Unbounding discrete oriented polytopes

Abstract

. We propose an efficient algorithm to compute k-sided unbounding discrete oriented polytopes ( 𝑘 -UDOPs) in arbitrary dimensions. These convex polytopes are constructed for a fixed set of directions and a given center point. The interior of 𝑘 -UDOPs does not intersect the scene geometry. We discuss several types of general geometric queries on these constructs, such as intersection with rays, and provide an empirical investigation on the limit of these shapes as the number of sides increases. In the 2D case, we extend our construction to planar shapes enclosed by arbitrary parametric boundaries with known derivative bounds.