# matrix rotations (vector rotation around an arbitrary axis, y = 0)

Hello…
I have found a formula to rotate a vector about an arbitrary axis at
http://www.cise.ufl.edu/~cmccann/seniorp…or%20rotation’
… I wish to find the counterclockwise rotation around the arbitrary vector (u, 0, w); I’m setting v to 0 since my arbitrary vector involves rotations not including the y-axis.
Since I don’t have the matrix to invert it and only the final vector formula, I thought I could rotate the vector (u, 0, w) by 180 degrees around the y axis getting (-u, 0, -w). Plugging those values in didn’t hold…
Am I doing something wrong or is there another way to do it?

Thank you,
-TS…

rotations are specified via the rotation matrix

e.g. a rotation about the z axis (the axis about to be rotated stays fixed thus the 0,0,1)

cos x -sin x 0 0
sin x cos x 0 0
0 0 1 0
0 0 0 1

the inverse rotation can be easily obtained by knowing the trigonemtric laws for

cos -x = cos x
sin -x = - sin x

thus the inverse rotation for the above described rotation about the z axis would be

cos x sin x 0 0
-sin x cos x 0 0
0 0 1 0
0 0 0 1

to rotate about a arbitrary axis you have to move your coordinate system to this axis because rotations are specified around the center.

I hope that helps a bit …