	root path of JSON
[in]	non_conforming	if true, the mesh will be non-conforming

Returns: created Mesh object

Definition at line 25 of file GeometryReader.cpp.

References polyfem::utils::Selection::build_selections(), construct_affine_transformation(), polyfem::Units::convert(), polyfem::mesh::Mesh::create(), polyfem::utils::is_param_valid(), polyfem::Units::length(), polyfem::log_and_throw_error(), polyfem::logger(), and polyfem::utils::resolve_path().

Referenced by read_fem_geometry().

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◆ read_obstacle_geometry()

Obstacle polyfem::mesh::read_obstacle_geometry	(	const Units &	units,
		const json &	geometry,
		const std::vector< json > &	displacements,
		const std::vector< json > &	dirichlets,
		const std::string &	root_path,
		const int	dim,
		const std::vector< std::string > &	names = `std::vector< std::string >()`,
		const std::vector< Eigen::MatrixXd > &	vertices = `std::vector< Eigen::MatrixXd >()`,
		const std::vector< Eigen::MatrixXi > &	cells = `std::vector< Eigen::MatrixXi >()`,
		const bool	non_conforming = `false`
	)

read a FEM mesh from a geometry JSON

Parameters

[in]	geometry	geometry JSON object(s)
[in]	displacements	displacements JSON object(s)
[in]	dirichlets	dirichlet bc JSON object(s)
[in]	root_path	root path of JSON

Returns: created Obstacle object

Definition at line 438 of file GeometryReader.cpp.

References polyfem::mesh::Obstacle::append_mesh(), polyfem::mesh::Obstacle::append_mesh_sequence(), polyfem::mesh::Obstacle::append_plane(), faces, polyfem::utils::is_param_valid(), polyfem::utils::json_as_array(), polyfem::log_and_throw_error(), read_obstacle_mesh(), polyfem::utils::resolve_path(), and polyfem::mesh::Obstacle::set_units().

Referenced by polyfem::State::load_mesh(), and polyfem::State::load_mesh().

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◆ read_obstacle_mesh()

void polyfem::mesh::read_obstacle_mesh	(	const Units &	units,
		const json &	j_mesh,
		const std::string &	root_path,
		const int	dim,
		Eigen::MatrixXd &	vertices,
		Eigen::VectorXi &	codim_vertices,
		Eigen::MatrixXi &	codim_edges,
		Eigen::MatrixXi &	faces
	)

read a obstacle mesh from a geometry JSON

Parameters

[in]	j_mesh	geometry JSON
[in]	root_path	root path of JSON
[out]	vertices	V x 3/2 output vertices positions
[out]	codim_vertices	indicies in vertices for the codimensional vertices
[out]	codim_edges	indicies in vertices for the codimensional edges
[out]	faces	indicies in vertices for the surface faces

Definition at line 327 of file GeometryReader.cpp.

References construct_affine_transformation(), polyfem::Units::convert(), faces, polyfem::utils::is_param_valid(), polyfem::Units::length(), polyfem::log_and_throw_error(), read_surface_mesh(), and polyfem::utils::resolve_path().

Referenced by read_obstacle_geometry().

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◆ read_surface_mesh()

bool polyfem::mesh::read_surface_mesh	(	const std::string &	mesh_path,
		Eigen::MatrixXd &	vertices,
		Eigen::VectorXi &	codim_vertices,
		Eigen::MatrixXi &	codim_edges,
		Eigen::MatrixXi &	faces
	)

read a surface mesh

Parameters

[in]	mesh_path	path to mesh file
[out]	vertices	V x 3/2 output vertices positions
[out]	codim_vertices	indicies in vertices for the codimensional vertices
[out]	codim_edges	indicies in vertices for the codimensional edges
[out]	faces	indicies in vertices for the surface faces

Definition at line 1091 of file MeshUtils.cpp.

References polyfem::utils::StringUtils::endswith(), extract_triangle_surface_from_tets(), faces, find_codim_vertices(), is_planar(), polyfem::io::MshReader::load(), polyfem::logger(), and polyfem::io::OBJReader::read().

Referenced by load_collision_proxy_mesh(), and read_obstacle_mesh().

