Here's the problem: I want to modify truetype.c in the POV-Ray source to
allow text objects to be bent around a circle (without distorting the
characters). I would like to be able to specify either an inner radius
for the text or a desired total arc angle. The characters would be
separated by chords equal in length to the distance normally separating
each character, plus two more chords equal to half of the character
widths on each end.
Now when radius is specified, the total angle is easy to compute because
it's the sum of all the chord angles. Given the radius, those angles are
easy to find. But when the problem is reversed, only a total angle and
the individual chords are known, but so far I haven't figured out any
way to calculate the radius that fits. (It's pretty easy to determine
that there is such a radius, and the minimum possible value of that
radius is easy to find. But the exact value I can only think to find by
guessing.)
Without a radius given, finding the radius is awfully hard. Yet the
value of this solution is obvious, since being able to fill in a
specific arc angle will often be far more useful than fitting text
around a specific radius.
This seems like it should be a simple problem, so I've asked elsewhere,
but so far with no results. Since it came up in the course of my working
with POV-Ray, I figured I'd take a whack at asking here.

Lummox JR

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