Multiple rectangles intersection points

I would like to ask if you could give me a reference of processing code or library that works with intersection of polygons.

The idea of the script is having multiple polygons intersecting with each other. 

For example, there are two polygons. Usually you can draw one line between intersecting rectangles, between points A and B. Then I need to cut the part of polygon in the line AB and delete it.

I uploaded dropbox idea sketch for it. IDEA

Could you give me ideas how to start thinking about this script development?

Best,

Petras.