- #1

sodemus

- 29

- 0

I'm looking for an appropriate rotation representation for the following situation.

I have two (always non-zero) vectors, v1, v2, that may or may not be parallel. The rotation relating the two vectors is obviously non-unique having one degree of freedom, parametrized by p. So my question is: Is there a "simple" way (in terms of quaternions, rotation matrices, Euler angles ... or whatever you prefer) to express the

*unique*(2 DOF) rotation in terms of the two vectors and the "free" parameter p, parametrizing the one degree of freedom mentioned above? What is the simplest way you can come up with?

I can do this myself but whatever I've come up with is algebraically pretty messy.

In case I haven't made myself clear, what I want is the "simplest" possible form of

R = R(v1,v2,p)

Many thanks in advance!

Edit: If it could be done without using cross-products that is an extra bonus!