Procedural Generation

The mouette.procedural module implements various functions to generate surface meshes or various shapes directly from code

Procedural shapes

`triangle(P0, P1, P2)`

Generates a triangle from three vertices

Parameters:

Name	Type	Description	Default
`P0,P1,P2`	`Vec`	three points	required

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a triangle

`unit_triangle(nu, nv, generate_uvs=False)`

Generate a subdivided unit right triangle (half of a unit grid)

Parameters:

Name	Type	Description	Default
`nu`	`int`	number of subdivisions on the horizontal axis	required
`nv`	`int`	number of subdivisions on the vertical axis	required
`generate_uvs`	`bool`	whether to generate uv-coordinates. Defaults to False.	`False`

Returns SurfaceMesh: a subdivided unit triangle

`quad(P0, P1, P2, triangulate=False)`

Generates a quad from three vertices

   P1-------
  /        /
 /        / 
P0-------P2

Parameters:

Name	Type	Description	Default
`P0,P1,P2`	`Vec`	coordinates of corners. The fourth point is deduced as P2 + P1 - 2*P0	required
`triangulate`	`bool`	whether to output two triangles instead of a quad. Defaults to False.	`False`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a quad

`unit_grid(nu, nv, triangulate=False, generate_uvs=False)`

Generates a subdivided regular unit grid

Parameters:

Name	Type	Description	Default
`nu`	`int`	number of subdivisions on the horizontal axis	required
`nv`	`int`	number of subdivisions on the vertical axis	required
`triangulate`	`bool`	whether to split quads into two triangles. Defaults to False.	`False`
`generate_uvs`	`bool`	whether to generate uv-coordinates. Defaults to False.	`False`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a subdivided unit grid of size nu*nv

`ring(N, defect, open=False, n_cover=1)`

Computes a ring of triangles with prescribed number of triangles and angle defect at the center.

Parameters:

Name	Type	Description	Default
`N`	`int`	number of triangles in the ring	required
`defect`	`float`	target angle defect to achieve. Position of the central point is adjusted via dichotomy to match this value.	required
`open`	`bool)`	whether to connect the last vertex to the first.	`False`
`n_cover`	`int`	Number of covering of the ring. Defaults to 1.	`1`

Raises:

Type	Description
`Exception`	Fails if N<3

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	the ring

`flat_ring(N, defect, n_cover=1)`

`tetrahedron(P1, P2, P3, P4, volume=False)`

Simple tetrahedron from four points

Parameters:

Name	Type	Description	Default
`P1`	`Vec`	first point	required
`P2`	`Vec`	second point	required
`P3`	`Vec`	third point	required
`P4`	`Vec`	fourth point	required
`volume`	`bool`	whether to generate a cell or just a surface. Defaults to False.	`False`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	description

`hexahedron(P1, P2, P3, P4, P5, P6, P7, P8, colored=False, triangulate=False, volume=False)`

Generate an hexahedron in arbitrary configuration given 8 points. Order and connectivity of points is:

   7--------6
  /|       /|
 / |      / |
4--------5  |
|  |     |  |
|  3-----|--2
| /      | /
|/       |/
0--------1

Parameters:

Name	Type	Description	Default
`P1`	`to P8 (Vec`	coordinates of eight vertices	required
`colored`	`bool`	if set to true, will add a color attribute on faces. Defaults to False.	`False`
`triangulate`	`bool`	if set to true, will triangulate the faces. Defaults to False.	`False`
`volume`	`bool`	if set to true, will also generate three tetrahedra to fill the volume. Defaults to False.	`False`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a cube

`hexahedron_4pts(P1, P2, P3, P4, colored=False, volume=False)`

Generate an hexahedron given by an absolute position and three points building a basis.

4
|
|  3
| /
|/
1--------2

Parameters:

Name	Type	Description	Default
`P1`	`to P4 (Vec`	coordinates of vertices	required
`colored`	`bool`	if set to true, will add a color attribute on faces to determine. Defaults to False.	`False`
`volume`	`bool`	if set to true, will also generate three tetrahedra to fill the volume. Defaults to False.	`False`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	[description]

`axis_aligned_cube(colored=False, triangulate=False)`

generated an axis aligned cube as 6 quad faces.

   7--------6
  /|       /|
 / |      / |
4--------5  |
|  |     |  |
|  3-----|--2
| /      | /
|/       |/
0--------1

Parameters:

Name	Type	Description	Default
`colored`	`bool`	if set to true, will add a colo rattribute on faces to determine. Defaults to False.	`False`
`triangulate`	`bool`	if set to true, will triangulate the faces. Defaults to False.	`False`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a cube

`octahedron()`

Generate a unit octahedron as the dual mesh of the unit hexahedron

Reference

https://danielsieger.com/blog/2021/01/03/generating-platonic-solids.html

`icosahedron(center=Vec(0, 0, 0), radius=1.0, uv=False)`

Generate a unit icosahedron

Parameters:

Name	Type	Description	Default
`center`	`Vec`	center position. Defaults to Vec(0,0,0).	`Vec(0, 0, 0)`
`uv`	`bool`	whether to generate uv coordinates. Defaults to False.	`False`

Returns:

Name	Type	Description
`_type_`		description

`dodecahedron()`

Generate a unit dodecahedron as the dual mesh of an icosahedron

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a dodecahedron

`cylinder(P1, P2, radius=1.0, N=50, fill_caps=True)`

Generates a cylinder around the segment defined by P1 and P2

Parameters:

