Object Partitioning Considered Harmful: Space Subdivision for BVHs

Stefan Popov Space Subdivision for BVHs

Stefan Popov, Iliyan Georgiev, Rossen Dimov, and Philipp Slusallek

Object Partitioning Considered Harmful: Space Subdivision for

BVHs


Motivation Classical BVH construction is not perfect

Looks only at primitive’s centroids

How much more performance is there?

Classical : Create leaf Correct solution

Tested sp

lits


Background

SAH:

Cost based BVH construction: Top-down Partition set of N’s primitives into NL and NR

Take partition with minimal cost Exhaustive search: O(2N)

)(

)()()(

NSA

NNSANNSACNcost RRLLT

0 1 0 1 1 0 0 1

\NL NR

N


Classical BVH Construction

P2

P1

P3

P4

Assumes finely tessellated geometry Primitive point


Can We Do Better?

Optimal partition Cost ≈ 100

CBVH split Cost ≈ 700


Geometric Partitioning Regular approach: Partition N’s primitives

Evaluate AABBs, and use to compute cost O(2N) partitions to test

Geometric partitioning: Fix child AABBs and put primitives according to SAH Some configurations are infeasible Child AABB boundaries ≡ boundaries of primitives O(N12) configurations to test


Geometric Partitioning Example

Boundaries of NL or R incident with dotted lines P4 shared put into node with smaller SA

P1

P2

P3P4

NL NR


Geometric Partitioning Example

Configuration infeasible P2 is not covered

P1

P2

P3P4

NL NR


Practical Considerations O(N12) is actually O(N6)

Each side of the parent AABB is inherited by a child Select child AABBs on a regular grid

Run-time: O(G6N0.5) including cost calculation Choosing G=RN1/6 yields O(N1.5)

Look at CBVH configurations as well

P1

P2

P3P4

NL NR


Results: FPS Random Rays

Bunny Fairy Forest Sponza Venice Soda Hall

0.70000000000000

1

1

0.4

0.8 0.8

0.70000000000000

1

0.70000000000000

1

0.3

0.5 0.5

0.70000000000000

1

0.4

Classical BVH Our Method (R=64) Our Method (R=4K)

Hig

he

r is

be

tte

r


Results: Surface Area Cost


66 58

142

95

166

68 68

167

108

167

80

150

Classical BVH Our Method (R=64) Our Method (R=4K)

Lo

we

r is

be

tte

r


Result Analysis Suspect: SAH

Overlap + locally minimizing SAH has adverse effect Experiment: Use recursive cost evaluation

Tree cost better than CBVH but slower FPS! Hypothesis: SA model needs space partitioning

Intuition: Early ray termination New algorithm

Penalize overlap in cost function Refine search space by allowing primitive splitting


Splitting Primitives Feasible and infeasible configurations

Two possible ways to split a primitive

SAH cost is the same

P3

P1 P2

NL

NRP3

P1 P2

NL

NR

P3

P1 P2

NL

NRP3

P1 P2

NL

NR


Search Spaces

Child AABBs continuum inside parent’s AABB Not limited to boundary of primitives anymore

Limit search to a grid for practical purposes Augment with search space of other algorithms

CBVH & KD-tree construction search spaces

P3

P1P2

NL

NR P3

P1P2

NL

NR


Penalizing Overlap

Bias SAH to account for overlap

CO – the overlap penalty Standard SAH: CO = 0 Standard SAH with space partitioning: CO ∞

)(

)()(

)(

)(1)(

NSA

NNSANNSA

NV

NNVCCNcost RRLLRLOT


The Generic Algorithm Parameters:

Search space Overlap penalty

Algorithm Take configuration search space with lowest cost

Interesting parameters CBVH: BVH, CO = 0 Full: Grid + KD tree + BVH, CO ∞ KDBVH: KD tree, CO irrelevant


Results: FPS Random Rays


0.70000000000000

1

1

0.4

0.8 0.80.81

0.8

1.11.2

0.81

0.8

1.2 1.2

CBVH Full Search KDBVH

Hig

he

r is

be

tte

r


Results: FPS Frustum Traversal


11

5.1 4.83.3

5.4

9.3

5.15.9

3.7

8.79.3

5.1 5.83.9

8.7

CBVH Full Search KDBVH

Hig

he

r is

be

tte

r


Comparison to Pre-Splitting

CBVH EVH (t=14)

EVH (t=16)

ESC (e=80)

ESC (e=200)

Full Search

KDBVH

0.110.25 0.28 0.29

0.26

0.590.57

0.6 0.6 0.60.5 0.55

0.95 0.96

Sponza Rotated Sponza

Hig

he

r is

be

tte

r


Role of Overlap Penalty

0 2 4 6 8 1060

65

70

75

80

85

1.2

1.6

2

2.4

2.8

Ray Cost Size in MB

Overlap Penalty

Ray

Co

st

MB


Spatial Build Algorithm Implement KDBVH using sweep plane Extensions:

Combine with CBVH to control size using CO

Sampling of cost function Issues: Might miss cost minimum

Cost is quadratic between split plane positions

P3

P2


Conclusion & Future Work

SAH inadequate without space partitioning! Generic framework to study BVH construction

Can explore full 2N search space Spatial build algorithm

Fast with near optimal results Research early termination aware cost function


Thank you!

Documents

Object Partitioning Considered Harmful: Space Subdivision for BVHs