19 th Eurographics Symposium on Rendering Compact Fast

19 th Eurographics Symposium on Rendering Compact, Fast and Robust Grids for Ray Tracing Ares Lagae & Philip Dutré EGSR 2008 Wednesday, June 25 th

Introduction • Acceleration structures for ray tracing – Kd-tree, BVH, … • Build time: slower (super-linear) • Render time: faster – Grid • Build time: faster (linear) • Render time: slower Minimize time to image – Time to image = render time + build time – Especially for dynamic scenes

Introduction • Algorithms in general – CPU-bound • Execution time = f( CPU speed ) – Memory-bound • Execution time = f( memory speed ) Accelerate by decreasing memory footprint Minimize memory footprint – Especially for large models

Grid Data Structures • Grid and linearized grid 0 ariz e 2 D 0 1 2 2 0 line 1 2 0 1 D 1 1 2 3 4 5 6 7 8

Grid Data Structures • Data structure using linked lists 0 1 2 3 4 5 6 7 8 1 1 0 2 2 1 1 • 1 word / cell • 2/3 words / object reference 0

Grid Data Structures • Data structure using dynamic arrays 0 2 1 0 2 2 1 3 1 2 1 4 0 5 3 2 6 2 2 0 1 1 2 7 1 2 0 8 1 2 2 • 3 words / cell • 1 -2 words / object reference : unused space

Compact Grid • Data structure – Concatenate object lists, store begin index 0 1 2 3 4 5 6 7 8 0 0 1 2 3 6 8 9 10 11 1 1 0 0 1 2 0 2 2 0 1 2 3 4 5 6 7 8 9 10 1 word / cell, 1 word / object reference 11

Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 1. Bound Compute bounding box of objects Determine grid resolution Grid size linear in number of objects

Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 2. Count Compute size of object lists (1 st pass) 0 1 2 3 4 5 6 7 8 0 1 1 1 3 2 1 1 1 0 1 2 3 4 5 6 7 8 9 10 11

Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 3. Accumulate Compute indices of object lists 0 1 2 3 4 5 6 7 8 0 1 2 3 6 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11

Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 4. Insert Reversely insert the object references (2 nd pass) 0 1 2 3 4 5 6 7 8 0 0 1 2 3 6 8 9 10 1 1 0 0 1 2 0 2 2 0 1 2 3 4 5 6 7 8 9 10 11

Compact Grid • Build algorithm – Time complexity Linear in the number of objects – Space complexity Linear in the number of objects • Traversal algorithm – Any grid traversal algorithm

Hashed Grid • Reduce memory footprint even further – Fast build algorithm – Efficient access during traversal • Redundancy – Object lists? no Experiments with object list compression failed – Cells? yes Grid is sparse, up to 99% of the cells are empty

Hashed Grid • Row displacement compression C 1 5 11 12 15

Hashed Grid • Row displacement compression C O 1 5 11 12 15 H

Hashed Grid • Row displacement compression C O 1 0 1 5 11 12 15 H 1

Hashed Grid • Row displacement compression C O 1 0 5 1 1 5 11 12 15 H 1 5

Hashed Grid • Row displacement compression C O 1 0 5 1 11 12 1 5 1 11 15 H 1 5 11

Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11 1 15 3 1 5 11 H 1 5 12 11 15

Hashed Grid • Row displacement compression O 0 1 1 3 C[i, j] H[O[i] + j] H 1 5 12 11 15

Hashed Grid • Row displacement compression D O 0 1 1 3 |D| + |O| + |H| << |C| H 1 5 12 11 15

Hashed Grid • Build algorithm – – – Bound Compute domain bits Compute hash function Count Accumulate Insert • Time complexity:

Results • Comparison traditional grid data structures Memory usage Build time

Results • Hashed grid Cruiser • Scene: 3. 64 M triangles, 124. 84 MB • Memory object lists: 28. 84 MB • Memory cells: 55. 48 MB 6. 20 MB • Build time: 0. 39 s 0. 72 s • Render time: 2. 49 s 2. 52 s Thai Statue • Scene: 28. 06 M triangles, 343. 32 MB • Memory object lists: 69. 78 MB • Memory cells: 152. 75 MB 8. 97 MB • Build time: 1. 17 s 1. 76 s • Render time: 1. 55 s 1. 43 s

Applications • Interactive ray tracing of dynamic scenes Scene: 260 K triangles - FPS: 8. 38 FPS (512 x 512)

Applications St. Matthew David • Ray tracing large models • Scene: 56. 23 M triangles, 1. 89 GB • Time to image: 7. 55 s / 10. 21 s • Memory usage: 1. 17 GB / 379. 94 MB • Scene: 372. 77 M triangles, 12. 50 GB • Time to image: - / 60. 75 s • Memory usage: - / 2. 36 GB

Conclusion & Future Work • Conclusion – Compact grid method Optimal grid representation (1 word / cell, 1 word / object reference) – Hashed grid method Applied perfect spatial hashing to grids for ray tracing • Future Work – Extend to hierarchical grids – Extend to other acceleration structures

Thanks! • Questions? Acknowledgments Ares Lagae is a Postdoctoral Fellow of the Research Foundation Flanders (FWO) The Stanford 3 D Scanning Repository, The Digital Michelangelo Project, the bwfirt benchmark, Matthias Rolf, Bernhard Finkbeiner and Greg Ward

Robust Grid Traversal • Discard intersections outside of cell Not robust {} {…}

Robust Grid Traversal • Discard intersections outside of cell Not robust Regular grid traversal

Robust Grid Traversal Do not discard intersections outside of cell – Keep closest intersection, terminate after the intersection Regular grid traversal Robust grid traversal

Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature

Results • Comparison traditional grid data structures Memory usage Build time

Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature

Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11 1 15 3 C[i, j] H[O[i] + j] 1 5 11 H 1 5 12 11 15