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◆ reduced_L2_projection()

void polyfem::mesh::reduced_L2_projection	(	const Eigen::MatrixXd &	M,
		const Eigen::MatrixXd &	A,
		const Eigen::Ref< const Eigen::MatrixXd > &	y,
		const std::vector< int > &	boundary_nodes,
		Eigen::Ref< Eigen::MatrixXd >	x
	)

Definition at line 47 of file L2Projection.cpp.

References x, and y.

◆ refine_edge()

Eigen::MatrixXd polyfem::mesh::refine_edge	(	const VectorNd &	a,
		const VectorNd &	b,
		const double	max_edge_length
	)

Refine an edge (a, b) so each refined edge has length at most max_edge_length.

Parameters

a	first vertex of the edge
b	second vertex of the edge
max_edge_length	maximum edge length

Returns: vertices of the refined edge (in order)

Definition at line 183 of file UpsampleMesh.cpp.

References max_edge_length(), and V.

Referenced by refine_triangle_edges().

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◆ refine_polygonal_mesh() [1/2]

void polyfem::mesh::refine_polygonal_mesh	(	const GEO::Mesh &	M_in,
		GEO::Mesh &	M_out,
		bool	refine_polygons = `false`,
		double	t = `0.5`
	)

inline

Definition at line 137 of file Refinement.hpp.

References polyfem::mesh::Polygons::no_split_func(), polyfem::mesh::Polygons::polar_split_func(), and refine_polygonal_mesh().

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◆ refine_polygonal_mesh() [2/2]

void polyfem::mesh::refine_polygonal_mesh	(	const GEO::Mesh &	M_in,
		GEO::Mesh &	M_out,
		Polygons::SplitFunction	split_func
	)

Refine a polygonal mesh.

Quads and triangles are split into quads. If refine_polygons is set to true, then polygonal facets are also split into a layer of padding quads, and a new polygon is created around the barycenter

Parameters

[in]	M_in	Surface mesh to subdivide
[out]	M_out	Refined mesh
[in]	split_func	Functional used to split the new polygon interiors (boundary has already been split)

Definition at line 620 of file Refinement.cpp.

References polyfem::mesh::Navigation::Index::edge, polyfem::F, facet_barycenter(), polyfem::mesh::Navigation::get_index_from_face(), mesh_create_vertex(), mesh_vertex(), polyfem::mesh::Navigation::next_around_face(), polyfem::mesh::Navigation::switch_edge(), polyfem::mesh::Navigation::switch_vertex(), V, and polyfem::mesh::Navigation::Index::vertex.

Referenced by polyfem::mesh::CMesh2D::refine(), and refine_polygonal_mesh().

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◆ refine_quad_mesh()

void polyfem::mesh::refine_quad_mesh	(	const Eigen::MatrixXd &	IV,
		const Eigen::MatrixXi &	IF,
		Eigen::MatrixXd &	OV,
		Eigen::MatrixXi &	OF
	)

Definition at line 507 of file Refinement.cpp.

References instantiate_pattern().

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◆ refine_triangle_edges()

void polyfem::mesh::refine_triangle_edges	(	const VectorNd &	a,
		const VectorNd &	b,
		const VectorNd &	c,
		const double	max_edge_len,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	E
	)

Refine the edges of a triangle (a, b, c) so each refined edge has length at most max_edge_length.

Parameters

a	first vertex of the triangle
b	second vertex of the triangle
c	third vertex of the triangle
max_edge_len	maximum edge length
V	vertices of the refined edges
E	refined edges

Definition at line 194 of file UpsampleMesh.cpp.

References refine_edge(), and V.

Referenced by irregular_triangle().

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◆ refine_triangle_mesh()

void polyfem::mesh::refine_triangle_mesh	(	const GEO::Mesh &	M_in,
		GEO::Mesh &	M_out
	)

Refine a triangle mesh.

Each input triangle is split into 4 new triangles

Parameters

[in]	M_in	Input surface mesh
[out]	M_out	Output surface mesh

Definition at line 736 of file Refinement.cpp.

References polyfem::mesh::Navigation::Index::edge, polyfem::mesh::Navigation::get_index_from_face(), mesh_create_vertex(), mesh_vertex(), polyfem::mesh::Navigation::next_around_face(), polyfem::mesh::Navigation::switch_edge(), polyfem::mesh::Navigation::switch_vertex(), and polyfem::mesh::Navigation::Index::vertex.

Referenced by polyfem::mesh::CMesh2D::refine().

