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- 1. High Performance Graphics 2013 - 8/21/13 Out-Of-Core Construction of Sparse Voxel Octrees Jeroen Baert, Ares Lagae & Philip Dutré Computer Graphics Group, KU Leuven, Belgium
- 2. Out-Of-Core Construction of Sparse Voxel Octrees 2 / 34 Voxel-related research ● Voxel Ray Casting – Gigavoxels (Crassin, 2009-...) – Efficient SVO's (Laine, Karras, 2010) ● Voxel Cone Tracing – Indirect Illumination (Crassin, 2011) ● Voxel-based Visibility – Voxelized Shadow Volumes (Wyman, 2013, later today!) ● ... Crassin2009 Laine/Karras2010 Crassin2011
- 3. Out-Of-Core Construction of Sparse Voxel Octrees 3 / 34 Why voxels? ● Regular structure ● Hierarchical representation in Sparse Voxel Octrees (SVO's) – Level of Detail / Filtering ● Generic representation for geometry and appearance – In a single data structure CreativeCommons–Wikipedia
- 4. Out-Of-Core Construction of Sparse Voxel Octrees 4 / 34 Polygon mesh to SVO ● We want large, highly detailed SVO scenes ● Where do we find content? ● Let's voxelize massive polygon meshes – Majority of current content pipelines is polygon-based
- 5. Out-Of-Core Construction of Sparse Voxel Octrees 5 / 34 What do we want? ● Algorithm requirements: – Need an out-of-core method ● Because polygon mesh & intermediary structures could be >> system memory – Data should be streamed in/out ● from disk / network / other process – Ideally: out-of-core as fast as in-core Algorithm Polygon Mesh Sparse Voxel Octree
- 6. Out-Of-Core Construction of Sparse Voxel Octrees 6 / 34 Pipeline construction (1) ● Voxelization step – Polygon mesh → Voxel grid ● Followed by SVO construction step – Voxel grid → Sparse Voxel Octree Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction
- 7. Out-Of-Core Construction of Sparse Voxel Octrees 7 / 34 Pipeline construction (2) ● Key insight: – If voxel grid is Morton-ordered – SVO construction can be done out-of-core ● Logarithmic in memory usage ~ octree size ● In a streaming manner – So voxelization step should deliver ordered voxels Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction Morton Ordered Grid
- 8. Out-Of-Core Construction of Sparse Voxel Octrees 8 / 34 Pipeline construction (3) ● High-resolution 3D voxel grid may be >> system memory – So partitioning step (into subgrids) is needed – Seperate triangle streams for each subgrid Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction Morton Ordered Grid Partitioning Mesh Parts
- 9. Out-Of-Core Construction of Sparse Voxel Octrees 9 / 34 Final Pipeline ● Now, every step in detail ... Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction Morton Ordered Grid Partitioning Mesh Parts
- 10. Out-Of-Core Construction of Sparse Voxel Octrees 10 / 34 Morton order / Z-order ● Linearization of n-dimensional grid – Post-order depth-first traversal of 2 n -tree ● Space-filling curve, Z-shaped
- 11. Out-Of-Core Construction of Sparse Voxel Octrees 11 / 34 Morton order / Z-order ● Hierarchical in nature ● Cell at position (x,y) → Morton code – Efficiently computed – (x,y,z) = (5,9,1) → (0101,1001,0001) → 010001000111 → 1095th cell along Z-curve
- 12. Out-Of-Core Construction of Sparse Voxel Octrees 12 / 34 Partitioning subprocess ● Partitioning (1 linear pass) – Into power-of-2 subgrids until it fits in memory – Subgrids temporarily stored on disk – Subgrids correspond to contiguous range in Morton order ● If we voxelize subgrids in Morton order, output will be Morton-ordered Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction Morton Ordered Grid Partitioning Mesh Parts
- 13. Out-Of-Core Construction of Sparse Voxel Octrees 13 / 34 Voxelization subprocess (1) ● Voxelize each subgrid in Morton order – Input: Subgrid triangle stream ● Each triangle voxelized independently – Output: Morton codes of non-empty cells ● Typically, majority of grid is empty Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction Morton Ordered Grid Partitioning Mesh Parts
- 14. Out-Of-Core Construction of Sparse Voxel Octrees 14 / 34 Voxelization subprocess (2) ● We use a simple voxelization method – But any method that works one triangle at a time will do 111011010100 101111010111 ... HuangetAl. Morton codes of non-empty cells
- 15. Out-Of-Core Construction of Sparse Voxel Octrees 15 / 34 Out-of-core SVO Construction ● Input: Morton-ordered voxel grid ● Output: SVO nodes + referenced dataevel Morton code Voxelization Polygon Mesh Sparse Voxel Octree SVO Construction Morton Ordered Grid Partitioning Mesh Parts
- 16. Out-Of-Core Construction of Sparse Voxel Octrees 16 / 34 SVO Construction algorithm in 2D 0 0 3... 1 4 7... 2 8 11... 3 12 15... ● Required: queues of 2 d nodes / octree level – Ex: 20483 grid → 11 * 8 octree nodes-l Octree representationSVO Builder queues Input position In Memory / On-disk Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- 17. Out-Of-Core Construction of Sparse Voxel Octrees 17 / 34 SVO Construction algorithm in 2D ● Read Morton codes 0 → 3 (+ voxel data) – Store them in level 2 queue – Level 2 queue = full 0 3 Octree representationSVO Builder queues 0 1 2 3 Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- 18. Out-Of-Core Construction of Sparse Voxel Octrees 18 / 34 SVO Construction algorithm in 2D ● Create internal parent node – With level 1 Morton code 0 – Store parent-child relations – Write non-empty level 2 nodes to disk+clear level 2 Octree representationSVO Builder queues 0 1 2 3 0 0 0 3 Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- 19. Out-Of-Core Construction of Sparse Voxel Octrees 19 / 34 SVO Construction algorithm in 2D ● Read Morton codes 4 → 7 (+ voxel data) – Store them in level 2 queue Octree representationSVO Builder queues 4 5 6 7 0 0 0 3 4 7... Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- 20. Out-Of-Core Construction of Sparse Voxel Octrees 20 / 34 SVO Construction algorithm in 2D ● Create internal parent node – With level 1 Morton code 1 – Store parent-child relations (there are none) – Write non-empty level 2 nodes to disk+clear level 2 Octree representationSVO Builder queues 4 5 6 7 0 1 0 0 3... 1 Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 4 7...
