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
template<std::floating_point T>
std::array< T, 3 >	compute_distance_gjk (std::span< const T > p, std::span< const T > q)
	Compute the distance between two convex bodies p and q, each defined by a set of points.
template<std::floating_point T>
std::vector< T >	shortest_vector (const mesh::Mesh< T > &mesh, int dim, std::span< const std::int32_t > entities, std::span< const T > points)
	Compute the shortest vector from a mesh entity to a point.
template<std::floating_point T>
T	compute_squared_distance_bbox (std::span< const T, 6 > b, std::span< const T, 3 > x)
	Compute squared distance between point and bounding box.
template<std::floating_point T>
std::vector< T >	squared_distance (const mesh::Mesh< T > &mesh, int dim, std::span< const std::int32_t > entities, std::span< const T > points)
	Compute the squared distance between a point and a mesh entity.
template<std::floating_point T>
BoundingBoxTree< T >	create_midpoint_tree (const mesh::Mesh< T > &mesh, int tdim, std::span< const std::int32_t > entities)
	Create a bounding box tree for the midpoints of a subset of entities.
template<std::floating_point T>
std::vector< std::int32_t >	compute_collisions (const BoundingBoxTree< T > &tree0, const BoundingBoxTree< T > &tree1)
	Compute all collisions between two bounding box trees.
template<std::floating_point T>
graph::AdjacencyList< std::int32_t >	compute_collisions (const BoundingBoxTree< T > &tree, std::span< const T > points)
	Compute collisions between points and leaf bounding boxes.
template<std::floating_point T>
std::int32_t	compute_first_colliding_cell (const mesh::Mesh< T > &mesh, std::span< const std::int32_t > cells, std::array< T, 3 > point, T tol)
	Given a set of cells, find the first one that collides with a point.
template<std::floating_point T>
std::vector< std::int32_t >	compute_closest_entity (const BoundingBoxTree< T > &tree, const BoundingBoxTree< T > &midpoint_tree, const mesh::Mesh< T > &mesh, std::span< const T > points)
	Compute closest mesh entity to a point.
template<std::floating_point T>
graph::AdjacencyList< std::int32_t >	compute_colliding_cells (const mesh::Mesh< T > &mesh, const graph::AdjacencyList< std::int32_t > &candidate_cells, std::span< const T > points)
	Compute which cells collide with a point.
template<std::floating_point T>
std::tuple< std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< T >, std::vector< std::int32_t > >	determine_point_ownership (const mesh::Mesh< T > &mesh, std::span< const T > points, T padding)
	Given a set of points, determine which process is colliding, using the GJK algorithm on cells to determine collisions.

Detailed Description

Geometry data structures and algorithms.

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

Function Documentation

compute_closest_entity()

template<std::floating_point T>

std::vector< std::int32_t > compute_closest_entity	(	const BoundingBoxTree< T > &	tree,
		const BoundingBoxTree< T > &	midpoint_tree,
		const mesh::Mesh< T > &	mesh,
		std::span< const T >	points
	)

Compute closest mesh entity to a point.

Note

Returns a vector filled with index -1 if the bounding box tree is empty.

Parameters

[in]	tree	The bounding box tree for the entities
[in]	midpoint_tree	A bounding box tree with the midpoints of all the mesh entities. This is used to accelerate the search.
[in]	mesh	The mesh
[in]	points	The set of points (shape=(num_points, 3)). Storage is row-major.

Returns

For each point, the index of the closest mesh entity.

compute_colliding_cells()

template<std::floating_point T>

graph::AdjacencyList< std::int32_t > compute_colliding_cells	(	const mesh::Mesh< T > &	mesh,
		const graph::AdjacencyList< std::int32_t > &	candidate_cells,
		std::span< const T >	points
	)

Compute which cells collide with a point.

Note

Uses the GJK algorithm, see geometry::compute_distance_gjk for details.

candidate_cells can for instance be found by using dolfinx::geometry::compute_collisions between a bounding box tree and the set of points.

Parameters

[in]	mesh	The mesh
[in]	candidate_cells	List of candidate colliding cells for the ith point in points
[in]	points	Points to check for collision (shape=(num_points, 3)). Storage is row-major.

Returns

For each point, the cells that collide with the point.

compute_collisions() [1/2]

template<std::floating_point T>

graph::AdjacencyList< std::int32_t > compute_collisions	(	const BoundingBoxTree< T > &	tree,
		std::span< const T >	points
	)

Compute collisions between points and leaf bounding boxes.

Bounding boxes can overlap, therefore points can collide with more than one box.

Parameters

[in]	tree	The bounding box tree
[in]	points	The points (shape=(num_points, 3)). Storage is row-major.

Returns

For each point, the bounding box leaves that collide with the point.

compute_collisions() [2/2]

template<std::floating_point T>

std::vector< std::int32_t > compute_collisions	(	const BoundingBoxTree< T > &	tree0,
		const BoundingBoxTree< T > &	tree1
	)

Compute all collisions between two bounding box trees.

