Quaternion * Vector3?

[Baldrake]

I've been reading up on quaternions. So far so good, but...

Ogre defines a '*' operation over a Quaternion and a Vector3, which doesn't seem to be a standard one. From the code, I can see that this is defined as:

Code: Select all

Let q=<x,y,z,w> be a quaternion and v be a vector in 3-space. Then:

q * v = v + 2w (<x,y,z> x v)
           + 2 (<x,y,z> x (<x,y,z> x v))

Ok, but what does this actually mean? Can someone give me the intuition behind this definition?

Thanks!

[haffax]

Ogre's Quaternion operator* actually calculates q*v*q^1. Thus applying the rotation. There is no use for the mathematically correct multiplication as a stand-alone in a 3D application, because you only use it to apply the rotation anyway and you therefor had to call it twice with some float multiplications overhead.