polyfem::mesh Namespace Reference

Namespaces
namespace	MeshProcessing3D
namespace	Navigation
namespace	Navigation3D
namespace	Polygons

Classes
class	CMesh2D
class	CMesh3D
struct	Edge
struct	Element
struct	Face
class	GeometryLoader
	Applies geometry JSON semantics while delegating all decoding to MeshLoader. More...
class	LoadedGeometry
class	LocalBoundary
	Boundary primitive IDs for a single element. More...
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	MeshData
	Format-independent input used to construct a runtime Mesh. More...
class	MeshLoader
	The only non-legacy decoder from a logical resource path to mesh data. More...
class	MeshNodes
class	MeshReader
	Stateless format decoders used exclusively by MeshLoader and in-memory adapters. More...
struct	MeshWithID
class	NCMesh2D
class	NCMesh3D
class	Obstacle
class	SurfaceMeshData
struct	Vertex

Typedefs
typedef std::function< void(const Eigen::MatrixXd &, Eigen::MatrixXd &, int)>	EvalParametersFunc
typedef std::function< std::tuple< int, int, bool >(int, int)>	GetAdjacentLocalEdge
using	SurfaceMesh = SurfaceMeshData

Enumerations
enum class	CollisionProxyTessellation { REGULAR , IRREGULAR }
enum class	BoundaryType {   TRI_LINE , QUAD_LINE , PRISM , PYRAMID ,   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 , PRISM , PYRAMID ,   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 }

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 io::ResourceIO &resources, 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 resources.
void	load_collision_proxy_mesh (const io::ResourceIO &resources, 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 resource.
void	load_collision_proxy_displacement_map (const io::ResourceIO &resources, 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 a resource.
	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::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.
std::vector< std::pair< Navigation::Index, Navigation::Index > >	compute_mesh_interface (const Mesh2D &first, const Mesh2D &second)
	Pair coincident boundary edges, including nonconforming leader/follower edges.
std::vector< std::pair< Navigation3D::Index, Navigation3D::Index > >	compute_mesh_interface (const Mesh3D &first, const Mesh3D &second)
	Pair coincident boundary faces, including nonconforming leader/follower faces.
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	find_triangle_surface_from_tets (const Eigen::MatrixXi &tets, Eigen::MatrixXi &faces)
	Boundary triangles of a tet mesh, indexing the tets' vertices.
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	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
bool	apply_slim (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const Eigen::MatrixXd &V_new, Eigen::MatrixXd &V_smooth, const int max_iters)

Variables
constexpr long	MESH_SCHEMA_VERSION = 1
	The canonical typed mesh schema shared by HDF5 bundles and checkpoints.

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.

SurfaceMesh

using polyfem::mesh::SurfaceMesh = typedef SurfaceMeshData

Definition at line 12 of file MeshLoader.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.
PRISM
PYRAMID
TRI
QUAD
POLYGON
POLYHEDRON
INVALID

Definition at line 12 of file LocalBoundary.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 17 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.
PRISM	Boundary polytope.
PYRAMID	Prism.
UNDEFINED	Pyramid.

Definition at line 31 of file Mesh.hpp.

MeshType

enum class polyfem::mesh::MeshType

strong

Enumerator
TRI
QUA
H_SUR
TET
HYB
HEX

Definition at line 57 of file Mesh3DStorage.hpp.

Function Documentation

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::utils::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 75 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::varform::NonlinearElasticVarForm::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 170 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_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 94 of file MeshUtils.cpp.

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

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compute_mesh_interface() [1/2]

std::vector< std::pair< polyfem::mesh::Navigation::Index, polyfem::mesh::Navigation::Index > > polyfem::mesh::compute_mesh_interface	(	const Mesh2D &	first,
		const Mesh2D &	second
	)

Pair coincident boundary edges, including nonconforming leader/follower edges.

Definition at line 834 of file MeshUtils.cpp.

References polyfem::mesh::Mesh2D::get_index_from_face(), polyfem::mesh::Mesh::is_boundary_edge(), polyfem::mesh::Mesh::n_face_vertices(), polyfem::mesh::Mesh::n_faces(), polyfem::mesh::Mesh2D::next_around_face(), polyfem::mesh::Mesh::point(), and polyfem::mesh::Mesh2D::switch_vertex().

Referenced by polyfem::varform::NavierStokesFSIVarForm::load_mesh().

