Surface meshes

SurfaceMesh

Bases: Mesh

A data structure for representing polygonal surfaces.

Attributes:

Name	Type	Description
`vertices`	`DataContainer`	the container for all vertices
`edges`	`DataContainer`	the container for all edges
`faces`	`DataContainer`	the container for all faces
`face_corners`	`DataContainer`	the container for all corner of faces
`boundary_edges`	`list`	list of all edge indices on the boundary
`interior_edges`	`list`	list of all interior edge indices (all edges \ boundary_edges)
`boundary_vertices`	`list`	list of all vertex indices on the boundary
`interior_vertices`	`list`	list of all interior verticex indices (all vertices \ boundary_vertices)
`connectivity`	`_SurfaceConnectivity`	the connectivity utility class

`id_corners` `property`

Shortcut for range(len(self.face_corners))

`id_edges` `property`

Shortcut for range(len(self.edges))

`id_faces` `property`

Shortcut for range(len(self.faces))

`id_vertices` `property`

Shortcut for range(len(self.vertices))

`clear_boundary_data()`

Clear all boundary data. Next call to a boundary/interior container or method will recompute everything

`is_edge_on_border(u, v)`

whether edge (u,v) is a boundary edge or not

Parameters:

Name	Type	Description	Default
`u`	`int`	vertex id	required
`v`	`int`	vertex id	required

Returns:

Name	Type	Description
`bool`	`bool`	whether edge (u,v) is a boundary edge or not. Returns False if (u,v) is not a valid edge.

`is_quad()`

Returns:

Name	Type	Description
`bool`	`bool`	True if the mesh is quadrangular (all faces are quad)

`is_triangular()`

Returns:

Name	Type	Description
`bool`	`bool`	True if the mesh is triangular (all faces are triangles)

`is_vertex_on_border(u)`

whether vertex u is a boundary vertex or not.

Parameters:

Name	Type	Description	Default
`u`	`int`	vertex id	required

Returns:

Name	Type	Description
`bool`	`bool`	whether vertex `u` is a boundary vertex or not.

`ith_vertex_of_face(fid, i)`

helper function to get the i-th vertex of a face, i.e. self.faces[fid][i]

Parameters:

Name	Type	Description	Default
`fid`	`int`	face id	required
`i`	`int`	vertex id in face. Should be 0 <= vid < len(face)	required

Returns:

Name	Type	Description
`int`	`int`	the id of the i-th vertex in face `fid` (`self.faces[fid][i]`)

`pt_of_face(fid)`

point coordinates of vertices of face fid

Parameters:

Name	Type	Description	Default
`fid`	`int`	face id	required

Returns:

Name	Type	Description
`Iterable`		iterator of Vec objects representing point coordinates of vertices

Surface Connectivity

Bases: _Connectivity

Connectivity for surface meshes. Is accessed via the .connectivity attribute of the SurfaceMesh class.

Warning

If your mesh is not manifold, there is no guarantee that the connectivity arrays will be correct.

`clear()`

Resets connectivity. The next query in the code will regenerate internal arrays.

`common_edge(iF1, iF2)`

Returns the two vertices (u,v) of the edge that separates faces iF1 and iF2 if it exists, and (None,None) otherwise.

Parameters:

Name	Type	Description	Default
`iF1`	`int`	first face index	required
`iF2`	`int`	second face index	required

Returns:

Type	Description
`(int, int)`	(u,v) pair of vertex indices, or (None,None)

`corner_to_face(C)`

The face inside which corner C belongs.

Parameters:

Name	Type	Description	Default
`C`	`int`	corner id	required

Returns:

Name	Type	Description
`int`	`int`	face id

`direct_face(u, v, return_inds=False)`

Pair (u,v) of vertex -> triangle to the left of edge (u,v) if edge (u,v) exists, None otherwise Also returns local indexes of u and v in the triangle (and None if (u,v) does not exists)

Calling this function with edge (v,u) yield the triangle of the other side of the edge

Parameters:

Name	Type	Description	Default
`u`	`int`	first vertex index	required
`v`	`int`	second vertex index	required
`return_inds`	`bool`	Whether to return local indices of u and v in the face. Defaults to False.	`False`

Returns:

Type	Description
	Index of a face or None. If return_inds is True, tuple made of index of face and local indices of u and v in face or (None,None,None).

