Voxel-based rendering has recently received significant attention due to its potential in the context of efficiently rendering massively large and highly detailed scenes. Unfortunately, few or no scenes are available in the form of sparse voxel octrees. In this paper, we present an out-of-core algorithm for constructing a sparse voxel octree from a triangle mesh. Our algorithm allows the input triangle mesh, the output sparse voxel octree, and, most importantly, the intermediate high-resolution 3D voxel grid, to be larger than available memory. We demonstrate that our out-of-core algorithm can construct sparse voxel octrees from triangle meshes using only a fraction of the memory required by an in-core algorithm in roughly the same time, and that our out-of-core algorithm can also handle extremely large triangle meshes.

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