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## Copyright (C) 2003-2017 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 centroid = polyhedronCentroid(vertices, faces) %#ok<INUSD>
%POLYHEDRONCENTROID Compute the centroid of a 3D convex polyhedron
%
% CENTRO = polyhedronCentroid(V, F)
% Computes the centroid (center of mass) of the polyhedron defined by
% vertices V and faces F.
% The polyhedron is assumed to be convex.
%
% Example
% % Creates a polyhedron centered on origin, and add an arbitrary
% % translation
% [v, f] = createDodecahedron;
% v2 = bsxfun(@plus, v, [3 4 5]);
% % computes the centroid, that should equal the translation vector
% centroid = polyhedronCentroid(v2, f)
% centroid =
% 3.0000 4.0000 5.0000
%
%
% See also
% meshes3d, meshVolume, meshSurfaceArea, polyhedronMeanBreadth
%
% ------
% Author: David Legland
% e-mail: david.legland@nantes.inra.fr
% Created: 2012-04-05, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012 INRA - Cepia Software Platform.
% 2015.11.13 use delaunayTriangulation instead of delaunayn (strange bug
% with icosahedron...)
% compute set of elementary tetrahedra
DT = delaunayTriangulation(vertices);
T = DT.ConnectivityList;
% number of tetrahedra
nT = size(T, 1);
% initialize result
centroid = zeros(1, 3);
vt = 0;
% Compute the centroid and the volume of each tetrahedron
for i = 1:nT
% coordinates of tetrahedron vertices
tetra = vertices(T(i, :), :);
% centroid is the average of vertices.
centi = mean(tetra);
% compute volume of tetrahedron
vol = det(tetra(1:3,:) - tetra([4 4 4],:)) / 6;
% add weighted centroid of current tetraedron
centroid = centroid + centi * vol;
% compute the sum of tetraedra volumes
vt = vt + vol;
end
% compute by sum of tetrahedron volumes
centroid = centroid / vt;
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