Am 02.05.2017 um 22:58 schrieb Kenneth:
> clipka <ano### [at] anonymousorg> wrote:
> 
>>
>> Mathematically, "natural splines" are only marginally different from
>> what POV-Ray calls "cubic splines": Both are 3rd order polynomial
>> splines... [snip]
> 
> Thinking back to the v3.62 days, I'm ashamed to admit that you probably
> explained this long ago-- and probably in response to a similar post by me! Mea
> culpa.

I'm an explainer by nature. It's difficult to tire me out on
re-iterating stuff I've explained over and over again. Ask me again
tomorrow, and I'll explain once more.

> Since both 'natural splines' and 'cubic splines' ARE both 3-rd order, I'm
> willing to guess(!) that the problem is not in POV-ray's mathematical
> implementation of the cubic spline, but rather in some kind of co-dependent
> problem with the 'difference-ing' operation. Based on nothing but my nutty
> intuition ;-)

There _is_ (or so I think by now) a fundamental flaw of that infamous
"FS#81 Patch" that specifically screws up difference ops (and other
cases where the interior of the sphere sweep is exposed). However, the
issue the patch was originally intended to fix does hit 3rd order
splines even without a difference op. (In a nutshell, any 3rd order
sphere sweep will be screwed up anywhere the spline runs approximately
perpendicular to the viewing direction.)

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