Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!sdd.hp.com!spool.mu.edu!munnari.oz.au!bruce!sol4!damian From: damian@sol4.cs.monash.edu.au (Damian Conway) Newsgroups: comp.graphics Subject: Elusive ellipsoid equation escapes explicit expression Message-ID: Date: 19 Jun 91 21:41:16 GMT Sender: news@bruce.cs.monash.OZ.AU Distribution: comp Lines: 24 Still not a student, still not an assignment :-) Still unable to explicitly find the shortest distance to an ellipsoid :-( In fact, the problem seems to unavoidably reduce to the implicit 6th order polynomial I posted as one of the forms of the problem. Trigonometric, geometric and calculus methods all yield the same result. The conclusion is that the problem has no explicit solution in the general case, although special cases (sphere, spheroid) can be solved explicitly. However, that implicit 6th order equation responds well to various iterative root-finding techniques. My thanks to the many individuals around the world who devoted time to the question. My condolences to the many, many individuals who asked me to post _the_ solution when I found it. 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