1. Ray Tracing Acceleration (5)

2. Ray Tracing Acceleration Techniques Too Slow! Uniform grids Spatial hierarchies K-D Octtree BSP Hierarchical grids Hierarchical bounding volumes (HBV) Tighter bounds Faster intersector Early ray termination Adaptive sampling Beam tracing Cone tracing Pencil tracing Faster intersection N1 Fewer raysGeneralized rays

3. Roadmap (LRT book, ch 4 – Intersection Acceleration) Approaches To Reducing Intersections –Ray-Box Intersections –Regular Grid –Hierarchical bounding volumes –BSP trees and friends –Meta-Hierarchies –Refinements to basic approaches Hierarchical Grid Accelerator –Creation –Traversal Kd Tree –Tree Representation –Tree construction –Traversal Further Reading

4. Grids 3-D array of cells Each cell contains list of all objects it intersects Ray intersected with all objects in a given cell’s list Cells visited in Bresenham order

5. Bounding Volume Hierarchies

6. Hierarchical Bounding Volumes (HBV) Trees of bounding volumes are constructed in a similar way to spatial hierarchy HBV does not partition space: the bounding volumes can overlap each other. HBV can be created from existing model hierarchy or by running a clustering algorithm.

7. Bounding Volume Ray-bunny intersection takes 70K ray-triangle intersections even if ray misses the bunny Place a sphere around bunny –Ray A misses sphere so ray A misses bunny without checking 70K ray-triangle intersections –Ray B intersects sphere but still misses bunny after checking 70K intersections –Ray C intersects sphere and intersects bunny Can also use axis-aligned bounding box –Easier to create for triangle mesh A B C

8. Bounding Volume Hierarchy Associate bounding volume with each node of scene graph If ray misses a node’s bounding volume, then no need to check any node beneath it If ray hits a node’s BV, then replace it with its children’s BV’s (or geometry) Breadth first search of tree –Maintain heap ordered by ray- BV intersection t-values –Explore children of node w/least pos. ray-BV t-value A B C Bunny BV Body BV Head BV L.EarFaceR.Ear BV

9. Choosing Bounding Volumes

10. Hierarchical Bounding Volumes

11. Heuristics for an Effective Bounding Hierarchy

12. Bounding Volume Hierarchy

13. Find bounding box of objects

14. Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups

15. Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse

16. Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse

17. Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse

18. Bounding Volume Hierarchy Find bounding box of objects Split objects into two groups Recurse

19. Where to split objects? At midpoint OR Sort, and put half of the objects on each side OR Use modeling hierarchy

20. Intersection with BVH Check subvolume with closer intersection first

21. Intersection with BVH Don't return intersection immediately if the other subvolume may have a closer intersection

22. Hierarchical Bounding Volumes Create tree of bounding volumes Children are contained within parent Creation preprocess –From model hierarchy –Automatic clustering Search intersect(node,ray,hits) { if( intersectp(node->bound,ray) if( leaf(node) ) intersect(node->prims,ray,hits) else for each child intersect(child,ray,hits) }

23. Bounding Volume Hierarchy Discussion Advantages –easy to construct –easy to traverse –binary Disadvantages –may be difficult to choose a good split for a node –poor split may result in minimal spatial pruning

24. Ray Tracing Acceleration Techniques Too Slow! Uniform grids Spatial hierarchies K-D Octtree BSP Hierarchical grids Hierarchical bounding volumes (HBV) Tighter bounds Faster intersector Early ray termination Adaptive sampling Beam tracing Cone tracing Pencil tracing Faster intersection N1 Fewer raysGeneralized rays

25. Uniform Spatial Partition

26. Spatial Partition Structures

27. Pitfalls!

28. 3-d Trees (K-d Trees)

29. Octrees

31. BSP Trees

32. Ray Tracing BSP Trees

33. Wrap-up Uniform Grids, Spatial Hierarchies, Hierarchical Grids, HBVs Question: Which one of the above is best? Answer: I don’t know. Here all techniques are heuristics.

34. Wrap-up Vlastimil Havran’s Best E.ciency Scheme Project at http://sgi.felk.cvut.cz/BES/ compares different accelerators. Basically every one of them works better in some cases and worse in some other cases. Worst case for ”Uniform Grid” is sparse scenes, –for example, a very complicated bunny model put at the center of a huge stadium.