Am 06.03.2016 um 18:10 schrieb Le_Forgeron:
> Le 06/03/2016 17:31, Bald Eagle a écrit :
>> So, there are cubic and "natural" splines that can be used independently, and
>> then there's the bezier spline that seems to only be invoked with lathe and sor.
>>
>> Is there a true bezier spline that can be used as a regular spline?  Is it the
>> same as natural spline?  (I would think that given the different name, the
>> answer is no)
> 
...
> 
> 2. linear, quadratic and cubic are "regular" splines, of Bézier.
> 
> https://en.wikipedia.org/wiki/B%C3%A9zier_curve

Actually, no -- Bezier splines are a particular sub-type of cubic
splines, not vice versa.

The mathematical terms "linear spline", "quadratic spline" and "cubic
spline" refer to the type of functions that make up the spline's
individual segments, in this case 1st, 2nd and 3rd order polynomials
respectively.

Terms like "natural spline", "Bezier spline" or "Catmull-Rom spline" do
not refer to the type of underlying functions, but to specific schemes
of how these functions are parameterized via a set of control points.


It is true, however, that every possible cubic spline can be represented
as a Bezier spline.


As for POV-Ray's "cubic_spline", that's actually a misnomer insofar as
it's not the only cubic spline supported by POV-Ray;
"catmull_rom_spline" would have been a more accurate name.

Post a reply to this message