%% Copyright (c) 2011, INRA
%% 2004-2011, 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{p} = } ellipseAsPolygon (@var{ell}, @var{n})
%% Convert an ellipse into a series of points
%%
%%   P = ellipseAsPolygon(ELL, N);
%%   converts ELL given as [x0 y0 a b] or [x0 y0 a b theta] into a polygon
%%   with N edges. The result P is (N+1)-by-2 array containing coordinates
%%   of the N+1 vertices of the polygon.
%%   The resulting polygon is closed, i.e. the last point is the same as the
%%   first one.
%%
%%   P = ellipseAsPolygon(ELL);
%%   Use a default number of edges equal to 72. This result in one piont for
%%   each 5 degrees.
%%   
%%   [X Y] = ellipseAsPolygon(...);
%%   Return the coordinates o fvertices in two separate arrays.
%%
%%   @seealso{ellipses2d, circleAsPolygon, rectAsPolygon, drawEllipse}
%% @end deftypefn

function varargout = ellipseAsPolygon(ellipse, N)

  % default value for N
  if nargin < 2
      N = 72;
  end

  % angle of ellipse
  theta = 0;
  if size(ellipse, 2) > 4
      theta = ellipse(:,5);
  end

  % get ellipse parameters
  xc = ellipse(:,1);
  yc = ellipse(:,2);
  a  = ellipse(:,3);
  b  = ellipse(:,4);

  % create time basis
  t = linspace(0, 2*pi, N+1)';

  % pre-compute trig functions (angles is in degrees)
  cot = cosd(theta);
  sit = sind(theta);

  % position of points
  x = xc + a * cos(t) * cot - b * sin(t) * sit;
  y = yc + a * cos(t) * sit + b * sin(t) * cot;

  % format output depending on number of a param.
  if nargout == 1
      varargout = {[x y]};
  elseif nargout == 2
      varargout = {x, y};
  end

endfunction

