Graph Laplacian

MeshProcessing.graphlaplacian — Method
L = graphlaplacian(mesh[; edges = Undirected, mode = :plain)

Get Graph Laplacian L with

  • edges = Undirected: ignore edge orientation,
  • edged ∈ [InEdges, OutEdges]: consider only given orientation.

and

  • mode = :plain graph Laplacian $D - A$ (for adjacency matrix $A$ and diagonal matrix with valencies $D$),
  • mode = :normalized normalized graph Laplacian $D^{-1}\,(D-A)$,
  • mode = :normalizedsymmetric symmetrically normalized graph Laplacian $I\,-\,D^{-\tfrac{1}{2}}\,(D-A)\,D^{-\tfrac{1}{2}}$.

See also umbrella, adjacencymatrix

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MeshProcessing.umbrella — Method
Ls = umbrella(mesh[; symmetric = true])
Lv = umbrella(mesh; symmetric = false)

Get uniform Laplacian (Leif Kobbelt's umbrella operator) either as symmetric Ls (with valencies on matrix diagonal) or as Lv (with unit-diagonal).

Note: This implementation does not treat the boundary as a univariate polygon.

See also graphlaplacian

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