Simple Polygon Collision and (!) getting the intersection area

Game Mechanics
#1

Hello,

I know there a A LOT of collision threads and tutorials and what not, but after searching for ~1 hour I decided to create yet another thread:

I’m familiar with the SAT and (to same degree) PIP (Point in Polygon) algorithms and they’re working fine, but I need additional information:
I need to know the “line” or set of vectors representing the intersection “cut” area:

I need either the red or the blue edge(part)s (depending on which polygon intersects which) as a set of vectors / lines. I know I can get the minimum translation vector via SAT but I can’t come up with or find any ideas that give me what I want.

If someone has a link for me or can discribe how to get my intersection cut?
Thank you in advance!

#2

Here´s a link how to get the point of two intersecting lines (you have to scroll down a bit)

http://paulbourke.net/geometry/pointlineplane/

There´s even some source. Even though it´s not java it´s really easy to port. Hope it helps.