Systems and methods of geometry processing, for rasterization and ray tracing processes provide for pre-processing of source geometry, such as by tessellating or other procedural modification of source geometry, to produce final geometry on which a rendering will be based. An acceleration structure (or portion thereof) for use during ray tracing is defined based on the final geometry. Only coarse-grained elements of the acceleration structure may be produced or retained, and a fine-grained structure within a particular coarse-grained element may be Produced in response to a collection of rays being ready for traversal within the coarse grained element. Final geometry can be recreated in response to demand from a rasterization engine, and from ray intersection units that require such geometry for intersection testing with primitives. Geometry at different resolutions can be generated to respond to demands from different rendering components.