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Kris Hauser

specular component of 5d subspace quaternion voxel rotations

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I have a heirarchal procedural voxel system set up using blended quaternion rotations in a 6-d world. Now how would i go about finding the specular component of the voxel subspace volume (5d in this case) with a 4-d hyper-light of an arbitrary form?

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Well you take this REALLY big piece of swiss cheese, and stuff it in your mouth, chew it for a long time, and then tell your girlfriend that you''ve been reading too many Star Trek books

#pragma DWIM // Do What I Mean!
~ Mad Keith ~
**I use Software Mode**

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OK. I''ll play. How can quaternions be used in a six-dimensional world? You get undefined results.

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well, they aren't TRUE quaternions, that would be rediculous. They're pseudo-quaternions, about which you can find out more in my thesis which can be found here . The gist of it is that it turns out if you examine the hyper-super-symmetry of the transformation the results from solution of the corresponding inifinite-order differential equation, it works out quite nicely to be an approximation to the transformation in 6 dimensions.

Edited by - Kris Hauser on 4/26/00 10:01:37 PM

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Why, to encode the Plucker space visibility calculations of course!



#pragma DWIM // Do What I Mean!
~ Mad Keith ~
**I use Software Mode**

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C''mon, Plucker''s overkill in games... unless, of course, you''re planning on implementing the Greenstein-Hiroyuki space-time graviton flux approximator. But anyways, the specular component is rather easy to find - take the quaternion, approximate it in 7D and iterate T=dXdYdU+lDZ until it converges, then rotate the basic 6D projection plane to match the hyper-light.

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I actually think that an approximating elliptical curve with weighted averaging would be faster.
*lol*
this is getting silly.


#pragma DWIM // Do What I Mean!
~ Mad Keith ~
**I use Software Mode**

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