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 % 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 % INRAE - BIA Research Unit - BIBS Platform (Nantes)
0022 % Created: 2021-09-22,    using Matlab 9.10.0.1684407 (R2021a) Update 3
0023 % Copyright 2021 INRAE.
0024 
0025 % determines number of iterations
0026 nIters = 3;
0027 if ~isempty(varargin)
0028     nIters = varargin{1};
0029 end
0030     
0031 % apply smoothing on scalar function
0032 nv = max(faces(:));
0033 
0034 % compute normalized averaging matrix
0035 W = meshAdjacencyMatrix(faces) + speye(nv);
0036 D = spdiags(full(sum(W,2).^(-1)), 0, nv, nv);
0037 W = D * W;
0038 
0039 % do averaging to smooth the field
0040 for j = 1:size(f, 2)
0041     for k = 1:nIters
0042         f(:,j) = W * f(:,j);
0043     end
0044 end