--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/geometry/inst/polygons2d/polygonArea.m	Wed Aug 15 10:36:54 2012 +0000
@@ -0,0 +1,98 @@
+%% Copyright (C) 2003-2011 David Legland <david.legland@grignon.inra.fr>
+%% Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%% 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.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{area} = } polygonArea (@var{points})
+%% @deftypefnx {Function File} {@var{area} = } polygonArea (@var{px},@var{py})
+%% Compute the signed area of a polygon.
+%%
+%% Compute area of a polygon defined by @var{points}. @var{points} is a N-by-2
+%% matrix containing coordinates of vertices.
+%%
+%% Vertices of the polygon are supposed to be oriented Counter-Clockwise
+%% (CCW). In this case, the signed area is positive.
+%% If vertices are oriented Clockwise (CW), the signed area is negative.
+%%
+%% If polygon is self-crossing, the result is undefined.
+%%
+%% If @var{points} is a cell, each element is considered a polygon and the area
+%% of each one is returned in the matrix @var{area}. The matrix has the same shape
+%% as the cell.
+%%
+%% References:
+%% Algorithm adapted from P. Bourke web page
+%% http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
+%%
+%% @seealso{polygons2d, polygonCentroid, drawPolygon}
+%% @end deftypefn
+
+function area = polygonArea(varargin)
+
+  var = varargin{1};
+
+  % in case of polygon sets, computes several areas
+  if iscell (var)
+     area = cellfun (@func, var);
+
+%     area = zeros(length(var), 1);
+%          for i = 1:length(var)
+%              area(i) = polygonArea(var{i}, varargin{2:end});
+%          end
+%          return;
+%      end
+  else
+    % extract coordinates
+    if nargin == 1
+
+      area = func(var)
+
+    elseif nargin == 2
+
+      px = varargin{1};
+      py = varargin{2};
+
+      % indices of next vertices
+      N = length(px);
+      iNext = [2:N 1];
+
+      % compute area (vectorized version)
+      area = sum(px .* py(iNext) - px(iNext) .* py) / 2;
+
+    end
+
+  end
+
+endfunction
+
+function a = func (c)
+
+  N = length (c);
+  iNext = [2:N 1];
+  a = sum (c(:,1) .* c(iNext,2) - c(iNext,1) .* c(:,2)) / 2;
+
+endfunction

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/geometry/inst/polygons2d/polygonCentroid.m	Wed Aug 15 10:36:54 2012 +0000
@@ -0,0 +1,82 @@
+%% Copyright (C) 2003-2011 David Legland <david.legland@grignon.inra.fr>
+%% Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%% 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.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {[ @var{pt}, @var{area} ] = } polygonCentroid (@var{points})
+%% @deftypefnx {Function File} {[ @dots{} ]= } polygonCentroid (@var{ptx},@var{pty})
+%% Compute the centroid (center of mass) of a polygon.
+%%
+%% Computes the center of mass of a polygon defined by @var{points}. @var{points} is a
+%% N-by-2 matrix. The two columns can be given separately using @var{ptx} and @var{pty}
+%% for the x and y component respectively.
+%%
+%% The area of the polygon is returned in the second output argument.
+%%
+%% Adapted from @url{http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/}
+%%
+%% @seealso{polygons2d, polygonArea, drawPolygon}
+%% @end deftypefn
+
+function [pt A] = polygonCentroid(varargin)
+
+  if nargin==1
+      var = varargin{1};
+
+      px = var(:,1);
+      py = var(:,2);
+
+  elseif nargin==2
+
+      px = varargin{1};
+      py = varargin{2};
+
+  end
+
+  % Algorithme P. Bourke (vectorized)
+  inext  = [2:N 1];
+
+  cros = (px.*py(inext) - px(inext).*py);
+  sx_  = sum ( (px + px(inext)) .*  cros);
+  sy_  = sum ( (py + py(inext)) .*  cros);
+
+  A = sum(cros) / 2;
+
+  pt_ = [sx_ sy_]/A/6;
+
+  %  sx = 0;
+  %  sy = 0;
+  %  N = length(px);
+  %  for i=1:N-1
+  %      sx = sx + (px(i)+px(i+1))*(px(i)*py(i+1) - px(i+1)*py(i));
+  %      sy = sy + (py(i)+py(i+1))*(px(i)*py(i+1) - px(i+1)*py(i));
+  %  end
+  %  sx = sx + (px(N)+px(1))*(px(N)*py(1) - px(1)*py(N));
+  %  sy = sy + (py(N)+py(1))*(px(N)*py(1) - px(1)*py(N));
+  %  pt = [sx sy]/6/polygonArea(px, py)
+
+endfunction