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

Question

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