A method of decomposing a three-dimensional representation of an object into a plurality of convex hulls can include instantiating a cluster priority queue in a computing system memory that initially contains a cluster corresponding to the three-dimensional representation of the object, computing with a processor of the computing system a concavity measure for each cluster in the cluster priority queue, and, for the cluster with the highest concavity measure: (1) computing with the processor a cut plane that divides the cluster corresponding to the three-dimensional representation of the object into two new clusters, each of the two new clusters having a corresponding convex hull, wherein computing a cut plane includes performing a hierarchical search of potential cut planes, (2) removing the cluster corresponding to the three-dimensional representation of the object from the cluster priority queue, and (3) adding the two new clusters to the cluster priority queue.