Group 4 Christopher Thorpe Jonghyun Kim ELEG652 Principles

Group 4 : Christopher Thorpe Jonghyun Kim ELEG-652 Principles of Parallel Computer Architectures Instructor : Dr. Gao Mentor : Joseph Data : 12/9/05

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Divide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Divide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Algorithm for a basic ray-tracing ▶ Three types of tiles 1. Border 2. Building 3. Open space Border T 7 Border T 1 Building Border T 2 T 3 T 4 Src T 5 Border ▶ Three channel models 1. Open space 2. Absorption 3. Reflection T 6 - Devide the map by four areas - Only consider one area - Recursive algorithm

Distribution algorithm for the ray-tracing ▶ Without balanced tasks Node 1 takes care of this ray range Node 0 takes care of this ray range 1200 Node 2 takes care of this ray range Assume we use three nodes

Distribution algorithm for the ray-tracing ▶ With balanced tasks Equal ray range for buildings is (R 1+R 2+R 3+R 4)/3 R 6 R 2 R 5 Equal ray range for borders is (R 5+R 6+R 7+R 8)/3 R 1 R 3 R 7 R 4 Assume we use three nodes R 8 Each node takes care of both ray ranges

Ray direction graph When the number of rays is 200

Ray direction graph When the number of rays is 10, 000

Intensity graph of the received power When the number of rays is 200

Intensity graph of the received power When the number of rays is 10, 000

Test bed

Varying the size of tiles - Map area : 100 ⅹ 100 m 2 - Number of rays : 3000 - Number of nodes : 6

Varying the number of rays - Map area : 100 ⅹ 100 m 2 - Tile size : 0. 5 m - Number of nodes : 6

Varying the number of rays - Map area : 100 ⅹ 100 m 2 - Tile size : 0. 5 m - Number of nodes : 6

Varying the number of nodes Another map SRC - Map area : 100 ⅹ 100 m 2 - Tile size : 0. 2 m - Number of rays : 3000 - Runtime of serial version : 231 s

Varying the number of nodes Another map SRC - Map area : 100 ⅹ 100 m 2 - Tile size : 0. 2 m - Number of rays : 3000

Varying the number of nodes - Map area : 100 ⅹ 100 m 2 - Number of rays : 3000

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.

List of references and tools ▶ 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 Geometry - http: //www. eecis. udel. edu/~bohacek/UDel. Models/index. html - http: //en. wikipedia. org/wiki/Ray_tracer - http: //www. cc. gatech. edu/grads/h/helcyon 1/ raytracing/raytracing. html ▶ MPI - http: //www-unix. mcs. anl. gov/mpi/tutorial/mpibasics/index. htm http: //www. mpi-forum. org/docs/mpi-20 -html/mpi 2 -report. html http: //www. lam-mpi. org/tutorials/ http: //www-unix. mcs. anl. gov/mpich