Multiresolution sphere packing tree: a hierarchical multiresolution 3D data structure

Abstract

Sphere packing arrangements are frequently found in nature, exhibiting efficient space-filling and energy minimization properties. Close sphere packings provide a tight, uniform, and highly symmetric spatial sampling at a single resolution. We introduce the Multiresolution Sphere Packing Tree (MSP-tree): a hierarchical spatial data structure based on sphere packing arrangements suitable for 3D space representation and selective refinement. Compared to the commonly used octree, MSP-tree offers three advantages: a lower fanout (a factor of four compared to eight), denser packing (about 24% denser), and persistence (sphere centers at coarse resolutions persist at finer resolutions). We present MSP-tree both as a region-based approach that describes the refinement mechanism succintly and intuitively, and as a lattice-based approach better suited for implementation. The MSP-tree offers a robust, highly symmetric tessellation of 3D space with favorable image processing properties.