What I mean is:

The "usual" array is {P1, P2, P3, P4}

The initial suggestion was to do:
> >      array { P1, P2, P2, P3 },
(seemed totally reasonable to me, and seemed to give good results)

Which is just P3 = P2.

Now you're saying:
>    SphereSweep_Approx
>    ( SSWP_BEZIER_SPLINE,
array {
P1,
P1 * 1/3 + P2 * 2/3,
P2 * 2/3 + P3 * 1/3,
P3 },

So what I'm asking is: why aren't ALL 3 control points appearing as terms in the
equations for each of the array elements?

I'm not doubting that the correction you're proposing is right, I'd just like
you to articulate, for my own benefit, why, in light of the corrections to the
2nd and 3rd elements, the first and last elements are still solitary control
points, and why the second doesn't have a term for P3, and the third doesn't
have a term for P1.

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