%% Copyright (c) 2011, INRA
%% 2009-2011, David Legland <david.legland@grignon.inra.fr>
%% 2011 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


