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function [A,b]=affinemap(pfrom,pto)
%  [A,b]=affinemap(pfrom,pto)
%
%  calculate an affine transform (A matrix and b vector) to map n
%  vertices from one space to the other using least square solutions
%
%  author: Qianqian Fang <q.fang at neu.edu>
%  date: 12/12/2008
%
% parameters: 
%      pfrom: nx3 matrix, each row is a 3d point in original space
%      pto: nx3 matrix, each row is a 3d point in the mapped space
%
% outputs:
%      A: 3x3 matrix, the calculated affine A matrix
%      b: 3x1 vector, the calculated affine b vector
%
% the solution will satisfy the following equation: A*pfrom'+b=pto
%
% Please find more information at http://iso2mesh.sf.net/cgi-bin/index.cgi?metch
%
% this function is part of "metch" toobox, see COPYING for license

bsubmat=eye(3);
ptnum=size(pfrom,1);
if(size(pto,1)~=ptnum)
        error('two inputs should have the same size');
end
amat=zeros(ptnum*3,9);
for i=1:ptnum
        amat(i*3-2:i*3,:)=kron(bsubmat,pfrom(i,:));
end
amat=[amat,repmat(bsubmat,ptnum,1)];

bvec=pto';
bvec=bvec(:);

x=amat\bvec;
A=reshape(x(1:9),3,3)';
b=x(end-2:end);