`edge_id(V1, V2)`

id of an edge. If self.edges[i] contains edges (A,B), then edge_id(A,B)=edge_id(B,A)=i If (A,B) is not a valid edge of the mesh, returns None

Parameters:

Name	Type	Description	Default
`V1`	`int`	first vertex of the edge	required
`V2`	`int`	second vertex of the edge	required

Returns:

Name	Type	Description
`int`	`int`	the id of edge (V1,V2), or `None` if the edge does not exist.

`edge_to_vertices(E)`

Returns the two vertex indices that are adjacent to edge `E

Parameters:

Name	Type	Description	Default
`E`	`int`	edge index	required

Returns:

Name	Type	Description
`list`	`list`	two vertex indices

`face_id(*args)`

The id of a face Args: int*: integers representing indices of vertices of the face (not necessarily in the correct order)

Returns:

Name	Type	Description
`int`	`int`	A face index or None if the given tuple is invalid

`face_to_corners(F)`

list of corners of face F

Parameters:

Name	Type	Description	Default
`F`	`int`	face id	required

Returns:

Name	Type	Description
`list`	`list`	list of corners of face `F`

`face_to_edges(F)`

List of edges that bound face F.

Parameters:

Name	Type	Description	Default
`F`	`int`	face id	required

Returns:

Name	Type	Description
`list`	`list`	list of edges `E` such that `E` is a boundary edge of face `F`

`face_to_faces(F)`

List of faces that are adjacent to face `F

Parameters:

Name	Type	Description	Default
`F`	`int`	face id	required

Returns:

Name	Type	Description
`list`	`list`	list of faces `G` that are adjacent to `F`

`face_to_first_corner(F)`

One corner C of the face F (the first in order of appearance in the face_corners container)

Parameters:

Name	Type	Description	Default
`F`	`int`	face id	required

Returns:

Name	Type	Description
`int`	`int`	corner id

`face_to_vertices(F)`

Neighborhood of face F in terms of vertices.

Note

Equivalent to mesh.faces[F]

Parameters:

Name	Type	Description	Default
`F`	`int`	face id	required

Returns:

Name	Type	Description
`list`	`list`	list of vertices `V` such that `V` is a vertex of `F`.

`in_face_index(F, V)`

Index of vertex V in face F. None if V is not in face F

Parameters:

Name	Type	Description	Default
`F`	`int`	face index	required
`V`	`int`	vertex index	required

Returns:

Type	Description
	int

`next_corner(C)`

Next corner of C around its associated face

Parameters:

Name	Type	Description	Default
`C`	`int`	corner index	required

Returns:

Name	Type	Description
`int`	`int`	index of the next corner

`opposite_corner(C)`

Opposite corner of C in terms of half edges. If C.vertex = A and C.next.vertex = B, then returns the corner D such that D.vertex = B and D.vertex.next = A

Parameters:

Name	Type	Description	Default
`C`	`int`	corner index	required

Returns:

Name	Type	Description
`int`	`int`	index of the opposite corner

`opposite_face(u, v, T, return_inds=False)`

Given a pair of vertices (u,v) and a face T, returns the face (and local indexes of u and v) on the other side of edge (u,v)

if (u,v) are not two vertices of the face T, returns None

`other_edge_end(E, V)`

Vertex at the opposite end of edge E from vertex V. Returns None if V is not adjacent to edge E

Parameters:

Name	Type	Description	Default
`E`	`int`	edge id	required
`V`	`int`	vertex id	required

Returns:

Name	Type	Description
`int`	`int`	the vertex `W` such that `E` is the edge `(V,W)`. Returns `None` if `V` is not adjacent to edge `E`

`previous_corner(C)`

Previous corner of C around its associated face

Parameters:

Name	Type	Description	Default
`C`	`int`	corner index	required

Returns:

Name	Type	Description
`int`	`int`	index of the previous corner

`vertex_to_corner_in_face(V, F)`

The corner C corresponding to vertex V in face F.

