polygonCentroid3d

POLYGONCENTROID3D Centroid (or center of mass) of a polygon.

   PTC = polygonCentroid3d(POLY)
   Computes center of mass of a polygon defined by POLY. POLY is a N-by-3
   array of double containing coordinates of polygon vertices.

   PTC = polygonCentroid3d(VX, VY, VZ)
   Specifies vertex coordinates as three separate arrays.

   Example
     % compute centroid of a basic polygon
     poly = [0 0 0; 10 0 10;10 10 20;0 10 10];
     centro = polygonCentroid3d(poly)
     centro =
         5.0000    5.0000    10.0000

   See also
   polygons3d, polygonArea3d, polygonCentroid

0001 function centroid = polygonCentroid3d(varargin)
0002 %POLYGONCENTROID3D Centroid (or center of mass) of a polygon.
0003 %
0004 %   PTC = polygonCentroid3d(POLY)
0005 %   Computes center of mass of a polygon defined by POLY. POLY is a N-by-3
0006 %   array of double containing coordinates of polygon vertices.
0007 %
0008 %   PTC = polygonCentroid3d(VX, VY, VZ)
0009 %   Specifies vertex coordinates as three separate arrays.
0010 %
0011 %   Example
0012 %     % compute centroid of a basic polygon
0013 %     poly = [0 0 0; 10 0 10;10 10 20;0 10 10];
0014 %     centro = polygonCentroid3d(poly)
0015 %     centro =
0016 %         5.0000    5.0000    10.0000
0017 %
0018 %   See also
0019 %   polygons3d, polygonArea3d, polygonCentroid
0020 %
0021 
0022 % ------
0023 % Author: David Legland
0024 % e-mail: david.legland@inra.fr
0025 % Created: 2007-09-18
0026 % Copyright 2007 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas).
0027 
0028 
0029 if nargin == 1
0030     % polygon is given as a single argument
0031     pts = varargin{1};
0032     
0033 elseif nargin == 3
0034     % polygon is given as 3 coordinate arrays
0035     px = varargin{1};
0036     py = varargin{2};
0037     pz = varargin{3};
0038     pts = [px py pz];
0039 end
0040 
0041 % create supporting plane (assuming first 3 points are not colinear...)
0042 plane = createPlane(pts(1:3, :));
0043 
0044 % project points onto the plane
0045 pts = planePosition(pts, plane);
0046 
0047 % compute centroid in 2D
0048 centro2d = polygonCentroid(pts);
0049 
0050 % project back in 3D
0051 centroid = planePoint(plane, centro2d);