

Cousin Ricky <ric### [at] yahoocom> wrote:
> That is wrong! Something didn't look right about the curve, so I went
> back and doublechecked the Bézier theory. The correct solution is this:
>
> SphereSweep_Approx
> ( SSWP_BEZIER_SPLINE,
> array { P1, P2 * 2/3 + P1 / 3, P2 * 2/3 + P3 / 3, P3 },
> array { Line, Line, Line, Line}, 100, 0
> )
>
> I will post an example illustration in p.b.i.
Without picking through the underlying code of the spheresweep, I'll just say
that the curve indeed looks correct, but (now, to me,)
array { P1, P2 * 2/3 + P1 / 3, P2 * 2/3 + P3 / 3, P3 }
does not.
Since a Bezier spline uses some fraction of all of the control points across the
entire spline (except for the absolute endpoints), shouldn't there be a P3 and a
P1 term in there  or does that somehow get (partially) accounted for under the
hood?
I was too tired to work out the correct derivatives of the Bernstein polynomial
terms the other day, and I have things to do before I will have a chance to look
into this any further.
Just asking to clarify and triple check. ;)
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