I would like to know the math concepts behind shape based games like http://www.miniclip.com/games/fat-slice/en/
To be specific, I would like to know on
- how to model shapes programmatically
- finding areas of shapes
- intersection of areas
- curvy shapes instead of polygons
I searched for tutorials / guides to the best of my knowledge, but couldn't find anything appropriate.
Edit: I am looking at C++ libraries, that would support iOS / Android.