cortex.polyutils.Surface.laplace_operator

property Surface.laplace_operator

Laplace-Beltrami operator for this surface. A sparse adjacency matrix with edge weights determined by the cotangents of the angles opposite each edge. Returns a 4-tuple (B,D,W,V) where D is the ‘lumped mass matrix’, W is the weighted adjacency matrix, and V is a diagonal matrix that normalizes the adjacencies. The ‘stiffness matrix’, A, can be computed as V - W.

The full LB operator can be computed as D^{-1} (V - W).

B is the finite element method (FEM) ‘mass matrix’, which replaces D in FEM analyses.

See ‘Discrete Laplace-Beltrami operators for shape analysis and segmentation’ by Reuter et al., 2009 for details.