Polygon shape comes from a sketch I draw with many clouds of random shapes:

Doing some experiments with the great and powerful paperjs library (http://paperjs.org/) I first tests the different parameters to smooth a path :

I choose the continuous parameter to smooth the path created with random points. To recreate random path, one option is simply to create random points in a square:

But this option has some issues, in particular when points are too close : that creates shapes that are not very nice. In fact, I saw that you can actually generate interesting shapes using a path that randomly picks up points evenly distributed around a circle. For example if you have 4 points (in red) or 5 points (in blue) that are evenly distributed around a circle, you can create different shape by using a path that randomly picks up the points in the circle:

With 4 points you have two different shapes, for 5 points 5 different shapes. With 6 points, there are 14 different shapes.

Polygon shape uses paths with 4 to 12 evenly distributed around a circle, that creates a lot of different shapes:



