Mesh Laplacian

MESH_LAPLACIAN: Laplacian of irregular triangular mesh

Useage: [lap,edge] = mesh_laplacian(vertex,face)

Returns 'lap', the Laplacian (2nd spatial derivative) of an irregular triangular mesh, and 'edge', the linear distances between vertices of 'face'. 'lap' and 'edge' are square, [Nvertices,Nvertices] in size, sparse in nature.

It is assumed that 'vertex' contains the (x,y,z) Cartesian coordinates of each vertex and that 'face' contains the triangulation of vertex with indices into 'vertex' that are numbered from 1:Nvertices. For information about triangulation, see 'help convhull' or 'help convhulln'.

The neighbouring vertices of vertex 'i' is given by:

k = find(edge(i,:));

The math of this routine is given by:

Oostendorp, Oosterom & Huiskamp (1989), Interpolation on a triangulated 3D surface. Journal of Computational Physics, 80: 331-343.

See also the "Mesh Laplacian Interpolation Operator" on the matlab central file exchange.