Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!asuvax!ncar!tank!cps3xx!flynn
From: flynn@pixel.cps.msu.edu (Patrick J. Flynn)
Newsgroups: comp.graphics
Subject: Re: Superquadrics
Message-ID: <5991@cps3xx.UUCP>
Date: 11 Jan 90 19:59:55 GMT
References: <438@fsu.scri.fsu.edu>
Sender: usenet@cps3xx.UUCP
Reply-To: flynn@pixel.cps.msu.edu (Patrick J. Flynn)
Organization: Perestroika Pixels
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In article <438@fsu.scri.fsu.edu> prem@geomag.gly.fsu.edu (Prem Subrahmanyam) writes:
>     One of the new shapes that [DBW_render] supports is called a 
>     superquadric.  Now, I've attempted to look up info in IEEE CG&A about
>     them and found out that the first issue ever to come out had an article
>     about these, however, our library does not have this issue.  So, can   
>     anyone point out another source for info about these (the full equation
>     used for them, and how to do a ray-superquadric intersection (complete
>     with normal calculation for a given point))?  Thanks in advance......

The computer vision community has been using superquadrics for
representation for a few years.  Alexander Pentland developed a solid
modeler (SuperSketch) around them, and recent papers have dealt
with fitting them to 3D data.

Parametric form for a point on a superquad.:

Let c(e,x) = (cos x)^e
    s(e,x) = (sin x)^e

(x(u,v),y(u,v),z(u,v)) = ( c(e1,u)*c(e2,v) , c(e1,u)*s(e2,v), s(e1,u) )

u and v are parameters of latitude and longitude.  The parameters e1 and
e2 control the shape of the primitive obtained when you sweep u and v
over the sphere.  The normal can be obtained by differentiation.

Ref:
Pentland, A.P., Perceptual Organization and the Representation of
Natural Form, Art. Intell. J. 28: 293-331, 5/86.

Fitting problems have been attacked by Ruzena Bajcsy and colleagues at
U. Pennsylvania, Terry Boult and Students at Columbia, and others.
If you're interested, check out Proceedings of the first and second
Int. Confs. on Computer Vision (IEEE), the AAAI workshop on Spatial
Reasoning and Multisensor Fusion (1987),  and the recent IEEE workshop
on 3D scene interpretation.
--
Patrick Flynn, CS, Mich. State U., flynn@cps.msu.edu