what is “kink”?

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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:-? do u know what is "kink" in general? – narges May 4 '12 at 6:16
Hello and welcome to math.SE! Since it's your first time here, I recommend you read the faq, which will help you ask better questions and thus get better answers. Another tip: it is generally a good idea to leave non-mathematical content out of your questions, such as requesting a prompt answer. It won't prompt users to answer sooner, and may annoy members of the community. – Alex Becker May 4 '12 at 6:17
Hello.thank you,shure,sorry,but do u know what is "kink"? – narges May 4 '12 at 6:21
You have to be more precise about what you mean by "curvature". Are you talking about curvature on a surface? What kind of curvature? Gaussian? – Alex Becker May 4 '12 at 6:28
You should ask that as a separate question and be a little more precise about what you are looking for. – Austin Mohr May 4 '12 at 6:29

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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 thank you,what is relationship between gradiant and curvature from geometry? – narges May 4 '12 at 6:28

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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 thank you,got it! – narges May 4 '12 at 6:38

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

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 Nice images! $\Large \;\; \ddot\smile\;\;+^{{+^+}^+}$ – amWhy May 5 at 0:30 @Babak S.:❁_❁ Your work was excellent ✔ – faranak50 May 5 at 15:53