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Parallel Reinsertion for Bounding Volume Hierarchy Optimization Daniel Meister and Ji r Bittner Department of Computer Graphics and Interaction Faculty of Electrical Engineering Czech Technical University in Prague Motivation:

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Parallel Reinsertion for Bounding Volume Hierarchy Optimization

Daniel Meister and Jiˇ r´ ı Bittner

Department of Computer Graphics and Interaction Faculty of Electrical Engineering Czech Technical University in Prague

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Motivation: High-Performance Ray Tracing

Movie industry - saving hours of computational time Computer games - precomputed BVH for static geometry camera image plane

[courtesy of Martin Lubich] Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 2/27

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Bounding Volume Hierarchy (BVH)

Ray tracing, collision detection, visibility culling Rooted tree of arbitrary branching factor

References to geometric primitives in leaves Bounding volumes in interior nodes

A B A B [Clark 1976]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 3/27

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Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + P(NL∣N)c(NL) + P(NR∣N)c(NR) if N is interior node cI∣N∣

  • therwise

[MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + P(NL∣N)c(NL) + P(NR∣N)c(NR) if N is interior node cI∣N∣

  • therwise

[MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + P(NL∣N)c(NL) + P(NR∣N)c(NR) if N is interior node cI∣N∣

  • therwise

[MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + SA(NL)

SA(N) c(NL) + P(NR∣N)c(NR)

if N is interior node cI∣N∣

  • therwise

[MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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SLIDE 8

Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + SA(NL)

SA(N) c(NL) + SA(NR) SA(N) c(NR)

if N is interior node cI∣N∣

  • therwise

[MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + SA(NL)

SA(N) c(NL) + SA(NR) SA(N) c(NR)

if N is interior node cI∣N∣

  • therwise

c(Nroot) = 1 SA(Nroot) ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ cT ∑

Ni

SA(Ni) + cI ∑

Nl

SA(Nl)∣Nl∣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ [MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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Surface Area Heuristic (SAH)

c(N) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ cT + SA(NL)

SA(N) c(NL) + SA(NR) SA(N) c(NR)

if N is interior node cI∣N∣

  • therwise

c(Nroot) = 1 SA(Nroot) ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ cT ∑

Ni

SA(Ni) + cI ∑

Nl

SA(Nl)∣Nl∣ ⎤ ⎥ ⎥ ⎥ ⎥ ⎦ ∝ ∑

Ni

SA(Ni) if ∣Nl∣ = 1 [MacDonald and Booth 1990]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 4/27

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BVH Construction Methods

Top-down Surface Area Heuristic [Hunt et al. 2007] Binning [Ize et al. 2007, Wald 2007] k-means clustering [Meister and Bittner 2016] Bottom-up Agglomerative clustering [Walter et al. 2008, Gu et al. 2013]

  • Approx. aggl. clustering [Gu et al. 2013, Meister and Bittner 2017]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 5/27

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BVH Construction Methods

Insertion Heuristic greedy search [Goldsmith and Salmon 1987] Online construction [Bittner et al. 2015] Optimization Rotations [Kensler 2008, Kopta et al. 2012] Insertion-based optimization [Bittner 2013 et al.] Treelet restructuring [Karras and Aila 2013, Domingues and Pedrini 2015]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 6/27

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BVH Construction Methods

Insertion Heuristic greedy search [Goldsmith and Salmon 1987] Online construction [Bittner et al. 2015] Optimization Rotations [Kensler 2008, Kopta et al. 2012] Insertion-based optimization [Bittner 2013 et al.] Treelet restructuring [Karras and Aila 2013, Domingues and Pedrini 2015]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 6/27

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Sequential Insertion-Based Optimization

!

[Bittner et al. 2013]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 7/27

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Sequential Insertion-Based Optimization

Remove a node causing the cost overhead and update bounding boxes

!

[Bittner et al. 2013]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 7/27

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Sequential Insertion-Based Optimization

Remove a node causing the cost overhead and update bounding boxes Search for a new position using branch-and-bound search with priority queue

!

[Bittner et al. 2013]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 7/27

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Sequential Insertion-Based Optimization

Remove a node causing the cost overhead and update bounding boxes Search for a new position using branch-and-bound search with priority queue Insert the child nodes into the found position decreasing the global cost

!

[Bittner et al. 2013]

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 7/27

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Parallel Insertion-Based Optimization

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 8/27

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Parallel Insertion-Based Optimization

Search for new positions for all nodes in parallel

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 8/27

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Parallel Insertion-Based Optimization

Search for new positions for all nodes in parallel Resolve conflicts prioritizing nodes with the higher cost reduction in parallel

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 8/27

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Parallel Insertion-Based Optimization

Search for new positions for all nodes in parallel Resolve conflicts prioritizing nodes with the higher cost reduction in parallel Reinsert not conflicting nodes in parallel

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 8/27

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Reinsertion = Removal + Insertion

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 9/27

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Reinsertion = Removal + Insertion

Removal - remove input node and its parent

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 9/27

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Reinsertion = Removal + Insertion

Removal - remove input node and its parent Insertion - use parent as a common parent for input and output nodes

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 9/27

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Bounding Boxes on Path

Positive zone - removals shrinking bounding boxes Zero zone - removals and insertions not changing bounding boxes Negative zone - insertions enlarging bounding boxes

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 10/27

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Bounding Boxes on Path

Positive zone - removals shrinking bounding boxes Zero zone - removals and insertions not changing bounding boxes Negative zone - insertions enlarging bounding boxes

We can track cost reduction without removing the node!

