Curvature of Catmullrom spline

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

haruspex

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

HallsofIvy

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

haruspex

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