2D lines with round joints using WebGL shaders

In Neon Made I need as much cpu time as possible for physics, so to render chain objects as lines that the user is making I need to be as efficient as possible. In this post I'll explain what I am doing to get round line joints and an arbitrary amount of lines using virtually only WebGL shaders for all the work. All the cpu does is push the data once per frame. Here I'll describe you how you can do that.
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