Polyline offset with closed polygon and islands

Question

I have unsorted set of line segments without any binding to each other. Each line described with 2 points (x,y). I can search for lines with the same points, which means they should be connected.

Every line have a thickness attribute. I need to offset each path by this thickness, and create 4 points describing the final plygon (for each line).

Screenshot 1

now I need to refine it to handle corners (joins) correctly. but have no idea how to do it.

Desired result: Screenshot 2

Answer 1

See here for one method of offsetting a polygon using it's skeleton (which is what you are trying to do here).