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◆ regular_grid_tessellation()

void polyfem::mesh::regular_grid_tessellation	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const double	max_edge_length,
		Eigen::MatrixXd &	V_out,
		Eigen::MatrixXi &	F_out
	)

Tessilate a triangle mesh (V, F) with regular grids of triangles of maximum edge length.

Parameters

V	vertices
F	triangular faces
max_edge_length	maximum edge length
V_out	tessilated vertices
F_out	tessilated faces

Definition at line 148 of file UpsampleMesh.cpp.

References polyfem::F, max_edge_length(), regular_grid_triangle_barycentric_coordinates(), stitch_mesh(), and V.

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◆ regular_grid_triangle_barycentric_coordinates()

void polyfem::mesh::regular_grid_triangle_barycentric_coordinates	(	const int	n,
		Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F
	)

Compute the barycentric coordinates of a regular grid of triangles.

Parameters

[in]	n	Number of triangles along each edge
[out]	V	Vertices of the regular grid
[out]	F	Faces of the regular grid

Definition at line 104 of file UpsampleMesh.cpp.

References polyfem::F, and V.

Referenced by build_collision_proxy(), and regular_grid_tessellation().

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◆ reorder_mesh()

void polyfem::mesh::reorder_mesh	(	Eigen::MatrixXd &	V,
		Eigen::MatrixXi &	F,
		const Eigen::VectorXi &	C,
		Eigen::VectorXi &	R
	)

Reorder vertices of a mesh using color tags, so that vertices are ordered by increasing colors.

Parameters

[in,out]	V	V x d input mesh vertices
[in,out]	F	F x k input mesh faces
[in]	C	V per vertex color tag
[out]	R	max(C)+1 vector of starting indices for each colors (last value is the total number of vertices)

Definition at line 325 of file MeshUtils.cpp.

References V.

◆ sample_polygon()

void polyfem::mesh::sample_polygon	(	const Eigen::MatrixXd &	IV,
		int	num_samples,
		Eigen::MatrixXd &	S
	)

Sample points on a polygon, evenly spaced from each other.

Parameters

[in]	IV	#IV x 2 vertex positions for the input polygon
[in]	num_samples	Desired number of samples
[out]	S	#S x 2 output sample positions

Definition at line 265 of file PolygonUtils.cpp.

Referenced by polyfem::basis::PolygonalBasis2d::build_bases().

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◆ sample_surface()

void polyfem::mesh::sample_surface	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		int	num_samples,
		Eigen::MatrixXd &	P,
		Eigen::MatrixXd *	N = `nullptr`,
		int	num_lloyd = `10`,
		int	num_newton = `10`
	)

Samples points on a surface.

Parameters

[in]	V	V x 3 input mesh vertices
[in]	F	F x 3 input mesh facets
[in]	num_samples	Number of desired samples
[out]	P	num_samples x 3 sample points positions
[out]	N	num_samples x 3 of normals estimated from the original surface (optional argument)
[in]	num_lloyd	Number of Lloyd iterations
[in]	num_newton	Number of Newton iterations

Definition at line 884 of file MeshUtils.cpp.

References to_geogram_mesh(), and V.

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◆ signed_squared_distances()

void polyfem::mesh::signed_squared_distances	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const Eigen::MatrixXd &	P,
		Eigen::VectorXd &	D
	)

Computes the signed squared distance from a list of points to a triangle mesh.

This function build a AABB tree of the input mesh, computes the distance for each query point to the closest triangle, and then determines the sign by casting a vertical ray from the query point and counting the number of intersections with the input mesh

Parameters

[in]	V	V x 3 input mesh vertices
[in]	F	F x 3 input mesh faces
[in]	P	#P x 3 query points
	D	#P x 1 computed signed distances, negative inside, positive outside

Definition at line 669 of file MeshUtils.cpp.

References to_geogram_mesh(), and V.

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◆ signed_volume()

double polyfem::mesh::signed_volume	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F
	)

Compute the signed volume of a surface mesh.

Parameters

[in]	V	V x 3 input mesh vertices
[in]	F	F x 3 input mesh facets

Returns: Signed volume of the surface

Definition at line 681 of file MeshUtils.cpp.

References V.

Referenced by orient_closed_surface(), and polyfem::mesh::MeshProcessing3D::refine_red_refinement_tet().

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◆ singular_edges()

void polyfem::mesh::singular_edges	(	const GEO::Mesh &	M,
		const Eigen::VectorXi &	V,
		Eigen::MatrixX2i &	E
	)

Definition at line 48 of file Singularities.cpp.

