smoothMeshFunction

SMOOTHMESHFUNCTION Apply smoothing on a functions defines on mesh vertices.

   FS = smoothMeshFunction(VERTICES, FACES, F, NITERS)
   Performs smoothing on the function F defined on vertices of the mesh.
   The mesh is specified by VERTICES and FACES array. At each iteration,
   the value for each vertex is obtained as the average of values obtained
   from neighbor vertices.
   NITERS is the number of times the iteration must be repeated. By
   default it equals 3.

   Example
   smoothMeshFunction

   See also
     meshes3d, meshCurvatures

0001 function f = smoothMeshFunction(vertices, faces, f, varargin) %#ok<INUSL>
0002 %SMOOTHMESHFUNCTION Apply smoothing on a functions defines on mesh vertices.
0003 %
0004 %   FS = smoothMeshFunction(VERTICES, FACES, F, NITERS)
0005 %   Performs smoothing on the function F defined on vertices of the mesh.
0006 %   The mesh is specified by VERTICES and FACES array. At each iteration,
0007 %   the value for each vertex is obtained as the average of values obtained
0008 %   from neighbor vertices.
0009 %   NITERS is the number of times the iteration must be repeated. By
0010 %   default it equals 3.
0011 %
0012 %   Example
0013 %   smoothMeshFunction
0014 %
0015 %   See also
0016 %     meshes3d, meshCurvatures
0017 
0018 % ------
0019 % Author: David Legland
0020 % E-mail: david.legland@inrae.fr
0021 % Created: 2021-09-22, using Matlab 9.10.0.1684407 (R2021a) Update 3
0022 % Copyright 2021-2024 INRAE - BIA Research Unit - BIBS Platform (Nantes)
0023 
0024 % determines number of iterations
0025 nIters = 3;
0026 if ~isempty(varargin)
0027     nIters = varargin{1};
0028 end
0029     
0030 % apply smoothing on scalar function
0031 nv = max(faces(:));
0032 
0033 % compute normalized averaging matrix
0034 W = meshAdjacencyMatrix(faces) + speye(nv);
0035 D = spdiags(full(sum(W,2).^(-1)), 0, nv, nv);
0036 W = D * W;
0037 
0038 % do averaging to smooth the field
0039 for j = 1:size(f, 2)
0040     for k = 1:nIters
0041         f(:,j) = W * f(:,j);
0042     end
0043 end