Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / centroid.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/centroid.m b/octave_packages/geometry-1.5.0/geom2d/centroid.m
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+%% Copyright (c) 2011, INRA
+%% 2003-2011, David Legland <david.legland@grignon.inra.fr>
+%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% 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 COPYRIGHT HOLDER 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 copyright holder.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{c} = } centroid (@var{points})
+%% @deftypefnx {Function File} {@var{c} = } centroid (@var{px}, @var{py})
+%% @deftypefnx {Function File} {@var{c} = } centroid (@dots{}, @var{mass})
+%% Compute centroid (center of mass) of a set of points.
+%%
+%%   Computes the ND-dimensional centroid of a set of points. 
+%%   @var{points} is an array with as many rows as the number of points, and as
+%%   many columns as the number of dimensions. 
+%%   @var{px} and @var{py} are two column vectors containing coordinates of the
+%%   2-dimensional points.
+%%   The result @var{c} is a row vector with ND columns.
+%%
+%%   If @var{mass} is given, computes center of mass of @var{points}, weighted by coefficient @var{mass}.
+%%   @var{points} is a Np-by-Nd array, @var{mass} is Np-by-1 array, and @var{px} and @var{py} are
+%%   also both Np-by-1 arrays.
+%%
+%%   Example:
+%% 
+%% @example
+%%   pts = [2 2;6 1;6 5;2 4];
+%%   centroid(pts)
+%%   ans =
+%%        4     3
+%%@end example
+%%
+%%   @seealso{points2d, polygonCentroid}
+%% @end deftypefn
+
+function center = centroid(varargin)
+
+  %% extract input arguments
+
+  % use empty mass by default
+  mass = [];
+
+  if nargin==1
+      % give only array of points
+      pts = varargin{1};
+      
+  elseif nargin==2
+      % either POINTS+MASS or PX+PY
+      var = varargin{1};
+      if size(var, 2)>1
+          % arguments are POINTS, and MASS
+          pts = var;
+          mass = varargin{2};
+      else
+          % arguments are PX and PY
+          pts = [var varargin{2}];
+      end
+      
+  elseif nargin==3
+      % arguments are PX, PY, and MASS
+      pts = [varargin{1} varargin{2}];
+      mass = varargin{3};
+  end
+
+  %% compute centroid
+
+  if isempty(mass)
+      % no weight
+      center = mean(pts);
+      
+  else
+      % format mass to have sum equal to 1, and column format
+      mass = mass(:)/sum(mass(:));
+      
+      % compute weighted centroid
+      center = sum(bsxfun(@times, pts, mass), 1);
+      % equivalent to:
+      % center = sum(pts .* mass(:, ones(1, size(pts, 2))));
+  end
+
+endfunction
+
+%!test 
+%!  points = [0 0;10 0;10 10;0 10];
+%!  centro = centroid(points);
+%!   assert ([5 5], centro, 1e-6);
+
+%!test 
+%!  points = [0 0;10 0;10 10;0 10];
+%!  centro = centroid(points(:,1), points(:,2));
+%!   assert ([5 5], centro, 1e-6);
+
+%!test 
+%!  points = [0 0;30 0;30 30;0 30];
+%!  centro = centroid(points, [1;1;1;3]);
+%!   assert ([10 20], centro, 1e-6);
+
+%!test 
+%!  points = [0 0;30 0;30 30;0 30];
+%!  centro = centroid(points(:,1), points(:,2), [1;1;1;3]);
+%!   assert ([10 20], centro, 1e-6);
+