How to create this 2D dynamic light and shadow system?

Here is the system I want to implement:

http://ncase.me/sight-and-light/ https://www.assetstore.unity3d.com/en/#!/content/25933

What I understand by now is that I will do many raycasts to every collider's borders and draw a polygon to cover it. But I'm pretty much clueless about how to use this polygon to create the fog using Unity components or shaders.