Advanced Ray Tracing Acceleration Techniques and Spatial Hierarchies for Faster Intersection

1. Approaches Faster Intersection Fewer Rays Generalized Rays N 1 Uniform grids Spatial hierarchies k-d, oct-tree, bsp hierarchical grids Hierarchical bounding volumes (HBV) Tighter bounds Faster intersector Early ray termination Adaptive sampling Beam tracing Cone tracing Pencil tracing Ray Tracing Acceleration Techniques

2. Primitives • pbrt primitive base class • Shape • Material and emission (area light) • Primitives • Basic geometric primitive • Primitive instance • Transformation and pointer to basic primitive • Aggregate (collection) • Treat collections just like basic primitives • Incorporate acceleration structures into collections • May nest accelerators of different types • Types: grid.cpp and kdtree.cpp

3. Uniform Grids • Preprocess scene • Find bounding box

4. Uniform Grids • Preprocess scene • Find bounding box • Determine resolution

5. Uniform Grids • Preprocess scene • Find bounding box • Determine resolution • Place object in cell, if object overlaps cell

6. Uniform Grids • Preprocess scene • Find bounding box • Determine resolution • Place object in cell, if object overlaps cell • Check that object intersects cell

7. Uniform Grids • Preprocess scene • Traverse grid 3D line – 3D-DDA 6-connected line • Section 4.3

8. Caveat: Overlap • Optimize for objects that overlap multiple cells • Traverse until tmin(cell) > tmax(ray) • Problem: Redundant intersection tests: • Solution: Mailboxes • Assign each ray an increasing number • Primitive intersection cache (mailbox) • Store last ray number tested in mailbox • Only intersect if ray number is greater

9. Spatial Hierarchies A A Letters correspond to planes (A) Point Location by recursive search

10. A B B A Spatial Hierarchies Letters correspond to planes (A, B) Point Location by recursive search

11. A B B C C D A Spatial Hierarchies D Letters correspond to planes (A, B, C, D) Point Location by recursive search

12. Variations kd-tree oct-tree bsp-tree

13. Ray Traversal Algorithms • Recursive inorder traversal • [Kaplan, Arvo, Jansen] Intersect(L,tmin,tmax) Intersect(L,tmin,t*) Intersect(R,t*,tmax) Intersect(R,tmin,tmax)

14. ? Build Hierarchy Top-Down • Choose splitting plane • Midpoint • Median cut • Surface area heuristic

15. Surface Area and Rays • Number of rays in a given direction that hit an • object is proportional to its projected area • The total number of rays hitting an object is • Crofton’s Theorem: • For a convex body • For example: sphere

16. Surface Area and Rays • The probability of a ray hitting a convex shape • that is completely inside a convex cell equals

17. Surface Area Heuristic Intersection time Traversal time b a

18. b a Surface Area Heuristic 2n splits

19. Comparison V. Havran, Best Efficiency Scheme Project http://sgi.felk.cvut.cz/BES/

20. Comparison

21. Univ. Saarland RTRT Engine • Ray-casts per second = FPS @ 1K × 1K • Pentium-IV 2.5GHz laptop • Kd-tree with surface-area heuristic [Havran] • Wald et al. 2003 [http://www.mpi-sb.mpg.de/~wald/]

22. Interactive Ray Tracing • Highly optimized software ray tracers • Use vector instructions; Cache optimized • Clusters and shared memory MPs • Ray tracing hardware • AR250/350 ray tracing processor www.art-render.com • SaarCOR • Ray tracing on programmable GPUs

23. Theoretical Nugget 1 • Computational geometry of ray shooting • 1. Triangles (Pellegrini) • Time: • Space: • 2. Sphere (Guibas and Pellegrini) • Time: • Space:

24. Theoretical Nugget 2 • Optical computer = Turing machine • Reif, Tygar, Yoshida • Determining if a ray • starting at y0 arrives • at yn is undecidable y = y+1 y = -2*y if( y>0 )