I have been wondering for a long time, why we use quaternions in CG. Even more, dual quaternions are used in CG recently. Today I just find one possible reason.
The act of rotating a vector r by an angular displacement (theta, n) is the same as tacking this angular displacement, 'lifting' it into quaternion space, by representing it as the unit quaternion (cos(theta/2), sin(theta/2)n) and performing the operation q*()*conjugate(q) on the quaternion (0,r).
Why use Quaternions in CG?
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