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From: trainor@lanai.cs.ucla.edu (Vulture of Light)
Newsgroups: comp.graphics
Subject: Re: Superquadrics
Message-ID: <10919@shemp.CS.UCLA.EDU>
Date: 5 Apr 88 17:58:17 GMT
References: <8340@agate.BERKELEY.EDU>
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Reply-To: trainor@lanai.UUCP (Vulture of Light)
Organization: UCLA Computer Science Department
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In article <8340@agate.BERKELEY.EDU> doug@mica.berkeley.edu (Doug Merritt) writes:
>A few years ago I read a paper by a guy at Stanford who came up
>with an interesting model that allowed two way transformations:
>model => rendered image, and digitized image => model. It was
>based on "superquadrics"; his paper did not adequately define these.
>
>Can someone explain "superquadrics", or give an easily accesible reference
>that does?

Just for the other people, this is a computer vision system whose model
of the world is comprised of superquadrics, akin to earlier systems
that used, say, generalized cylinders.

Superquadrics are fun, easy, and are a generalization of quadric surfaces.
All you do is fiddle with exponents in the equations!  To illustrate the
concept, take a circle:

            _   [             ]   [    1        ]
            X = [ cos (theta) ] = [ cos (theta) ]
                [             ]   [    1        ]
                [ sin (theta) ]   [ sin (theta) ]

And to make it "super" just paramaterize the exponent:

            _   [    r        ]
            X = [ cos (theta) ]
                [    r        ]
                [ sin (theta) ]

Play with "r" and you get all sorts of cool shapes.  Now just do this
with the quadrics (too messy in ascii...).  If you want to find out 
more I suggest reading:

    Barr, A.H. ``Superquadrics and Angle-Preserving Transformations,''
    IEEE Computer Graphics and Applications, Vol. 1, No. 1, 1981.