1. Fast BVH Construction on GPUs (Eurographics 2009) Park, Soonchan KAIST (Korea Advanced Institute of Science and Technology)

2. 2 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

3. 3 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

4. 4 What is BVH? ● Bounding Volume Hierarchy ● A tree structure on a set of geometric objects ● “Fast Computation” ● Ray tracing ● Collision detection ● Visibility Culling

5. 5 What is BVH? ● Issues of BVH construction ● Construction Time ● Effectiveness of Construction ● How much improvement BVH makes –Median Subdivision & Surface Area Heuristic

6. 6 Motivation ● BVH Construction Almost all prior works are about “Purely serial construction algorithms” Make Efficient Parallel algorithms! on manycore processors  How to make processes of BVH construction appropriate for parallel computation

7. 7 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

8. 8 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

9. 9 LBVH ● Linear Bounding Volume Hierarchy ● Simplest approach to parallelizing BVH Construction ● Sorting input primitives by Morton Codes ● BVH Construction  Sorting ( O(nlogn) )

10. 10 Morton Codes (Z-order) ● Space-filling curve ● Morton Codes (Z-order) ● Good locality-preserving ● Express space as bits

11. 11 Morton Codes (Z-order)

12. 12 LBVH ● Linear B.V.H. ● Sorting primitives along the curve parallel radix sort [SHG08] ● Each primitive has bit expression of position ● How to make the Hierarchy?

13. 13 LBVH ● Make Hierarchy ● Test all Primitive i with Primitive i+1 ● What levels they are separated ● Make list ( (Primitive index), ( separate level) ) ● Resort the list by level  We can have intervals at each level!

14. 14 Example (6, 1) (3, 2) (6, 2) (2,3) (3,3) (4,3) (5,3) (6,3) (7,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (7,4) Split list (Prim.Index, Separate Lev.)

15. 15 7 8 1 2 3 4 5 6 LEVEL 1 1 2 3 4 5 6 7 8

16. 16 7 8 1 2 3 4 5 6 123 456 LEVEL 1 LEVEL 2 1 2 3 4 5 6 7 8

17. 17 7 8 1 2 3 4 5 6 123 456 3 12 4 5 678 LEVEL 1 LEVEL 2 LEVEL 3 1 2 3 4 5 6 7 8

18. 18 7 8 1 2 3 4 5 6 123 456 3 12 4 5 678 12 LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 1 2 3 4 5 6 7 8

19. 19

20. 20 LBVH ● Pros ● Very fast – same complexity as sorting ● + we use parallel radix sort [SHG 08] ● Cons ● Constructed Hierarchy is not optimized ● It uniformly subdivides space at the median ● Leaf can has multiple primitives

21. 21 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

22. 22 What is SAH ● Surface Area Heuristic ● Answer for optimized architecture ● “which of a number of partitions of primitives will be better? ● “which of a number of possible positions to split space will be better?”

23. 23 What is SAH ● SAH optimized construction can also be achieved in O(nlogn) [WH06] ● Processes for SAH ● Recursively splitting the set of geometric primitives (usually two parts per step-binary tree) ● Evaluate with “cost function” ● Cost function can be defined ● Find the one with lowest cost ● Check all possible split position can be costly ● Sampling method can be applied

24. 24 GPU SAH Construction ● Breadth-first construction using work queues ● Parallelization! Input queue Output queue

25. 25 Data-Parallel SAH Split ● Two steps for performing SAH split ● Determine the best split position by evaluating the SAH ● Reorder the primitives ( corresponds to the new split )

26. 26 Data-Parallel SAH Split ● Determine the best split position ● Approximate SAH computation ● Generate k uniformly sampled split candidates for three axes ( test all the samples in parallel by using 3k threads ) ● Each thread computes the SAH cost for its split candidate ● Find split candidate with lowest cost ● Reorder the Primitives ● In corresponds to the new splits ● Only reorder the indices ● No copy of geometry

27. 27 Small Split Operation ● Two main bottleneck ● Initial split at the top level of hierarchy is very slow ● Large # of primitives at Top level –By using hybrid method (discussed later) ● Large # of small splits at Low level ● Problems ● Higher compaction costs generated by large # of splits ● Vector utilizing is low (Few primitive per split) ● Large # of small size of split makes problem  Use different split kernel for small size

28. 28 Small Split Operation ● Main Idea ● Set Thresh hold to define “Small split” ● Depends on geometry data & cache size (32) ● Use processor’s local memory ● to maintain a local work queue ● Keep all the geometric primitives ● Pros ● Reduce memory bandwidth ● Decrease # of Thread ● Maximize utilization of vector operation ● Avoid waiting for memory access  15~20% speed up

29. 29 Small Split Operation Times # of active splits Level of splits

30. 30 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

31. 31 Hybrid GPU Construction Algorithm ● LBVH ● Not optimized at last ● Shallow hierarchy ● Large # of primitives at the leafs ● But FAST ● Problem of GPU SAH Construction ● Relatively Slow ● Overhead at first level ● But it can build optimized hierarchy ● Solution ● Top level  use LBVH ● Others  use GPU SAH Construction

32. 32 Contents ● What is BVH ● Motivation ● Three Algorithm to Construct BVH ● LBVH ● SAH Hierarchy Construction ● Hybrid GPU Construction Algorithm ● Results & Analysis

33. 33 Results ● Render several scenes ● Comparing with other environments ● One-core not optimized CPU SAH ● Full SAH ● Standard CPU BVH ray tracer using ray packets ● Compare with ● Construction time, Well Optimized, fps

34. 34 Results Construction Time Absolute/relative r.t. perf.

35. 35 Results Construction Time Absolute/relative r.t. perf.

36. 36 Results Construction Time Absolute/relative r.t. perf.

37. 37 Results ● GPU SAH ● Show better performance than CPU SAH ● Good optimization ● LBVH ● Fast, not optimized ● Scene dependent ● Hybrid ● Middle of GPU SAH & LBVH ● can be customized

38. 38 Analysis ● Current GPU architecture several features for constructing hierarchy ● Special Graphics memory  significantly higher memory bandwidth ● Manage fast local memory ● Discussed in Small Split Operation ● Memory ● 113 bytes/triangle ● Worst case: when one triangle per leaf  It allows multi-million triangle models on current GPU

39. 39 Analysis ● Bottleneck Analysis Core overhead Memory overhead

40. 40 Analysis ● Time Distribution *Rest = read/write BVH node information, setting up splits, join rest of steps “Note that Hybrid build is 10 times faster” Full SAH buildHybrid build

41. 41 Video ● Youtube Video Youtube Video

42. 42 Reference ● [SHG08] SATISH N., HARRIS M., GARLAND M.: Designing efficient sorting algorithms for manycore GPUs. Under review (2008). ● [WH06] WALD I., HAVRAN V.: On building fast kd-trees for ray tracing, and on doing that in O(N log N). In Proc. of IEEE Symp.on Interactive Ray Tracing (2006), pp. 61–69.