ellipseToPolygon

ELLIPSETOPOLYGON Convert an ellipse into a series of points.

   P = ellipseToPolygon(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 a N-by-2 array containing the coordinates
   of the N vertices of the polygon.

   P = ellipseToPolygon(ELL);
   Use a default number of edges equal to 72. This results in one point
   for each 5 degrees.
   
   [X, Y] = ellipseToPolygon(...);
   Return the coordinates of vertices in two separate arrays.

   Example
     poly = ellipseToPolygon([50 50 40 30 20], 60);
     figure; hold on;
     axis equal; axis([0 100 10 90]);
     drawPolygon(poly, 'b');
     drawPoint(poly, 'bo');

   See also:
   ellipses2d, drawEllipse, circleToPolygon, rectToPolygon

0001 function varargout = ellipseToPolygon(ellipse, N)
0002 %ELLIPSETOPOLYGON Convert an ellipse into a series of points.
0003 %
0004 %   P = ellipseToPolygon(ELL, N);
0005 %   converts ELL given as [x0 y0 a b] or [x0 y0 a b theta] into a polygon
0006 %   with N edges. The result P is a N-by-2 array containing the coordinates
0007 %   of the N vertices of the polygon.
0008 %
0009 %   P = ellipseToPolygon(ELL);
0010 %   Use a default number of edges equal to 72. This results in one point
0011 %   for each 5 degrees.
0012 %
0013 %   [X, Y] = ellipseToPolygon(...);
0014 %   Return the coordinates of vertices in two separate arrays.
0015 %
0016 %   Example
0017 %     poly = ellipseToPolygon([50 50 40 30 20], 60);
0018 %     figure; hold on;
0019 %     axis equal; axis([0 100 10 90]);
0020 %     drawPolygon(poly, 'b');
0021 %     drawPoint(poly, 'bo');
0022 %
0023 %   See also:
0024 %   ellipses2d, drawEllipse, circleToPolygon, rectToPolygon
0025 %
0026 
0027 %   ---------
0028 %   author : David Legland
0029 %   INRA - TPV URPOI - BIA IMASTE
0030 %   created the 06/04/2005.
0031 %
0032 
0033 % HISTORY
0034 % 2011-03-30 use angles in degrees, add default value for N
0035 % 2011-12-09 rename to ellipseToPolygon
0036 % 2017-08-31 returns N vertices instead of N+1
0037 
0038 % default value for N
0039 if nargin < 2
0040     N = 72;
0041 end
0042 
0043 % angle of ellipse
0044 theta = 0;
0045 if size(ellipse, 2) > 4
0046     theta = ellipse(:,5);
0047 end
0048 
0049 % get ellipse parameters
0050 xc = ellipse(:,1);
0051 yc = ellipse(:,2);
0052 a  = ellipse(:,3);
0053 b  = ellipse(:,4);
0054 
0055 % create time basis
0056 t = linspace(0, 2*pi, N+1)';
0057 t(end) = [];
0058 
0059 % pre-compute trig functions (angles is in degrees)
0060 cot = cosd(theta);
0061 sit = sind(theta);
0062 
0063 % position of points
0064 x = xc + a * cos(t) * cot - b * sin(t) * sit;
0065 y = yc + a * cos(t) * sit + b * sin(t) * cot;
0066 
0067 % format output depending on number of a param.
0068 if nargout == 1
0069     varargout = {[x y]};
0070 elseif nargout == 2
0071     varargout = {x, y};
0072 end