Applications of interval arithmetic for reduction of number of computations in ray tracing problems

Embodiments provide for ray tracing traversal that relies on selected geometrical properties of the application to reduce the number of operations required during each traversal step. The traversal algorithm does not depend on the number of rays in the group. As a result, multi-level traversal schemes may be implemented, starting with a large number of rays in a group and then reducing it as needed to maintain group coherency. Multi-level traversal schemes may be created by splitting large groups of rays while traversing acceleration structures.