Multi-Resolution Geometric Representation using Bounding Volume Hierarchy for Ray Tracing

Overview

The paper proposes a multi‑resolution geometric representation that leverages the Bounding Volume Hierarchy (BVH) already built for ray tracing. By treating the axis‑aligned bounding boxes (AABBs) of BVH nodes as coarse geometric proxies, the method can dynamically select a level of detail (LOD) during ray traversal without any extra pre‑processing, additional storage, or separate LOD meshes. To make this approximation usable for global illumination (i.e., non‑occlusion rays), the authors introduce stochastic material sampling, which retrieves material information from the underlying triangles of a BVH node at runtime. The approach is implemented with only two extra integer fields per BVH node and can be integrated into existing ray‑tracing pipelines by a modest change to the BVH traversal logic. Experimental results on several scenes show up to ~14 % reduction in total rendering time and ~12 % reduction in ray‑casting time, with visual errors that are generally acceptable for many real‑time applications.

Main Contributions

1. Multi‑Resolution Geometry via BVH AABBs

Concept: Use the AABB of any BVH node as a geometric proxy for all triangles in its subtree.
LOD Selection: During traversal, test whether the proxy is “good enough” for the current ray. If it passes, the traversal stops at that node; otherwise, the algorithm descends to children for finer detail.
Ray‑Cone Test: A ray cone with spread angle θᵣ is tracked. The proxy is accepted when the virtual sphere enclosing the AABB lies completely inside the cone, i.e.,

\[\| \mathbf{d} \| \;<\; 2\|\mathbf{c}\|\tan(\theta_r) \;+\; 2 w_r,\]

where d is the AABB diagonal vector, c the vector from ray origin to the AABB centre, and wᵣ the cone width from the previous path segment.

Dynamic Spread Angle: The cone angle is adapted per ray bounce:

\[\theta_r \;=\; \max\!\bigl( H(b_d\!-\!2)\,T,\; H(b_d\!-\!1)\,\theta_\delta \bigr),\]

with b_d the number of diffuse bounces, T a user‑specified spread, θ_δ a small fallback angle (3°), and H(x) the Heaviside step function

\[H(x)=\begin{cases} 1 & x\ge 0,\\ 0 & x<0. \end{cases}\]

2. Stochastic Material Sampling

Problem: A coarse proxy lacks per‑triangle material data, which is required for shading in path tracing.
Solution: Store, for each BVH node, the range of triangle indices belonging to its subtree (two integers). When a proxy is hit, a triangle is uniformly sampled from this range, and its material (including complex shading networks) is used for the hit point.
Texture Coordinates & Barycentrics: After selecting a triangle, a random barycentric coordinate is sampled to interpolate texture coordinates. The geometric normal of the AABB is used as a sufficient shading normal.

3. Hardware‑Ray‑Tracing Extension (Conceptual)

Proposes extending the AMD image_bvh_intersect_ray instruction to return, for each child AABB, the hit distance, a validity flag, and the hit face (encoded in 32 bits). This enables the approximation test to be performed entirely inside the hardware instruction, minimizing extra work in shader code.

Limitations

Aspect	Limitation
Approximation Accuracy	The coarse AABB proxy can introduce noticeable errors for rays that interact with fine geometry (e.g., specular reflections, refractions, or when a light source is hidden by a small opening).
Material Sampling Bias	Uniform triangle sampling assumes a uniform distribution of triangles in direction space; highly non‑uniform meshes may lead to biased material selection.
Area Light Handling	Geometric approximation changes the effective area of emissive geometry. The authors mitigate this by flagging BVH nodes that contain area lights and disabling the proxy for them, but this adds a per‑scene preprocessing step.
Hardware Dependency	The proposed hardware instruction extension is not yet available on current GPUs; practical adoption would require ISA changes.
Performance Bottlenecks	In scenes where shading/shader execution dominates (e.g., heavy use of complex materials), the speed‑up from reduced traversal is limited.

Conclusion

The authors demonstrate that BVH‑based multi‑resolution geometry combined with stochastic material sampling can effectively reduce ray‑tracing workload for both occlusion and global‑illumination rays. The method requires only minimal changes to existing traversal code and a negligible memory overhead (two integers per BVH node). Empirical results show up to 40 % speed‑up for ambient‑occlusion ray casting and ~14 % overall rendering time reduction in full path‑tracing workloads, while maintaining visual fidelity that is acceptable for many real‑time scenarios.

Future Directions

Transmissive Surfaces – Extend the stochastic material sampling and proxy acceptance criteria to handle refraction and volumetric scattering.
Improved Approximation Criteria – Develop more sophisticated tests (e.g., considering hole preservation) to avoid large errors when a proxy would hide important geometric features such as torus openings.
Adaptive Sampling – Incorporate triangle area and orientation into the stochastic material selection to reduce bias on non‑uniform meshes.
Hardware Realization – Implement and evaluate the proposed image_bvh_intersect_ray extension on upcoming GPU architectures, measuring actual hardware‑level benefits.
Animation & Temporal Coherence – Investigate how the proxy selection can be made temporally stable across frames to avoid flickering in animated scenes.