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Is there a source/cookbook of equations that approximate geometric shapes?

Computational Science Asked by Friasco on July 31, 2021

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:
    $(-x+1.2a)^{1.7}+(y-b)^2 < r^2$

One Answer

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.

Answered by nicoguaro on July 31, 2021

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