- 21. Out-Of-Core Construction of Sparse Voxel Octrees 21 / 34 SVO Construction algorithm in 2D ● Same for Morton codes 8 → 11 Octree representationSVO Builder queues 0 1 0 0 3 1 2 9 2 Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
- 22. Out-Of-Core Construction of Sparse Voxel Octrees 22 / 34 SVO Construction algorithm in 2D ● Same for Morton codes 12 → 15 Octree representationSVO Builder queues 0 1 2 3 3 12 15... Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 3 1 2 9
- 23. Out-Of-Core Construction of Sparse Voxel Octrees 23 / 34 SVO Construction algorithm in 2D ● Now level 1 is full – Create parent node (root node) – Store parent-child relations – Write non-empty level 1 nodes to disk+clear level 1 Octree representationSVO Builder queues 0 1 2 3 R R ... ... Level 0 Level 1 Level 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 12 15... 0 0 3 2 9 1
- 24. Out-Of-Core Construction of Sparse Voxel Octrees 24 / 34 SVO Construction: optimization ● Lots of processing time for empty nodes – Sparseness = typical for high-res voxelized meshes ● Insight for optimization – Pushing back 2 d empty nodes in a queue at level n = Pushing back 1 empty node at level n-1 n-1 n ... SVO Builder queues
- 25. Out-Of-Core Construction of Sparse Voxel Octrees 25 / 34 SVO Construction: optimization ● Implementation details in paper ● Optimization exploits sparseness of voxelized meshes ● Speedup: two orders of magnitude – Building SVO from grid: ● David: 471 vs 0.55 seconds ● San Miguel: 453 vs 1.69 seconds
- 26. Out-Of-Core Construction of Sparse Voxel Octrees 26 / 34 Results: Tests ● Resolution: 2048 3 ● Memory limits – 8 Gb (in-core) – 1 Gb (out-of-core) – 128 Mb (out-of-core) ● Models – David (8.25 M polys) – San Marco (7.88 M polys) – XYZRGB Dragon (7.2 M polys)
- 27. Out-Of-Core Construction of Sparse Voxel Octrees 27 / 34 Results: Out-Of-Core performance ● Out-Of-Core method = ~ as fast as In-Core – Even when available memory is 1/64
- 28. Out-Of-Core Construction of Sparse Voxel Octrees 28 / 34 Results: Time breakdown ● Partitioning speedup from skipping empty space
- 29. Out-Of-Core Construction of Sparse Voxel Octrees 29 / 34 Results: Extremely large models ● 4096 3 – In-core: 64 Gb ● Atlas model – 17.42 Gb, 507 M tris – < 11 min at 1 Gb ● St. Matthew model – 13.1 Gb, 372 M tris – < 9 min at 1 Gb
- 30. Out-Of-Core Construction of Sparse Voxel Octrees 30 / 34 Results: SVO Construction ● SVO output stream – Good locality of reference ● Nonempty siblings on same level always stored next to each other – Nodes separated from data itself (separation hot/cold data) ● Using data pointers + offsets as reference
- 31. Out-Of-Core Construction of Sparse Voxel Octrees 31 / 34 Appearance ● Pipeline: binary voxelization ● Extend with appearance data? – Interpolate vertex attributes (color, normals, tex) – Propagate appearance data upwards ● Global data access ↔ Out-Of-Core algorithms – Multi-pass approach DecreasingSVOlevel
- 32. Out-Of-Core Construction of Sparse Voxel Octrees 32 / 34 Conclusion ● Voxelization and SVO construction algorithm – Out-of-core as fast as in-core – Support for extremely large meshes ● Future work – Combine with GPU method to speed up voxelization – Handle global appearance data
- 33. Out-Of-Core Construction of Sparse Voxel Octrees 33 / 34 Thanks! ● Source code / binaries will be available at project page ● Contact – jeroen.baert @ cs.kuleuven.be – @jbaert ● Acknowledgements: – Jeroen Baert funded by Agency for Innovation by Science and Technology in Flanders (IWT), Ares Lagae is a Postdoctoral Fellow of the Research Foundation – Flanders (FWO), David / Atlas / St. Matthew models : Digital Michelangelo project, San Miguel model : Guillermo M. Leal Llaguno (Evolucien VIsual)
- 34. Out-Of-Core Construction of Sparse Voxel Octrees 34 / 34

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