PolyFEM
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#include <Mesh3D.hpp>
Public Member Functions | |
Mesh3D ()=default | |
virtual | ~Mesh3D ()=default |
Mesh3D (Mesh3D &&)=default | |
Mesh3D & | operator= (Mesh3D &&)=default |
Mesh3D (const Mesh3D &)=default | |
Mesh3D & | operator= (const Mesh3D &)=default |
bool | is_volume () const override |
checks if mesh is volume | |
virtual int | n_cell_edges (const int c_id) const =0 |
virtual int | n_cell_faces (const int c_id) const =0 |
virtual int | cell_face (const int c_id, const int lf_id) const =0 |
virtual int | cell_edge (const int c_id, const int le_id) const =0 |
void | elements_boxes (std::vector< std::array< Eigen::Vector3d, 2 > > &boxes) const override |
constructs a box around every element (3d cell, 2d face) | |
void | barycentric_coords (const RowVectorNd &p, const int el_id, Eigen::MatrixXd &coord) const override |
constructs barycentric coodiantes for a point p. | |
void | compute_cell_jacobian (const int el_id, const Eigen::MatrixXd &reference_map, Eigen::MatrixXd &jacobian) const |
virtual RowVectorNd | kernel (const int cell_id) const =0 |
double | tri_area (const int gid) const override |
area of a tri face of a tet mesh | |
std::pair< RowVectorNd, int > | edge_node (const Navigation3D::Index &index, const int n_new_nodes, const int i) const |
std::pair< RowVectorNd, int > | face_node (const Navigation3D::Index &index, const int n_new_nodes, const int i, const int j) const |
std::pair< RowVectorNd, int > | cell_node (const Navigation3D::Index &index, const int n_new_nodes, const int i, const int j, const int k) const |
void | get_edges (Eigen::MatrixXd &p0, Eigen::MatrixXd &p1) const override |
Get all the edges. | |
void | get_edges (Eigen::MatrixXd &p0, Eigen::MatrixXd &p1, const std::vector< bool > &valid_elements) const override |
Get all the edges according to valid_elements selection. | |
virtual Navigation3D::Index | get_index_from_element (int hi, int lf, int lv) const =0 |
virtual Navigation3D::Index | get_index_from_element (int hi) const =0 |
virtual Navigation3D::Index | get_index_from_element_edge (int hi, int v0, int v1) const =0 |
virtual Navigation3D::Index | get_index_from_element_face (int hi, int v0, int v1, int v2) const =0 |
virtual std::vector< uint32_t > | vertex_neighs (const int v_gid) const =0 |
virtual std::vector< uint32_t > | edge_neighs (const int e_gid) const =0 |
virtual Navigation3D::Index | switch_vertex (Navigation3D::Index idx) const =0 |
virtual Navigation3D::Index | switch_edge (Navigation3D::Index idx) const =0 |
virtual Navigation3D::Index | switch_face (Navigation3D::Index idx) const =0 |
virtual Navigation3D::Index | switch_element (Navigation3D::Index idx) const =0 |
virtual Navigation3D::Index | next_around_edge (Navigation3D::Index idx) const =0 |
virtual Navigation3D::Index | next_around_face (Navigation3D::Index idx) const =0 |
void | to_face_functions (std::array< std::function< Navigation3D::Index(Navigation3D::Index)>, 6 > &to_face) const |
void | to_vertex_functions (std::array< std::function< Navigation3D::Index(Navigation3D::Index)>, 8 > &to_vertex) const |
void | to_edge_functions (std::array< std::function< Navigation3D::Index(Navigation3D::Index)>, 12 > &to_edge) const |
std::array< int, 8 > | get_ordered_vertices_from_hex (const int element_index) const |
virtual std::array< int, 4 > | get_ordered_vertices_from_tet (const int element_index) const |
virtual void | get_vertex_elements_neighs (const int v_id, std::vector< int > &ids) const =0 |
virtual void | get_edge_elements_neighs (const int e_id, std::vector< int > &ids) const =0 |
void | compute_element_barycenters (Eigen::MatrixXd &barycenters) const override |
utility for 2d/3d. | |
Public Member Functions inherited from polyfem::mesh::Mesh | |
