A packing algorithm for three-dimensional convex particles

Simulation of granular particles is an important tool in many fields. However, simulation of particles of complex shapes remains largely out of reach even in two-dimension. One of the major hurdles is the difficulty in representing particles in an efficient, flexible, and accurate manner. By representing particles as convex polyhedrons which are themselves the intersection of a set of half spaces, we develop a method that allows one to efficiently carry out key operations, including particle-particle and particle-container wall overlapping detection, precise identification of the overlapping region, particle shifting, particle rotation, and others. The simulation of packing 1,000 particles into a container takes only a few minutes with this approach. We further demonstrate the potential of this approach with a simulation that re-generates the "Brazil nut" phenomenon by mixing and shaking particles of two different sizes.