Compact, Fast and RobustGrids for Ray Tracing

Ares Lagae & Philip Dutré

19th Eurographics Symposium on Rendering

EGSR 2008 Wednesday, June 25th

Introduction

• Acceleration structures for ray tracing– Kd-tree, BVH, …

• Build time: slower (super-linear)• Render time: faster

– Grid• Build time: faster (linear)• Render time: slower

Minimize time to image– Time to image = render time + build time– Especially for dynamic scenes

Introduction

• Algorithms in general– CPU-bound

• Execution time = f( CPU speed )

– Memory-bound• Execution time = f( memory speed )

Accelerate by decreasing memory footprint

Minimize memory footprint– Especially for large models

Grid Data Structures

• Grid and linearized grid

2

1

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0 1 2

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2D

1D

linea

rize

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Grid Data Structures

• Data structure using linked lists0 1 2 3 4 5 6 7 8

1 1 0 2

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2 0 2 2

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• 1 word / cell

• 2/3 words / object reference

Grid Data Structures

• Data structure using dynamic arrays0 1 2 3 4 5 6 7 8

1 1 0 0

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0 2 2

2 0 2 1 2 1 2 1 4 3 2 2 2 1 2 1 2 1

• 3 words / cell

• 1-2 words / object reference : unused space

Compact Grid

• Data structure– Concatenate object lists, store begin index

0 0 1 2 6 8 9 10

0 1 2 3 4 5 6 7 8

11

1 1 0 0 1 1 2 0 2 2

0 1 2 3 4 5 6 7 8 9 10 11

1 word / cell, 1 word / object reference

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NM S

V

Compact Grid

• Build algorithm (Bound – Count – Accumulate – Insert)

1. Bound Compute bounding box of objects

Determine grid resolution

Grid size linear in number of objects

Compact Grid

• Build algorithm (Bound – Count – Accumulate – Insert)

2. Count Compute size of object lists (1st pass)

0 1 1 1 2 1 1 1

0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8 9 10 11

3

Compact Grid

• Build algorithm (Bound – Count – Accumulate – Insert)

3. Accumulate Compute indices of object lists

0 1 2 3 8 9 10 11

0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8 9 10 11

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Compact Grid

• Build algorithm (Bound – Count – Accumulate – Insert)

4. Insert Reversely insert the object references (2nd pass)

0 0 1 2 6 8 9 10

0 1 2 3 4 5 6 7 8

1 1 0 0 1 1 2 0 2 2

0 1 2 3 4 5 6 7 8 9 10 11

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Compact Grid

• Build algorithm– Time complexity

Linear in the number of objects

– Space complexity Linear in the number of objects

• Traversal algorithm– Any grid traversal algorithm

Hashed Grid

• Reduce memory footprint even further– Fast build algorithm– Efficient access during traversal

• Redundancy– Object lists? no

Experiments with object list compression failed

– Cells? yesGrid is sparse, up to 99% of the cells are empty

Hashed Grid

• Row displacement compression

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12 15

C

Hashed Grid

• Row displacement compression

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12 15

C O

H

Hashed Grid

• Row displacement compression

1

5

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12 15

1

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C O

H

0

Hashed Grid

• Row displacement compression

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12 15

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C O

H

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Hashed Grid

• Row displacement compression

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12 15

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111 5

C O

H

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Hashed Grid

• Row displacement compression

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12 15

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12 15

12 11 151 5

C O

H

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Hashed Grid

• Row displacement compression

12 11 151 5

O

HC[i,j] H[O[i] + j]

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Hashed Grid

• Row displacement compression

12 11 151 5

D O

H|D| + |O| + |H| << |C|

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4/3( ) ( )O M O M

Hashed Grid

• Build algorithm– Bound– Compute domain bits– Compute hash function– Count– Accumulate– Insert

• Time complexity:

Results

• Comparison traditional grid data structures

Memory usage Build time

Results

• Hashed grid

Tha

i Sta

tue

• Scene: 28.06 M triangles, 343.32 MB

• Memory object lists: 69.78 MB

• Memory cells: 152.75 MB 8.97 MB

• Build time: 1.17 s 1.76 s

• Render time: 1.55 s 1.43 s

Cru

iser

• Scene: 3.64 M triangles, 124.84 MB

• Memory object lists: 28.84 MB

• Memory cells: 55.48 MB 6.20 MB

• Build time: 0.39 s 0.72 s

• Render time: 2.49 s 2.52 s

Applications

• Interactive ray tracing of dynamic scenes

Scene: 260 K triangles - FPS: 8.38 FPS (512 x 512)

Applications

• Ray tracing large models

St.

Mat

thew • Scene: 372.77 M triangles, 12.50 GB

• Time to image: - / 60.75 s

• Memory usage: - / 2.36 GB

Dav

id

• Scene: 56.23 M triangles, 1.89 GB

• Time to image: 7.55 s / 10.21 s

• Memory usage: 1.17 GB / 379.94 MB

Conclusion & Future Work

• Conclusion– Compact grid method

Optimal grid representation (1 word / cell, 1 word / object reference)

– Hashed grid method Applied perfect spatial hashing to grids for ray tracing

• Future Work– Extend to hierarchical grids– Extend to other acceleration structures

Thanks!

• Questions?

AcknowledgmentsAres Lagae is a Postdoctoral Fellow of the Research Foundation Flanders (FWO)The Stanford 3D Scanning Repository, The Digital Michelangelo Project, the bwfirt benchmark, Matthias Rolf, Bernhard Finkbeiner and Greg Ward

Robust Grid Traversal

• Discard intersections outside of cell Not robust

{}

{…}

Robust Grid Traversal

• Discard intersections outside of cell Not robust

Regular grid traversal

Robust Grid Traversal

Do not discard intersections outside of cell– Keep closest intersection, terminate after the intersection

Regular grid traversal Robust grid traversal

Parallelization

• Using sort-middle approach of Ize et al.

Asian Dragon Nature

Results

• Comparison traditional grid data structures

Memory usage Build time

Parallelization

• Using sort-middle approach of Ize et al.

Asian Dragon Nature

Hashed Grid

• Row displacement compression

1

5

11

12 15

1

5

11

12 15

12 11 151 5

C O

HC[i,j] H[O[i] + j]

0

1

1

3