virtual std::unique_ptr< Mesh > | copy () const =0 |
Create a copy of the mesh. | |
virtual | ~Mesh ()=default |
Destroy the Mesh object. | |
Mesh (Mesh &&)=default | |
Construct a new Mesh object. | |
Mesh & | operator= (Mesh &&)=default |
Copy constructor. | |
Mesh (const Mesh &)=default | |
Construct a new Mesh object. | |
Mesh & | operator= (const Mesh &)=default |
virtual void | refine (const int n_refinement, const double t)=0 |
refine the mesh | |
int | dimension () const |
utily for dimension | |
virtual bool | is_conforming () const =0 |
if the mesh is conforming | |
int | n_elements () const |
utitlity to return the number of elements, cells or faces in 3d and 2d | |
int | n_boundary_elements () const |
utitlity to return the number of boundary elements, faces or edges in 3d and 2d | |
virtual int | n_cells () const =0 |
number of cells | |
virtual int | n_faces () const =0 |
number of faces | |
virtual int | n_edges () const =0 |
number of edges | |
virtual int | n_vertices () const =0 |
number of vertices | |
virtual int | n_face_vertices (const int f_id) const =0 |
number of vertices of a face | |
virtual int | n_cell_vertices (const int c_id) const =0 |
number of vertices of a cell | |
virtual int | edge_vertex (const int e_id, const int lv_id) const =0 |
id of the edge vertex | |
virtual int | face_vertex (const int f_id, const int lv_id) const =0 |
id of the face vertex | |
virtual int | cell_vertex (const int f_id, const int lv_id) const =0 |
id of the vertex of a cell | |
int | element_vertex (const int el_id, const int lv_id) const |
id of the vertex of a element | |
std::vector< int > | element_vertices (const int el_id) const |
list of vids of an element | |
int | boundary_element_vertex (const int primitive_id, const int lv_id) const |
virtual bool | is_boundary_vertex (const int vertex_global_id) const =0 |
is vertex boundary | |
virtual bool | is_boundary_edge (const int edge_global_id) const =0 |
is edge boundary | |
virtual bool | is_boundary_face (const int face_global_id) const =0 |
is face boundary | |
virtual bool | is_boundary_element (const int element_global_id) const =0 |
is cell boundary | |
virtual bool | save (const std::string &path) const =0 |
virtual void | attach_higher_order_nodes (const Eigen::MatrixXd &V, const std::vector< std::vector< int > > &nodes)=0 |
attach high order nodes | |
const Eigen::MatrixXi & | orders () const |
order of each element | |
bool | is_rational () const |
check if curved mesh has rational polynomials elements | |
void | set_is_rational (const bool in_is_rational) |
Set the is rational object. | |
virtual void | normalize ()=0 |
normalize the mesh | |
virtual void | compute_elements_tag ()=0 |
compute element types, see ElementType | |
virtual void | update_elements_tag () |
Update elements types. | |
virtual double | edge_length (const int gid) const |
edge length | |
virtual double | quad_area (const int gid) const |
area of a quad face of an hex mesh | |
virtual RowVectorNd | point (const int global_index) const =0 |
point coordinates | |
virtual void | set_point (const int global_index, const RowVectorNd &p)=0 |
Set the point. | |
virtual RowVectorNd | edge_barycenter (const int e) const =0 |
edge barycenter | |
virtual RowVectorNd | face_barycenter (const int f) const =0 |
face barycenter | |
virtual RowVectorNd | cell_barycenter (const int c) const =0 |
cell barycenter | |
void | edge_barycenters (Eigen::MatrixXd &barycenters) const |
all edges barycenters | |
void | face_barycenters (Eigen::MatrixXd &barycenters) const |
all face barycenters | |
void | cell_barycenters (Eigen::MatrixXd &barycenters) const |
all cells barycenters | |
virtual void | bounding_box (RowVectorNd &min, RowVectorNd &max) const =0 |
computes the bbox of the mesh | |
