ellipsoid_tree::SimplexMesh Class Reference

Simplicial mesh in R^d (cells are d-simplices) with point location, closest-point, CG1 evaluation, and ellipsoid queries. More...

#include <ellipsoid_tree/simplex_mesh.hpp>

Public Member Functions
	SimplexMesh (const Eigen::Ref< const Eigen::MatrixXd > &vertices, const Eigen::Ref< const Eigen::MatrixXi > &cells, int num_threads=0)
	Builds a d-simplex mesh from vertex coordinates (dim, num_vertices) and cell vertex-index columns (dim+1, num_cells); the boundary is extracted as the faces belonging to exactly one cell.
int	dim () const
	Spatial dimension d.
int	num_vertices () const
	Number of mesh vertices.
int	num_cells () const
	Number of cells (d-simplices).
int	num_boundary_faces () const
	Number of boundary faces (faces belonging to exactly one cell).
const Eigen::MatrixXd &	vertices () const
	Vertex coordinates, shape (dim, num_vertices).
const Eigen::MatrixXi &	cells () const
	Cell vertex indices, shape (dim+1, num_cells).
const Eigen::MatrixXi &	boundary_faces () const
	Boundary-face vertex indices, shape (dim, num_boundary_faces).
const SimplexTree &	cell_tree () const
	Underlying spatial index over the cells.
const SimplexTree &	boundary_face_tree () const
	Underlying spatial index over the boundary faces.
std::pair< Eigen::VectorXi, Eigen::MatrixXd >	locate_points (const Eigen::Ref< const Eigen::MatrixXd > &points, int num_threads=0) const
	For each query point (column): the index of a containing cell (-1 if outside the mesh) and its barycentric coordinates in that cell (columns of the second output; zero-filled for outside points).
Eigen::Array< bool, Eigen::Dynamic, 1 >	point_is_in_mesh (const Eigen::Ref< const Eigen::MatrixXd > &points, int num_threads=0) const
	For each query point (column), true if it lies inside the meshed domain (some cell contains it).
Eigen::VectorXd	closest_point (const Eigen::Ref< const Eigen::VectorXd > &p) const
	Closest point of the meshed domain to p: p itself if p is inside the mesh, otherwise the closest point on the mesh boundary.
Eigen::MatrixXd	closest_points (const Eigen::Ref< const Eigen::MatrixXd > &points, int num_threads=0) const
	Closest domain point to each query point (column), shape (dim, num_points); see closest_point.
Eigen::MatrixXd	eval_cg1 (const Eigen::Ref< const Eigen::MatrixXd > &functions_at_vertices, const Eigen::Ref< const Eigen::MatrixXd > &points, bool reflect_exterior=false, int num_threads=0) const
	functions_at_vertices: one function per row, shape (num_functions, num_vertices); points: shape (dim, num_points).
std::vector< int >	cells_intersecting (const Ellipsoid &E, double tau) const
	Indices of the cells intersecting the ellipsoid E at scale tau.
std::vector< std::pair< int, int > >	cell_ellipsoid_pairs (const EllipsoidTree &ellipsoids) const
	All (cell, ellipsoid) collision pairs against an EllipsoidTree, via dual-tree traversal.
std::vector< std::pair< int, int > >	cell_pairs (const SimplexMesh &other) const
	All (cell of this mesh, cell of the other mesh) pairs whose closed cells intersect — the geometric kernel of supermeshing / conservative field transfer between non-matching meshes.

Detailed Description

Simplicial mesh in R^d (cells are d-simplices) with point location, closest-point, CG1 evaluation, and ellipsoid queries.

Constructor & Destructor Documentation

SimplexMesh()

ellipsoid_tree::SimplexMesh::SimplexMesh ( const Eigen::Ref< const Eigen::MatrixXd > &  vertices, const Eigen::Ref< const Eigen::MatrixXi > &  cells, int  num_threads = 0  )

inline

Builds a d-simplex mesh from vertex coordinates (dim, num_vertices) and cell vertex-index columns (dim+1, num_cells); the boundary is extracted as the faces belonging to exactly one cell.

