"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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