bool | is_spline_compatible (const int el_id) const |
checks if element is spline compatible | |
bool | is_cube (const int el_id) const |
checks if element is cube compatible | |
bool | is_polytope (const int el_id) const |
checks if element is polygon compatible | |
bool | is_simplex (const int el_id) const |
checks if element is simples compatible | |
const std::vector< ElementType > & | elements_tag () const |
Returns the elements types. | |
void | set_tag (const int el, const ElementType type) |
changes the element type | |
void | compute_node_ids (const std::function< int(const size_t, const RowVectorNd &, bool)> &marker) |
computes boundary selections based on a function | |
virtual void | load_boundary_ids (const std::string &path) |
loads the boundary selections for a file | |
virtual void | compute_boundary_ids (const std::function< int(const size_t, const std::vector< int > &, const RowVectorNd &, bool)> &marker)=0 |
computes boundary selections based on a function | |
virtual void | compute_body_ids (const std::function< int(const size_t, const std::vector< int > &, const RowVectorNd &)> &marker)=0 |
computes boundary selections based on a function | |
virtual void | set_boundary_ids (const std::vector< int > &boundary_ids) |
Set the boundary selection from a vector. | |
virtual void | set_body_ids (const std::vector< int > &body_ids) |
Set the volume sections. | |
virtual int | get_default_boundary_id (const int primitive) const |
Get the default boundary selection of an element (face in 3d, edge in 2d) | |
virtual int | get_boundary_id (const int primitive) const |
Get the boundary selection of an element (face in 3d, edge in 2d) | |
virtual int | get_node_id (const int node_id) const |
Get the boundary selection of a node. | |
void | update_nodes (const Eigen::VectorXi &in_node_to_node) |
Update the node ids to reorder them. | |
virtual int | get_body_id (const int primitive) const |
Get the volume selection of an element (cell in 3d, face in 2d) | |
virtual const std::vector< int > & | get_body_ids () const |
Get the volume selection of all elements (cells in 3d, faces in 2d) | |
bool | has_node_ids () const |
checks if points selections are available | |
bool | has_boundary_ids () const |
checks if surface selections are available | |
virtual bool | has_body_ids () const |
checks if volumes selections are available | |
const std::vector< double > & | cell_weights (const int cell_index) const |
weights for rational polynomial meshes | |
void | set_cell_weights (const std::vector< std::vector< double > > &in_cell_weights) |
Set the cell weights for rational polynomial meshes. | |
virtual void | prepare_mesh () |
method used to finalize the mesh. | |
bool | has_poly () const |
checks if the mesh has polytopes | |
bool | is_simplicial () const |
checks if the mesh is simplicial | |
bool | is_linear () const |
check if the mesh is linear | |
std::vector< std::pair< int, int > > | edges () const |
list of sorted edges. | |
std::vector< std::vector< int > > | faces () const |
list of sorted faces. | |
std::unordered_map< std::pair< int, int >, size_t, polyfem::utils::HashPair > | edges_to_ids () const |
map from edge (pair of v id) to the id of the edge | |
std::unordered_map< std::vector< int >, size_t, polyfem::utils::HashVector > | faces_to_ids () const |
map from face (tuple of v id) to the id of the face | |
const Eigen::VectorXi & | in_ordered_vertices () const |
Order of the input vertices. | |
const Eigen::MatrixXi & | in_ordered_edges () const |
Order of the input edges. | |
const Eigen::MatrixXi & | in_ordered_faces () const |
Order of the input edges. | |
virtual void | append (const Mesh &mesh) |
appends a new mesh to the end of this | |
void | append (const std::unique_ptr< Mesh > &mesh) |
