This seems like it ought to be obvious, but I¹m not seeing it. I¹m interested in the problem of deciding whether a point is inside/outside a polygon. Given the vertexes of a polygon, there are a several of ³classic² ways known to compute this test (eg for graphics applications) . Furthermore, it¹s a commonplace computational optimization, to enable quicker culling of points far from the polygon, to construct a bounding box (eg a rectangle aligned with the axes) so that any point outside the box is certainly outside the polygon (eg box corner coordinates are min/max of the polygon¹s). I¹m wondering: how hard is it to compute a sort of ³conceptual dual², a ³binding box², such that any point inside the box is certainly inside the polygon? We can restrict the problem to non-self intersecting polygons, but they may have zigzagging concavities. Perhaps easier would be to use circles, maybe some kind of projective inversion?