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

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

## 1 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.

• 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. – Friasco Jan 7 at 7:26
• @Friasco You should check MathMod, it has some interesting ones. – nicoguaro Jan 7 at 18:54