rotmat2vec

 [R,s]=rotmat2vec(u,v)

 the rotation matrix from vector u to v, satisfying R*u*s=v

 author: Bruno Luong
 URL:http://www.mathworks.com/matlabcentral/newsreader/view_original/827969

 input: 
   u: a 3D vector in the source coordinate system;
   v: a 3D vector in the target coordinate system;

 output:
   R: a rotation matrix to transform normalized u to normalized v
   s: a scaling factor, so that R*u(:)*s=v(:)

 -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)

0001 function [R,s]=rotmat2vec(u,v)
0002 %
0003 % [R,s]=rotmat2vec(u,v)
0004 %
0005 % the rotation matrix from vector u to v, satisfying R*u*s=v
0006 %
0007 % author: Bruno Luong
0008 % URL:http://www.mathworks.com/matlabcentral/newsreader/view_original/827969
0009 %
0010 % input:
0011 %   u: a 3D vector in the source coordinate system;
0012 %   v: a 3D vector in the target coordinate system;
0013 %
0014 % output:
0015 %   R: a rotation matrix to transform normalized u to normalized v
0016 %   s: a scaling factor, so that R*u(:)*s=v(:)
0017 %
0018 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0019 %
0020 
0021 s=norm(v(:))/norm(u(:));
0022 u1=u(:)/norm(u(:));
0023 v1=v(:)/norm(v(:));
0024 
0025 k = cross(u1,v1);
0026 if(~any(k)) % u and v are parallel
0027     R=eye(3);
0028     return;
0029 end
0030 % Rodrigues's formula:
0031 costheta = dot(u1,v1);
0032 R =[ 0 -k(3) k(2);
0033      k(3) 0 -k(1);
0034     -k(2) k(1) 0];
0035 R = costheta*eye(3) + R + k*k'*(1-costheta)/sum(k.^2);