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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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:-? do u know what is "kink" in general? – narges May 4 '12 at 6:16
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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
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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
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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
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3 Answers

up vote 4 down vote

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
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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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thank you,got it! – narges May 4 '12 at 6:38
up vote 2 down vote

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

enter image description here

enter image description here

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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

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