Sphere polygon interaction to fill volume objects

Abstract

Volume computation can be approximated by filling with regular convex geometric primitives. Volume filling simulation using spheres in a 3D environment, requires the motion and interaction between the geometric primitives, specifically collision detection and collision response. The object to be filled is represented by a polygonal mesh, and the problem arises when there are many spheres moving around, operations increase, and the simulation becomes unstable. We propose an algorithm to fill solid objects with spheres, by discarding geometric primitives (spheres and polygons) to speed up the simulation. We emphasize in the benefit of the method, which is shown mathematically and computationally with experiments of convex and non-convex objects.