A hardware-based traversal coprocessor provides acceleration of tree traversal operations searching for intersections between primitives represented in a tree data structure and a ray. The primitives may include opaque and alpha triangles used in generating a virtual scene. The hardware-based traversal coprocessor is configured to determine primitives intersected by the ray, and return intersection information to a streaming multiprocessor for further processing. The hardware-based traversal coprocessor is configured to omit reporting of one or more primitives the ray is determined to intersect. The omitted primitives include primitives which are provably capable of being omitted without a functional impact on visualizing the virtual scene.