Describing Curvature of a Non-Uniform Curve Using Second Derivative Average?

[ice109]

suppose a curve is not uniformly curved and i would like to describe how "curvy" a segment of this curve is? how would i do to this? i imagine i can take the second derivative and find the average of it over the entire segment and the closer the average is to zero the straight the segment is but immediately I'm dealing with a set of data points.

 

[CRGreathouse]

http://en.wikipedia.org/wiki/Radius_of_curvature ?

 

[ice109]

http://en.wikipedia.org/wiki/Radius_of_curvature ?

this is for continuous distributions which i do not have.

 

[Kummer]

Curvature.

 

[Emmanuel114]

Variance? I don't even know why you would be talking about curvature of a set of points.

 

[ice109]

Variance? I don't even know why you would be talking about curvature of a set of points.

yea variance is probably it, i want to find the flattest part of a distrubtion of points

 

[Hurkyl]

this is for continuous distributions which i do not have.

You can always use discrete approximations to curvature, and/or apply some smoothing.

 

[arildno]

Since you are dealing with a discrete set of points, and wish to make some sort of interpolation, you have to decide what niceties you want the interpolating function to have.