The reason a "bounding box" works so much better than a "binding box" is that the intersection of boxes is a box, but the union of boxes isn't, so the bounding box is just the intersection of all (grid-aligned) boxes that bound, while the union of binding boxes isn't a box, but is the entire interior. Andy On Sun, Oct 7, 2012 at 3:30 PM, Marc LeBrun <mlb@well.com> wrote:
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?
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