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.

The full LB operator can be computed as D^{-1} (V - W). The ‘stiffness matrix’, A, can be computed as V - W.

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

Returns:

Bsparse matrix

Finite element method (FEM) ‘mass matrix’, which replaces D in FEM analyses.

Dsparse matrix, dia

‘Lumped mass matrix’.

Wsparse matrix

Weighted adjacency matrix, with edge weights given by cotangent_weights.

Vsparse matrix, dia

Diagonal matrix that normalizes the adjacencies (row sums of W).