Parameters

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

Returns

List of pairs of intersecting box indices from each tree, flattened as a vector of size num_intersections*2

compute_distance_gjk()

template<std::floating_point T>

std::array< T, 3 > compute_distance_gjk	(	std::span< const T >	p,
		std::span< const T >	q
	)

Compute the distance between two convex bodies p and q, each defined by a set of points.

Uses the Gilbert–Johnson–Keerthi (GJK) distance algorithm.

Parameters

[in]	p	Body 1 list of points, shape (num_points, 3). Row-major storage.
[in]	q	Body 2 list of points, shape (num_points, 3). Row-major storage.

Returns

shortest vector between bodies

compute_first_colliding_cell()

template<std::floating_point T>

std::int32_t compute_first_colliding_cell	(	const mesh::Mesh< T > &	mesh,
		std::span< const std::int32_t >	cells,
		std::array< T, 3 >	point,
		T	tol
	)

Given a set of cells, find the first one that collides with a point.

A point can collide with more than one cell. The first cell detected to collide with the point is returned. If no collision is detected, -1 is returned.

Note

cells can for instance be found by using dolfinx::geometry::compute_collisions between a bounding box tree for the cells of the mesh and the point.

Parameters

[in]	mesh	The mesh
[in]	cells	The candidate cells
[in]	point	The point (shape=(3,))
[in]	tol	Tolerance for accepting a collision (in the squared distance)

Returns

The local cell index, -1 if not found

compute_squared_distance_bbox()

template<std::floating_point T>

T compute_squared_distance_bbox	(	std::span< const T, 6 >	b,
		std::span< const T, 3 >	x
	)

Compute squared distance between point and bounding box.

Parameters

[in]	b	Bounding box coordinates
[in]	x	A point

Returns

The shortest distance between the bounding box b and the point x. Returns zero if x is inside box.

create_midpoint_tree()

template<std::floating_point T>

BoundingBoxTree< T > create_midpoint_tree	(	const mesh::Mesh< T > &	mesh,
		int	tdim,
		std::span< const std::int32_t >	entities
	)

Create a bounding box tree for the midpoints of a subset of entities.

Parameters

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

Returns

Bounding box tree for midpoints of entities

determine_point_ownership()

template<std::floating_point T>

std::tuple< std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< T >, std::vector< std::int32_t > > determine_point_ownership	(	const mesh::Mesh< T > &	mesh,
		std::span< const T >	points,
		T	padding
	)

Given a set of points, determine which process is colliding, using the GJK algorithm on cells to determine collisions.

Todo:

This docstring is unclear. Needs fixing.

Parameters

[in]	mesh	The mesh
[in]	points	Points to check for collision (shape=(num_points, 3)). Storage is row-major.
[in]	padding	Amount of absolute padding of bounding boxes of the mesh. Each bounding box of the mesh is padded with this amount, to increase the number of candidates, avoiding rounding errors in determining the owner of a point if the point is on the surface of a cell in the mesh.

Returns

Tuple (src_owner, dest_owner, dest_points, dest_cells), where src_owner is a list of ranks corresponding to the input points. dest_owner is a list of ranks corresponding to dest_points, the points that this process owns. dest_cells contains the corresponding cell for each entry in dest_points.

Note

dest_owner is sorted

Returns -1 if no colliding process is found

dest_points is flattened row-major, shape (dest_owner.size(), 3)

Only looks through cells owned by the process

A large padding value can increase the runtime of the function by orders of magnitude, because that for non-colliding cells one has to determine the closest cell among all processes with an intersecting bounding box, which is an expensive operation to perform.

shortest_vector()

template<std::floating_point T>

std::vector< T > shortest_vector	(	const mesh::Mesh< T > &	mesh,
		int	dim,
		std::span< const std::int32_t >	entities,
		std::span< const T >	points
	)

Compute the shortest vector from a mesh entity to a point.

Parameters

[in]	mesh	The mesh
[in]	dim	Topological dimension of the mesh entity
[in]	entities	List of entities
[in]	points	Set of points (shape=(num_points, 3)), using row-major storage.

Returns

An array of vectors (shape=(num_points, 3)) where the ith row is the shortest vector between the ith entity and the ith point. Storage is row-major.

squared_distance()

template<std::floating_point T>

std::vector< T > squared_distance	(	const mesh::Mesh< T > &	mesh,
		int	dim,
		std::span< const std::int32_t >	entities,
		std::span< const T >	points
	)

Compute the squared distance between a point and a mesh entity.

The distance is computed between the ith input points and the ith input entity.

Note

Uses the GJK algorithm, see geometry::compute_distance_gjk for details.

Uses a convex hull approximation of linearized geometry

Parameters

[in]	mesh	Mesh containing the entities
[in]	dim	The topological dimension of the mesh entities
[in]	entities	The indices of the mesh entities (local to process)
[in]	points	The set points from which to computed the shortest (shape=(num_points, 3)). Storage is row-major.

Returns

Squared shortest distance from points[i] to entities[i]