Abstract: The classical Z-buffer visibility algorithm samples a scene at regularly spaced points on an image plane. Previously, we introduced an extension of this algorithm called the irregular Z-buffer that permits sampling of the scene from arbitrary points on the image plane. These sample points are stored in a two-dimensional spatial data structure. Here we present a set of architectural enhancements to the classical Z-buffer acceleration hardware which supports efficient execution of the irregular Z-buffer. These enhancements enable efficient parallel construction and query of certain irregular data structures, including the grid of linked lists used by our algorithm. The enhancements include flexible atomic read-modify-write units located near the memory controller, an internal routing network between these units and the fragment processors, and a MIMD fragment processor design. We simulate the performance of this new architecture and demonstrate that it can be used to render high-quality shadows in geometrically complex scenes at interactive frame rates. We also discuss other uses of the irregular Z-buffer algorithm and the implications of our architectural changes in the design of chip-multiprocessors.