Tutte's Embedding

Usage

import mouette as M
mesh = M.mesh.load(args.model)
tutte = M.parametrization.TutteEmbedding(mesh, [boundary_mode], use_cotan=True, verbose=True)
tutte.run()
M.mesh.save(mesh, "tutte_model.obj")
M.mesh.save(tutte.flat_mesh, "tutte_flat.obj")

TutteEmbedding

Bases: BaseParametrization

Tutte's embedding parametrization method for a disk inside a fixed boundary. The parametrization is locally injective (Floater, 1997) provided the boundary is convex.

References

[1] How to draw a graph, Tutte W.T., 1963
[2] Parametrization and smooth approximation of surface triangulations, Floater M.S., 1997

Example

https://github.com/GCoiffier/mouette/blob/main/examples/parametrization/tutte.py

Parameters:

Name	Type	Description	Default
`mesh`	`SurfaceMesh`	the mesh to embed. Should be a surface with disk topology.	required
`boundary_mode`	`str`	Shape of the boundary. Possible choices are ["square", "circle"]. Defaults to "circle".	`'circle'`
`use_cotan`	`bool`	If True, uses cotangents as weights in the Laplacian matrix [2]. Otherwise, use Tutte's original barycentric embedding [1]. Defaults to False.	`False`
`verbose`	`bool`	verbose mode. Defaults to False.	`False`

Other Parameters:

Name	Type	Description
`save_on_corners`	`bool`	if True, the resulting uv-coordinates will be stored in an attribute on face corners. Otherwise, they are stored in an attribute on vertices. Defaults to True
`custom_boundary`	`(ndarray, optionnal)`	a Nx2 array containing custom coordinates for the boundary vertices (N being the number of boundary vertices).

Attributes:

Name	Type	Description
`uvs`	`Attribute`	an attribute containing the uv-coordinates of the parametrization
`save_on_corners`	`bool`	whether the coordinates are saved as a vertex attribute or a face_corner attribute

Raises:

Type	Description
`InvalidArgumentValueError`	if 'boundary_mode' is not "square" or "circle".

`flat_mesh` `property`

A flat representation of the mesh where uv-coordinates are copied to xy.

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	the flat mesh

`run()`

Computes the parametrization. Result is stored in the uvs attribute