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From: leech@homer.cs.unc.edu (Jonathan Leech)
Newsgroups: comp.graphics
Subject: Re: Cones and Cylinders
Message-ID: <16530@thorin.cs.unc.edu>
Date: 4 Oct 90 14:52:53 GMT
References: <15822@rouge.usl.edu>
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Reply-To: leech@homer.cs.unc.edu (Jonathan Leech)
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In article <15822@rouge.usl.edu> pcb@cacs.usl.edu (Peter C. Bahrs) writes:
>Suppose I am modeling cones and cylinders algebraically and parametrically.
>How can I draw these?	I do not want to do ray tracing.  Is there a common
>technique(s) that will rendering these things without having to make a
>zillion polygons?

    See Jim Blinn's wonderful short paper, ``The Algebraic Properties
of Homogeneous Second Order Surfaces.'' This describes direct
rendering of arbitrary quadrics (synopsis: represent the surface as a
homogeneous matrix; similarity transform the matrix for modelling,
viewing, and perspective; find screenspace boundaries of the quadric;
solve the resulting equation for Z-depth and normal vector at each
pixel).

    I believe this appeared in SIGGRAPH course notes in '84 or '85; my
copy is a draft so I'm not sure which course.

--
    Jon Leech (leech@cs.unc.edu)    __@/
    "We've already learned something we didn't know and that's fun!"
	- Dr. James Westphal on the first Hubble photo