polylineCentroid

 Computes the centroid of a curve defined by a series of points.

   PT = polylineCentroid(POINTS);
   Computes center of mass of a polyline defined by POINTS. POINTS is a
   N-by-D array of double, representing a set of N points in a
   D-dimensional space.

   PT = polylineCentroid(PTX, PTY);
   PT = polylineCentroid(PTX, PTY, PTZ);
   Specifies points as separate column vectors

   PT = polylineCentroid(..., TYPE);
   Specifies if the last point is connected to the first one. TYPE can be
   either 'closed' or 'open'.

   Example
   poly = [0 0;10 0;10 10;20 10];
   polylineCentroid(poly)
   ans = 
       [10 5]

   See also:
     polygons2d, centroid, polygonCentroid, polylineLength

0001 function center = polylineCentroid(varargin)
0002 % Computes the centroid of a curve defined by a series of points.
0003 %
0004 %   PT = polylineCentroid(POINTS);
0005 %   Computes center of mass of a polyline defined by POINTS. POINTS is a
0006 %   N-by-D array of double, representing a set of N points in a
0007 %   D-dimensional space.
0008 %
0009 %   PT = polylineCentroid(PTX, PTY);
0010 %   PT = polylineCentroid(PTX, PTY, PTZ);
0011 %   Specifies points as separate column vectors
0012 %
0013 %   PT = polylineCentroid(..., TYPE);
0014 %   Specifies if the last point is connected to the first one. TYPE can be
0015 %   either 'closed' or 'open'.
0016 %
0017 %   Example
0018 %   poly = [0 0;10 0;10 10;20 10];
0019 %   polylineCentroid(poly)
0020 %   ans =
0021 %       [10 5]
0022 %
0023 %   See also:
0024 %     polygons2d, centroid, polygonCentroid, polylineLength
0025 %
0026 
0027 %   ---------
0028 %   author : David Legland
0029 %   INRA - TPV URPOI - BIA IMASTE
0030 %   created the 22/05/2006.
0031 %
0032 
0033 
0034 
0035 %% process input arguments
0036 
0037 % check whether the curve is closed
0038 closed = false;
0039 var = varargin{end};
0040 if ischar(var)
0041     if strcmpi(var, 'closed')
0042         closed = true;
0043     end
0044     % remove last argument
0045     varargin(end) = [];
0046 end
0047 
0048 % extract point coordinates
0049 if length(varargin)==1
0050     points = varargin{1};
0051 elseif length(varargin)==2
0052     points = [varargin{1} varargin{2}];
0053 end
0054 
0055 
0056 %% Main computation
0057 
0058 % compute centers and lengths composing the curve
0059 if closed
0060     centers = (points + points([2:end 1],:))/2;
0061     lengths = sqrt(sum(diff(points([1:end 1],:)).^2, 2));
0062 else
0063     centers = (points(1:end-1,:) + points(2:end,:))/2;
0064     lengths = sqrt(sum(diff(points).^2, 2));
0065 end
0066 
0067 % centroid of edge centers weighted by edge length
0068 %weigths = repmat(lengths/sum(lengths), [1 size(points, 2)]);
0069 center = sum(centers .* repmat(lengths, [1 size(points, 2)]), 1) / sum(lengths);
0070