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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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Following there are some resources that might be useful.

  • Wikipedia has a List of curves. They are listed according to some classification criteria and link to the article of each curve, where you can further read.

  • Shikin, E. V. (1995). Handbook and atlas of curves. CRC Press. This books presents an atlas where the curves are listed in alphabetical order.

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  • $\begingroup$ Thanks, Shikin has a few useful entries. Still a bit thin on the curves of interest, i.e. closed, bounded, mainly convex and, especially, approximations for polygons. $\endgroup$ – Friasco Jan 7 at 7:26
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    $\begingroup$ @Friasco You should check MathMod, it has some interesting ones. $\endgroup$ – nicoguaro Jan 7 at 18:54

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