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I've been trying to find an elegant model for a function of two variables $(x,y)$ with the following constraints:

  • $x \geq 0$
  • $y \leq 0$
  • $f(x,y) < 0$ when $x < 2$
  • $f(x,y) < 0$ when $y \leq -2$
  • $f(x,y) \geq 0$ when $x \geq 2$ and $y > -2$

It seems like I could use the hyperbolic paraboloid function as the starting point, but I haven't been able to figure out how to adjust the formula to get the function to come close to my constraints.

My intent is to use the resulting function to construct a feature for a machine learning algorithm, so it's not important that it's a hyperbolic paraboloid, just that it models the constraints well.

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    Posting all of your previous work would make this a much easier thing to help with. – 2017-01-11
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    It's not going to be continuous, because $f^{-1}([0,\infty))$ isn't open – 2017-01-11

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