Boundary First Flattening

Example

import mouette as M

mesh = M.mesh.load("path/to/mesh")
bff = M.parametrization.BoundaryFirstFlattening(mesh, bnd_scale_fctr=scale, verbose=True)
mesh = bff.run() # /!\ mesh is not modified in place

`BoundaryFirstFlattening(mesh, bnd_scale_fctr=None, bnd_curvature=None, verbose=False, **kwargs)`

Bases: BaseParametrization

Boundary First Flattening: A conformal flattening algorithm with control over the boundary conditions, either in terms of scale factor or curvature

References

[1] Boundary First Flattening, Rohan Sawhney and Keenan Crane, ACM ToG, 2017

Warning

This algorithm reorders the vertices so that boundary vertices are labeled [0, N-1] in order. Therefore, the uvs coordinates are not computed on the original mesh but on a reordered copy. Access the final result with self.mesh

Example

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

Parameters:

Name	Type	Description	Default
`mesh`	`SurfaceMesh`	the input surface. Should be a triangulation of a topological disk.	required
`bnd_scale_fctr`	`Attribute`	Scale factor on the boundary. Ignores values for interior vertices. Defaults to None. If provided, will automatically compute boundary curvature and ignore the `bnd_curvature`a argument.	`None`
`bnd_curvature`	`Attribute`	Geodesic curvature on the boundary. Ignores values for interior vertices. Defaults to None. If provided (and no `bnd_scale_fctr` is provided), will automatically compute boundary scale factors.	`None`
`verbose`	`bool`	verbose mode. Defaults to False.	`False`

Other Parameters:

Name	Type	Description
`save_on_corners`	`bool`	if True, stores the results on face corners instead of vertices. Defaults to True
`use_cotan`	`bool`	if True, uses the cotan Laplacian instead of the connectivity Laplacian. Defaults to True.
`hilbert_transform`	`bool`	if True, extends the boundary values with the Hilbert transform

Attributes:

Name	Type	Description
`uvs`	`Attribute`	an attribute containing the uv-coordinates of the parametrization

Raises:

Type	Description
`Exception`	if the mesh is not the triangulation of a topological disk

Note

If neither of bnd_scale_fctr and bnd_curvature are provided, the algorithm will run in default mode with scale factors = 0 on the boundary. Otherwise, provided scale factors have priority over provided curvatures.

`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()`

Run the algorithm

Raises:

Type	Description
`Exception`	If the mesh is not a triangulation of a topological disk

Returns:

Name	Type	Description
`SurfaceMesh`	`SurfaceMesh`	a copy of the original mesh with reordered vertices and computed uv-coordinates

Boundary First Flattening

Example