Volume meshes

A tetrahedral mesh

VolumeMesh

Bases: Mesh

boundary_mesh property

The boundary of the VolumeMesh as a SurfaceMesh. Shortcut for `self.boundary_connectivity.mesh

Returns:

Name	Type	Description
None		if the boundary connectivity is not enabled (mesh was not built). See enable_connectivity
SurfaceMesh		the boundary mesh otherwise

id_cells property

Shortcut for range(len(self.cells))

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))

_BoundaryConnectivity(master)

Bases: _Connectivity

Attributes:

Name	Type	Description
m2b_vertex	dict	volume mesh -> boundary indirection for vertices
m2b_edge	dict	volume mesh -> boundary indirection for edges
m2b_face	dict	volume mesh -> boundary indirection for faces
b2m_vertex	dict	boundary -> volume mesh indirection for vertices
b2m_edge	dict	boundary -> volume mesh indirection for edges
b2m_face	dict	boundary -> volume mesh indirection for faces

_extract_surface_boundary()

Builds indirection maps. This is performed automatically upon first connectivity request.

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)

Identifier 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_faces(u, v)

For an edge (u,v), returns the indices of faces that are direct and indirect from (u,v)(see direct_face method). If one of the faces does not exist, returns a None instead of its index.

Parameters:

Name	Type	Description	Default
u	int	index of first vertex	required
v	int	index of second vertex	required

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

Note

Equivalent to mesh.edges[E]

Returns:

Name	Type	Description
list	list	two vertex indices

face_id(*args)

The identifier of a face.

Parameters:

Name	Type	Description	Default
int*		integers representing indices of vertices of the face (not necessarily in the correct order)	required

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_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

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, F, return_inds=False)

Returns the index of the face adjacent to edge (u,v) that is at the opposite of face F. Returns None if such a face does not exist, or if F is not adjacent to edge (u,v)

Parameters:

Name	Type	Description	Default
u	int	index of edge's first vertex	required
v	int	index of edge's second vertex	required
F	int	index of face	required
return_inds	bool	If True, also returns local indices of u and v in opposite face. If input is invalid, will return None,None,None instead of None. Defaults to False.	False

Returns:

Name	Type	Description
int		index of a face

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

_Connectivity(master)

Bases: _Connectivity

_sort_edge_neighborhoods()

Sorts cells adjacent to an edge so that they are in direct order

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)

Identifier 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_faces(u, v)

For an edge (u,v), returns the indices of faces that are direct and indirect from (u,v)(see direct_face method). If one of the faces does not exist, returns a None instead of its index.

Parameters:

Name	Type	Description	Default
u	int	index of first vertex	required
v	int	index of second vertex	required

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

Note

Equivalent to mesh.edges[E]

Returns:

Name	Type	Description
list	list	two vertex indices

face_id(*args)

The identifier of a face.

Parameters:

Name	Type	Description	Default
int*		integers representing indices of vertices of the face (not necessarily in the correct order)	required

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_cell_index(C, V)

Index of vertex V in cell C. None if V is not in cell C

Parameters:

Name	Type	Description	Default
C	int	cell index	required
V	int	vertex index	required

Returns:

Type	Description
	int

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, F, return_inds=False)

Returns the index of the face adjacent to edge (u,v) that is at the opposite of face F. Returns None if such a face does not exist, or if F is not adjacent to edge (u,v)

Parameters:

Name	Type	Description	Default
u	int	index of edge's first vertex	required
v	int	index of edge's second vertex	required
F	int	index of face	required
return_inds	bool	If True, also returns local indices of u and v in opposite face. If input is invalid, will return None,None,None instead of None. Defaults to False.	False

Returns:

Name	Type	Description
int		index of a face

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.

enable_boundary_connectivity()

Builds the indirection maps to the boundary surface mesh, which then can be accessed via the self.boundary_connectivity attribute.

See documentation for VolumeMesh._BoundaryConnectivity for more details.

is_cell_tet(ic)

Returns True if the cell given by idic` is a tetrahedron (i.e. has 4 vertices)

Parameters:

Name	Type	Description	Default
ic	int	cell index	required

Returns:

Name	Type	Description
bool	bool	len(self.cells[ic])==4

is_edge_on_border(*args)

Simple test to determine if a given edge is on the boundary of the mesh.

Parameters:

Name	Type	Description	Default
*args		Either an integer index representing an edge, or two integer indices representing two (adjacent) vertices	()

Returns:

Name	Type	Description
bool	bool	Returns True if the given edge is on the boundary of the mesh.

is_face_on_border(*args)

Simple test to determine if a given face is on the boundary of the mesh.

Parameters:

Name	Type	Description	Default
*args		Either an integer index representing a face, or n integer indices representing the vertices	()

Returns:

Name	Type	Description
bool	bool	Returns True is the given face exists and is on the boundary of the mesh

is_tetrahedral()

Returns:

Name	Type	Description
bool	bool	True if the mesh is tetrahedral (all cells are tetrahedra)

Volume Connectivity

Warning

Volume connectivity is a work in progress and will be available soon.

BoundaryConnectivity

In some applications, you may need to access the boundary surface mesh of a volume mesh in a self-contained way while keeping links to the original volume. It allows requests like "return the list of all vertices adjacent to boundary vertex i that are on the boundary"

It implements the same methods as the Connectivity class of surface meshes for the boundary mesh, as well as indirection arrays to move from volume indices to surface indices. Returned indices of connectivity queries are indices with relation to the volume mesh.

To save time and memory, the boundary indirections are not computed by default. Use the enable_boundary_connectivity() method of the VolumeMesh to explicitly generate a BoundaryConnectivity object, stored in the .boundary_connectivity attribute.

Example

import mouette as M
m = M.mesh.load("my_volume_mesh.tet")

# if enable_boundary_connectivity is not called, `m.boundary_connectivity` is None
m.enable_boundary_connectivity() # builds the indirection
bnd_m = m.boundary_mesh # access the boundary mesh as an independent surface mesh
boundary_neighbors = m.boundary_connectivity.vertex_to_vertices(4) # query connectivity

Bases: _Connectivity

Attributes:

Name	Type	Description
m2b_vertex	dict	volume mesh -> boundary indirection for vertices
m2b_edge	dict	volume mesh -> boundary indirection for edges
m2b_face	dict	volume mesh -> boundary indirection for faces
b2m_vertex	dict	boundary -> volume mesh indirection for vertices
b2m_edge	dict	boundary -> volume mesh indirection for edges
b2m_face	dict	boundary -> volume mesh indirection for faces

clear()

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