Bounding Volume Hierarchy Optimization through Agglomerative Treelet Restructuring

Transcription

1 Bounding Volume Hierarchy Optimization through Agglomerative Treelet Restructuring Leonardo R. Domingues Helio Pedrini Eldorado Research Institute Institute of Computing - University of Campinas Brazil High-Performance Graphics Conference August 07, 2015 Leonardo R. Domingues, Helio Pedrini ATRBVH 1 / 30

2 Summary 1 Introduction 2 Related Work 3 Methodology 4 Results 5 Conclusion Leonardo R. Domingues, Helio Pedrini ATRBVH 2 / 30

3 1 Introduction 2 Related Work 3 Methodology 4 Results 5 Conclusion Leonardo R. Domingues, Helio Pedrini ATRBVH 3 / 30

4 Introduction Motivation Construction time x structure quality Lower construction time is important for: Animated scenes Interactive applications Higher quality is important for: Tracing a large number of rays GPU methods typically increase speed but reduce quality Leonardo R. Domingues, Helio Pedrini ATRBVH 4 / 30

5 Introduction Objectives Objectives Expand on the current state of the art 1 Test heuristics to replace exhaustive search Reduce construction times further Keep quality competitive with the most time demanding algorithms 1 T. Karras and T. Aila. Fast parallel construction of high-quality bounding volume hierarchies. High-Performance Graphics Conference, pages ACM, Leonardo R. Domingues, Helio Pedrini ATRBVH 5 / 30

6 1 Introduction 2 Related Work 3 Methodology 4 Results 5 Conclusion Leonardo R. Domingues, Helio Pedrini ATRBVH 6 / 30

7 Related Work Bounding Volume Hierarchies (BVHs) a 1 2 b 3 c 4 b c a Figure: Bounding Volume Hierarchy Leonardo R. Domingues, Helio Pedrini ATRBVH 7 / 30

8 Related Work BVH Quality The quality of a BVH can be measured using the Surface Area Heuristic (SAH) ( ) SAH = 1 C i A(n) + C t A(n)N(n) A t n I n L (1) A t = surface area of the root node A(n) = surface area of node n C i = relative cost for traversing an internal node C t = relative cost for performing ray-triangle intersection I = set of internal nodes L = set of leaves N(n) = number of triangles referenced by leaf n Leonardo R. Domingues, Helio Pedrini ATRBVH 8 / 30

9 Related Work BVH Construction GPU construction: Faster methods Lower quality trees LBVH 2 is the fastest method: LBVH Sort triangles along the Z curve Split the sorted array to create the internal nodes 2 C. Lauterbach, M. Garland, S. Sengupta, D. P. Luebke, and D. Manocha. Fast BVH construction on GPUs. Computer Graphics Forum, 28(2): , Apr Leonardo R. Domingues, Helio Pedrini ATRBVH 9 / 30

10 Related Work BVH Optimization Karras and Aila (2013) is the state of the art on GPU optimization TRBVH Treelets = small neighborhood of nodes Bottom-up traversal of the tree Form a treelet for each traversed node Restructure treelet nodes to find the optimal topology Leonardo R. Domingues, Helio Pedrini ATRBVH 10 / 30

11 1 Introduction 2 Related Work 3 Methodology 4 Results 5 Conclusion Leonardo R. Domingues, Helio Pedrini ATRBVH 11 / 30

12 Methodology ATRBVH Improvement on TRBVH Approximate the search for the optimal treelet structure Greedy Bottom-up Agglomerative Leonardo R. Domingues, Helio Pedrini ATRBVH 12 / 30

13 Methodology ATRBVH Algorithm 1: RearrangeTreelets 1 for internal node i in BVH do 2 treelet FormTreelet(i) 3 clusters treeletleaves 4 while length(clusters) > 1 do 5 distances [] 6 foreach pair of clusters (x, y) do 7 d Dissimilarity(x, y) 8 distances (d, x, y) 9 end 10 (m, n) FindMinimumDistance(distances) 11 o MergeClusters(m, n) 12 clusters.remove(m) 13 clusters.remove(n) 14 clusters.add(o) 15 end 16 end Leonardo R. Domingues, Helio Pedrini ATRBVH 13 / 30

14 Methodology ATRBVH R R 1 A C 4 B D R A B D C B A C D Figure: Agglomerative treelet restructuring Leonardo R. Domingues, Helio Pedrini ATRBVH 14 / 30

