Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!samsung!munnari.oz.au!bruce!damian From: damian@sol4.cs.monash.edu.au (Damian Conway) Newsgroups: comp.graphics Subject: Nearest point on an ellipsoid Keywords: help! Message-ID: Date: 5 Jun 91 05:26:26 GMT Sender: news@bruce.cs.monash.OZ.AU Distribution: comp Lines: 33 This is not an exercise. I am not a student. Is there an analytical solution to either of these (equivalent) problems. They both sound very simple (even trivial) to solve, but the math soon begins to snarl and bare its claws: Version 1: Given a point P = and an ellipsoid with half-axes (A,B,C), find the point Q on the ellipsoid which is nearest P. Version 2: Given a point P, find the point Q on an ellipsoid such that the normal at Q passes through P. Why do I need this? Q marks the brightest point on a diffuse ellipsoid illuminated from P. I need to find that point in order to do fast rendering of objects. BTW: Please don't reply: 6 5 4 3 2 "Sure, you just solve K + iK + jK + kK + lK + mK + n" (Unless _you_ can solve it, of course :-) Any assistance greatly appreciated (and gratefully credited). damian ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ who: Damian Conway email: damian@bruce.cs.monash.edu.au where: Dept. Computer Science phone: +61-3-565-5184 Monash University quote: "A pessimist is never disappointed." Clayton 3168 AUSTRALIA