/usr/share/octave/packages/geometry-1.7.0/geom2d/fitAffineTransform2d.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{T} = } fitAffineTransform2d (@var{pts1}, @var{pts2})
## Fit an affine transform using two point sets.
##
## Example
##
## @example
## N = 10;
## pts = rand(N, 2)*10;
## trans = createRotation(3, 4, pi/4);
## pts2 = transformPoint(pts, trans);
## pts3 = pts2 + randn(N, 2)*2;
## fitted = fitAffineTransform2d(pts, pts2)
##@end example
##
## @seealso{transforms2d}
## @end deftypefn
function trans = fitAffineTransform2d(pts1, pts2)
# number of points
N = size(pts1, 1);
# main matrix of the problem
A = [...
pts1(:,1) pts1(:,2) ones(N,1) zeros(N, 3) ; ...
zeros(N, 3) pts1(:,1) pts1(:,2) ones(N,1) ];
# conditions initialisations
B = [pts2(:,1) ; pts2(:,2)];
# compute coefficients using least square
coefs = A\B;
# format to a matrix
trans = [coefs(1:3)' ; coefs(4:6)'; 0 0 1];
endfunction
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