# Composing rotations

When importing 3d stuidos .ASE files into my OpenGL program, I noted something strange, it used following information to record state of Pivot:

• translation vector
• scale factors for x, y, z axis
• rotation angle and rotation axis (which is represented with x,y,z coords)

Transformations are ment to be used in following order: M = TRS (I’ve tested this)

Now, strange thing is that all rotations are represented with only 4 variables: angle and axis. Is it posible that composition of N rotations can be substituted with single rotation around arbitrary axis??

If this is true, can I find more about it and similiar facts in form of mathematical theorem/theory?

Thanks for every info!

yes its sufficient

here is some info about matrix/quaternions
I think there is also some euler conversion stuff in it

http://skal.planet-d.net/demo/matrixfaq.htm

http://www.sjbrown.co.uk/quaternions.html

This introduction to quaternions is a bit better structured. It’s a bit more mathematical, but it shouldn’t be too hard to understand.

Thanks for links, they look great!
I’ll check them tonight.

Cheers,