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compute_mesh_interface() [2/2]

std::vector< std::pair< polyfem::mesh::Navigation3D::Index, polyfem::mesh::Navigation3D::Index > > polyfem::mesh::compute_mesh_interface	(	const Mesh3D &	first,
		const Mesh3D &	second
	)

Pair coincident boundary faces, including nonconforming leader/follower faces.

Definition at line 880 of file MeshUtils.cpp.

References polyfem::mesh::Mesh3D::cell_face(), polyfem::mesh::Mesh::face_vertex(), faces, polyfem::mesh::Mesh3D::get_index_from_element(), polyfem::mesh::Mesh::is_boundary_face(), polyfem::mesh::Mesh3D::n_cell_faces(), polyfem::mesh::Mesh::n_cells(), polyfem::mesh::Mesh::n_face_vertices(), polyfem::mesh::Mesh3D::next_around_face(), and polyfem::mesh::Mesh::point().

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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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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 1253 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 1140 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 924 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 1214 of file MeshUtils.cpp.

References find_triangle_surface_from_tets().

Referenced by polyfem::mesh::MeshReader::read_msh_surface().

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facet_barycenter()

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

Definition at line 61 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 341 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::io::ResourceIO::glob(), polyfem::mesh::MeshProcessing3D::refine_catmul_clark_polar(), and polyfem::mesh::NCMesh2D::switch_edge().

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find_triangle_surface_from_tets()

void polyfem::mesh::find_triangle_surface_from_tets	(	const Eigen::MatrixXi &	tets,
		Eigen::MatrixXi &	faces
	)

Boundary triangles of a tet mesh, indexing the tets' vertices.

Parameters

[in]	tets	#T x 4 tet indices
[out]	faces	F x 3 boundary triangle indices

Definition at line 1180 of file MeshUtils.cpp.

References faces.

Referenced by extract_triangle_surface_from_tets(), and polyfem::mesh::MeshReader::read_msh_surface().

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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 635 of file MeshUtils.cpp.

References F, and 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 1303 of file MeshUtils.cpp.

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

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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 276 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 239 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 28 of file MeshUtils.cpp.

Referenced by polyfem::mesh::MeshReader::from_geogram(), and polyfem::mesh::MeshReader::read_geogram_surface().

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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 149 of file PolygonUtils.cpp.

References compute_visibility_kernel(), and F.

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 416 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 io::ResourceIO &	resources,
		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 resources.

Parameters

[in]	mesh_filename	Mesh resource path
[in]	weights_filename	Weights resource path
[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 317 of file CollisionProxy.cpp.

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

Referenced by polyfem::varform::NonlinearElasticVarForm::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 io::ResourceIO &	resources,
		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 a resource.

Parameters

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

Definition at line 375 of file CollisionProxy.cpp.

References polyfem::io::ResourceIO::is_group(), load_collision_proxy_displacement_map(), polyfem::io::ResourceIO::materialize(), polyfem::io::ResourceIO::read_double_vector(), polyfem::io::ResourceIO::read_int_vector(), polyfem::io::ResourceIO::read_shape_attribute(), and weights.

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 io::ResourceIO &	resources,
		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 resource.

Parameters

[in]	mesh_filename	Mesh resource path
[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 333 of file CollisionProxy.cpp.

References polyfem::mesh::SurfaceMeshData::edges, faces, polyfem::mesh::SurfaceMeshData::faces, load_collision_proxy_mesh(), polyfem::mesh::MeshLoader::load_surface(), polyfem::mesh::SurfaceMeshData::points, and polyfem::mesh::SurfaceMeshData::vertices.

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(), 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 74 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 41 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 175 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 698 of file MeshUtils.cpp.

References F, 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 300 of file MeshUtils.cpp.

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

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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 613 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 502 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 727 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 321 of file MeshUtils.cpp.

References F, and 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 261 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 1078 of file MeshUtils.cpp.

References F, 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 665 of file MeshUtils.cpp.

References F, 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 677 of file MeshUtils.cpp.

References F, and 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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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 571 of file MeshUtils.cpp.

References F, and V.

Referenced by polyfem::mesh::NCMesh2D::build_topology(), sample_surface(), 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 1020 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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Variable Documentation

MESH_SCHEMA_VERSION

constexpr long polyfem::mesh::MESH_SCHEMA_VERSION = 1

inlineconstexpr

The canonical typed mesh schema shared by HDF5 bundles and checkpoints.

Definition at line 10 of file MeshLoader.hpp.

Referenced by polyfem::mesh::MeshLoader::validate_group(), and polyfem::io::CheckpointWriter::write_mesh().