Parameters:

Name	Type	Description	Default
`V`	`int`	vertex id	required
`F`	`int`	face id	required

Returns:

Name	Type	Description
`int`	`int`	corner id, or `None` if `V` is not a vertex of `F`.

`vertex_to_corners(V)`

List of face corners that correspond to vertex V

Parameters:

Name	Type	Description	Default
`V`	`int`	vertex id	required

Returns:

Name	Type	Description
`list`	`list`	the list of corners `C` such that `mesh.corners[C]==V`

`vertex_to_edges(V)`

Neighborhood of vertex V in terms of edges.

Parameters:

Name	Type	Description	Default
`V`	`int`	vertex id	required

Returns:

Name	Type	Description
`list`	`list`	list of edges E such that V belongs to E.

`vertex_to_faces(V)`

Neighborhood of vertex V in terms of faces.

Parameters:

Name	Type	Description	Default
`V`	`int`	vertex id	required

Returns:

Name	Type	Description
`list`	`list`	list of faces `F` such that `V` is a vertex of `F`.

`vertex_to_vertices(V)`

Neighborhood of vertex V in terms of vertices.

Parameters:

Name	Type	Description	Default
`V`	`int`	vertex id	required

Returns:

Name	Type	Description
`list`	`list`	list of vertices `W` such that `(V,W)` is a valid edge in the polyline.

Surface meshes

SurfaceMesh

id_corners property

id_edges property

id_faces property

id_vertices property

clear_boundary_data()

is_edge_on_border(u, v)

is_quad()

is_triangular()

is_vertex_on_border(u)

ith_vertex_of_face(fid, i)

pt_of_face(fid)

Surface Connectivity

clear()

common_edge(iF1, iF2)

corner_to_face(C)

direct_face(u, v, return_inds=False)

edge_id(V1, V2)

edge_to_vertices(E)

face_id(*args)

face_to_corners(F)

face_to_edges(F)

face_to_faces(F)

face_to_first_corner(F)

face_to_vertices(F)

in_face_index(F, V)

next_corner(C)

opposite_corner(C)

opposite_face(u, v, T, return_inds=False)

other_edge_end(E, V)

previous_corner(C)

vertex_to_corner_in_face(V, F)

vertex_to_corners(V)

vertex_to_edges(V)

vertex_to_faces(V)

vertex_to_vertices(V)

`id_corners` `property`

`id_edges` `property`

`id_faces` `property`

`id_vertices` `property`

`clear_boundary_data()`

`is_edge_on_border(u, v)`

`is_quad()`

`is_triangular()`

`is_vertex_on_border(u)`

`ith_vertex_of_face(fid, i)`

`pt_of_face(fid)`

`clear()`

`common_edge(iF1, iF2)`

`corner_to_face(C)`

`direct_face(u, v, return_inds=False)`

`edge_id(V1, V2)`

`edge_to_vertices(E)`

`face_id(*args)`

`face_to_corners(F)`

`face_to_edges(F)`

`face_to_faces(F)`

`face_to_first_corner(F)`

`face_to_vertices(F)`

`in_face_index(F, V)`

`next_corner(C)`

`opposite_corner(C)`

`opposite_face(u, v, T, return_inds=False)`

`other_edge_end(E, V)`

`previous_corner(C)`

`vertex_to_corner_in_face(V, F)`

`vertex_to_corners(V)`

`vertex_to_edges(V)`

`vertex_to_faces(V)`

`vertex_to_vertices(V)`