rot(V,theta)

Returns the 3D rotation matrix about an arbitary vector

This function returns the 3D rotation matrix about an arbitary vector V passing the origin.
This may serves as an extension to the matlab built in funciton : rotx, roty and rotz.
This can also be extended for V not going through origin by simple translation
Input:
V: 3 by 1 or 1 by 3 arbitrary rotation vector, it does not need to be normalized
theta:The rotation angle is positive if the rotation is in the counter-clockwise direction when viewed by an observer looking along the V towards the origin.
Output:
R: 3 by 3 rotation matrix
To use R on a column vector v: R*v
To use R on a row vector w: w*R'
Glenn Murray's step by step approach

(1) Translate space so that the rotation axis passes through the origin.
(2) Rotate space about the z axis so that the rotation axis lies in the xz plane.
(3) Rotate space about the y axis so that the rotation axis lies along the z axis.
(4) Perform the desired rotation by θ about the z axis.
(5) Apply the inverse of step (3).
(6) Apply the inverse of step (2).
(7) Apply the inverse of step (1).

Glenn Murray's online article :
http://inside.mines.edu/fs_home/gmurray/ArbitraryAxisRotation/

Example:
Rotate pi/3 about x-axis
rot([1,0,0],pi/3)
=

1.0000 0 0
0 0.5000 -0.8660
0 0.8660 0.5000

By Tianxiao Jiang
Unversity of Houston
[e-mail]