# Curvature of Catmullrom spline

1. Jul 20, 2012

### gingaz

Hello guys!

I'm stuck with this for a 4th day now..

I have a set of data and for every data point I want to calculate a curvature. In order to do that I use Catmullrom spline to interpolate points and get derivatives f' and f". Curvature is defined as y"/ (1+y'^2)^3/2.

However, at some points calculated curvature is incorrect.

It is known, that Catmullrom is C1 continuous, so f" is NOT continuous.
I have read somewhere, that f' means slope and f" - curvature.

My question would be: for curvature calculations, can I rely on Catmullrom spline if it is only C1 continuous (not C2)?
Or should i use NURBS? Any easier approach?

Thank you very much!

Ginga

Last edited: Jul 20, 2012
2. Jul 20, 2012

### haruspex

Does http://tom.cs.byu.edu/~455/bs.pdf [Broken] help?

Last edited by a moderator: May 6, 2017
3. Jul 20, 2012

### HallsofIvy

Probably not. B-spline are piecewise cubic and the second derivative is always continuous at knots, unlike Catmullrom splines.

4. Jul 21, 2012

### haruspex

The OP appeared to be open to the possibility of using different splines, so I was suggesting B-splines.