Path: utzoo!attcan!uunet!wuarchive!zaphod.mps.ohio-state.edu!ncar!boulder!speer
From: speer@boulder.Colorado.EDU (Rick Speer)
Newsgroups: comp.graphics
Subject: Re:  ray tracing superquadrics
Keywords: raytracing
Message-ID: <28825@boulder.Colorado.EDU>
Date: 28 Oct 90 21:46:19 GMT
Sender: news@boulder.Colorado.EDU
Organization: University of Colorado, Boulder
Lines: 65
Originator: speer@anchor.colorado.edu

In Article 14754 of comp.graphics, ojt@cs.brown.edu (Oren J. Tversky)
writes-

    ----------------------------------------------------------------
    From: ojt@cs.brown.edu (Oren J. Tversky)
    Newsgroups: comp.graphics
    Subject: ray tracing super quadrics
    Date: 28 Oct 90 01:21:00 GMT

    To whom it may concern-

     I have been thinking over ways to ray trace super quadrics (including
    super-toroids).  Despite possessing an implicit form, I couldn't come up
    with any obvious method for doing this.  I would be interested in any method
    anybody has of accomplishing this.

    If anyone has any ideas, please mail me at:

    ojt@cs.brown.edu
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I've sent mail to Oren but am posting my reply too in case others are
interested.

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Oren,

Here's some material that may be of assistance. The following paper-

  "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 paper-

  "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.

focuses in particular on root-finding when intersecting a ray with an
implicit surface. Mathematical and pictorial examples of tracing super-
quadrics are given, along with data on the time-cost of intersections
(when run on a SPARCstation). There's also some discussion of using the
method for CSG.

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.

Hope this helps.

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| Rick Speer               | "Can I try another world?" - Question overheard |
| speer@anchor.colorado.edu|  from a guy trying out the system at the VPL    |
|                          |  Research (virtual reality) booth at Siggraph.  |
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