Maximizing Parallelism in the Construction of BVHs, Octrees, and k-d Trees

Tero Karras

NVIDIA Research

Trees

2

Trees

Path tracingPharr & Humphreys

Real-time ray tracingNVIDIA

Collision detectionAgeia

Particle simulationNVIDIA

Voxel-basedglobal illumination

Crassin et al.

Surface reconstructionAmenta et al.

Photon mappingUchida

Better Faster

3

Outline

Fastest existing methods are sequential Parallelize within each hierarchy level But not between levels

4

Outline

Fastest existing methods are sequential Parallelize within each hierarchy level But not between levels

Lack of parallelism Small workloads bottlenecked by top levels Sub-linear scaling of performance

5

Outline

Novel way to build the entire tree in parallel Two algorithmic “building blocks” Fast, scalable

6

Outline

Novel way to build the entire tree in parallel Two algorithmic “building blocks” Fast, scalable

Main focus: BVHs Point-based octrees and k-d trees also covered

in the paper

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Bounding volume hierarchy

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Bounding volume hierarchy

?

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LBVH - Lauterbach et al. [2009]

1. Assign Morton codes2. Sort primitives3. Generate hierarchy4. Fit bounding boxes

p

px = 0.py = 0.pz = 0.

1 0 1 00 1 1 11 1 0 0

10

01

0

LBVH - Lauterbach et al. [2009]

1. Assign Morton codes2. Sort primitives3. Generate hierarchy4. Fit bounding boxes

p

px = 0.py = 0.pz = 0.

1 1 00 1 11 1 0

1 0 1 00 1 1 1

1 1 0 0

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LBVH - Lauterbach et al. [2009]

1. Assign Morton codes2. Sort primitives3. Generate hierarchy4. Fit bounding boxes

p

px = 0.py = 0.pz = 0.

1 0 1 00 1 1 1

1 1 0 01 0 1 01 1 0 0code =

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LBVH - Lauterbach et al. [2009]

1. Assign Morton codes2. Sort primitives3. Generate hierarchy4. Fit bounding boxes

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LBVH - Lauterbach et al. [2009]

1. Assign Morton codes2. Sort primitives3. Generate hierarchy4. Fit bounding boxes

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Binary radix tree

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Longest common prefix

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δ(5,6) = 4

δ(5,6) = 4

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Longest common prefix

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δ(5,6) = 4

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δ(0,3) = 2δ(0,3) = 2

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Garanzha et al. [2011]

Level 3 1 node

Level 2 3 nodes

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Our method

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Our method

Define a numbering scheme for the nodes Gain some knowledge of their identity Establish a connection with the keys

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Our method

Define a numbering scheme for the nodes Gain some knowledge of their identity Establish a connection with the keys

Find the children of a given node Only look at node index and nearby keys

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Our method

Define a numbering scheme for the nodes Gain some knowledge of their identity Establish a connection with the keys

Find the children of a given node Only look at node index and nearby keys

Do this for all nodes in parallel27

Numbering scheme

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Numbering scheme

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Numbering scheme

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Numbering scheme

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Algorithm

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δ(2,3) = 4

Algorithm

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δ(3,4) = 03

δ(2,3) = 4

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Algorithm

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δ(3,4) = 03

δ(2,3) = 4

?δ(1,3) = 2 δ(0,3) = 2

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Algorithm

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δ(0,3) = 2

? δ(2,3) = 4 δ(1,3) = 2

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Algorithm

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For each node i=0..n-2 in parallel:1. Determine direction of the range2. Expand the range as far as possible3. Find where to split the range4. Identify children

Algorithm

Binary search

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Duplicate keys

The algorithm only works with unique keys Duplicates are common in practice

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Duplicate keys

The algorithm only works with unique keys Duplicates are common in practice

Trick: Augment each key with its index Distinguishes between duplicates Keys are still in lexicographical order

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Duplicate keys

The algorithm only works with unique keys Duplicates are common in practice

Trick: Augment each key with its index Distinguishes between duplicates Keys are still in lexicographical order

Tie-break when evaluating δ(i,j)40

LBVH

1. Assign Morton codes2. Sort primitives3. Generate hierarchy4. Fit bounding boxes

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Lauterbach et al. [2009]

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Our method

Need a different approach How many levels are there? Which nodes are located on a given level?

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Our method

Need a different approach How many levels are there? Which nodes are located on a given level?

Traverse paths in the tree in parallel Start from leaves, advance toward the root Terminate threads using per-node atomic flags

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Our method

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Results

Evaluate performance on GTX 480 (Fermi) CUDA, 30-bit Morton codes

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Results

Evaluate performance on GTX 480 (Fermi) CUDA, 30-bit Morton codes

Compare against Garanzha et al. [2011] Identical tree (top-level SAH splits disabled)

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Results

Evaluate performance on GTX 480 (Fermi) CUDA, 30-bit Morton codes

Compare against Garanzha et al. [2011] Identical tree (top-level SAH splits disabled)

Simulate large GPUs N times as many cores N times the memory bandwidth 48

Results

49

Our method Garanzha et al.

Fairy Forest174K triangles

milliseconds

Morton Sort Build AABB Morton Sort Build AABB

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Morton Sort Build AABB Morton Sort Build AABB

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2 ×1 × cores

4 ×

Results

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Our method Garanzha et al.

Fairy Forest174K triangles

milliseconds

Morton Sort Build AABB Morton Sort Build AABB

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Morton Sort Build AABB Morton Sort Build AABB

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1.7 ×1.1 ×

12.5 ×

33.6 ×

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Results

51

Our method

Turbine Blade1.77M triangles

milliseconds

Garanzha et al.

Morton Sort Build AABB Morton Sort Build AABB

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Morton Sort Build AABB Morton Sort Build AABB

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3.7 ×

7.0 ×

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11.625

2.252.875 3.5

4.1254.75

5.375 66.625

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Results

11.625

2.252.875 3.5

4.1254.75

5.375 66.625

7.257.875

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Garanzha et al.

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Stanford Dragon871K triangles

Morton

Sort

Build

AABB

milliseconds

Our method

milliseconds

Acknowledgements

Timo Aila Samuli Laine David Luebke Jacopo Pantaleoni Jaakko Lehtinen

For helpful suggestions and proofreading.

53

Thank You

Questions

Backup slides

Pseudocode

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ResultsCommon Build AABB

Scene Cores Eval Sort Our Prev Our Prev

Fairy Forest(174K tris)

1x 0.05 0.56 0.15 1.88 0.23 0.292x 0.03 0.33 0.09 1.75 0.13 0.224x 0.02 0.30 0.05 1.68 0.08 0.19

Conference Room(283K tris)

1x 0.08 0.78 0.24 1.93 0.35 0.382x 0.04 0.51 0.13 1.72 0.19 0.264x 0.03 0.31 0.08 1.58 0.12 0.20

Stanford Dragon(871K tris)

1x 0.22 1.67 0.65 3.14 1.10 1.032x 0.12 1.09 0.34 2.38 0.57 0.604x 0.06 0.64 0.18 1.97 0.30 0.38

Turbine Blade(1.77M tris)

1x 0.45 2.73 1.28 4.73 2.10 1.772x 0.23 1.63 0.65 3.19 1.07 0.964x 0.12 1.08 0.34 2.37 0.56 0.55

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Algorithm

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Algorithm

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δ(1,2) = 2 δ(2,3) = 4 δ(2,3) = 4

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δ(2,4) = 0

Algorithm

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δ(2,3) = 4

Algorithm

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? δ(2,3) = 4

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δ(2,3) = 4

Algorithm

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