Terminating Spatial Hierarchies by A Priori Bounding Memory

We consider the efficient top-down construction of spatial hierarchies for accelerating ray tracing and present a new termination criterion that allows for a priori fixing the memory footprint of the data structure. The resulting simplification of memory management makes algorithms shorter, more efficient, and more widely applicable, especially when considering hardware implementations and kd-trees. Even the on demand construction of parts of the hierarchy becomes close to trivial. In addition it proves to be the case that the hierarchy construction time easily can be predicted by the size of the provided memory block. This in turn allows for automatically balancing construction and ray tracing time in order to minimize the total time needed to render a frame from scratch.