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I came across this link when searching for an algorithm for spline smoothing. Though I understand basically what I have to do, I need further clarifications on the formula chosen for curvature quantification (the next formula after "To quantify the curvature we integrate the square of the second derivative").

Also any other examples, links are welcome.

Thanks,

Iulian

PS: I have an engineer background but I understand some math.

PS2: Since I am a new user, could you create 'spline' and 'curvature' tags (or tag this more appropriately)?

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  • $\begingroup$ "approximation-theory" already exists as a tag, "splines" can be viewed as a technique of approximation-theory, therefore I added that tag. $\endgroup$
    – Tim van Beek
    Commented Feb 24, 2011 at 12:45
  • $\begingroup$ I checked en.wikipedia.org/wiki/Smoot carefully but I fail to see the relevance :-) $\endgroup$
    – Neil Strickland
    Commented Feb 24, 2011 at 13:36

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Here is a short article explaining the motivation behind using the square of the second derivative.

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