isPointInEllipse

ISPOINTINELLIPSE Check if a point is located inside a given ellipse.

   B = isPointInEllipse(POINT, ELLIPSE) 
   Returns true if point is located inside the given ellipse.

   B = isPointInEllipse(POINT, ELLIPSE, TOL) 
   Specifies the tolerance value

   Example:
   isPointInEllipse([1 0], [0 0 2 1 0])
   ans =
       1
   isPointInEllipse([0 0], [0 0 2 1 0])
   ans =
       1
   isPointInEllipse([1 1], [0 0 2 1 0])
   ans =
       0
   isPointInEllipse([1 1], [0 0 2 1 30])
   ans =
       1

   See also:
     ellipses2d, isPointInCircle

0001 function b = isPointInEllipse(point, ellipse, varargin)
0002 %ISPOINTINELLIPSE Check if a point is located inside a given ellipse.
0003 %
0004 %   B = isPointInEllipse(POINT, ELLIPSE)
0005 %   Returns true if point is located inside the given ellipse.
0006 %
0007 %   B = isPointInEllipse(POINT, ELLIPSE, TOL)
0008 %   Specifies the tolerance value
0009 %
0010 %   Example:
0011 %   isPointInEllipse([1 0], [0 0 2 1 0])
0012 %   ans =
0013 %       1
0014 %   isPointInEllipse([0 0], [0 0 2 1 0])
0015 %   ans =
0016 %       1
0017 %   isPointInEllipse([1 1], [0 0 2 1 0])
0018 %   ans =
0019 %       0
0020 %   isPointInEllipse([1 1], [0 0 2 1 30])
0021 %   ans =
0022 %       1
0023 %
0024 %   See also:
0025 %     ellipses2d, isPointInCircle
0026 %
0027 
0028 %   ---------
0029 %   author : David Legland
0030 %   INRA - TPV URPOI - BIA IMASTE
0031 %   created the 11/03/2011
0032 %
0033 
0034 %   HISTORY
0035 
0036 % extract computation tolerance
0037 tol = 1e-14;
0038 if ~isempty(varargin)
0039     tol = varargin{1};
0040 end
0041 
0042 % compute ellipse to unit circle transform
0043 rot = createRotation(-deg2rad(ellipse(5)));
0044 sca = createScaling(1./ellipse(3:4));
0045 trans = sca * rot;
0046 
0047 % transform points to unit circle basis
0048 pTrans = bsxfun(@minus, point, ellipse(:,1:2));
0049 pTrans = transformPoint(pTrans, trans);
0050 
0051 % test if distance to origin smaller than 1
0052 b = sqrt(sum(power(pTrans, 2), 2)) - 1 <= tol;
0053