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Bavid
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Measure of the "Sharpness of a curve"
I have a set of curves that belong to the family of curves [itex]y=\frac{c}{x^m}[/itex], where [itex]m[/itex] and [itex]c[/itex] are parameters.
The attached picture (save.png) shows three such curves for different values of [itex]m[/itex] and [itex]c[/itex].
Now these curves have different 'sharpenss' of curvature (to see what I mean by sharpness, observe how 'sharp' a corner the lowermost curve forms compared to the uppermost).
I am trying to find a function F of [itex]m[/itex] and [itex]c[/itex] that can quantify this sharpness, i.e., larger value of F(m,c) indicates that the corresponding curve has a sharper corner or the vice versa.
Any ideas how to go about constructing the function F?
I have a set of curves that belong to the family of curves [itex]y=\frac{c}{x^m}[/itex], where [itex]m[/itex] and [itex]c[/itex] are parameters.
The attached picture (save.png) shows three such curves for different values of [itex]m[/itex] and [itex]c[/itex].
Now these curves have different 'sharpenss' of curvature (to see what I mean by sharpness, observe how 'sharp' a corner the lowermost curve forms compared to the uppermost).
I am trying to find a function F of [itex]m[/itex] and [itex]c[/itex] that can quantify this sharpness, i.e., larger value of F(m,c) indicates that the corresponding curve has a sharper corner or the vice versa.
Any ideas how to go about constructing the function F?