References V.

Referenced by singularity_graph().

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◆ singular_vertices()

void polyfem::mesh::singular_vertices	(	const GEO::Mesh &	M,
		Eigen::VectorXi &	V,
		int	regular_degree = `4`,
		bool	ignore_border = `true`
	)

Definition at line 8 of file Singularities.cpp.

References V.

Referenced by singularity_graph().

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◆ singularity_graph()

void polyfem::mesh::singularity_graph	(	const GEO::Mesh &	M,
		Eigen::VectorXi &	V,
		Eigen::MatrixX2i &	E,
		int	regular_degree = `4`,
		bool	ignore_border = `true`
	)

Definition at line 75 of file Singularities.cpp.

References singular_edges(), singular_vertices(), and V.

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◆ stitch_mesh() [1/2]

void polyfem::mesh::stitch_mesh	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const std::vector< Eigen::Triplet< double > > &	W,
		Eigen::MatrixXd &	V_out,
		Eigen::MatrixXi &	F_out,
		std::vector< Eigen::Triplet< double > > &	W_out,
		const double	epsilon = `1e-5`
	)

Stitch a triangle mesh (V, F) together by removing duplicate vertices.

Also removes weights in W that correspond to duplicate vertices.

Parameters

[in]	V	Input vertices
[in]	F	Input faces
[in]	W	Input weights
[out]	V_out	Output vertices (duplicate vertices removed)
[out]	F_out	Output faces (updated to use V_out)
[out]	W_out	Output weights (updated to use V_out)
[in]	epsilon	Tolerance for duplicate vertices

indices: #V_out by 1 list of indices so V_out = V(indices,:) inverse: V by 1 list of indices so V = V_out(inverse,:)

Definition at line 46 of file UpsampleMesh.cpp.

References polyfem::F, polyfem::utils::inverse(), and V.

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◆ stitch_mesh() [2/2]

void polyfem::mesh::stitch_mesh	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		Eigen::MatrixXd &	V_out,
		Eigen::MatrixXi &	F_out,
		const double	epsilon = `1e-5`
	)

Stitch a triangle mesh (V, F) together by removing duplicate vertices.

Parameters

[in]	V	Input vertices
[in]	F	Input faces
[out]	V_out	Output vertices (duplicate vertices removed)
[out]	F_out	Output faces (updated to use V_out)
[in]	epsilon	Tolerance for duplicate vertices

Definition at line 35 of file UpsampleMesh.cpp.

References polyfem::F, stitch_mesh(), and V.

Referenced by build_collision_proxy(), irregular_tessellation(), regular_grid_tessellation(), and stitch_mesh().

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◆ tertrahedralize_star_shaped_surface()

void polyfem::mesh::tertrahedralize_star_shaped_surface	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		const Eigen::RowVector3d &	kernel,
		Eigen::MatrixXd &	OV,
		Eigen::MatrixXi &	OF,
		Eigen::MatrixXi &	OT
	)

Tetrahedralize a star-shaped mesh, with a given point in its kernel.

Parameters

[in]	V	V x 3 input mesh vertices
[in]	F	F x 3 input mesh triangles
[in]	kernel	A point in the kernel
[out]	OV	#OV x 3 output mesh vertices
[out]	OF	#OF x 3 output mesh surface triangles
[out]	OT	#OT x 4 output mesh tetrahedra

Definition at line 869 of file MeshUtils.cpp.

References V.

Referenced by polyfem::quadrature::PolyhedronQuadrature::get_quadrature(), and polyfem::utils::RefElementSampler::sample_polyhedron().

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◆ to_geogram_mesh() [1/2]

void polyfem::mesh::to_geogram_mesh	(	const Eigen::MatrixXd &	V,
		const Eigen::MatrixXi &	F,
		GEO::Mesh &	M
	)

Converts a triangle mesh to a Geogram mesh.

Parameters

[in]	V	V x 3 input mesh vertices
[in]	F	F x 3 input mesh surface
[out]	M	Output Geogram mesh

Definition at line 575 of file MeshUtils.cpp.

References V.

Referenced by polyfem::mesh::CMesh2D::build_from_matrices(), polyfem::mesh::NCMesh2D::build_from_matrices(), sample_surface(), polyfem::mesh::CMesh3D::save(), and signed_squared_distances().

