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Curvature of Catmullrom spline

  1. Jul 20, 2012 #1
    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. jcsd
  3. Jul 20, 2012 #2

    haruspex

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    Does http://tom.cs.byu.edu/~455/bs.pdf [Broken] help?
     
    Last edited by a moderator: May 6, 2017
  4. Jul 20, 2012 #3

    HallsofIvy

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    Probably not. B-spline are piecewise cubic and the second derivative is always continuous at knots, unlike Catmullrom splines.
     
  5. Jul 21, 2012 #4

    haruspex

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