TSS BVHs: Tetrahedron Swept Sphere BVHs for Ray Tracing Subdivision Surfaces

• Published in: Computer graphics forum Vol. 35; no. 7; pp. 279 - 288
• Main Authors: Du, P., Kim, Y. J., Yoon, S. E.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.10.2016
• Subjects: Analysis; Categories and Subject Descriptors (according to ACM CCS); Complexity; Computation; Computer graphics; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Raytracing; Image processing systems; Mathematical models; Order disorder; Ray tracing; Studies; Subdivisions; Tetrahedrons; Theorems; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.13025

We present a novel, compact bounding volume hierarchy, TSS BVH, for ray tracing subdivision surfaces computed by the Catmull‐Clark scheme. We use Tetrahedron Swept Sphere (TSS) as a bounding volume to tightly bound limit surfaces of such subdivision surfaces given a user tolerance. Geometric coordinates defining our TSS bounding volumes are implicitly computed from the subdivided mesh via a simple vertex ordering method, and each level of our TSS BVH is associated with a single distance bound, utilizing the Catmull‐Clark scheme. These features result in a linear space complexity as a function of the tree depth, while many prior BVHs have exponential space complexity. We have tested our method against different benchmarks with path tracing and photon mapping. We found that our method achieves up to two orders of magnitude of memory reduction with a high culling ratio over the prior AABB BVH methods, when we represent models with two to four subdivision levels. Overall, our method achieves three times performance improvement thanks to these results. These results are acquired by our theorem that rigorously computes our TSS bounding volumes.