polyhedronCentroid

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

0001 function centroid = polyhedronCentroid(vertices, faces) %#ok<INUSD>
0002 %POLYHEDRONCENTROID Compute the centroid of a 3D convex polyhedron.
0003 %
0004 %   CENTRO = polyhedronCentroid(V, F)
0005 %   Computes the centroid (center of mass) of the polyhedron defined by
0006 %   vertices V and faces F.
0007 %   The polyhedron is assumed to be convex.
0008 %
0009 %   Example
0010 %     % Creates a polyhedron centered on origin, and add an arbitrary
0011 %     % translation
0012 %     [v, f] = createDodecahedron;
0013 %     v2 = bsxfun(@plus, v, [3 4 5]);
0014 %     % computes the centroid, that should equal the translation vector
0015 %     centroid = polyhedronCentroid(v2, f)
0016 %     centroid =
0017 %         3.0000    4.0000    5.0000
0018 %
0019 %
0020 %   See also
0021 %   meshes3d, meshVolume, meshSurfaceArea, polyhedronMeanBreadth
0022 %
0023 
0024 % ------
0025 % Author: David Legland
0026 % e-mail: david.legland@nantes.inra.fr
0027 % Created: 2012-04-05,    using Matlab 7.9.0.529 (R2009b)
0028 % Copyright 2012 INRA - Cepia Software Platform.
0029 
0030 % 2015.11.13 use delaunayTriangulation instead of delaunayn (strange bug
0031 %       with icosahedron...)
0032 
0033 % compute set of elementary tetrahedra
0034 DT = delaunayTriangulation(vertices);
0035 T = DT.ConnectivityList;
0036 
0037 % number of tetrahedra
0038 nT  = size(T, 1);
0039 
0040 % initialize result
0041 centroid = zeros(1, 3);
0042 vt = 0;
0043 
0044 % Compute the centroid and the volume of each tetrahedron
0045 for i = 1:nT
0046     % coordinates of tetrahedron vertices
0047     tetra = vertices(T(i, :), :);
0048     
0049     % centroid is the average of vertices.
0050     centi = mean(tetra);
0051     
0052     % compute volume of tetrahedron
0053     vol = det(tetra(1:3,:) - tetra([4 4 4],:)) / 6;
0054     
0055     % add weighted centroid of current tetraedron
0056     centroid = centroid + centi * vol;
0057     
0058     % compute the sum of tetraedra volumes
0059     vt = vt + vol;
0060 end
0061 
0062 % compute by sum of tetrahedron volumes
0063 centroid = centroid / vt;