Abstract: We present a set of new techniques to compute an exact polygon-to-polygon visibility in Plücker space. The contributions are based on the definition of the minimal representation of lines stabbing two convex polygons. The new algorithms are designed to indicate useless computations, which results in more compact visibility data, faster to exploit, and in a reduced computation time. We also define a simple robust and exact solution to handle degeneracies, where previous methods proposed aggressive solutions.