1. LCTS: Ray Shooting using Longest Common Traversal Sequences
Vlastimil Havran, Jiří Bittner
Dept. of Computer Science Czech Technical University in Prague
Department of Computer Science and Engineering
Computer Graphics Group
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

2. 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

3. 1) Introduction - ray shooting
Given a ray, find out the first object intersected. A B D C
ray
Input: a scene and a ray
Output: the object C
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

4. 1) Introduction to BSP trees - constructionA 4 B C A 2 B y C 3 C D D x
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

5. 1) Introduction to BSP trees - recursive ray traversal algorithm
Left only L R
Left, then right
Interior node of
BSP tree L R
Right only L R
Right, then left
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

6. 1) Introduction to BSP trees - recursive ray traversal algorithm4 L R A 2 L R A B 3 4 y
ray 2 C R R D B C1 C2
Left | Right 3
Intersection
found D
Stack: x
Left | Right 4 2
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

7. 1) Introduction to BSP trees - Efficiency of ray shooting
Total ray shooting time =
time for ray-object intersection tests +
time for ray traversal of BSP tree
1) Decreasing number of ray-object intersection tests
2) Faster ray-object intersection tests
3) Decreasing number of traversal steps
4) Faster traversal step
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

8. 2) LCTS - MAIN IDEA 1 B 3 C 2 A D R2 R1: 1 1 3 A D R1 2 3 A B x y B 2
Ray origin A B
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

9. 3) Simple LCTS = sequence of leaves
R1, R2: 1 2 3 A B R2
Traversal History for R1:
head A
tail 1 3 A D B R1
Traversal History for R2: x y B
head 2 A
tail C B
SLCTS(R1, R2):
head A
tail
Ray origin B
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

10. 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. A C B D 1 3 2 4 x y R1 x y A C B D 1 3 4 2 R1 R2 ; R2
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

11. 4) Hierarchial LCTS 1 B 3 C 2 A D Traversal History for R1: 1(R,L) 1 3x y B 2 R1
Ray origin C
Traversal History for R2:
1(R,L)
2(R)
3(R,L) A B D
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

12. 4) Hierarchial LCTS - contd.
Matching two traversal histories into common one:
Traversal History for R1: 1 B 3 C 2 A D
1(R,L)
2(L)
3(R,L) C B D
Common Traversal History
for all rays between R1 and R2:
Traversal History for R2:
= HLCTS(R1, R2):
head
1(R,L)
tail
2(?) D B
2(R)
3(R,L) A B D
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

13. 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
HLCTS1 - constructed from
traversal history of R1 and R2
HLCTS2 R3
HLCTS1
Ray R3 - traversal uses HLCTS1 R2
HLCTS2 - constructed from
HLCTS1 and
traversal history of R3
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

14. 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

15. 5) Unification of empty leaves
LCTS(R1,R2):
head
tail
2(?)
2(?) 1 3 D B 5 A 4 R2 y 2 R1
Ray origin
head
Simplified LCTS(R1,R2): = C x
2(?)
tail
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

16. Termination object must be convex !
tail
head
Simplified LCTS(R1,R2): C D B 5 A 4
Ray origin y R2 2 R1 C 1 3
= tail
head
More simplified
LCTS(R1,R2): C x
Termination object must be convex !
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

17. 5) Initial Leaf Sequence - only for HLCTS
Use: 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
HLCTS2 R3
HLCTS1 R2
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

18. 6) LCTS Application and Results
Application - where rays exhibit similarities.
1) Hidden Surface Removal A C B D 1 2 3 x y 4 5 A B
2) Shooting between
two patches.
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

19. ad 6) Application and Results - contd.
Hidden Surface Removal
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

20. ad 6) Application and Results - contd.
Hidden Surface Removal: four methods
- use of SLCTS and HLCTS
- using LCTS concept in one or two dimensions
SLCTS + scanline:
SLCTS + two dimensions:
SLCTS 1 3 4
SLCTS 2 6 7 5
SLCTS 1 5 6
SLCTS 2 15 16 13 7 8 9 17 18 19 10 11 12 20 21 22 3 4 14
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences

21. 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

22. 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

23. 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

24. - Eduard Groeller and Jan Prikryl from
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.
Vlastimil Havran, Jiri Bittner: LCTS: Ray Shooting using Longest Common Traversal Sequences