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From: uad1077@dircon.uucp
Newsgroups: comp.graphics
Subject: Re: Lunar Distortions
Keywords: raytracing, distortions.
Message-ID: <1990Nov20.204506.27184@dircon.uucp>
Date: 20 Nov 90 20:45:06 GMT
References: <27332@cs.yale.edu> <1097@shakti.ncst.ernet.in>
Organization: The Direct Connection, UK
Lines: 42

In article <1097@shakti.ncst.ernet.in> dilip@ncst.ernet.in (Dilip Khandekar) writes:
>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.)
>>  Can anyone out there prove this conjecture right or wrong, or demonstrate
>>some nice workaround?
>>
>
>   I also encountered the same problem and would be interested in any method
>or projection-model which circumvents this problem. If the pin-hole camera
>model is not a good model for the human eye-brain system then is there any
>other model which is more accurate?

YOu might like to experiment with mimcking the disorting effect of
camera lenses.  Lenses which behave like renderers are very expensive,
and are called something like `flat-plane lenses' (surprise).  Ordinary
lenses exhibit distortion (it's called that in optics books).  Positive
distortion makes flat squares look like pillowcases, negative makes
them look weird.  A way to model positive distortion is to move points
in the picture closer to the centre.  A point that starts off at
(r, theta) on the image plane in polar co-ordinates would move to
(r', theta) where, in two popular approximations:
r' = r (1 - C * r * r)
r' = r * cos (C * r)
for appropriate (small) constants C.  Of course, I was working with
images.  In a ray-tracer, you would distort the directions of the rays
by using the inverse transformation to splay the rays from the camera
outwards.

NO guarantees that it will fix the problem, but it is not a million
miles away from this discussion....

-- 
Ian D. Kemmish                    Tel. +44 767 601 361
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