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 10/27

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Search Overview

Proceeding up to the root visiting sibling subtrees Pre-order traversal using parent links (no priority queue!) Incrementally tracking the cost reduction Pruning the search using the best output node found so far

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 11/27

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Search Overview

Proceeding up to the root visiting sibling subtrees Pre-order traversal using parent links (no priority queue!) Incrementally tracking the cost reduction Pruning the search using the best output node found so far

Many nodes can search independently in parallel

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 11/27

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Search - Example

in

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest= out

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot parent cannot be

  • utput node!
  • utbest

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot pruning!

  • utbest
  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot better position found!

  • utbest= out

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut =

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest
  • ut

pruning!

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • utbest

= out

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Search - Example

in pivot

  • ut

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 12/27

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Parallel Reinsertion

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 13/27

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Parallel Reinsertion

Topological conflicts - concurrent modification of topology

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 13/27

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Parallel Reinsertion

Topological conflicts - concurrent modification of topology Path conflicts - sharing nodes on the paths

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 13/27

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Parallel Reinsertion

Topological conflicts - concurrent modification of topology Path conflicts - sharing nodes on the paths Conflict resolution by atomic locks prioritizing paths with higher cost reduction

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 13/27

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Conservative Strategy

Resolve both topological and path conflicts

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 14/27

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Conservative Strategy

Resolve both topological and path conflicts

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 14/27

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Conservative Strategy

Resolve both topological and path conflicts

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 14/27

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Aggressive Strategy

Resolve only topological conflicts

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 15/27

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Aggressive Strategy

Resolve only topological conflicts

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 15/27

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Aggressive Strategy

Resolve only topological conflicts

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 15/27

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Aggressive Strategy

Resolve only topological conflicts

Experiments showed that aggressive strategy converges faster to lower costs

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 15/27

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Superiority of Aggressive Strategy

Significantly more reinsertions performed in parallel Total cost reduction is not sum of costs reductions of individual reinsertions

Detailed analysis can be found in the paper

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 16/27

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Performance Optimization - Sparse Search

Search phase is the bottleneck Chance of conflicts between neighboring nodes Process every µ-th node shifted by index of iteration (parameter µ)

  • iter. 0
  • iter. 1
  • iter. 2
  • iter. 3

... ... ... ... ...

µ = 3

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 17/27

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Termination Criteria

Optimization iteration

yes yes no no μ > 1 cprev - c < ε μ = μ - 1 end

parameter ε (reasonable choice ε = 0.1)

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 18/27

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Implementation in CUDA

Atomic lock 64-bit integers with atomic max Comparison of positive floats in integer representation Using node index to prevent deadlocks Path encoding Only necessary for the conservative strategy Path in binary tree encoded in bitset 128 bits enough for all paths

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 19/27

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Results

8 scenes (1-8.6M tris) Path tracing (GPU ray tracing kernel [Aila and Laine 2009]) Intel Core I7-3770 3.4 GHz CPU (4 cores), 16 GB RAM CUDA 9.1, NVIDIA GeForce GTX TITAN X (Maxwell), 12 GB RAM

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 20/27

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Tested Methods

LBVH [Karras 2012] Spatial medians ATRBVH [Domingues and Pedrini 2015] Treelet restructuring by agglomertive clustering PLOC [Meister and Bittner 2017] Parallel locally-ordered clustering RBVH [Bittner et. al 2013] Sequential insertion-based optimization PRBVH Parallel insertion-based optimization (our algorithm) Adaptive leaf sizes, SAH cost constants cT = 3, cI = 2

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 21/27

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Pompeii

5632k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 22/27

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Pompeii

5632k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 22/27

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Pompeii

5632k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 22/27

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Pompeii

5632k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 22/27

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Pompeii

5632k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 22/27

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Pompeii

5632k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 22/27

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San Miguel

7880k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 23/27

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San Miguel

7880k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 23/27

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San Miguel

7880k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 23/27

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San Miguel

7880k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 23/27

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San Miguel

7880k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 23/27

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San Miguel

7880k tris, aggressive strategy, µ = 9, ε = 0.1

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 23/27

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San Miguel

Influence of sparse search (the µ parameter)

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 24/27

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San Miguel

Influence of sparse search (the µ parameter)

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 24/27

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Crown

Aggressive and conservative strategies

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 25/27

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Conclusion and Future Work

Parallel BVH optimization Parallel search and locking scheme Two orders of magnitude faster than sequential method Trace performance w.r.t. state-of-the-art GPU builders

speedup 8% - 31% w.r.t. PLOC speedup 4% - 12% w.r.t. ATRBVH

Implementation in CUDA with released source codes Future work Wide BVHs Spatial splits

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 26/27

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Thank you for your attention!

The project website with source codes http://dcgi.felk.cvut.cz/projects/prbvh/

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Manuscript

Initial BVH built by LBVH and ATRBVH

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 28/27

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Manuscript

Initial BVH built by LBVH and ATRBVH

Daniel Meister and Jiˇ r´ ı Bittner Parallel Reinsertion for Bounding Volume Hierarchy Optimization 28/27