createRotationVector3d

CREATEROTATIONVECTOR3D Calculates the rotation between two vectors.

   ROT = createRotationVector3d(A, B) returns the 4x4 rotation matrix ROT
   to transform vector A in the same direction as vector B.

   Example
     A=[ .1  .2  .3];
     B=-1+2.*rand(1,3);
     ROT = createRotationVector3d(A,B);
     C = transformVector3d(A,ROT);
     figure('color','w'); hold on; view(3)
     O=[0 0 0];
     drawVector3d(O, A,'r');
     drawVector3d(O, B,'g');
     drawVector3d(O, C,'r');

   See also
   transformPoint3d, createRotationOx, createRotationOy, createRotationOz

   Source
     https://math.stackexchange.com/a/897677

 ---------
 Author: oqilipo
 Created: 2017-08-07
 Copyright 2017

0001 function ROT = createRotationVector3d(A,B)
0002 %CREATEROTATIONVECTOR3D Calculates the rotation between two vectors.
0003 %
0004 %   ROT = createRotationVector3d(A, B) returns the 4x4 rotation matrix ROT
0005 %   to transform vector A in the same direction as vector B.
0006 %
0007 %   Example
0008 %     A=[ .1  .2  .3];
0009 %     B=-1+2.*rand(1,3);
0010 %     ROT = createRotationVector3d(A,B);
0011 %     C = transformVector3d(A,ROT);
0012 %     figure('color','w'); hold on; view(3)
0013 %     O=[0 0 0];
0014 %     drawVector3d(O, A,'r');
0015 %     drawVector3d(O, B,'g');
0016 %     drawVector3d(O, C,'r');
0017 %
0018 %   See also
0019 %   transformPoint3d, createRotationOx, createRotationOy, createRotationOz
0020 %
0021 %   Source
0022 %     https://math.stackexchange.com/a/897677
0023 %
0024 % ---------
0025 % Author: oqilipo
0026 % Created: 2017-08-07
0027 % Copyright 2017
0028 
0029 if isParallel3d(A,B)
0030     if A*B'>0
0031         ROT = eye(4);
0032     else
0033         ROT = -1*eye(4); ROT(end)=1;
0034     end
0035 else
0036     a=normalizeVector3d(A);
0037     b=normalizeVector3d(B);
0038     a=reshape(a,3,1);
0039     b=reshape(b,3,1);
0040     
0041     v = cross(a,b);
0042     ssc = [0 -v(3) v(2); v(3) 0 -v(1); -v(2) v(1) 0];
0043     ROT = eye(3) + ssc + ssc^2*(1-dot(a,b))/(norm(v))^2;
0044     
0045     ROT = [ROT, [0;0;0]; 0 0 0 1];
0046 end
0047 
0048 end