Mesh Laplacian

Calculate Laplacian for triangulated mesh.

Description

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.

• MATLAB release: MATLAB 6.0 (R12)

[ghr lililp]

comment fair le mayage(meshe)

[yuga cnkf]

|Fr|Le maillage, c'est juste un tableau de coordonnées (vertex).

Généralement on utilise un générateur d'objets 3D (comme Lynx) qui crée un fichier texte avec les coordonnées des points et les numéros de ces points qui sont reliés dans une face.

Tu peux aussi essayer la fonction GenMesh de Matlab.

[Duane Hanselman]

A function should not produce command window output unless there is warning or error feedabck. Let the user place tic and toc around the function rather than include them in the function itself. Get rid of:

fprintf('MESH_LAPLACIAN: Calc Laplacian matrix for %5d vertices...',nvertex);
tic
...
t = toc;
fprintf('done (%6.2f sec).\n',t);

Can you describe the input arguments or revise them to match the way MATLAB uses triangulation, e.g., from TRIMESH
% TRIMESH(TRI,X,Y,Z,C) displays the triangles defined in the M-by-3
% face matrix TRI as a mesh. A row of TRI contains indexes into the X,Y, and Z vertex vectors to define a single triangular face.

[Jeremy Hall]