Determining the intersection of polytope and hyperplane in arbitrary dimension is of central interest in computational geometry. In some paper(this one in particular: https://pdfs.semanticscholar.org/f4a6/4713dbf19883878e1357a6dc2bdfc2a04f30.pdf) author mentioned the "Naive Algorithm" of finding all the intersection between edges and hyperplane.
However, I couldn't find a proof that the intersection of polytope and hyperplane is determined by the intersection of the hyperplane and polytope's edges; is this unproven? If it is can someone post a source?
The polygon lies in a plane. The intersection of a hyperplane and a plane is either the entire plane or a line in the plane. Thus, if a hyperplane intersects the polygon in some point, it intersect the polygon's plane in a line through that point. This line necessarily crosses the edges of the polygon. Thus you can find the polygon's intersection with a hyperplane by finding the intersections of its edges with the hyperplane.