Group 4 :Christopher Thorpe

Jonghyun Kim

ELEG-652 Principles of Parallel Computer ArchitecturesInstructor : Dr. GaoMentor : JosephData : 12/9/05

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Divide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Divide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Algorithm for a basic ray-tracing

T7

T1 T2

T3 T4

T5

T6

Border

Border

BorderBorder

Building

Src

▶ Three types of tiles 1. Border 2. Building 3. Open space

▶ Three channel models 1. Open space 2. Absorption 3. Reflection

- Devide the map by four areas- Only consider one area- Recursive algorithm

Distribution algorithm for the ray-tracing

1200

1200

1200

Node 0 takes care ofthis ray range

Node 1 takes care ofthis ray range

Node 2 takes care ofthis ray range

▶ Without balanced tasks

Assume we use three nodes

Distribution algorithm for the ray-tracing▶ With balanced tasks

R1

R2

R3

R4

R5R6

R7 R8

(R1+R2+R3+R4)/3

Assume we use three nodes

Equal ray rangefor buildings is

(R5+R6+R7+R8)/3

Equal ray rangefor borders is

Each node takes careof both ray ranges

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Ray direction graph

When the number of rays is 200

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Ray direction graph

When the number of rays is 10,000

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Intensity graph of the received power

When the number of rays is 200

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Intensity graph of the received power

When the number of rays is 10,000

Test bed

Varying the size of tiles

0

200

400

600

800

1000

1200

1400

1600

1800

0.5 0.4 0.3 0.2 0.1Size of tiles (m)

Runtim

e (

s)

Serial version

Parallel versionwithout balancedtasks

Parallel versionwith balancedtasks

- Map area : 100 ⅹ100 m2

- Number of rays : 3000- Number of nodes : 6

050

100150200250300350400

3000 6000 9000 12000 15000

Number of rays

Runt

ime

(s)

Serial version

Parallel versionwithout balancedtasksParallel version withbalanced tasks

Varying the number of rays

- Map area : 100 ⅹ100 m2

- Tile size : 0.5 m- Number of nodes : 6

00.5

11.5

22.5

33.5

4

Number of rays

Spee

dup

Withoutbalanced tasksWith balancedtasks

Varying the number of rays

- Map area : 100 ⅹ100 m2

- Tile size : 0.5 m- Number of nodes : 6

Varying the number of nodes

020406080

100120140

2 3 4 5 6 7

Number of nodes

Runt

ime

(s)

Without balancedtasksWith balancedtasks

- Map area : 100 ⅹ100 m2 - Runtime of serial version : 231 s- Tile size : 0.2 m- Number of rays : 3000

SRC

Another map

Varying the number of nodes

- Map area : 100 ⅹ100 m2 - Tile size : 0.2 m- Number of rays : 3000

0

1

2

3

4

5

6

2 3 4 5 6 7

Number of nodes

Spe

edup

Withoutbalanced tasksWith balancedtasks

SRC

Another map

Varying the number of nodes

- Map area : 100 ⅹ100 m2

- Number of rays : 3000

0

5

10

15

20

25

30

35

40

45

1 2 3 4 5 6 7 8

Number of nodes

Variance

Tile size : 0.5Tile size : 0.3Tile size : 0.1

Conclusion

• Performace depends on tile size, number of rays, and distribution of builings

• With balanced tasks, performance shows better than without balanced tasks

• Implementation overhead is mitigated for any practical map size.

▶ Ray tracing - V. Sridhara, Models and Methodologies for Simulating Urban Mesh Networks - S. Bohacek, The Graph Properties of MANETs in Urban Environments - J. Hansen, Efficient Indoor Radio Channel Modeling Based on Integral Geomet

ry - http://www.eecis.udel.edu/~bohacek/UDelModels/index.html - http://en.wikipedia.org/wiki/Ray_tracer - http://www.cc.gatech.edu/grads/h/helcyon1/ raytracing/raytracing.html

▶ MPI - http://www-unix.mcs.anl.gov/mpi/tutorial/mpibasics/index.htm - http://www.mpi-forum.org/docs/mpi-20-html/mpi2-report.html - http://www.lam-mpi.org/tutorials/ - http://www-unix.mcs.anl.gov/mpi/mpich

List of references and tools