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[Octave-bug-tracker] [bug #45295] Division by Zero in 2nd derivative of
From: |
Carlo de Falco |
Subject: |
[Octave-bug-tracker] [bug #45295] Division by Zero in 2nd derivative of NURBS surface |
Date: |
Mon, 15 Jun 2015 11:43:25 +0000 |
User-agent: |
Mozilla/5.0 (Macintosh; Intel Mac OS X 10.9; rv:38.0) Gecko/20100101 Firefox/38.0 |
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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