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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;