damian@sol4.cs.monash.edu.au (Damian Conway) (06/20/91)
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