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From: fournier@cs.ubc.ca (Alain Fournier)
Newsgroups: comp.graphics
Subject: Re: Lunar Distortions
Message-ID: <10507@ubc-cs.UUCP>
Date: 19 Nov 90 04:48:55 GMT
References: <27332@cs.yale.edu>
Sender: news@cs.ubc.ca
Organization: UBC Department of Computer Science, Vancouver, B.C., Canada
Lines: 22

In article <27332@cs.yale.edu> musgrave-forest@CS.YALE.EDU (F. Ken Musgrave) writes:
>
>  Here's another little question spawned by moon-renderings:
>
>  A very wide-angle view of a scene (i.e., a landscape), with a sphere
>(i.e., a moon) in an extreme corner of the image, sports one very distorted
>sphere in the image, when rendered using the standard virtual-screen model
>for ray tracing.  (See the cover of Jan. '89 IEEE CG&A for an example.)
>....

This one is easy (and frustrating to behold). The projection of a sphere
on a screen using standard viewing transformation is the intersection
of a cone (the eye at apex, with a circular cross section defined by the 
circle on the sphere tangent to the cone) and the plane of the window.
This (as known for two to three thousands of years) is a conic (ellipse -including
circle, parabola or hyperbola).
Most of the times in a CG picture it's an ellipse, and most of these times
it's close enough to a circle that the difference is not noticeable.
Ken got cases where it is. Why do we think it's not "normal"? I guess
because in real life we don't look at the "corners" of our field of vision,
and our retina is curved to begin with (just a guess here about the reasons).
bbb