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)

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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)

1. Have a look at

https://github.com/LeForgeron/povray/wiki/Splines



2. linear, quadratic and cubic are "regular" splines, of Bézier.

https://en.wikipedia.org/wiki/B%C3%A9zier_curve


So what is your true Bézier spline ?

In lathe, the bezier_spline is made of segments of spline, point 4 of segment N must
be identical to point 1 of segment N+1
but otherwise there is no requirement of continuity of derivative at that point.
Points 2 & 3 of each segments are only control points and are only involved in one
single segment.

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> 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)
>
>
>
>

For the "natural" spline, it looks like it's similar to the cubic 
spline, but continuing up to the first and last point with curve been 
out of controll at those points.

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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.

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clipka <ano### [at] anonymousorg> wrote:

So, If I'm interpreting that correctly,

1. the cubic spline is a cubic spline of the CR type.
2. the natural spline is a cubic spline of another.
3. bezier_spline cannot be use in a spline or sphere sweep declaration

Thanks

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Am 06.03.2016 um 22:45 schrieb Bald Eagle:
> clipka <ano### [at] anonymousorg> wrote:
> 
> So, If I'm interpreting that correctly,
> 
> 1. the cubic spline is a cubic spline of the CR type.
> 2. the natural spline is a cubic spline of another.

That is correct.

> 3. bezier_spline cannot be use in a spline or sphere sweep declaration

That's correct as well. It's an inconsistency, and it's /somewhere/ on
the agenda to be resolved, but at present that's how it is.

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clipka <ano### [at] anonymousorg> wrote:

> > 3. bezier_spline cannot be use in a spline or sphere sweep declaration
>
> That's correct as well. It's an inconsistency, and it's /somewhere/ on
> the agenda to be resolved, but at present that's how it is.

Right on.   Not complaining.
Until it's resolved, I always have
http://news.povray.org/web.55fe784eb76273e03fda44f40%40news.povray.org
and
http://www.joshuarenglish.com/cyclopedia/bezier.html

I was just trying to clarify what the status of the splines was.
Thanks

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