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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 = isPointInEllipsoid(point, elli, varargin)
%ISPOINTINELLIPSOID Check if a point is located inside a 3D ellipsoid.
%
% output = isPointInEllipsoid(input)
%
% Example
% % create an ellipsoid
% elli = [10 20 30 50 30 10 5 10 0];
% display it
% figure; hold on;
% drawEllipsoid(elli, 'FaceColor', 'g', 'FaceAlpha', .5, ...
% 'drawEllipses', true, 'EllipseColor', 'b', 'EllipseWidth', 3);
% view(3); axis equal;
% % check for a point inside the ellipsoid
% p1 = [20 30 35];
% b1 = isPointInEllipsoid(p1, elli)
% ans =
% 1
% % check for a point outside the ellipsoid
% p2 = [-20 10 25];
% b2 = isPointInEllipsoid(p2, elli)
% ans =
% 0
%
%
% See also
% equivalentEllipsoid, drawEllipsoid, isPointInEllipse
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2020-11-19, using Matlab 9.8.0.1323502 (R2020a)
% Copyright 2020-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
% extract computation tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% compute ellipse to unit circle transform
rot = eulerAnglesToRotation3d(elli(7:9));
sca = createScaling3d(elli(4:6));
trans = inv(rot * sca);
% transform points to unit sphere basis
pTrans = bsxfun(@minus, point, elli(1:3));
pTrans = transformPoint3d(pTrans, trans);
% test if norm is smaller than 1
b = sqrt(sum(power(pTrans, 2), 2)) - 1 <= tol;
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