what is "kink"?

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Pleas tell me that what a "Kink" is and what this sentence means:

Distance functions have a kink at the interface where $d = 0$ is a local minimum.

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3 Answers

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A "kink" in a curve would be a point where the curve is continuous, yet the first derivative (gradient) is not continuous. The curvature would be infinite at a kink because the direction changes a finite amount in an infinitesimal distance.

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In this case, I believe a "kink" in the function refers to a point at which the function fails to be differentiable. For example, the function $f(x)=|x|$ (which gives the distance between $x$ and $0$) is not differentiable at $x=0$, where the function is $0$ as well.

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As above you can find it via the web as Cusp (singularity). See the following graphs:

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