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Hi All,
Is there a reason why Bezier splines that can be used for lathes and prisms
can't be declared as splines?
On simular notes:
What is the difference between Natural and Cubic splines?
and
Sence POV doesn't like them as splines, can someone link me to the formual
for Bezier splines given 4 control points?
Thanks
JFMILLER
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In article <3df68bd5@news.povray.org>,
"jfmiller" <jfm### [at] hotmail com> wrote:
> Is there a reason why Bezier splines that can be used for lathes and prisms
> can't be declared as splines?
Historical reasons, mainly: these shapes were created long before the
spline feature was added to POV Ray, and use their own spline code.
--
Christopher James Huff <cja### [at] earthlinknet>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: chr### [at] tagpovrayorg
http://tag.povray.org/
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On Tue, 10 Dec 2002 19:50:14 -0500, jfmiller quoth:
> Hi All,
>
> Is there a reason why Bezier splines that can be used for lathes and
> prisms can't be declared as splines?
>
> On simular notes:
>
> What is the difference between Natural and Cubic splines?
Natural splines are a type of cubic spline where the entire spline is
controlled by all control points at once: changing one control point
affects the entire spline, with the greatest effect near the control
point. These splines produce the smoothest path (mathematically, they
have second-derivative continuity). Cubic splines are the same type of
cubic spline (Catmull-Rom) that is used in lathe and prism objects. Each
section of the spline is affected only by the four control points around
it, making it easier to control than the natural cubic spline, but not as
smooth.
--
Mark
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"Mark Wagner" wrote:
> On Tue, 10 Dec 2002 19:50:14 -0500, jfmiller quoth:
>
> > Hi All,
> >
> > Is there a reason why Bezier splines that can be used for lathes and
> > prisms can't be declared as splines?
> >
> > On simular notes:
> >
> > What is the difference between Natural and Cubic splines?
>
> Natural splines are a type of cubic spline where the entire spline is
> controlled by all control points at once: changing one control point
> affects the entire spline, with the greatest effect near the control
> point. These splines produce the smoothest path (mathematically, they
> have second-derivative continuity). Cubic splines are the same type of
> cubic spline (Catmull-Rom) that is used in lathe and prism objects. Each
> section of the spline is affected only by the four control points around
> it, making it easier to control than the natural cubic spline, but not as
> smooth.
>
>
In the "original" type of cubic interpolating splines (second order
derivative continuity) normally two types are used:
- the natural cubic spline: the second derivative in the first and last
control point equals zero; ask people to sketch by hand a nice curve
passing through a number of given points and in most cases you obtain a
curve where in the endpoints the curvature is zero!
- a clamped cubic spline: one has to give the value of the first
derivative in the first and last control point
In this sense "natural" is opposed to "clamped".
A Catmull-Rom cubic spline is an other type of cubic spline, determined
by other conditions
Herman
--
HermanS <url:http://cage.rug.ac.be/~hs>
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