[Octave-bug-tracker] [bug #45295] Division by Zero in 2nd derivative of NURBS surface

[Carlo de Falco]

Follow-up Comment #4, bug #45295 (project octave):

Hi,

nrbderiv is based on bspderiv that implements
the algorith A3.3 on page 98 of the book:

Piegl, Les and Tiller, Wayne
The Nurbs Book
Springer, New York, 1997 (2nd ed.) 

which assumes the input knot vector has at most
p repetitions per knot, p being the degree, 
corresponding to C0 continuity.

therefore you can compute the first derivative of a C0
curve but not its second derivative.

On the other hand, I believe that, if you take the C(-1) curve
obtained by performing the first derivative,  
the knots and control points of each knot span
should define a Bezier curve. 

So if you have a BSpline curve you should be able to
compute the second derivative by cycling over each knotspan
and taking the local knotvector.

I am not sure how this works for rational BSplines, 
maybe Rafael can comment on this.

c. 

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