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From: aaa@pixar.UUCP (Tony Apodaca)
Newsgroups: comp.graphics
Subject: Re: Tough geometry problem
Message-ID: <280@pixar.UUCP>
Date: Mon, 24-Nov-86 16:38:00 EST
Article-I.D.: pixar.280
Posted: Mon Nov 24 16:38:00 1986
Date-Received: Tue, 25-Nov-86 20:43:28 EST
References: <13111@glacier.ARPA>
Reply-To: aaa@pixar.UUCP (Tony Apodaca)
Organization: Pixar -- Marin County, California
Lines: 27
Keywords: superquadrics, computational geometry, vector calculus
Summary: Ask the original author.

In article <13111@glacier.ARPA> jbn@glacier.ARPA (John B. Nagle) writes:
>     I need to calculate the distance between two objects described using
>the superquartic primitives proposed by Pentland (in SRI Tech Note 357).

>     Pentland has an extension to this.  Instead of limiting the objects to
>quartics, (things describable with exponents no larger than 2), he uses
>superquartics, which allow bigger exponents.

	I don't have SRI Tech Note 357, but I *think* I know what you're
talking about, since it sound's awfully familiar.
	Things which are "describable with exp no larger than 2" are QUADRICS.
The extensions are therefore called SUPERQUADRICS, and are due to Al Barr,
formerly of Rensselar Polytechnic Institute, now of Cal Tech (he developed
them as part of his PhD research) (credit where credit is due).  Al's work
is a 3-D extension of 2-D superquadric work done by an earlier mathematician
whose name escapes me at the moment.  The key is not "bigger" exponents,
but "any" exponents (specifically, real numbers).  Squareness is reached at
the limit of exp -> 0, not exp -> infinity.
	These shapes are fun, since they model cubes, spheres, cones,
cylinders, ellipsoids as special cases, and do dice, pillows, "jax",
helixes etc etc etc in the more general forms.

	References: "Superquadrics and Angle-Preserving Transformations",
IEEE Computer Graphics and Applications, Vol 1, No 1, January 1981.
	"Global and Local Deformations of Solid Primitives", Proceedings
of SIGGRAPH 1984.
	etc.