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find all shapes from 2 intersecated rects

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i have two parallel rectangles (so no rotation) and i want to find all shapes formed by intersection.

this is an example:

| |
| 5----9----6
| | | |
3----10----4 |
| |
| |

first rectangle: 1,2,3,4
second: 5,6,7,8
intersection points: 9,10 (getted by brute force intersecting all segment of first rect with each other of second one.. there is a better way?)

desired output:

i hope you understand, sorry for my bad english

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