appends a new mesh to the end of this, utility that takes pointer, calls other one | |
void | apply_affine_transformation (const MatrixNd &A, const VectorNd &b) |
Apply an affine transformation \(Ax+b\) to the vertex positions \(x\). | |
Additional Inherited Members | |
Static Public Member Functions inherited from polyfem::mesh::Mesh | |
static std::unique_ptr< Mesh > | create (const std::string &path, const bool non_conforming=false) |
factory to build the proper mesh | |
static std::unique_ptr< Mesh > | create (GEO::Mesh &M, const bool non_conforming=false) |
factory to build the proper mesh | |
static std::unique_ptr< Mesh > | create (const Eigen::MatrixXd &vertices, const Eigen::MatrixXi &cells, const bool non_conforming=false) |
factory to build the proper mesh | |
static std::unique_ptr< Mesh > | create (const int dim, const bool non_conforming=false) |
factory to build the proper empty mesh | |
Protected Member Functions inherited from polyfem::mesh::Mesh | |
Mesh ()=default | |
Construct a new Mesh object. | |
virtual bool | load (const std::string &path)=0 |
loads a mesh from the path | |
virtual bool | load (const GEO::Mesh &M)=0 |
loads a mesh from a geo mesh | |
Protected Attributes inherited from polyfem::mesh::Mesh | |
std::vector< ElementType > | elements_tag_ |
list of element types | |
std::vector< int > | node_ids_ |
list of node labels | |
std::vector< int > | boundary_ids_ |
list of surface labels | |
std::vector< int > | body_ids_ |
list of volume labels | |
Eigen::MatrixXi | orders_ |
list of geometry orders, one per cell | |
bool | is_rational_ = false |
stores if the mesh is rational | |
std::vector< EdgeNodes > | edge_nodes_ |
high-order nodes associates to edges | |
std::vector< FaceNodes > | face_nodes_ |
high-order nodes associates to faces | |
std::vector< CellNodes > | cell_nodes_ |
high-order nodes associates to cells | |
std::vector< std::vector< double > > | cell_weights_ |
weights associates to cells for rational polynomail meshes | |
Eigen::VectorXi | in_ordered_vertices_ |
Order of the input vertices. | |
Eigen::MatrixXi | in_ordered_edges_ |
Order of the input edges. | |
Eigen::MatrixXi | in_ordered_faces_ |
Order of the input faces, TODO: change to std::vector of Eigen::Vector. | |
Definition at line 18 of file Mesh3D.hpp.
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default |
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virtualdefault |
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default |
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default |
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overridevirtual |
constructs barycentric coodiantes for a point p.
WARNING works only for simplices
[in] | p | query point |
[in] | el_id | element id |
[out] | coord | matrix containing the barycentric coodinates |
Implements polyfem::mesh::Mesh.
Definition at line 410 of file Mesh3D.cpp.
References get_ordered_vertices_from_tet(), polyfem::mesh::Mesh::is_simplex(), and polyfem::mesh::Mesh::point().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by get_edges(), and polyfem::refinement::APriori::p_refine().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::io::Evaluator::interpolate_boundary_function().
std::pair< RowVectorNd, int > polyfem::mesh::Mesh3D::cell_node | ( | const Navigation3D::Index & | index, |
const int | n_new_nodes, | ||
const int | i, | ||
const int | j, | ||
const int | k | ||
) | const |
Definition at line 199 of file Mesh3D.cpp.
References polyfem::mesh::Mesh::cell_barycenter(), polyfem::mesh::Mesh::cell_nodes_, polyfem::mesh::Navigation3D::Index::element, polyfem::mesh::Mesh::is_cube(), polyfem::mesh::Mesh::is_simplex(), polyfem::mesh::Mesh::orders_, polyfem::mesh::Mesh::point(), switch_edge(), switch_face(), switch_vertex(), and polyfem::mesh::Navigation3D::Index::vertex.
