It's quite obvious to me that if I clip any convex polygon with a half-space, the resulting polygon will be convex. I explain it to myself by "a straight line can't introduce concavity", but is there a proper, mathematical proof to it?
I have used this property extensively in my thesis (computer science, not mathematics), but realized now I can't come up with any sound argument why my assumption holds. Proving it is out of scope of my work, but I would like to understand the proof myself. Points to any reading/papers that I could cite are also very welcome :)
The convex polygon and half-space are both convex sets, and the result of clipping the polygon by the half-space is merely their intersection, which will be convex from this result. So in case the intersection forms a polygon, it will be a convex one.