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. The result
   PTC is given as a 1-by-3 numeric array.
   The algorithm assumes (1) that the vertices of the polygon are within
   the same plane and (2) that the planar projection of the polygon (on
   the embedding plane) do not self-intersect.

   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, planePosition, planePoint

0001 function [centroid, area] = 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. The result
0007 %   PTC is given as a 1-by-3 numeric array.
0008 %   The algorithm assumes (1) that the vertices of the polygon are within
0009 %   the same plane and (2) that the planar projection of the polygon (on
0010 %   the embedding plane) do not self-intersect.
0011 %
0012 %   PTC = polygonCentroid3d(VX, VY, VZ)
0013 %   Specifies vertex coordinates as three separate arrays.
0014 %
0015 %   Example
0016 %     % compute centroid of a basic polygon
0017 %     poly = [0 0 0; 10 0 10;10 10 20;0 10 10];
0018 %     centro = polygonCentroid3d(poly)
0019 %     centro =
0020 %         5.0000    5.0000    10.0000
0021 %
0022 %   See also
0023 %     polygons3d, polygonArea3d, polygonCentroid, planePosition, planePoint
0024 %
0025 
0026 % ------
0027 % Author: David Legland
0028 % E-mail: david.legland@inrae.fr
0029 % Created: 2007-09-18
0030 % Copyright 2007-2024 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
0031 
0032 if nargin == 1
0033     % polygon is given as a single argument
0034     pts = varargin{1};
0035 elseif nargin == 3
0036     % polygon is given as 3 coordinate arrays
0037     px = varargin{1};
0038     py = varargin{2};
0039     pz = varargin{3};
0040     pts = [px py pz];
0041 end
0042 
0043 pts = parsePolygon(pts, 'repetition');
0044 
0045 % create supporting plane
0046 plane = fitPlane(pts);
0047 
0048 % project points onto the plane
0049 pts = planePosition(pts, plane);
0050 
0051 % compute centroid in 2D
0052 [centro2d, area] = polygonCentroid(pts);
0053 
0054 % project back in 3D
0055 centroid = planePoint(plane, centro2d);