Referenced by polyfem::mesh::MeshNodes::node_ids_from_cell().
void polyfem::mesh::Mesh3D::compute_cell_jacobian | ( | const int | el_id, |
const Eigen::MatrixXd & | reference_map, | ||
Eigen::MatrixXd & | jacobian | ||
) | const |
Definition at line 424 of file Mesh3D.cpp.
References get_ordered_vertices_from_tet(), polyfem::mesh::Mesh::is_simplex(), and polyfem::mesh::Mesh::point().
Referenced by polyfem::solver::AMIPSForm::AMIPSForm(), and polyfem::State::set_materials().
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inlineoverridevirtual |
utility for 2d/3d.
In 2d it returns face_barycenters, in 3d it returns cell_barycenters
[out] | barycenters | the barycenters |
Implements polyfem::mesh::Mesh.
Definition at line 88 of file Mesh3D.hpp.
References polyfem::mesh::Mesh::cell_barycenters().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::refinement::APriori::p_refine().
std::pair< RowVectorNd, int > polyfem::mesh::Mesh3D::edge_node | ( | const Navigation3D::Index & | index, |
const int | n_new_nodes, | ||
const int | i | ||
) | const |
Definition at line 80 of file Mesh3D.cpp.
References polyfem::mesh::Navigation3D::Index::edge, polyfem::mesh::Mesh::edge_nodes_, polyfem::mesh::Navigation3D::Index::element, polyfem::mesh::Mesh::orders_, polyfem::mesh::Mesh::point(), switch_vertex(), and polyfem::mesh::Navigation3D::Index::vertex.
Referenced by polyfem::mesh::MeshNodes::node_ids_from_edge().
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constructs a box around every element (3d cell, 2d face)
[out] | boxes | axis aligned bounding boxes |
Implements polyfem::mesh::Mesh.
Definition at line 388 of file Mesh3D.cpp.
References polyfem::mesh::Mesh::cell_vertex(), polyfem::mesh::Mesh::n_cell_vertices(), polyfem::mesh::Mesh::n_elements(), and polyfem::mesh::Mesh::point().
std::pair< RowVectorNd, int > polyfem::mesh::Mesh3D::face_node | ( | const Navigation3D::Index & | index, |
const int | n_new_nodes, | ||
const int | i, | ||
const int | j | ||
) | const |
Definition at line 99 of file Mesh3D.cpp.
References polyfem::mesh::Navigation3D::Index::element, polyfem::mesh::Navigation3D::Index::face, polyfem::mesh::Mesh::face_nodes_, polyfem::mesh::Mesh::is_cube(), polyfem::mesh::Mesh::is_simplex(), next_around_face(), polyfem::mesh::Mesh::orders_, polyfem::mesh::Mesh::point(), switch_edge(), switch_vertex(), and polyfem::mesh::Navigation3D::Index::vertex.
Referenced by polyfem::mesh::MeshNodes::node_ids_from_face().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
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Get all the edges.
[out] | p0 | edge first vertex |
[out] | p1 | edge second vertex |
Implements polyfem::mesh::Mesh.
Definition at line 33 of file Mesh3D.cpp.
References polyfem::mesh::Mesh::edge_vertex(), polyfem::mesh::Mesh::n_edges(), and polyfem::mesh::Mesh::point().
Referenced by polyfem::mesh::CMesh3D::normalize(), and polyfem::refinement::APriori::p_refine().
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Get all the edges according to valid_elements selection.
[out] | p0 | edge first vertex |
[out] | p1 | edge second vertex |
[in] | valid_elements | flag to compute the edge |
Implements polyfem::mesh::Mesh.
Definition at line 48 of file Mesh3D.cpp.
