Paperjs split line segments

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I am using paperjs and now have a need to do vector segmentation of freely drawn line segments. Specifically, it has a function similar to erasing, and the eraser itself has a volume. Then the intersecting parts of the eraser need to be removed and a new vector path generated。 I use the subtract and intersection methods from paperjs, but there are still many problems. I am not sure whether it is because I am not familiar with them or because paperjs is flawed. Or how to get some algorithm to solve this problem.

At the first, it will be first

at the finally,it should be final

i move the eraser in middle,and it should divide to 4 parts

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