# Is a contour's curvature stable under turning and also consistent scaling?

The title actually claim's all of it, once again is a contour's curvature stable under turning and also consistent scaling?

A contour's curvature is stable under turning. With ease, a contour transforms equally as much despite just how it is oriented. Extra officially, for a contour $\gamma(s)$ that is parametrized by arc size, the curvature is $\kappa(s) = ||\gamma''(s)||$. Turning does not transform the size of the $\gamma''(s)$ vector, just the instructions ; consequently, turning does not influence curvature.

A contour's curvature is not stable under consistent scaling, nonetheless. Take into consideration the instance of a circle. All circles coincide approximately scaling, yet they do not all have the very same curvature ; as a whole, a circle of distance r has curvature 1/r.

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