Curvature of Catmullrom spline

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Discussion Overview

The discussion revolves around the calculation of curvature using Catmull-Rom splines, particularly in the context of interpolating data points. Participants explore the implications of the spline's continuity properties on the accuracy of curvature calculations and consider alternative spline types.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) questions the reliability of using Catmull-Rom splines for curvature calculations due to their C1 continuity, which implies that the second derivative is not continuous.
  • The OP notes that curvature is defined as y"/(1+y'^2)^(3/2) and expresses concern about incorrect curvature values at certain points.
  • One participant suggests that a B-spline might be a better alternative, as they are piecewise cubic and have continuous second derivatives at knots.
  • Another participant reiterates the point about B-splines having continuous second derivatives, emphasizing their potential advantages over Catmull-Rom splines.

Areas of Agreement / Disagreement

Participants express differing views on the suitability of Catmull-Rom splines for curvature calculations, with some advocating for B-splines as a potentially better option. The discussion remains unresolved regarding the best approach for the OP's specific needs.

Contextual Notes

The discussion highlights the limitations of Catmull-Rom splines in terms of curvature calculation due to their continuity properties, but does not resolve the implications of these limitations or the specific conditions under which different spline types may be preferable.

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?
 
Last edited by a moderator:
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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