"Bald Eagle" <cre### [at] netscapenet> wrote:

> So I am a lot less frustrated, and a lot happier now that I'm managed to get
> that all set down into working code.

Well,
I am back to what I was struggling with in my first attempt:
orienting and placing the Villarceau circle equivalents.

To my knowledge, there is no clear documentation about where the centers lie, or
how to calculate the locus of all the centers, or if there is another parameter
like c, which lies along the a semimajor axis, but that lies along the b
semiminor axis.  There is also a movement in y.

My initial attempt involved modeling a torus, inverting it to a cyclide, and
then finding the tangent points of the Villlarceau circles on the torus,
inverting those, and finding the centers.  But orienting them is another step
entirely.

And although I love my circles almost as much as Archimedes, I'm getting a bit
frustrated going around and around this one.

Perhaps someone has a personal insight, a literature reference, an internet
link, or something that an AI actually gets right - to put me on the path to
solving this last critical step.

- BE

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