scott <sco### [at] scottcom> wrote:


> Wait... the two spheres are rotated different amounts:
>
> sphere{ <X, T1, Z1>, T1 pigment {Blue} rotate -y*Tooth1*AngularSpacing}
> sphere{ <X, T1, Z2>, T1 pigment {Blue} rotate -y*Tooth2*AngularSpacing}

Correct.   Because if you plot the involutes, one curves up, and the other
curves down.  I already (after 40 minutes worth of trigonometric algebra)
established where they cross the base circle, and then after some more searching
and some luck, did the same with the addendum circle.

The second sphere gets rotated by Tooth2, which is just Tooth1+0.5.  Therefore
it gets rotated above/past the other involute and so as it curls own and the
first involute curls up, they will eventually intersect.   As Jerome pointed
out, since these are "transcendental functions" - they will have an infinite
number of intersections, but I'm only interested at the first (at the moment
;).

I do think that his suggestion of "tracking" the curves and determining the
intersection from a change of sign will work - but that looks more "practical"
than mathematical and elegant.   But maybe that's the reality of how it's done.
 I'll play with it some and see where I get, but that could take all day
again...

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