/usr/share/octave/packages/geometry-1.7.0/geom2d/isPointInEllipse.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{b} = } isPointInellipse (@var{point}, @var{ellipse})
## 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
##
## @seealso{ellipses2d, isPointInCircle}
## @end deftypefn
function b = isPointInEllipse(point, ellipse, varargin)
# extract computation tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
# compute ellipse to unit circle transform
rot = createRotation(-deg2rad(ellipse(5)));
sca = createScaling(1./ellipse(3:4));
trans = sca * rot;
# transform points to unit circle basis
pTrans = bsxfun(@minus, point, ellipse(:,1:2));
pTrans = transformPoint(pTrans, trans);
# test if distance to origin smaller than 1
b = sqrt(sum(power(pTrans, 2), 2)) - 1 <= tol;
endfunction
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