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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## 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 AUTHOR 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 the copyright holders.
function b = isPointInEllipse(point, ellipse, varargin)
%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
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-03-11
% Copyright 2011-2023 INRA - TPV URPOI - BIA IMASTE
% 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;
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