Member Function Documentation

dim()

int ellipsoid_tree::SimplexMesh::dim ( ) const

inline

Spatial dimension d.

num_vertices()

int ellipsoid_tree::SimplexMesh::num_vertices ( ) const

inline

Number of mesh vertices.

num_cells()

int ellipsoid_tree::SimplexMesh::num_cells ( ) const

inline

Number of cells (d-simplices).

num_boundary_faces()

int ellipsoid_tree::SimplexMesh::num_boundary_faces ( ) const

inline

Number of boundary faces (faces belonging to exactly one cell).

vertices()

const Eigen::MatrixXd & ellipsoid_tree::SimplexMesh::vertices ( ) const

inline

Vertex coordinates, shape (dim, num_vertices).

cells()

const Eigen::MatrixXi & ellipsoid_tree::SimplexMesh::cells ( ) const

inline

Cell vertex indices, shape (dim+1, num_cells).

boundary_faces()

const Eigen::MatrixXi & ellipsoid_tree::SimplexMesh::boundary_faces ( ) const

inline

Boundary-face vertex indices, shape (dim, num_boundary_faces).

cell_tree()

const SimplexTree & ellipsoid_tree::SimplexMesh::cell_tree ( ) const

inline

Underlying spatial index over the cells.

boundary_face_tree()

const SimplexTree & ellipsoid_tree::SimplexMesh::boundary_face_tree ( ) const

inline

Underlying spatial index over the boundary faces.

locate_points()

std::pair< Eigen::VectorXi, Eigen::MatrixXd > ellipsoid_tree::SimplexMesh::locate_points ( const Eigen::Ref< const Eigen::MatrixXd > &  points, int  num_threads = 0  ) const

inline

For each query point (column): the index of a containing cell (-1 if outside the mesh) and its barycentric coordinates in that cell (columns of the second output; zero-filled for outside points).

point_is_in_mesh()

Eigen::Array< bool, Eigen::Dynamic, 1 > ellipsoid_tree::SimplexMesh::point_is_in_mesh ( const Eigen::Ref< const Eigen::MatrixXd > &  points, int  num_threads = 0  ) const

inline

For each query point (column), true if it lies inside the meshed domain (some cell contains it).

closest_point()

Eigen::VectorXd ellipsoid_tree::SimplexMesh::closest_point ( const Eigen::Ref< const Eigen::VectorXd > &  p ) const

inline

Closest point of the meshed domain to p: p itself if p is inside the mesh, otherwise the closest point on the mesh boundary.

closest_points()

Eigen::MatrixXd ellipsoid_tree::SimplexMesh::closest_points ( const Eigen::Ref< const Eigen::MatrixXd > &  points, int  num_threads = 0  ) const

inline

Closest domain point to each query point (column), shape (dim, num_points); see closest_point.

eval_cg1()

Eigen::MatrixXd ellipsoid_tree::SimplexMesh::eval_cg1 ( const Eigen::Ref< const Eigen::MatrixXd > &  functions_at_vertices, const Eigen::Ref< const Eigen::MatrixXd > &  points, bool  reflect_exterior = false, int  num_threads = 0  ) const

inline

functions_at_vertices: one function per row, shape (num_functions, num_vertices); points: shape (dim, num_points).

Returns function values at the points, shape (num_functions, num_points). Points outside the mesh evaluate to zero, unless reflect_exterior is set, in which case they are first reflected across the boundary through their closest boundary point (points whose reflection is still outside give zero).

cells_intersecting()

std::vector< int > ellipsoid_tree::SimplexMesh::cells_intersecting ( const Ellipsoid &  E, double  tau  ) const

inline

Indices of the cells intersecting the ellipsoid E at scale tau.

cell_ellipsoid_pairs()

std::vector< std::pair< int, int > > ellipsoid_tree::SimplexMesh::cell_ellipsoid_pairs ( const EllipsoidTree &  ellipsoids ) const

inline

All (cell, ellipsoid) collision pairs against an EllipsoidTree, via dual-tree traversal.

cell_pairs()

std::vector< std::pair< int, int > > ellipsoid_tree::SimplexMesh::cell_pairs ( const SimplexMesh &  other ) const

inline

All (cell of this mesh, cell of the other mesh) pairs whose closed cells intersect — the geometric kernel of supermeshing / conservative field transfer between non-matching meshes.

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The documentation for this class was generated from the following file:

• ellipsoid_tree/simplex_mesh.hpp