Curvature of Catmullrom spline

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The discussion centers on the challenges of calculating curvature using Catmull-Rom splines, which are C1 continuous but not C2 continuous, leading to incorrect curvature values at certain points. The curvature formula relies on the second derivative, which is not continuous in Catmull-Rom splines, raising concerns about their reliability for this purpose. Participants suggest considering alternative spline methods, such as B-splines, which maintain continuity of the second derivative at knots. The original poster is exploring whether to stick with Catmull-Rom or switch to NURBS or B-splines for more accurate curvature calculations. Ultimately, the choice of spline affects the accuracy of curvature computations in the given data set.
gingaz
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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
 
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Does http://tom.cs.byu.edu/~455/bs.pdf help?
 
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Probably not. B-spline are piecewise cubic and the second derivative is always continuous at knots, unlike Catmullrom splines.
 
HallsofIvy said:
Probably not. B-spline are piecewise cubic and the second derivative is always continuous at knots, unlike Catmullrom splines.
The OP appeared to be open to the possibility of using different splines, so I was suggesting B-splines.
 

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