datastructures

Meshes

The mesh is implemented as a half-edge datastructure. It is meant for the representation of polygonal “surface” meshes. A mesh can be connected or disconnected. A mesh can be closed or open. A mesh can be comprised of only vertices.

Mesh

Implementation of the base mesh data structure that adds some of the mesh algorithms as methods.

Data structure

`HalfEdge`	Base half-edge data structure for representing meshes.
`BaseMesh`	Geometric implementation of a half edge data structure for polygon meshses.

Algorithms

`mesh_bounding_box`	Compute the (axis aligned) bounding box of a mesh.
`mesh_bounding_box_xy`	Compute the (axis aligned) bounding box of a projection of the mesh in the XY plane.
`mesh_connected_components`
`mesh_contours_numpy`	Compute the contours of the mesh.
`mesh_delete_duplicate_vertices`	Cull all duplicate vertices of a mesh and sanitize affected faces.
`mesh_dual`	Construct the dual of a mesh.
`mesh_explode`	Explode a mesh into its disconnected parts.
`mesh_face_adjacency`	Build a face adjacency dict.
`mesh_flip_cycles`	Flip the cycle directions of all faces.
`mesh_geodesic_distances_numpy`	Compute geodesic from the vertices of a mesh to given source vertices.
`mesh_is_connected`	Verify that the mesh is connected.
`mesh_isolines_numpy`	Compute the isolines of a specified attribute of the vertices of a mesh.
`mesh_merge_faces`	Merge two faces of a mesh over their shared edge.
`mesh_offset`	Offset a mesh.
`mesh_oriented_bounding_box_numpy`	Compute the (axis aligned) bounding box of a mesh.
`mesh_oriented_bounding_box_xy_numpy`	Compute the (axis aligned) bounding box of a projection of the mesh in the XY plane.
`mesh_planarize_faces`	Planarise a set of connected faces.
`mesh_quads_to_triangles`
`mesh_slice_plane`	Slice a mesh with a plane and construct the resulting submeshes.
`mesh_smooth_centroid`	Smooth a mesh by moving every free vertex to the centroid of its neighbors.
`mesh_smooth_area`	Smooth a mesh by moving each vertex to the barycenter of the centroids of the surrounding faces, weighted by area.
`mesh_subdivide`	Subdivide the input mesh.
`mesh_subdivide_tri`	Subdivide a mesh using simple insertion of vertices.
`mesh_subdivide_corner`	Subdivide a mesh by cutting corners.
`mesh_subdivide_quad`	Subdivide a mesh such that all faces are quads.
`mesh_subdivide_catmullclark`	Subdivide a mesh using the Catmull-Clark algorithm.
`mesh_subdivide_doosabin`	Subdivide a mesh following the doo-sabin scheme.
`mesh_thicken`	Thicken a mesh.
`mesh_transform`	Transform a mesh.
`mesh_transformed`	Transform a copy of `mesh`.
`mesh_transform_numpy`	Transform a mesh.
`mesh_transformed_numpy`	Transform a copy of `mesh`.
`mesh_unify_cycles`	Unify the cycle directions of all faces.
`mesh_weld`	Weld vertices of a mesh within some precision distance.

`meshes_join`	Join meshes without welding.
`meshes_join_and_weld`	Join and and weld meshes within some precision distance.

Matrices

`mesh_adjacency_matrix`	Creates a vertex adjacency matrix from a Mesh datastructure.
`mesh_connectivity_matrix`	Creates a connectivity matrix from a Mesh datastructure.
`mesh_degree_matrix`	Creates a vertex degree matrix from a Mesh datastructure.
`mesh_face_matrix`	Construct the face matrix from a Mesh datastructure.
`mesh_laplacian_matrix`	Construct a Laplacian matrix with uniform weights from a mesh data structure.

Conway Operators

`mesh_conway_dual`	Generates the dual mesh from a seed mesh.
`mesh_conway_join`	Generates the join mesh from a seed mesh.
`mesh_conway_ambo`	Generates the ambo mesh from a seed mesh.
`mesh_conway_kis`	Generates the kis mesh from a seed mesh.
`mesh_conway_needle`	Generates the needle mesh from a seed mesh.
`mesh_conway_zip`	Generates the zip mesh from a seed mesh.
`mesh_conway_truncate`	Generates the truncate mesh from a seed mesh.
`mesh_conway_ortho`	Generates the ortho mesh from a seed mesh.
`mesh_conway_expand`	Generates the expand mesh from a seed mesh.
`mesh_conway_gyro`	Generates the gyro mesh from a seed mesh.
`mesh_conway_snub`	Generates the snub mesh from a seed mesh.
`mesh_conway_meta`	Generates the meta mesh from a seed mesh.
`mesh_conway_bevel`	Generates the bevel mesh from a seed mesh.

Triangle Meshes

Algorithms

`trimesh_descent`
`trimesh_face_circle`	Get data on circumcentre of triangular face.
`trimesh_gaussian_curvature`	Compute the gaussian curvature at the vertices of a triangle mesh using the angular deficit.

Networks

The network is a connectivity graph. It is meant for the representation of networks of vertices connected by edges. The edges are directed. A network does not have faces. A network can be connected or disconnected. A network with vertices only is also a valid network.

Network

Data structure

Graph

Base graph data structure for describing the topological relationships between nodes connected by edges.

Algorithms

`network_complement`	Generate the complement network of a network.
`network_count_crossings`	Count the number of crossings (pairs of crossing edges) in the network.
`network_embed_in_plane`	Embed the network in the plane.
`network_find_crossings`	Identify all pairs of crossing edges in a network.
`network_find_cycles`	Find the faces of a network.
`network_is_connected`	Verify that the network is connected.
`network_is_crossed`	Verify if a network has crossing edges.
`network_is_planar`	Check if the network is planar.
`network_is_planar_embedding`	Verify that a network is embedded in the plane without crossing edges.
`network_is_xy`	Verify that a network lies in the XY plane.
`network_transform`	Transform a network.
`network_transformed`	Transform a copy of `network`.

VolMesh

The volmesh is a cellular mesh. It is implemented as a half-plane, the three-dimensional equivalent of a half-edge. It can, for example, be used for the representation of subdivided/partitioned polyhedra.

VolMesh

Implementation of the base volmesh data structure that adds some of the mesh algorithms as methods.

datastructures

Meshes

Data structure

Algorithms

Matrices

Conway Operators

Triangle Meshes

Algorithms

Networks

Data structure

Algorithms

VolMesh

COMPAS