

On 20200908 1:36 PM (4), Bald Eagle wrote:
> 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 don't know what you mean; all 3 terms are in the array. The 2nd term
is 2/3 of the way from P1 to P2, and the 3rd term is 2/3 of the way from
P3 to P2.
Under the hood, the formula draws from all 4 control points, so each of
the 3 quadratic points gets its input.
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