Measuring Distortion

Utilities classes to compute distortions of elements between "real" \(xyz\)-space and "parametric" \(uv\)-space.

ParamDistortion(mesh, uv_attr='uv_coords', save_on_mesh=True, verbose=False)

Bases: Worker

Utility class to compute various distortion metrics for surface parametrization.

Initializes the distortion utility class.

Parameters:

Name	Type	Description	Default
mesh	SurfaceMesh	the supporting mesh	required
uv_attr	str	the attribute name that stores the uv-coordinates on face corners. Defaults to "uv_coords".	'uv_coords'
save_on_mesh	bool	If True, distortion values will be stored as attributes on the mesh. Defaults to True.	True
verbose	bool	verbose mode. Defaults to False.	False

Raises:

Type	Description
Exception	fails if the attribute 'uv_attr' does not exists.

conformal property

Conformal distortion, defined as \(\frac{||J||^2}{\det(J)}\)

iso property

Isometric distortion

Defined as the distance from (\(\sigma_1\), \(\sigma_2\)) to (1,1) where \(\sigma_1\) and \(\sigma_2\) are the eigenvalues of J

scale property

Scale distortion, defined as \(\frac12 (\det(J) + 1/\det(J))\)

shear property

Shear distortion

Defined as \(c1 \cdot c2\) where \(c1\) and \(c2\) are the columns of J

stretch property

Stretch distortion

Defined as the ratio \(\frac{\sigma_1}{\sigma_2}\) where \(\sigma_1\) and \(\sigma_2\) are the eigenvalues of J

summary property

Computes a summary dictionnary of all distortion values as an average over the mesh

Returns:

Name	Type	Description
dict	dict	a dictionnary with aggregated values over the mesh

run()

Run the distortion computation.

Raises:

Type	Description
Exception	fails if the mesh is not triangular.
ZeroDivisionError	if degenerated elements are present in the parametrization.

PointCloud(data=None)

Bases: Mesh

A data structure for representing point clouds

Attributes:

Name	Type	Description
vertices	DataContainer	the container for all vertices
__str__	str	Representation of the object and its elements as a string.

id_vertices property

Shortcut for range(len(self.vertices))

append(x)

Shortcut for self.vertices.append(x), since we can only append elements in the 'vertices' container

PolyLine(data=None)

Bases: Mesh

A data structure for representing polylines.

Attributes:

Name	Type	Description
vertices	DataContainer	the container for all vertices
edges	DataContainer	the container for all edges
__str__		Representation of the object and its elements as a string.

id_edges property

Shortcut for range(len(self.edges))

id_vertices property

Shortcut for range(len(self.vertices))

QuadQuality(mesh, save_on_mesh=True, verbose=False)

Bases: Worker

Utility class to compute various quality metrics on quad meshes

SurfaceMesh(data=None)

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()

Checks if the mesh is a quadrangulation

Returns:

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

is_triangular()

Checks if the mesh is a triangulation

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

VolumeMesh(data=None)

Bases: Mesh

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))

is_edge_on_border(*args)

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

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.

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)