Algorithms for congruent sphere packing and applications

The problem of packing congruent spheres (i.e., copies of the same sph ere) in a bounded domain arises in many applications. In this paper, we present a new pack-and-shake scheme for packing congruent spheres in various bounded 2-D domains. Our packing scheme is based on a number of interesting ideas, such as a trimming and packing approach, optimal lattice packing under translation and/or rotation, shaking procedures, etc. Our packing algorithms have fairly low time complexities. In certain cases, they even run in nearly linear time. Our techniques can be easily generalized to congruent packing of other shapes of objects, and are readily extended to higher dimensional spaces. Applications of our packing algorithms to treatment planning of radiosurgery are discussed. Experimental results suggest that our algorithms produce reasonably dense packings.