15 Methodology Distance Distance Metric Surface area of the bounding box containing the two nodes Minimizes SAH Distance Cache Cache distances in a triangular matrix Borrowed from Gu et al. (2013) 3 3 Y. Gu, Y. He, K. Fatahalian, and G. Blelloch. Efficient BVH construction via approximate agglomerative clustering. In Proceedings of the High-Performance Graphics Conference, pages ACM, Leonardo R. Domingues, Helio Pedrini ATRBVH 15 / 30

16 Methodology Update Distance Matrix Figure: Updating the distance matrix Leonardo R. Domingues, Helio Pedrini ATRBVH 16 / 30

17 Methodology Treelet Reconstruction Store modifications in a list Check if the new structure will reduce the tree SAH Only apply changes that improve the tree SAH Leonardo R. Domingues, Helio Pedrini ATRBVH 17 / 30

18 Methodology Post-processing Collapse the tree More than one triangle per node Compare cost of the subtree with cost of the collapsed subtree Cost of the collapsed tree c = C t A(n)N(n) (2) C t = Relative cost of ray-triangle intersection A(n) = Surface area of node n N(n) = Number of triangles contained in the subtree Leonardo R. Domingues, Helio Pedrini ATRBVH 18 / 30

19 1 Introduction 2 Related Work 3 Methodology 4 Results 5 Conclusion Leonardo R. Domingues, Helio Pedrini ATRBVH 19 / 30

20 Results Test Setup Compared methods LBVH TRBVH ATRBVH Leonardo R. Domingues, Helio Pedrini ATRBVH 20 / 30

21 Results Test Setup TRBVH is not publicly available Build times for our TRBVH are 3x higher than reported by the authors GTX 770 x GTX Titan Low-level optimizations TRBVH and ATRBVH share a large similarity Leonardo R. Domingues, Helio Pedrini ATRBVH 21 / 30

22 Results Test Setup NVIDIA GTX scenes Aila et al. (2009) 4 (2012) 5 traversal framework LBVH as basis for optimization Treelet size of 9 for ATRBVH All trees are collapsed as post-processing 4 T. Aila and S. Laine. Understanding the efficiency of ray traversal on GPUs. In Proceedings of the High-Performance Graphics Conference, pages ACM, T. Aila, S. Laine, and T. Karras. Understanding the efficiency of ray traversal on GPUs - Kepler and Fermi addendum. NVIDIA Technical Report NVR , NVIDIA Corporation, June Leonardo R. Domingues, Helio Pedrini ATRBVH 22 / 30

23 Results Measurements Arabic (412K) Method Mrays/s Time (ms) SAH Relative (%) LBVH TRBVH ATRBVH Method Mrays/s Time (ms) SAH Relative (%) Buddha (1.1M) LBVH TRBVH ATRBVH Method Mrays/s Time (ms) SAH Relative (%) Conference (282K) LBVH TRBVH ATRBVH Leonardo R. Domingues, Helio Pedrini ATRBVH 23 / 30

24 Results Measurements Dragon (870K) Time Machine (4.7M) Welsh Dragon (2.2M) Method Mrays/s Time (ms) SAH Relative (%) LBVH TRBVH ATRBVH Method Mrays/s Time (ms) SAH Relative (%) LBVH TRBVH ATRBVH Method Mrays/s Time (ms) SAH Relative (%) LBVH TRBVH ATRBVH Table: Test results Leonardo R. Domingues, Helio Pedrini ATRBVH 24 / 30

25 Results Average for all Scenes Method Performance (%) Time (%) LBVH TRBVH ATRBVH Table: Results averaged over all test scenes Leonardo R. Domingues, Helio Pedrini ATRBVH 25 / 30

26 1 Introduction 2 Related Work 3 Methodology 4 Results 5 Conclusion Leonardo R. Domingues, Helio Pedrini ATRBVH 26 / 30

27 Conclusions and Future Work Contributions ATRBVH 30% faster than TRBVH Virtually same quality (99.7%) Implementation publicly available Leonardo R. Domingues, Helio Pedrini ATRBVH 27 / 30

28 Conclusions and Future Work Future Work Treelet sizes > 32 Dynamically adjust treelet size Test with triangle splitting Leonardo R. Domingues, Helio Pedrini ATRBVH 28 / 30

29 Authors Contact Info Leonardo R. Domingues, Helio Pedrini ATRBVH 29 / 30

30 Bounding Volume Hierarchy Optimization through Agglomerative Treelet Restructuring Leonardo R. Domingues Helio Pedrini Eldorado Research Institute Institute of Computing - University of Campinas Brazil High-Performance Graphics Conference August 07, 2015 Leonardo R. Domingues, Helio Pedrini ATRBVH 30 / 30