References cell_edge(), polyfem::mesh::Mesh::edge_vertex(), n_cell_edges(), and polyfem::mesh::Mesh::point().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::mesh::extract_polyhedra(), get_ordered_vertices_from_hex(), and get_ordered_vertices_from_tet().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::basis::LagrangeBasis3d::hex_face_local_nodes(), and polyfem::basis::LagrangeBasis3d::tet_face_local_nodes().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::basis::LagrangeBasis3d::tet_face_local_nodes().
std::array< int, 8 > polyfem::mesh::Mesh3D::get_ordered_vertices_from_hex | ( | const int | element_index | ) | const |
Definition at line 322 of file Mesh3D.cpp.
References get_index_from_element(), polyfem::mesh::Mesh::is_cube(), and to_vertex_functions().
Referenced by polyfem::mesh::to_geogram_mesh().
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Reimplemented in polyfem::mesh::NCMesh3D.
Definition at line 346 of file Mesh3D.cpp.
References get_index_from_element(), next_around_face(), switch_edge(), switch_face(), and switch_vertex().
Referenced by polyfem::mesh::CMesh3D::barycentric_coords(), barycentric_coords(), and compute_cell_jacobian().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
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inlineoverridevirtual |
checks if mesh is volume
Implements polyfem::mesh::Mesh.
Definition at line 28 of file Mesh3D.hpp.
Referenced by polyfem::basis::PolygonalBasis3d::build_bases(), polyfem::basis::SplineBasis3d::build_bases(), polyfem::basis::PolygonalBasis3d::compute_integral_constraints(), and polyfem::compute_integral_constraints().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::mesh::extract_polyhedra().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by get_edges().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::mesh::extract_polyhedra(), and polyfem::io::Evaluator::interpolate_boundary_function().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::mesh::extract_polyhedra(), face_node(), get_ordered_vertices_from_tet(), polyfem::basis::LagrangeBasis3d::hex_face_local_nodes(), and polyfem::basis::LagrangeBasis3d::tet_face_local_nodes().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by cell_node(), face_node(), get_ordered_vertices_from_tet(), to_edge_functions(), to_face_functions(), and to_vertex_functions().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by polyfem::mesh::MeshNodes::node_ids_from_face().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by cell_node(), get_ordered_vertices_from_tet(), to_edge_functions(), to_face_functions(), and to_vertex_functions().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.
Referenced by cell_node(), edge_node(), face_node(), get_ordered_vertices_from_tet(), polyfem::basis::LagrangeBasis3d::hex_face_local_nodes(), polyfem::basis::LagrangeBasis3d::tet_face_local_nodes(), to_edge_functions(), to_face_functions(), and to_vertex_functions().
void polyfem::mesh::Mesh3D::to_edge_functions | ( | std::array< std::function< Navigation3D::Index(Navigation3D::Index)>, 12 > & | to_edge | ) | const |
Definition at line 298 of file Mesh3D.cpp.
References switch_edge(), switch_face(), and switch_vertex().
void polyfem::mesh::Mesh3D::to_face_functions | ( | std::array< std::function< Navigation3D::Index(Navigation3D::Index)>, 6 > & | to_face | ) | const |
Definition at line 267 of file Mesh3D.cpp.
References switch_edge(), switch_face(), and switch_vertex().
void polyfem::mesh::Mesh3D::to_vertex_functions | ( | std::array< std::function< Navigation3D::Index(Navigation3D::Index)>, 8 > & | to_vertex | ) | const |
Definition at line 285 of file Mesh3D.cpp.
References switch_edge(), switch_face(), and switch_vertex().
Referenced by get_ordered_vertices_from_hex().
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overridevirtual |
area of a tri face of a tet mesh
[in] | gid | global face id |
Reimplemented from polyfem::mesh::Mesh.
Definition at line 18 of file Mesh3D.cpp.
References polyfem::mesh::Mesh::face_vertex(), polyfem::mesh::Mesh::n_face_vertices(), polyfem::mesh::Mesh::n_vertices(), and polyfem::mesh::Mesh::point().
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pure virtual |
Implemented in polyfem::mesh::CMesh3D, and polyfem::mesh::NCMesh3D.