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From: rick@pangea.Stanford.EDU (Rick Ottolini)
Newsgroups: comp.graphics.visualization
Subject: Re: surface rendering of fuzzy cloud
Message-ID: <1991May2.204040.18691@leland.Stanford.EDU>
Date: 2 May 91 20:40:40 GMT
References: <73521@eerie.acsu.Buffalo.EDU> <1991Apr30.182711.2223@fido.wpd.sgi.com> <1991May1.205240.28361@bnlux1.bnl.gov>
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In article <1991May1.205240.28361@bnlux1.bnl.gov> bstewart@bnlux1.bnl.gov (Bruce Stewart) writes:
>In article <1991Apr30.182711.2223@fido.wpd.sgi.com> robert@sgi.com writes:
>>In article <73521@eerie.acsu.Buffalo.EDU>, okeefe@cs.Buffalo.EDU (Paul O'Keefe) writes:
>>|> 
>>|> In article <2594@amethyst.math.arizona.edu>, winfree@.math.arizona.edu (Art Winfree) writes:
>>|> |> 
>>|> |> Does anybody know how to render the surface of a fuzzy 3D cloud of
>>|> |> data points? The "cloud" is actually supposed to be a 2D surface, but
>>
>>For some time I've wanted to construct and visualize the surface of a
>>chaotic attractor, given an unordered list of points on the surface.

Many of the current graphics representation techniques using the concept
of a lighting model to project an illusion of 3-D.  The lighting models
are either reflective- a light source in front of the object that reflects
to the viewpoint- or transmissive- goes through an object of various degrees
of opacity.  Now consider the reflective lighting model.  It requires some
idea of surface tangency (the normal is the perpendicular).  A tangency is
only well-defined if the object is differentiable.  Many chaotic or fractal
datasets are not differentiable.  Graphics people cheat sometimes and assume
a smooth connection between sampled points for the purpose of rendering.