Geometry (dolfinx::geometry
)

namespace dolfinx::geometry
Geometry data structures and algorithms.
Tools for geometric data structures and operations, e.g. searching.
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.
 Parameters
p – [in] Body 1 list of points, shape (num_points, 3)
q – [in] Body 2 list of points, shape (num_points, 3)
 Returns
shortest vector between bodies

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.
 Parameters
mesh – [in] The mesh
tdim – [in] The topological dimension of the entity
entity_indices – [in] List of local entity indices
 Returns
Bounding box tree for midpoints of mesh entities

std::vector<std::array<int, 2>> compute_collisions(const BoundingBoxTree &tree0, const BoundingBoxTree &tree1)
Compute all collisions between two BoundingBoxTrees (local to process)
 Parameters
tree0 – [in] First BoundingBoxTree
tree1 – [in] Second BoundingBoxTree
 Returns
List of pairs of intersecting box indices from each tree

graph::AdjacencyList<std::int32_t> compute_collisions(const BoundingBoxTree &tree, const xt::xtensor<double, 2> &points)
Compute all collisions between bounding boxes and for a set of points.
 Parameters
tree – [in] The bounding box tree
points – [in] The points (shape=(num_points, 3))
 Returns
An adjacency list where the ith node corresponds to the bounding box leaves that contain the ith point

std::vector<std::int32_t> compute_closest_entity(const BoundingBoxTree &tree, const BoundingBoxTree &midpoint_tree, const mesh::Mesh &mesh, const xt::xtensor<double, 2> &points)
Compute closest mesh entity to a point.
Note
Returns index 1 if the bounding box tree is empty
 Parameters
tree – [in] The bounding box tree for the entities
midpoint_tree – [in] A bounding box tree with the midpoints of all the mesh entities. This is used to accelerate the search
mesh – [in] The mesh
points – [in] The set of points (shape=(num_points, 3))
 Returns
Index of the closest mesh entity to a point. The ith entry is the index of the closest entity to the ith input point.

double compute_squared_distance_bbox(const xt::xtensor_fixed<double, xt::xshape<2, 3>> &b, const xt::xtensor_fixed<double, xt::xshape<3>> &x)
Compute squared distance between point and bounding box.
 Parameters
b – [in] Bounding box coordinates
x – [in] A point
 Returns
The shortest distance between the bounding box
b
and the pointx
. Returns zero ifx
is inside box.

xt::xtensor<double, 2> shortest_vector(const mesh::Mesh &mesh, int dim, const xtl::span<const std::int32_t> &entities, const xt::xtensor<double, 2> &points)
Compute the shortest vector from a mesh entity to a point.
 Parameters
mesh – [in] The mesh
dim – [in] The topological dimension of the mesh entity
entities – [in] The list of entities (local to process)
points – [in] The set of points (shape=(num_points, 3))
 Returns
An array of vectors where the ith row is the shortest vector from the ith entity and the ith point

xt::xtensor<double, 1> squared_distance(const mesh::Mesh &mesh, int dim, const xtl::span<const std::int32_t> &entities, const xt::xtensor<double, 2> &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.
Note
Uses a convex hull approximation of linearized geometry
 Parameters
mesh – [in] Mesh containing the entities
dim – [in] The topological dimension of the mesh entities
entities – [in] The indices of the mesh entities (local to process)
points – [in] The set points from which to computed the shortest (shape=(num_points, 3))
 Returns
Squared shortest distance from points[i] to entities[i]

graph::AdjacencyList<int> compute_colliding_cells(const mesh::Mesh &mesh, const graph::AdjacencyList<std::int32_t> &candidate_cells, const xt::xtensor<double, 2> &points)
From a Mesh, find which cells collide with a set of points.
Note
Uses the GJK algorithm, see geometry::compute_distance_gjk for details
Note
There may be nodes with no entries in the adjacency list
 Parameters
mesh – [in] The mesh
candidate_cells – [in] List of candidate colliding cells for the ith point in
points
points – [in] The points to check for collision (shape=(num_points, 3))
 Returns
Adjacency list where the ith node is the list of entities that collide with the ith point

class BoundingBoxTree
 #include <BoundingBoxTree.h>
AxisAligned bounding box binary tree. It is used to find entities in a collection (often a mesh::Mesh).

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