Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / fitAffineTransform2d.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/fitAffineTransform2d.m b/octave_packages/geometry-1.5.0/geom2d/fitAffineTransform2d.m
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+++ b/octave_packages/geometry-1.5.0/geom2d/fitAffineTransform2d.m
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+%% 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>
+%%
+%% All rights reserved.
+%% (simplified BSD License)
+%%
+%% 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 COPYRIGHT HOLDER 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 copyright holder.
+
+%% -*- 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
+
+