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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = smoothMesh(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.
%
% ... = smoothMesh(V, F, NITER)
% Repeat the smoothing procedure NITER times. This is equivalent to
% calling the smoothMesh function NITER times.
%
%
% 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, drawMesh
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2013-04-29, using Matlab 7.9.0.529 (R2009b)
% Copyright 2013-2023 INRA - Cepia Software Platform
var1 = varargin{1};
if isstruct(var1)
vertices = var1.vertices;
faces = var1.faces;
varargin(1) = [];
else
vertices = varargin{1};
faces = varargin{2};
varargin(1:2) = [];
end
% determine number of iterations
nIter = 1;
if ~isempty(varargin)
nIter = varargin{1};
end
% compute adjacency matrix,
% result is a Nv-by-Nv matrix with zeros on the diagonal
adj = meshAdjacencyMatrix(faces);
% ensure the size of the matrix is Nv-by-Nv
% (this can not be the case if some vertices are not referenced)
nv = size(vertices, 1);
if size(adj, 1) < nv
adj(nv, nv) = 0;
end
% Add "self adjacencies"
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
varargout = formatMeshOutput(nargout, v2, faces);
%% 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
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