Mesh Laplacian

Calculate Laplacian for triangulated mesh.
Updated 24 Jan 2003

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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.

Cite As

Darren Weber (2024). Mesh Laplacian (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R12
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Need a link in the description to the companion function: Mesh Laplacian Interpolation Operator