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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 line = fitLine3d(points)
%FITLINE3D Fit a 3D line to a set of points.
%
% LINE = fitLine3d(PTS)
%
% Example
% pts = randn(300, 3);
% pts = transformPoint3d(pts, createScaling3d([6 4 2]));
% pts = transformPoint3d(pts, createRotationOx(pi/6));
% pts = transformPoint3d(pts, createRotationOy(pi/4));
% pts = transformPoint3d(pts, createRotationOz(pi/3));
% pts = transformPoint3d(pts, createTranslation3d([5 4 3]));
% elli = equivalentEllipsoid(pts);
% figure; drawPoint3d(pts); axis equal;
% hold on; drawEllipsoid(elli, ...
% 'drawEllipses', true, 'EllipseColor', 'b', 'EllipseWidth', 3);
% line = fitLine3d(pts);
% drawLine3d(line, 'color', 'm', 'LineWidth', 4);
%
% See also
% lines3d, equivalentEllipsoid, fitPlane, fitLine
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-11-11, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRA - Cepia Software Platform
% number of points
n = size(points, 1);
% compute centroid
center = mean(points);
% compute the covariance matrix
covPts = cov(points)/n;
% perform a principal component analysis with 2 variables,
% to extract inertia axes
[U, S] = svd(covPts);
% sort axes from greater to lower
[dummy, ind] = sort(diag(S), 'descend'); %#ok<ASGLU>
% format U to ensure first axis points to positive x direction
U = U(ind, :);
if U(1,1) < 0
U = -U;
% keep matrix determinant positive
U(:,3) = -U(:,3);
end
% create row vector representing the line
line = [center U(:,1)'];
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