Am 03.05.2013 11:36, schrieb Kenneth:

> This cubic spine business has been causing problems with the sphere sweep for
> years (and apparently continues to do so.) At this point, I would venture an
> opinion: get rid of that spline. *If* there is a suitable replacement. (I'm no
> mathematician, so I don't know such things--not sure I even want to know! So
> this opinion might be a very naive one.)

There is no suitable replacement.

There are various levels of "smoothness" a spline may provide: Linear 
splines provide gradual change of position, but the direction changes 
abruptly at certain points; quadratic splines also provide a gradual 
change of direction, but the rate of change in direction (the 
"acceleration", so to speak) changes abruptly. Cubic splines also allow 
for gradual change of this acceleration.

There /are/ other splines that do allow the same level of smoothness; 
however, fun fact is that unless you're choosing some very exotic (and 
mathematically even more challenging) spline, they're all cubic (aka 3rd 
order polynomial) splines at heart, with just a different way of 
parameterizing them via a series of points.


That said, I suspect that all the problems with the cubic splines 
primitive in POV-Ray are implementation issues rather than inevitable 
mathematical problems.

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