spectralbrain.anisotropic_laplacian#

spectralbrain.anisotropic_laplacian(vertices, faces, *, anisotropy=1.0, direction='max_curvature', custom_directions=None)[source]#

Build an anisotropic Laplacian weighted by curvature direction.

Modifies the cotangent Laplacian by scaling diffusion along the principal curvature directions. When anisotropy=0, recovers the standard isotropic Laplacian. When anisotropy=1, diffusion is maximally biased along the chosen direction.

This is a simplified implementation inspired by Andreux, Rodolà, Aubry & Cremers (NORDIA 2014) and the Finsler-LBO of Jadhav & Cremers (CVPR 2024).

Parameters:

  • vertices (ndarray, shape (N, 3))

  • faces (ndarray, shape (F, 3))

  • anisotropy (float) – Anisotropy strength in [0, 1]. 0 = isotropic, 1 = fully directional.

  • direction (str) – "max_curvature" — bias along maximum curvature direction. "min_curvature" — bias along minimum curvature direction. "custom" — use custom_directions.

  • custom_directions (ndarray, shape (N, 3), optional) – Per-vertex preferred directions (unit vectors).

Returns:

  • L (SparseMatrix, shape (N, N))

  • M (MassMatrix, shape (N, N))

Return type:

tuple[spmatrix, spmatrix]