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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 trans = fitAffineTransform3d(ref, src)
%FITAFFINETRANSFORM3D Compute the affine transform that best register two 3D point sets.
%
% TRANS = fitAffineTransform3d(REF, SRC)
% Returns the affine transform matrix that minimizes the distance between
% the reference point set REF and the point set SRC after transformation.
% Both REF and SRC must by N-by-3 arrays with the same number of rows,
% and the points must be in correspondence.
% The function minimizes the sum of the squared distances:
% CRIT = sum(distancePoints3d(REF, transformPoint3d(PTS, TRANSFO)).^2);
%
% Example
% N = 50;
% pts = rand(N, 3)*10;
% trans = createRotationOx([5 4 3], pi/4);
% pts2 = transformPoint3d(pts, trans);
% pts3 = pts2 + randn(N, 3)*2;
% fitted = fitAffineTransform3d(pts, pts2);
%
%
% See also
% transforms3d, transformPoint3d, transformVector3d,
% fitAffineTransform2d, registerPoints3dAffine
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2009-07-31, using Matlab 7.7.0.471 (R2008b)
% Copyright 2009-2023 INRAE - Cepia Software Platform
% number of points
N = size(src, 1);
if size(ref, 1) ~= N
error('Requires the same number of points for both arrays');
end
% main matrix of the problem
tmp = [src(:,1) src(:,2) src(:,3) ones(N,1)];
A = [...
tmp zeros(N, 8) ; ...
zeros(N, 4) tmp zeros(N, 4) ; ...
zeros(N, 8) tmp ];
% conditions initialisations
B = [ref(:,1) ; ref(:,2) ; ref(:,3)];
% compute coefficients using least square
coefs = A\B;
% format to a matrix
trans = [coefs(1:4)' ; coefs(5:8)'; coefs(9:12)'; 0 0 0 1];
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