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

0001 function varargout = principalAxesTransform(pts)
0002 % Align a set of points along its principal axes.
0003 %
0004 %   TRANSFO = principalAxesTransform(PTS)
0005 %   Computes the affine transform that will transform the input array PTS
0006 %   such that its principal axes become aligned with main axes.
0007 %
0008 %   [TRANSFO, PTS2] = principalAxesTransform(PTS)
0009 %   Also returns the result of the transform applied to the points.
0010 %
0011 %   Example
0012 %   principalAxesTransform
0013 %
0014 %   See also
0015 %     principalAxes, equivalentEllipse, equivalentEllipsoid
0016 %
0017  
0018 % ------
0019 % Author: David Legland
0020 % e-mail: david.legland@inrae.fr
0021 % Created: 2020-03-06,    using Matlab 8.6.0.267246 (R2015b)
0022 % Copyright 2020 INRAE - Cepia Software Platform.
0023 
0024 % computes principal axes
0025 [center, rotMat] = principalAxes(pts);
0026 
0027 % concatenate into affine matrix
0028 nd = size(pts, 2);
0029 transfo = inv([rotMat center'; zeros(1, nd) 1]);
0030 
0031 
0032 % format output
0033 if nargout < 2
0034     varargout = transfo;
0035 else
0036     if nd == 2
0037         pts2 = transformPoint(pts, transfo);
0038     else
0039         pts2 = transformPoint3d(pts, transfo);
0040     end
0041     varargout = {transfo, pts2};
0042 end