Given a convex polygon P and a point A on P’s boundary, how do I compute a point B also on P’s boundary such that AB splits P into two areas of a given proportion?
Ideally I’d like an analytical solution. As a last resort I can draw a line anywhere on the polygon and gradually move it until the proportion is correct to a given precision.
I’ve worked out how to calculate B once I know between which two points on the polygon it should go. So if there’s a way to find out between which points it should go, I should be able to take it from there!
Split the polygon into triangles from the point A, and calculate their areas. Then you can add triangles from each end to each polygon depending on their proportions, until there is only one triangle left. Then you know that the point B is somewhere on the base of that triangle.