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I'm numerically modelling flows around various geometric 2D shapes. Is there a good source/cookbook of equations that approximate these? Some examples are

  1. Rectangle: $(x-a)^n+(y-b)^n < r^n$ where $r$ is side length and $n$ is even. The larger $n$, the sharper the corners. Also e.g. $\text{max}(500 |x-a|, 55 |y-b|) < r^2$ achieves this .
  2. Tilted square: $|x-a|+|y-b| < r^2$
  3. Bullet: $(-x+1.2a)^{1.7}+(y-b)^2 < r^2$
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