19 th Eurographics Symposium on Rendering Compact Fast
![19 th Eurographics Symposium on Rendering Compact, Fast and Robust Grids for Ray Tracing 19 th Eurographics Symposium on Rendering Compact, Fast and Robust Grids for Ray Tracing](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-1.jpg)
![Introduction • Acceleration structures for ray tracing – Kd-tree, BVH, … • Build time: Introduction • Acceleration structures for ray tracing – Kd-tree, BVH, … • Build time:](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-2.jpg)
![Introduction • Algorithms in general – CPU-bound • Execution time = f( CPU speed Introduction • Algorithms in general – CPU-bound • Execution time = f( CPU speed](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-3.jpg)
![Grid Data Structures • Grid and linearized grid 0 ariz e 2 D 0 Grid Data Structures • Grid and linearized grid 0 ariz e 2 D 0](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-4.jpg)
![Grid Data Structures • Data structure using linked lists 0 1 2 3 4 Grid Data Structures • Data structure using linked lists 0 1 2 3 4](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-5.jpg)
![Grid Data Structures • Data structure using dynamic arrays 0 2 1 0 2 Grid Data Structures • Data structure using dynamic arrays 0 2 1 0 2](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-6.jpg)
![Compact Grid • Data structure – Concatenate object lists, store begin index 0 1 Compact Grid • Data structure – Concatenate object lists, store begin index 0 1](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-7.jpg)
![Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 1. Bound Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 1. Bound](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-8.jpg)
![Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 2. Count Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 2. Count](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-9.jpg)
![Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 3. Accumulate Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 3. Accumulate](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-10.jpg)
![Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 4. Insert Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 4. Insert](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-11.jpg)
![Compact Grid • Build algorithm – Time complexity Linear in the number of objects Compact Grid • Build algorithm – Time complexity Linear in the number of objects](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-12.jpg)
![Hashed Grid • Reduce memory footprint even further – Fast build algorithm – Efficient Hashed Grid • Reduce memory footprint even further – Fast build algorithm – Efficient](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-13.jpg)
![Hashed Grid • Row displacement compression C 1 5 11 12 15 Hashed Grid • Row displacement compression C 1 5 11 12 15](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-14.jpg)
![Hashed Grid • Row displacement compression C O 1 5 11 12 15 H Hashed Grid • Row displacement compression C O 1 5 11 12 15 H](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-15.jpg)
![Hashed Grid • Row displacement compression C O 1 0 1 5 11 12 Hashed Grid • Row displacement compression C O 1 0 1 5 11 12](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-16.jpg)
![Hashed Grid • Row displacement compression C O 1 0 5 1 1 5 Hashed Grid • Row displacement compression C O 1 0 5 1 1 5](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-17.jpg)
![Hashed Grid • Row displacement compression C O 1 0 5 1 11 12 Hashed Grid • Row displacement compression C O 1 0 5 1 11 12](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-18.jpg)
![Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11 Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-19.jpg)
![Hashed Grid • Row displacement compression O 0 1 1 3 C[i, j] H[O[i] Hashed Grid • Row displacement compression O 0 1 1 3 C[i, j] H[O[i]](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-20.jpg)
![Hashed Grid • Row displacement compression D O 0 1 1 3 |D| + Hashed Grid • Row displacement compression D O 0 1 1 3 |D| +](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-21.jpg)
![Hashed Grid • Build algorithm – – – Bound Compute domain bits Compute hash Hashed Grid • Build algorithm – – – Bound Compute domain bits Compute hash](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-22.jpg)
![Results • Comparison traditional grid data structures Memory usage Build time Results • Comparison traditional grid data structures Memory usage Build time](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-23.jpg)
![Results • Hashed grid Cruiser • Scene: 3. 64 M triangles, 124. 84 MB Results • Hashed grid Cruiser • Scene: 3. 64 M triangles, 124. 84 MB](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-24.jpg)
![Applications • Interactive ray tracing of dynamic scenes Scene: 260 K triangles - FPS: Applications • Interactive ray tracing of dynamic scenes Scene: 260 K triangles - FPS:](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-25.jpg)
![Applications St. Matthew David • Ray tracing large models • Scene: 56. 23 M Applications St. Matthew David • Ray tracing large models • Scene: 56. 23 M](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-26.jpg)
![Conclusion & Future Work • Conclusion – Compact grid method Optimal grid representation (1 Conclusion & Future Work • Conclusion – Compact grid method Optimal grid representation (1](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-27.jpg)
![Thanks! • Questions? Acknowledgments Ares Lagae is a Postdoctoral Fellow of the Research Foundation Thanks! • Questions? Acknowledgments Ares Lagae is a Postdoctoral Fellow of the Research Foundation](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-28.jpg)
![](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-29.jpg)
![Robust Grid Traversal • Discard intersections outside of cell Not robust {} {…} Robust Grid Traversal • Discard intersections outside of cell Not robust {} {…}](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-30.jpg)
![Robust Grid Traversal • Discard intersections outside of cell Not robust Regular grid traversal Robust Grid Traversal • Discard intersections outside of cell Not robust Regular grid traversal](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-31.jpg)
![Robust Grid Traversal Do not discard intersections outside of cell – Keep closest intersection, Robust Grid Traversal Do not discard intersections outside of cell – Keep closest intersection,](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-32.jpg)
![Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-33.jpg)
![](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-34.jpg)
![Results • Comparison traditional grid data structures Memory usage Build time Results • Comparison traditional grid data structures Memory usage Build time](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-35.jpg)
![Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-36.jpg)
![Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11 Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-37.jpg)
- Slides: 37
