function [v2, faces] = smoothMesh(vertices, faces, varargin)
%SMOOTHMESH Smooth mesh by replacing each vertex by the average of its neighbors 
%
%   V2 = smoothMesh(V, F)
%   [V2, F2] = smoothMesh(V, F)
%   Performs smoothing of the values given in V, by using adjacency
%   information given in F. 
%   V is a numeric array representing either vertex coordinate, or value
%   field associated to each vertex. F is an array of faces, given either
%   as a NF-by-3 or NF-by-4 numeric array, or as a cell array. 
%   Artifact adjacencies are added if faces have more than 4 vertices.
%
%   Example
%     [v f] = torusMesh([50 50 50 30 10 30 45]);
%     v = v + randn(size(v));
%     [v2 f] = smoothMesh(v, f, 3);
%     figure; drawMesh(v2, f);
%     l = light; lighting gouraud
%
%   See also
%     meshes3d, meshAdjacencyMatrix, triangulateFaces
%

% ------
% Author: David Legland
% e-mail: david.legland@nantes.inra.fr
% Created: 2013-04-29,    using Matlab 7.9.0.529 (R2009b)
% Copyright 2013 INRA - Cepia Software Platform.

% determine number of iterations
nIter = 1;
if ~isempty(varargin)
    nIter = varargin{1};
end

% % ensure faces correspond to a triangulation
% if iscell(faces) || size(faces, 2) > 3
%     faces = triangulateFaces(faces);
% end

% compute adjacency matrix
adj = meshAdjacencyMatrix(faces);

% Add "self adjacencies"
nv = size(adj, 1);
adj = adj + speye(nv);

% weight each vertex by the number of its neighbors
w = spdiags(full(sum(adj, 2).^(-1)), 0, nv, nv);
adj = w * adj;

% do averaging to smooth the field
v2 = vertices;
for k = 1:nIter
    v2 = adj * v2;
end


%% Old version
% % Compute vertex adjacencies
% edges = computeMeshEdges(faces);
% v2 = zeros(size(vertices));
% 
% % apply several smoothing
% for iter = 1:nIter
%     
%     % replace the coords of each vertex by the average coordinate in the
%     % neighborhood
%     for i = 1:size(vertices, 1)
%         edgeInds = sum(edges == i, 2) > 0;
%         neighInds = unique(edges(edgeInds, :));
%         v2(i, :) = mean(vertices(neighInds, :));
%     end
%     
%     % update for next iteration
%     vertices = v2;
% end
