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From: markv@gauss.Princeton.EDU (Mark VandeWettering)
Newsgroups: comp.graphics
Subject: Re:  ray tracing superquadrics
Keywords: raytracing
Message-ID: <3684@idunno.Princeton.EDU>
Date: 30 Oct 90 15:22:52 GMT
References: <28825@boulder.Colorado.EDU> <1990Oct29.150528.11257@eye.com>
Sender: news@idunno.Princeton.EDU
Reply-To: markv@gauss.Princeton.EDU (Mark VandeWettering)
Organization: Princeton University
Lines: 28

>>  "Robust Ray Tracing with Interval Arithmetic", by Don Mitchell, pp.
>>  68-74 in the Proceedings of Graphics Interface '90, Canadian Infor-
>>  mation Processing Society (Toronto), 1990.
>
>    Interesting paper, though I admit to not having tried its method yet.
>Looks like a great general method for superquadrics and whole families of
>surfaces.  My favorite paper of this proceedings.

	Very interesting paper, but I believe that the convergence of the 
	method is quite slow, even slower than bisection.  I coded up 
	a version of it for the MTV raytracer, and was testing it out when
	it was clear it was converging VERY slowly.  If anyone has some
	hints, or wants to discuss this further, send me some email.

	The reason I was interested in this scheme is that it would allow
	you to trace non-linear rays (rays could be generalized to space 
	curves) which would allow more generic transformations of objects
	(ala Al Barr).

	You can use geometrical properties of the superquadric to figure
	out intersections.  There can be at most two intersections in any 
	octant of the superquad, so a primitive method would be to handle
	each octant separately and then use some favorite numerical method
	(Newtons or bisection) to home in on the roots.

Mark (markv@acm.princeton.edu)
Mark VandeWettering
markv@acm.princeton.edu