Point Sampling

`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))

`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)

`sample_AABB(box, n_pts, mode='uniform', return_point_cloud=False)`

Sample a point cloud uniformly at random inside an axis-aligned bounding box. Works by sampling the unit cube and applying an affine transformation.

Parameters:

Name	Type	Description	Default
`box`	`AABB`	the domain of sampling	required
`n_pts`	`int`	number of points to sample. If mode is 'grid', the function may return a slightly smaller number of points (nearest perfect n-th root).	required
`mode`	`str`	sampling mode. 'uniform' or 'grid'. Uniform takes points at random, while 'grid' generates a grid of regularly spaced points.	`'uniform'`
`return_point_cloud`	`bool`	whether to compile the points in a PointCloud object or return the raw numpy array. Is ignored if the bounding box has dimension >3. Defaults to False.	`False`

Raises:

Type	Description
`Exception`	fails if the bounding box is empty.
`ValueError`	fails if the dimension of the box is > 3 and return_point_cloud is set to True, so that no PointCloud object with dim > 3 is created.

Returns:

Type	Description
	PointCloud \| np.ndarray: a sampled point cloud of `n_pts` points

`sample_ball(center, radius, n_pts, return_point_cloud=False)`

Samples points uniformly inside a 3D ball.

Parameters:

Name	Type	Description	Default
`center`	`Vec`	center of the ball	required
`radius`	`float`	radius of the ball	required
`n_pts`	`int`	number of points to sample	required
`return_point_cloud`	`bool`	whether to compile the points in a PointCloud object or return the raw numpy array. Defaults to False.	`False`

Returns:

Type	Description
	PointCloud \| np.ndarray: a sampled point cloud of `n_pts` points

`sample_polyline(mesh, n_pts, return_point_cloud=False)`

Sample a point cloud uniformly at random from a polyline

Parameters:

Name	Type	Description	Default
`mesh`	`PolyLine`	the input polyline	required
`n_pts`	`int`	number of points to sample	required
`return_point_cloud`	`bool`	whether to compile the points in a PointCloud object or return the raw numpy array. Defaults to False.	`False`

Returns:

Type	Description
	PointCloud \| np.ndarray: a sampled point cloud of `n_pts` points

`sample_sphere(center, radius, n_pts, return_point_cloud=False)`

Samples points uniformly on the surface of a 3D sphere

Parameters:

Name	Type	Description	Default
`center`	`Vec`	center of the sphere	required
`radius`	`float`	radius of the spheres	required
`n_pts`	`int`	number of points to sample	required
`return_point_cloud`	`bool`	whether to compile the points in a PointCloud object or return the raw numpy array. Defaults to False.	`False`

Returns:

Type	Description
	PointCloud \| np.ndarray: a sampled point cloud of `n_pts` points

`sample_surface(mesh, n_pts, return_point_cloud=False, return_normals=False)`

Sample a point cloud uniformly at random from a surface mesh

Parameters:

Name	Type	Description	Default
`mesh`	`SurfaceMesh`	input mesh	required
`n_pts`	`int`	number of points to sample	required
`return_point_cloud`	`bool`	whether to compile the points in a PointCloud object or return the raw numpy array. Defaults to False.	`False`
`return_normals`	`bool`	wether to assign the normal of the faces to sampled points. Only has effect if return_point_cloud is set to True. Defaults to False.	`False`

Returns:

Type	Description
	PointCloud \| np.ndarray: a sampled point cloud of `n_pts` points
	np.ndarray : the associated normals (if sample_normals was set to True)

Point Sampling

PointCloud(data=None)

id_vertices property

append(x)

PolyLine(data=None)

id_edges property

id_vertices property

SurfaceMesh(data=None)

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)

VolumeMesh(data=None)

id_cells property

id_corners property

id_edges property

id_faces property

id_vertices property

is_edge_on_border(*args)

is_face_on_border(*args)

is_tetrahedral()

sample_AABB(box, n_pts, mode='uniform', return_point_cloud=False)

sample_ball(center, radius, n_pts, return_point_cloud=False)

sample_polyline(mesh, n_pts, return_point_cloud=False)

sample_sphere(center, radius, n_pts, return_point_cloud=False)

sample_surface(mesh, n_pts, return_point_cloud=False, return_normals=False)

`PointCloud(data=None)`

`id_vertices` `property`

`append(x)`

`PolyLine(data=None)`

`id_edges` `property`

`id_vertices` `property`

`SurfaceMesh(data=None)`

`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)`

`VolumeMesh(data=None)`

`id_cells` `property`

`id_corners` `property`

`id_edges` `property`

`id_faces` `property`

`id_vertices` `property`

`is_edge_on_border(*args)`

`is_face_on_border(*args)`

`is_tetrahedral()`

`sample_AABB(box, n_pts, mode='uniform', return_point_cloud=False)`

`sample_ball(center, radius, n_pts, return_point_cloud=False)`

`sample_polyline(mesh, n_pts, return_point_cloud=False)`

`sample_sphere(center, radius, n_pts, return_point_cloud=False)`

`sample_surface(mesh, n_pts, return_point_cloud=False, return_normals=False)`