Per element attributes

Vertices

angle_defects(mesh, zero_border=False, name='angleDefect', persistent=True, dense=True)

Computes the angle defect at each vertex, defined as 2*pi minus the sum of angles around the vertex.

Angle defect is an discrete approximation of the gaussian curvature. This function relies on the computation of cotangents on the mesh.

Warning

Only works for triangulated meshes.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the mesh	required
zero_border	bool	if set to true, ignores the defect on the boundary of the mesh. Defaults to False.	False
name	str	Name given to the attribute. Defaults to "angleDefect".	'angleDefect'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Type	Description
Attribute	Attribute(float) on vertices

Raises:

Type	Description
Exception	fails if the mesh is not triangulated (ie if a face is not a triangle)

border_normals(mesh, name='borderNormals', persistent=True, dense=False)

Computes the normal direction of the boundary curve.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the mesh	required
name	str	Name given to the attribute. Defaults to "borderNormals".	'borderNormals'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	False

Returns:

Type	Description
Attribute	Attribute(float,3) on vertices

degree(mesh, name='degree', persistent=True, dense=True)

Computes the degree of each vertex, that is the number of vertex that are adjacent.

Parameters:

Name	Type	Description	Default
mesh	Mesh	the input mesh. Pointclouds are forbidden	required
name	str	description. Defaults to "degree".	'degree'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Type	Description
Attribute	Attribute(int) on vertices

vertex_normals(mesh, name='normals', persistent=True, interpolation='area', dense=True, custom_fnormals=None)

Computes normal directions as 3d vectors for each vertex. Normal at a vertex is a weighted sum of normals of adjacent faces. This function essentially interpolates the face normals.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "normals".	'normals'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
interpolation	str	Interpolation weighting mode. 'uniform' : computes the mean for adjacent facet 'area' : the mean is weighted by facet area. Default value. 'angle' : the mean is weighted by internal angle at the vertex	'area'
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True
custom_fnormals	Attribute	custom values for the face normals to be interpolated. Defaults to None.	None

Raises:

Type	Description
Exception	if 'interpolation' is not one of {'uniform', 'area', 'angles'}

Returns:

Type	Description
Attribute	Attribute(float, 3) on vertices

Edges

cotan_weights(mesh, name='cotan_weight', persistent=True, dense=True)

Compute the cotan weights of edges. The weight of an edge separating T1 and T2 is the sum of cotangent of opposite angles in T1 and T2

Parameters:

Name	Type	Description	Default
mesh	Mesh	the input mesh.	required
name	str	name of the attribute. Defaults to "cotan_weight".	'cotan_weight'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

curvature_matrices(mesh)

Curvature matrix for each edge on the mesh, as defined in 'Restricted Delaunay Triangulations and Normal Cycle', David Cohen-Steiner and Jean-Marie Morvan, 2003

Note

See Curvature Frame Fields for their aggregation on triangles or vertices

edge_length(mesh, name='length', persistent=True, dense=True)

Compute edge lengths across the mesh.

Parameters:

Name	Type	Description	Default
mesh	Mesh	the input mesh. PointClouds are forbidden (no edges).	required
name	str	name of the attribute. Defaults to "length".	'length'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Faces

face_area(mesh, name='area', persistent=True, dense=True)

Computes the barycenter point of each face.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "area".	'area'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	a float per faces

face_barycenter(mesh, name='barycenter', persistent=True, dense=True)

Computes the barycenter point of each face.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "barycenter".	'barycenter'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	one 3D vector per face

face_circumcenter(mesh, name='circumcenter', persistent=True, dense=True)

Computes the circumcenter point of each triangular face.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "barycenter".	'circumcenter'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	one float per face

Raises:

Type	Description
Exception	fails if a face of the mesh is not a triangle

face_normals(mesh, name='normals', persistent=True, dense=True)

Computes the barycenter point of each face.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "normals".	'normals'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	3 floats per faces

faces_near_border(mesh, dist=2, name='near_border', persistent=True, dense=False)

Returns the faces that are at most at 'dist' neighbours from the boundary. Proceeds by region growing, starting from all faces touching the boundary and going inwards.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
dist	int	Extend to which we flag the faces. All faces with a path of length < dist to the boundary will be returned. Defaults to 2.	2
name	str	Name given to the attribute. Defaults to "barycenter".	'near_border'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to False	False

Returns:

Name	Type	Description
Attribute	Attribute	one bool per faces. If not persistent, returns a set.

parallel_transport_curvature(mesh, PT, name='curvature', persistent=True, dense=True)

Compute the curvature of each face associated to a given parallel transport pT

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	description	required
PT	dict	parallel transport. Dictionnary of keys (A,B) -> direction (angle) of edge (A,B) in local basis of A	required
name	str	Name given to the attribute.. Defaults to "curvature".	'curvature'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to False.	True

Returns:

Name	Type	Description
Attribute		One float per face.

triangle_aspect_ratio(mesh, name='aspect_ratio', persistent=True, dense=True)

Computes the aspect ratio of every triangular faces. Sets aspect ratio to -1 for every other faces

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "aspect_ratio".	'aspect_ratio'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to False.	True

Returns:

Name	Type	Description
Attribute	Attribute	One float per face.

Face Corners

corner_angles(mesh, name='angles', persistent=True, dense=True)

Attribute storing the angles of a face at a vertex

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "angles".	'angles'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	one float per face corner

cotangent(mesh, name='cotan', persistent=True, dense=True)

Attribute storing the cotangents of each face at each vertex.

Warning

Only works if the mesh is triangulated (ie every faces are triangles)

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "cotan".	'cotan'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Type	Description
Attribute	Attribute(: one float per face corner

Raises:

Type	Description
Exception	fails if the mesh is not triangulated

Cells

cell_barycenter(mesh, name='barycenter', persistent=True, dense=True)

Computes the barycenter point of each cell.

Parameters:

Name	Type	Description	Default
mesh	VolumeMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "barycenter".	'barycenter'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	3D vector per cell

cell_faces_on_boundary(mesh, name='boundary', persistent=True, dense=False)

Integer flag on cells. For each cell, computes the number of its faces that lay on the boundary

Parameters:

Name	Type	Description	Default
mesh	VolumeMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "boundary".	'boundary'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to False	False

Returns:

Name	Type	Description
Attribute	Attribute	bool per cell

cell_volume(mesh, name='volume', persistent=True, dense=True)

Computes the volume of each cell.

Parameters:

Name	Type	Description	Default
mesh	VolumeMesh	the input mesh	required
name	str	Name given to the attribute. Defaults to "volume".	'volume'
persistent	bool	If the attribute is persistent (stored in the mesh object) or not. Defaults to True.	True
dense	bool	Is the attribute dense (numpy array) or not (dict). Defaults to True	True

Returns:

Name	Type	Description
Attribute	Attribute	one float per cell