Name	Type	Description	Default
`P1`	`Vec`	start of the cylinder (center of bottom face)	required
`P2`	`Vec`	end of the cylinder (center of top face)	required
`radius`	`float`	radius. Defaults to 1..	`1.0`
`N`	`int`	number of segments. Defaults to 50.	`50`
`fill_caps`	`bool`	whether to also generate faces at caps. Defaults to True.	`True`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a cylinder

`torus(major_segments=50, minor_segments=30, major_radius=1.0, minor_radius=0.3, triangulate=False)`

Generates a torus Args: major_segments (int): number of major segments. Defaults to 50. minor_segments (int): number of minor segments. Defaults to 30. major_radius (float): global radius of the torus. Defaults to 1. minor_radius (float): thickness of the torus. Defaults to 0.3 triangulate (bool, optional): whether to output a triangular or quadmesh. Defaults to False.

References

https://danielsieger.com/blog/2021/05/03/generating-primitive-shapes.html

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a torus

`sphere_uv(n_lat=30, n_long=50, center=Vec(0.0, 0.0, 0.0), radius=1.0)`

Generates a sphere using classical spherical uv-coordinates

Parameters:

Name	Type	Description	Default
`n_lat`	`int`	number of different latitudes for points. Defaults to 30.	`30`
`n_long`	`int`	number of different longitudes for points. Defaults to 50.	`50`
`center`	`Vec`	Center position of the sphere. Defaults to Vec(0.,0.,0.).	`Vec(0.0, 0.0, 0.0)`
`radius`	`float`	Radius of the sphere. Defaults to 1.	`1.0`

References

https://danielsieger.com/blog/2021/03/27/generating-spheres.html

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	the sphere

`icosphere(n_refine=3, center=Vec(0.0, 0.0, 0.0), radius=1.0)`

Generates an icosphere, that is a subdivision of the icosahedron

Parameters:

Name	Type	Description	Default
`n_refine`	`int`	number of subdivisions. Defaults to 3.	`3`
`center`	`Vec`	center of the sphere. Defaults to Vec(0.,0.,0.).	`Vec(0.0, 0.0, 0.0)`
`radius`	`float`	radius of the sphere. Defaults to 1..	`1.0`

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	the sphere

`sphere_fibonacci(n_pts, radius=1.0, build_surface=True)`

Generates a point cloud or a surface mesh using fibonacci sampling of a sphere.

Parameters:

Name	Type	Description	Default
`n_pts`	`int`	total number of vertices	required
`radius`	`float`	Radius of the sphere. Defaults to 1.	`1.0`
`build_surface`	`bool`	If specified to True, the function will also compute a triangulation of the vertices. This is obtained through a convex hull algorithm (since points lay on a convex shape, the convex hull and the Delaunay triangulation are equivalent). Defaults to True.	`True`

Returns:

Type	Description
`SurfaceMesh`	[SurfaceMesh \| PointCloud]: the generated mesh

Polyline generation

`chain_of_vertices(vertices, loop=False)`

Creates a polyline that links the provided vertices in order.

Parameters:

Name	Type	Description	Default
`vertices`	`ndarray`	vertex positions.	required
`loop`	`bool`	whether to link the last vertex with the first, creating a closed loop. Defaults to False.	`False`

Returns:

Name	Type	Description
`PolyLine`	`PolyLine`	description

`vector_field(origins, vectors, length_mult=1.0)`

Creates the representation of a vector field from an array of origin points and an array of vectors.

Parameters:

Name	Type	Description	Default
`origins`	`ndarray`	size (N,K) with N the number of points and K<=3 the dimension. Origin of the vectors	required
`vectors`	`ndarray`	size (N,K) with N the number of points and K<=3 the dimension. Coordinates of each vector.	required
`length_mult`	`float`	factor multiplied to each vector to modulate their length for vizualisation purposes. Defaults to 1.	`1.0`

Raises:

Type	Description
`Exception`	fails if the two arrays (origins and vectors) have a different shape
`Exception`	fails if one of the two arrays have dimension > 3

Returns:

Name	Type	Description
`PolyLine`	`PolyLine`	the vector field represented as a polyline.

Transformations

`spherify_vertices(points, radius=0.01, n_subdiv=1)`

Transforms vertices of a point cloud as icospheres

Parameters:

Name	Type	Description	Default
`points`	`PointCloud`	the input point cloud	required
`radius`	`float`	radius of each sphere. Defaults to 1e-2.	`0.01`
`n_subdiv`	`int`	number of subdivisions of the icospheres. Defaults to 1.	`1`

Returns:

Type	Description
`SurfaceMesh`	SurfaceMesh

`cylindrify_edges(mesh, radius=0.05, N=50)`

Transforms edges of a polyline as cylinder surface

Parameters:

Name	Type	Description	Default
`mesh`	`PolyLine`	the input mesh	required
`radius`	`float`	Radius of the output cylinders. Defaults to 5e-2.	`0.05`
`N`	`int`	Number of points inside each circle of the cylinders. Defaults to 50.	`50`

Returns:

Type	Description
`SurfaceMesh`	SurfaceMesh

`dual_mesh(mesh)`

Computes the dual mesh of a mesh

Parameters:

Name	Type	Description	Default
`mesh`	`SurfaceMesh`	input surface	required

Returns:

Type	Description
`SurfaceMesh`	SurfaceMesh