lcts: ray shooting using longest common traversal sequences

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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LCTS: Ray Shooting using Longest Common Traversal Sequences

Vlastimil Havran, Jiří Bittner

havran@fel.cvut.cz

Dept. of Computer Science Czech Technical University

in Prague

Department of Computer Science and Engineering

Computer Graphics Group

http://www.cgg.cvut.cz

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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Outline

1) Introduction (ray shooting, BSP tree)

2) Key Idea of LCTS

3) Simple LCTS

4) Hierarchical LCTS

5) Improvements for LCTS

6) Application and Results

7) Conclusions and Future Work

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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A B

D

Cray

1) Introduction - ray shooting

Given a ray, find out the first object intersected.

Input: a scene and a ray

Output: the object C

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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1) Introduction to BSP trees - construction

A

C

B

D

1 1

A

3

3CD

2

24

B C

4

x

y

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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L R

Left only

L R

Left, then right

L R

Right only

L R

Right, then left

Interior node of BSP tree

1) Introduction to BSP trees - recursive ray traversal algorithm

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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A B

D

D B

x

y

1) Introduction to BSP trees - recursive ray traversal algorithm

BSP tree:

Stack:

2

R R

L R

4

ray

A

L R

C1C

42

412

3

3

1

IntersectionfoundLeft | Right

Left

| Rig

h t

C2

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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1) Introduction to BSP trees - Efficiency of ray shooting

1) Decreasing number of ray-object intersection tests

2) Faster ray-object intersection tests

3) Decreasing number of traversal steps

4) Faster traversal step

Total ray shooting time = time for ray-object intersection tests + time for ray traversal of BSP tree

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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R2:

R1:

2) LCTS - MAIN IDEA

A

C

B

D

1

2

3

x

yB

2

1

A

3

1

B

3

C

2

A D

B

2

1

3

A

R1

R2

Ray origin

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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Traversal History for R1:

head

3) Simple LCTS = sequence of leaves

R1, R2:

A

C

B

D

1

2

3

x

y

B

2

1

3

A

R1

R2

Ray origin

SLCTS(R1, R2):

B

head

B A

tail

Traversal History for R2:

B A

A

tail

head tail

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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;

A

C

B

D

1

3

2

4

x

y

R1

R2

3) Simple LCTS - Problems

1) No common sequence of leaves exists.

2) When accessing SLCTS, object was not found, and traversal has to continue further.

R1

R2

x

y A

C

B

D

1

3

4

2

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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4) Hierarchial LCTS

Traversal History for R2:

Traversal History for R1:

A

C

B

D

1

2

3

x

y

R1

R2

Ray origin

1

B

3

C

2

A D

BC

1(R,L)

D

3(R,L)2(L)

BA

1(R,L)

D

3(R,L)2(R)

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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Traversal History for R2:

Traversal History for R1:

Common Traversal History for all rays between R1 and R2:

= HLCTS(R1, R2):

4) Hierarchial LCTS - contd.

A

1(R,L)

3(R,L)2(R)

1

B

3

C

2

A D

head

D B

tail

2(?)

C

1(R,L)

3(R,L)2(L)

D

DB

B

Matching two traversal histories into common one:

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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4) Hierarchical LCTS - contd.

1) Matching traversal histories for two or more rays.

2) Matching traversal histories for rays with the previously constructed common traversal history.

R1

R2

HLCTS1

R3HLCTS2

HLCTS1 - constructed from traversal history of R1 and R2

HLCTS2 - constructed from HLCTS1 and

traversal history of R3

Ray R3 - traversal uses HLCTS1

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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5) Further Improvements of LCTS concept

1) Unification of empty leaves.

2) Common termination object.

3) Initial leaf sequence.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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head

Simplified LCTS(R1,R2):

2(?)

tail

2(?)

5) Unification of empty leaves

A

C

BD

1

2

3

x

y

R1

R2

Ray origin

45

head

LCTS(R1,R2):

tail

2(?)

=

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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5) Termination object

A

C

BD

1

2

3

x

y

R1

R2Ray origin

45 tail

head

Simplified LCTS(R1,R2):

C

= tailhead

More simplified LCTS(R1,R2):

CTermination object must be convex !

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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5) Initial Leaf Sequence - only for HLCTSUse: For matching common traversal sequence with new traversal history of ray.How: Initial leaf nodes of HLCTS need not be matched,but they are copied only.

R1

R2

HLCTS1

R3HLCTS2

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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A

C

B D

1

2

3

x

y

45

6) LCTS Application and Results

Application - where rays exhibit similarities.

2) Shooting between two patches.

1) Hidden Surface Removal

BA

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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ad 6) Application and Results - contd.

Hidden Surface Removal

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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SLCTS + two dimensions:

SLCTS

SLCTS + scanline:

SLCTS SLCTS

SLCTS

ad 6) Application and Results - contd.

Hidden Surface Removal: four methods - use of SLCTS and HLCTS - using LCTS concept in one or two dimensions

1 3 4 2 6 7 5 1

3 4

26

7

5

8 9

10 11 12

13

14

15 16

17 18 19

20 21 22

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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ad 6) Application and Results - contd.

- Number of traversal steps decreases typically by more than 60 %.

- Time devoted to ray shooting decreases typically by 20 %.

- Speedup achieved is scene and resolution dependent.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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7) Conclusions and Further Work

- New concept of traversal coherence introduced. (not restricted to BSP tree only.)

- SLCTS and HLCTS.

- Hidden Surface Removal tested.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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7) Further Work- automatic setting of image resolution for SLCTS.

- application for higher order rays in global illumination algorithms.

- other image sampling patterns for HLCTS in hidden surface removal.

- use of LCTS in rendering animation sequences.

Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

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Acknowledgements:

- Eduard Groeller and Jan Prikryl from Vienna University of Technology.

- Czech-Austrian scientific cooperation grant Aktion number 1999/17.

- IGP company for partially sponsoring my visit here.