Systems and methods for producing an acceleration structure provide for subdividing a 3-D scene into a plurality of volumetric portions, which have different sizes, each being addressable using a multipart address indicating a location and a relative size of each volumetric portion. A stream of primitives is processed by characterizing each according to one or more criteria, selecting a relative size of volumetric portions for use in bounding the primitive, and finding a set of volumetric portions of that relative size which bound the primitive. A primitive ID is stored in each location of a cache associated with each volumetric portion of the set of volumetric portions. A cache location is selected for eviction, responsive to each cache eviction decision made during the processing. An element of an acceleration structure according to the contents of the evicted cache location is generated, responsive to the evicted cache location.