Path: utzoo!utgpu!watserv1!watmath!att!att!bu.edu!rpi!uupsi!eye!erich
From: erich@eye.com (	Eric Haines)
Newsgroups: comp.graphics
Subject: Re:  ray tracing superquadrics
Summary: some comments
Keywords: raytracing
Message-ID: <1990Oct29.150528.11257@eye.com>
Date: 29 Oct 90 15:05:28 GMT
References: <28825@boulder.Colorado.EDU>
Sender: Eric Haines
Reply-To: erich@eye.com (Eric Haines)
Organization: 3D/Eye Inc., Ithaca, NY
Lines: 44

Rick gave a good answer to a request for information on how to ray trace
superquadrics.  Here are some comments on his references.

In article <28825@boulder.Colorado.EDU> speer@boulder.Colorado.EDU (Rick Speer) writes:
>
>  "An Introduction to Ray Tracing", by Roman Kuchkuda, pp. 1039-60 in
>  Theoretical Foundations of Computer Graphics and CAD, R. A. Earnshaw,
>  Ed., Springer-Verlag, 1988.
>
>is a good introduction to the tracing of superquadrics. In addition to
>the usual overview material it gives actual source code, in C.

    This code can be found in electronic form in Craig Kolb (& Roman
Kuchkuda's and others) RayShade ray tracer.  It works for the simple test
cases I tried, but I wouldn't bet my life on its stability for concave
superquadrics.  The site weedeater.math.yale.edu [130.132.23.17] has RayShade
available via anonymous FTP.


>  "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.


>Finally, this thesis-
>
>  "Implementation of a Ray-Tracing Algorithm for Rendering Superquadric
>  Solids", Bruce Edwards, Masters Thesis and Technical Report TR-82018,
>  Rensselaer Polytechnic Institute (Troy, NY), December 1982.
>
>probably goes into more detail than either of the papers mentioned
>above.

    My recollection of this thesis (I wanted to add superquadrics to the ray
tracer when I first got to Cornell in 1983) is that there is less than a page
on actually intersecting the beasts!  Essentially, it says something like "use
Newton's method to find the roots" and gives a reference.  The reference says 
"private discussions with Al Barr".  Not exactly revealing.

Eric Haines, erich@eye.com