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◆ to_geogram_mesh() [2/2]

void polyfem::mesh::to_geogram_mesh	(	const Mesh3D &	mesh,
		GEO::Mesh &	M
	)

Converts a hex mesh to a Geogram mesh.

Parameters

[in]	mesh	Input mesh
[out]	M	Output Geogram mesh

Definition at line 811 of file MeshUtils.cpp.

References polyfem::mesh::Mesh::face_vertex(), polyfem::mesh::Mesh3D::get_ordered_vertices_from_hex(), polyfem::mesh::Mesh::is_boundary_face(), polyfem::mesh::Mesh::is_cube(), polyfem::mesh::Mesh::n_cells(), polyfem::mesh::Mesh::n_face_vertices(), polyfem::mesh::Mesh::n_faces(), polyfem::mesh::Mesh::n_vertices(), and polyfem::mesh::Mesh::point().

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◆ unconstrained_L2_projection()

Eigen::MatrixXd polyfem::mesh::unconstrained_L2_projection	(	const Eigen::SparseMatrix< double > &	M,
		const Eigen::SparseMatrix< double > &	A,
		const Eigen::Ref< const Eigen::MatrixXd > &	y
	)

Definition at line 17 of file L2Projection.cpp.

References polyfem::logger(), x, and y.

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

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◆ unique_facet_tuples() [1/2]

void polyfem::mesh::unique_facet_tuples	(	const wmtk::TetMesh &	m,
		std::vector< wmtk::TetMesh::Tuple > &	tuples
	)

Definition at line 43 of file LocalMesh.cpp.

◆ unique_facet_tuples() [2/2]

void polyfem::mesh::unique_facet_tuples	(	const wmtk::TriMesh &	m,
		std::vector< wmtk::TriMesh::Tuple > &	tuples
	)

Definition at line 38 of file LocalMesh.cpp.

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

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Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ EvalParametersFunc

◆ GetAdjacentLocalEdge

◆ SizingFieldTetRemesher

◆ SizingFieldTriRemesher

◆ TetMesh

◆ TriMesh

◆ Tuple

◆ WildTetRemesher

◆ WildTriRemesher

Enumeration Type Documentation

◆ BoundaryType

◆ CollapseEdgeTo

◆ CollisionProxyTessellation

◆ ElementType

◆ MeshType

Function Documentation

◆ add_solver_timings()

◆ apply_slim()

◆ build_collision_proxy() [1/2]

◆ build_collision_proxy() [2/2]

◆ build_collision_proxy_displacement_map()

◆ clip_polygon_by_half_plane()

◆ compute_area_ratio_energy()

◆ compute_element_tags()

◆ compute_valence_energy()

◆ compute_visibility_kernel()

◆ constrained_L2_projection()

◆ construct_affine_transformation()

◆ count_faces()

◆ create_patch_around_singularities()

◆ edge_adjacency_graph()

◆ extract_parent_edges()

◆ extract_polyhedra()

◆ extract_triangle_surface_from_tets()

◆ facet_barycenter()

◆ find()

◆ from_geogram_mesh()

◆ generate_edges()

◆ get_quality()

◆ instantiate_pattern()

◆ irregular_tessellation()

◆ irregular_triangle()

◆ irregular_triangle_barycentric_coordinates()

◆ is_inside()

◆ is_planar()

◆ is_star_shaped()

◆ line_weight()

◆ load_collision_proxy()

◆ load_collision_proxy_displacement_map()

◆ load_collision_proxy_mesh()

◆ max_edge_length()

◆ mesh_create_vertex()

◆ mesh_vertex()

◆ NLOHMANN_JSON_SERIALIZE_ENUM()

◆ offset_polygon()

◆ operator<<()

◆ orient_closed_surface()

◆ orient_normals_2d()

◆ project_local_quantities()

◆ rank_edges()

◆ read_fem_geometry()

◆ read_fem_mesh()

◆ read_obstacle_geometry()

◆ read_obstacle_mesh()

◆ read_surface_mesh()

◆ reduced_L2_projection()

◆ refine_edge()

◆ refine_polygonal_mesh() [1/2]

◆ refine_polygonal_mesh() [2/2]

◆ refine_quad_mesh()

◆ refine_triangle_edges()

◆ refine_triangle_mesh()

◆ regular_grid_tessellation()

◆ regular_grid_triangle_barycentric_coordinates()