   reversing vertex transform
  Say I had a vertex that had a position and quaternion transform I wanted to transform from world space to object space, how would I do it?   
  You will want to multiply the vertex by the inverse of the world space transform to get the vertex back into object space. I assume you combine your quaternion and position into a single transformation matrix. You could invert that matrix or I believe you can invert the position and quaternion separately.   ;  The conjugate of a unit quaternion is analogous to the inverse of the equivalent 3x3 rotation matrix. The conjugate is extremely easy to calculate:If q = w + i x + j y + k z rotates from A to Bthen conj(q) = w - i x - j y - k z rotates from B to A   