Quaternion - Rotate To

Question

I have some object in world space, let\'s say at (0,0,0) and want to rotate it to face (10,10,10).

How do i do this using quaternions?

Answer 1

In response to your clarification and to just answer this, I've shamelessly copied a very interesting and neat algorithm for finding the quat between two vectors that looks like I have never seen before from here. Mathematically, it seems valid, and since your question is about the mathematics behind it, I'm sure you'll be able to convert this pseudocode into C++.

quaternion q;
vector3 c = cross(v1,v2);
q.v = c;
if ( vectors are known to be unit length ) {
    q.w = 1 + dot(v1,v2);
} else {
    q.w = sqrt(v1.length_squared() * v2.length_squared()) + dot(v1,v2);
}
q.normalize();
return q;

Let me know if you need help clarifying any bits of that pseudocode. Should be straightforward though.

dot(a,b) = a1*b1 + a2*b2 + ... + an*bn

and

cross(a,b) = well, the cross product. it's annoying to type out and
can be found anywhere.