## Numerically Identifying  Discontinuity

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Hey, I need to numerically identify discontinuity points for a function given by a general expression (formula). I am able to evaluate the values at any point. I need it to be fast bu not accurate. The goal is to correctly render functions. With my naive algorithm, I get vertical lines on $x=0$ for $1/x$ and $sign(x)$. The types of discontinuities I need to find are like in the functions $sign(x)$ and $1/x$, that is -,+ adjacent polars and step like functions. I would like to avoid false positives like in the function $sin(1/x)$ which may numerically turn out as discontinues as you approach 0.

Thank You!!!

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I don't think that this is appropriate for this site. You might have more luck at maths.stackexchange.com – Andrew Stacey Mar 18 2011 at 8:38

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I think this is appropriate for this site. – Paul Tupper Jul 18 2011 at 4:37

## 1 Answer

It's going to be hard to find a "fast" way of doing this, but there is an algorithm due to Jeff Tupper for reliably sketching discontinuous functions, which you should be able to adapt to your needs.

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