dolfinx::geometry Namespace Reference

Geometry data structures and algorithms. More...

Classes
class	BoundingBoxTree
	Axis-Aligned bounding box binary tree. It is used to find entities in a collection (often a mesh::Mesh). More...

Functions
xt::xtensor_fixed< double, xt::xshape< 3 > >	compute_distance_gjk (const xt::xtensor< double, 2 > &p, const xt::xtensor< double, 2 > &q)
	Calculate the distance between two convex bodies p and q, each defined by a set of points, using the Gilbert–Johnson–Keerthi (GJK) distance algorithm. More...
BoundingBoxTree	create_midpoint_tree (const mesh::Mesh &mesh, int tdim, const xtl::span< const std::int32_t > &entity_indices)
	Create a bounding box tree for a subset of entities (local to process) based on the entity midpoints. More...
std::vector< std::array< int, 2 > >	compute_collisions (const BoundingBoxTree &tree0, const BoundingBoxTree &tree1)
	Compute all collisions between two BoundingBoxTrees (local to process). More...
std::vector< int >	compute_collisions (const BoundingBoxTree &tree, const std::array< double, 3 > &p)
	Compute all collisions between bounding boxes and point. More...
std::pair< std::int32_t, double >	compute_closest_entity (const BoundingBoxTree &tree, const std::array< double, 3 > &p, const mesh::Mesh &mesh, double R=-1)
	Compute closest mesh entity (local to process) for the topological distance of the bounding box tree and distance and a point. More...
double	compute_squared_distance_bbox (const std::array< std::array< double, 3 >, 2 > &b, const std::array< double, 3 > &x)
	Compute squared distance between point and bounding box wih index "node". Returns zero if point is inside box.
double	squared_distance (const mesh::Mesh &mesh, int dim, std::int32_t index, const std::array< double, 3 > &p)
	Compute squared distance from a given point to the nearest point on a cell (only first order convex cells are supported at this stage) Uses the GJK algorithm, see geometry::compute_distance_gjk for details. More...
std::vector< std::int32_t >	select_colliding_cells (const dolfinx::mesh::Mesh &mesh, const xtl::span< const std::int32_t > &candidate_cells, const std::array< double, 3 > &p, int n)
	From the given Mesh, select up to n cells (local to process) from the list which actually collide with point p. n may be zero (selects all valid cells). Less than n cells may be returned. More...

Detailed Description

Geometry data structures and algorithms.

Tools for geometric data structures and operations, e.g. searching.

Function Documentation

compute_closest_entity()

std::pair< int, double > dolfinx::geometry::compute_closest_entity	(	const BoundingBoxTree &	tree,
		const std::array< double, 3 > &	p,
		const mesh::Mesh &	mesh,
		double	R = -1
	)

Compute closest mesh entity (local to process) for the topological distance of the bounding box tree and distance and a point.

Parameters

[in]	tree	The bounding box tree
[in]	p	The point
[in]	mesh	The mesh
[in]	R	Radius for search. Supplying a negative radius causes the function to estimate an initial search radius.

Returns

The local index of the entity and the distance from the point.

compute_collisions() [1/2]

std::vector< int > dolfinx::geometry::compute_collisions	(	const BoundingBoxTree &	tree,
		const std::array< double, 3 > &	p
	)

Compute all collisions between bounding boxes and point.

Parameters

[in]	tree	The bounding box tree
[in]	p	The point

Returns

Bounding box leaves (local to process) that contain the point

compute_collisions() [2/2]

std::vector< std::array< int, 2 > > dolfinx::geometry::compute_collisions	(	const BoundingBoxTree &	tree0,
		const BoundingBoxTree &	tree1
	)

Compute all collisions between two BoundingBoxTrees (local to process).

Parameters

[in]	tree0	First BoundingBoxTree
[in]	tree1	Second BoundingBoxTree

Returns

List of pairs of intersecting box indices (local to process) from each tree

compute_distance_gjk()

xt::xtensor_fixed< double, xt::xshape< 3 > > dolfinx::geometry::compute_distance_gjk	(	const xt::xtensor< double, 2 > &	p,
		const xt::xtensor< double, 2 > &	q
	)

Calculate the distance between two convex bodies p and q, each defined by a set of points, using the Gilbert–Johnson–Keerthi (GJK) distance algorithm.

Parameters

[in]	p	Body 1 list of points, shape (num_points, 3)
[in]	q	Body 2 list of points, shape (num_points, 3)

Returns

shortest vector between bodies

create_midpoint_tree()

geometry::BoundingBoxTree dolfinx::geometry::create_midpoint_tree	(	const mesh::Mesh &	mesh,
		int	tdim,
		const xtl::span< const std::int32_t > &	entity_indices
	)

Create a bounding box tree for a subset of entities (local to process) based on the entity midpoints.

Parameters

[in]	mesh	The mesh
[in]	tdim	The topological dimension of the entity
[in]	entity_indices	List of local entity indices

Returns

Bounding box tree for midpoints of mesh entities

select_colliding_cells()

std::vector< std::int32_t > dolfinx::geometry::select_colliding_cells	(	const dolfinx::mesh::Mesh &	mesh,
		const xtl::span< const std::int32_t > &	candidate_cells,
		const std::array< double, 3 > &	p,
		int	n
	)

From the given Mesh, select up to n cells (local to process) from the list which actually collide with point p. n may be zero (selects all valid cells). Less than n cells may be returned.

Parameters

[in]	mesh	Mesh
[in]	candidate_cells	List of cell indices to test
[in]	p	Point to check for collision
[in]	n	Maximum number of positive results to return

Returns

List of cells which collide with point

squared_distance()

double dolfinx::geometry::squared_distance	(	const mesh::Mesh &	mesh,
		int	dim,
		std::int32_t	index,
		const std::array< double, 3 > &	p
	)

Compute squared distance from a given point to the nearest point on a cell (only first order convex cells are supported at this stage) Uses the GJK algorithm, see geometry::compute_distance_gjk for details.

Note

Currently a convex hull approximation of linearized geometry.

Parameters

[in]	mesh	Mesh containing the mesh entity
[in]	dim	The topological dimension of the mesh entity
[in]	index	The index of the mesh entity (local to process)
[in]	p	The point from which to compouted the shortest distance to the mesh to compute the Point

Returns

shortest squared distance from p to entity