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From: news@cit-vax.Caltech.Edu (Usenet netnews)
Newsgroups: comp.graphics
Subject: Re: Tough geometry problem
Message-ID: <1231@cit-vax.Caltech.Edu>
Date: Mon, 24-Nov-86 15:46:39 EST
Article-I.D.: cit-vax.1231
Posted: Mon Nov 24 15:46:39 1986
Date-Received: Mon, 24-Nov-86 22:35:20 EST
References: <13111@glacier.ARPA>
Reply-To: jon@cit-vax.UUCP (Jon Leech)
Organization: California Institute of Technology
Lines: 35

Organization : California Institute of Technology
Keywords: superquartics, computational geometry, vector calculus
From: jon@oddhack.Caltech.Edu (Jon Leech)
Path: oddhack!jon

In article <13111@glacier.ARPA> jbn@glacier.ARPA (John B. Nagle) writes:
>     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.  Imagine a display of a
>sphere attached to a "squareness" control; as you turn up the "squareness",
>the corners become more square.  An intermediate figure looks like a TV
>screen, and higher values look like later model TV screens; eventually
>one gets a cube.  
>...
>     That's the basic figure.  One is then allowed three distortions of
>the superquartic; stretching, bending (in a circular sense only) and
>tapering.  All of these can be modelled as simple distortions of the
>metric.  The resulting distored primitives can then be combined, using
>the obvious operations of union and difference (which latter operation
>corresponds to making a "hole" in something) to make complex objects.

	You may be interested in two papers by my advisor, Alan Barr:

	'Superquadrics and Angle-Preserving Transformations', 
	IEEE Computer Graphics & Applications, Volume 1 #1 1981

	'Global and Local Deformations of Solid Primitives'
	Computer Graphics, Volume 18 #3, July 1984

	These do not address the issue of finding distance between
primitives but you may find other material of interest therein.

    -- Jon Leech (jon@csvax.caltech.edu || ...seismo!cit-vax!jon)
    Caltech Computer Science Graphics Group
    __@/