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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 varargout = principalAxesTransform(pts)
%PRINCIPALAXESTRANSFORM Align a set of points along its principal axes.
%
% TRANSFO = principalAxesTransform(PTS)
% Computes the affine transform that will transform the input array PTS
% such that its principal axes become aligned with main axes.
%
% [TRANSFO, PTS2] = principalAxesTransform(PTS)
% Also returns the result of the transform applied to the points.
%
% Example
% principalAxesTransform
%
% See also
% principalAxes, equivalentEllipse, equivalentEllipsoid
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2020-03-06, using Matlab 8.6.0.267246 (R2015b)
% Copyright 2020-2023 INRAE - Cepia Software Platform
% computes principal axes
[center, rotMat] = principalAxes(pts);
% concatenate into affine matrix
nd = size(pts, 2);
transfo = inv([rotMat center'; zeros(1, nd) 1]);
% format output
if nargout < 2
varargout = transfo;
else
if nd == 2
pts2 = transformPoint(pts, transfo);
else
pts2 = transformPoint3d(pts, transfo);
end
varargout = {transfo, pts2};
end
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