I'm working on my degree and have started getting into some deeper lin alg than I took previously regarding coordinate system transformations. I was hoping someone might be able to shed some light on it for me. I'll do my best to explain the problem ..

I have a global coordinate system for a volume in space created by a motion capture device. Thus three unit vectors representing the x, y and z vectors of the global space are

[1 0 0

0 1 0

0 0 1]

I then have a person standing in space, with markers on their hips in such a way I can determine a local system for the person's pelvis. The unit vectors representing this local system are as follows

[0.9625 -0.0326 -0.266

0.0268 0.9999 -0.0256

0.2671 0.6175 0.9627]

So the local system is oriented very close to the global system.

I then calculate two points in space, but in the global space. I in essence need to rotate them about the origin of my local system as much as my local system is rotated from my global system.

I'm sure I sound like a bumbling goon, but I hope you guys can make heads or tails of this. I'm guessing there's a way to come up with a rotation matrix from system 1 to system 2, and from there .. hmm.. somehow translate my points about the origin of my local system.

I can clarify anything if need be.