Path: utzoo!attcan!uunet!jarthur!usc!ucsd!hub.ucsb.edu!ucsbuxa!3003jalp From: 3003jalp@ucsbuxa.ucsb.edu (Applied Magnetics) Newsgroups: comp.graphics Subject: Re: Lunar Distortions Message-ID: <7297@hub.ucsb.edu> Date: 19 Nov 90 16:10:47 GMT References: <27332@cs.yale.edu> Sender: news@hub.ucsb.edu Lines: 28 In article <27332@cs.yale.edu> musgrave-forest@CS.YALE.EDU (F. Ken Musgrave) writes: > 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.) > Seems that this is a version of the sphere-to-plane mapping problem, and >therefore inadmissible to a non-distorting solution. > Can anyone out there prove this conjecture right or wrong, or demonstrate >some nice workaround? A stereographic projection maps circles on the sphere to circles in the plane (counting straight lines as degenerate circles). The inevitable distorsion is an increased magnification toward the edges of the scene. The distorsion is extreme on a world map, but it might be OK for a rendering if your wide angle stays below 180 degrees. (Never seen one myself, so I don't know.) If the distorsion is too large, look for conformal mappings. A conformal mapping would transform _small_ circles to circles. The most general conformal mapping from the sphere to the plane is a stereographic projection followed by an analytic transformation of the complex plane. Read the Shaum book on complex variables, do all the problems and start tinkering :-). Pierre Asselin, R&D, Applied Magnetics Corp.