![19 th Eurographics Symposium on Rendering Compact Fast and Robust Grids for Ray Tracing 19 th Eurographics Symposium on Rendering Compact, Fast and Robust Grids for Ray Tracing](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-1.jpg)
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 Kdtree BVH Build time Introduction • Acceleration structures for ray tracing – Kd-tree, BVH, … • Build time:](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-2.jpg)
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 CPUbound Execution time f CPU speed Introduction • Algorithms in general – CPU-bound • Execution time = f( CPU speed](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-3.jpg)
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 Grid Data Structures • Grid and linearized grid 0 ariz e 2 D 0](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-4.jpg)
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 Grid Data Structures • Data structure using linked lists 0 1 2 3 4](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-5.jpg)
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 Grid Data Structures • Data structure using dynamic arrays 0 2 1 0 2](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-6.jpg)
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 Compact Grid • Data structure – Concatenate object lists, store begin index 0 1](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-7.jpg)
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 Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 1. Bound](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-8.jpg)
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 Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 2. Count](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-9.jpg)
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 Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 3. Accumulate](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-10.jpg)
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 Compact Grid • Build algorithm (Bound – Count – Accumulate – Insert) 4. Insert](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-11.jpg)
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 Compact Grid • Build algorithm – Time complexity Linear in the number of objects](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-12.jpg)
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 Hashed Grid • Reduce memory footprint even further – Fast build algorithm – Efficient](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-13.jpg)
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 1 5 11 12 15](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-14.jpg)
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 5 11 12 15 H](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-15.jpg)
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 Hashed Grid • Row displacement compression C O 1 0 1 5 11 12](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-16.jpg)
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 Hashed Grid • Row displacement compression C O 1 0 5 1 1 5](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-17.jpg)
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 Hashed Grid • Row displacement compression C O 1 0 5 1 11 12](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-18.jpg)
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 Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-19.jpg)
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 Ci j HOi Hashed Grid • Row displacement compression O 0 1 1 3 C[i, j] H[O[i]](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-20.jpg)
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 Hashed Grid • Row displacement compression D O 0 1 1 3 |D| +](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-21.jpg)
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 Hashed Grid • Build algorithm – – – Bound Compute domain bits Compute hash](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-22.jpg)
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 • Comparison traditional grid data structures Memory usage Build time](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-23.jpg)
Results • Comparison traditional grid data structures Memory usage Build time
![Results Hashed grid Cruiser Scene 3 64 M triangles 124 84 MB Results • Hashed grid Cruiser • Scene: 3. 64 M triangles, 124. 84 MB](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-24.jpg)
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 Applications • Interactive ray tracing of dynamic scenes Scene: 260 K triangles - FPS:](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-25.jpg)
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 Applications St. Matthew David • Ray tracing large models • Scene: 56. 23 M](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-26.jpg)
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 Conclusion & Future Work • Conclusion – Compact grid method Optimal grid representation (1](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-27.jpg)
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 Thanks! • Questions? Acknowledgments Ares Lagae is a Postdoctoral Fellow of the Research Foundation](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-28.jpg)
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
![](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-29.jpg)
![Robust Grid Traversal Discard intersections outside of cell Not robust Robust Grid Traversal • Discard intersections outside of cell Not robust {} {…}](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-30.jpg)
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 • Discard intersections outside of cell Not robust Regular grid traversal](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-31.jpg)
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 Robust Grid Traversal Do not discard intersections outside of cell – Keep closest intersection,](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-32.jpg)
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 sortmiddle approach of Ize et al Asian Dragon Nature Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-33.jpg)
Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature
![](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-34.jpg)
![Results Comparison traditional grid data structures Memory usage Build time Results • Comparison traditional grid data structures Memory usage Build time](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-35.jpg)
Results • Comparison traditional grid data structures Memory usage Build time
![Parallelization Using sortmiddle approach of Ize et al Asian Dragon Nature Parallelization • Using sort-middle approach of Ize et al. Asian Dragon Nature](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-36.jpg)
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 Hashed Grid • Row displacement compression C 12 O 1 0 5 1 11](https://slidetodoc.com/presentation_image/d1553aa842e6bdad1c50ab5fed9dfaa7/image-37.jpg)
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
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