Mesh Laplacian Interpolation Operator

See also MESH_LAPLACIAN function on matlab central file exchange.

MESH_LAPLACIAN_INTERP: Computes the zero Laplacian interpolation matrix

Useage: [int, keepindex, repindex] = mesh_laplacian_interp(lap, index)

This function calculates an interpolation matrix that provides the coefficients for the calculation of potential values at all unknown vertices of a mesh, given known potential values at a subset of the mesh vertices (at 'index'). The interpolation solution is constrained by a minimal norm of the Laplacian of the mesh. See the reference below for details.

'lap' is the laplacian matrix for the full mesh (see mesh_laplacian) 'int' is the matrix which interpolates from the points in 'index' to the full mesh. 'index' is a row vector of indices into a subset of the vertices used to calculate 'lap'. This subset is where the electric potential is known and usually corresponds to the given electrode vertices, eg:

index = dsearchn(scalpvert,elecvert)';

If 'index' contains repeated indices, only the unique indices are useful. The 'keepindex' array can be used to select these. The 'repindex' array is the repeated indices. Interpolations can be done using matrix 'int', eg:

[int, keepindex, repindex] = mesh_laplacian_interp(lap,index);
if isempty(repindex),
Vint = int * Vknown;
else
Vint = int * Vknown(keepindex);
end

This implements interpolation method B (p. 336) of Oostendorp T, Oosterom A & Huiskamp G (1989), Interpolation on a triangulated 3D surface. Journal of Computational Physics, 80: 331-343.