Parallel Rendering. Jongwook Jin Kwangyun Wohn VR Lab. CS Dept. KAIST MAR

Transcription

1 Optimal Partition for Parallel Rendering Jongwook Jin Kwangyun Wohn VR Lab. CS Dept. KAIST Culture Technology Research Center MAR

2 Optimal Partition for Parallel Rendering Load balanced partition for rendering Adhoc and Scan-like Tries No Optimal Approaches for reducing Parallel rendering Hazards Partition algorithm for Parallel Rendering Load Balance with Minimization Parallel Rendering Hazards Realtime Partitioning Performance

3 Parallel Graphics Hazards Processing Hazard Unbalanced Graphics Processing vertices etcesa and dp pixel processing pocess overlap primitives between different partitions Management Hazard Unbalanced Management Processing frame coherency between each processor s partitions of animate frame se quence out of core rendering resources management

4 Optimal Partition Generation for Parallel Graphics Typical Load balancing for New Load balancing for Parallel processing Parallel Realtime Graphics Preprocessed, Static Partition Load Balance with Minimization Cutting Edge between Partitions (for communication minimization) Runtime, Dynamic Partition with computing time constraints Load Balance with minimizing Parallel Graphics Hazards

5 Optimal Partition Generation for Parallel Graphics Visibility Culling Graph Modeling Graph Partitioning View frustum Culling with Adapting graph size for Hazards Minimization i i Hierarchical Structure realtime partition algorithm within load balance condition Problem set per each image frame 3D or 2D Graph for problem set Graphics Hazards Modeling via Weighted Laplacian Fast, Efficient i and Scalable Graph Partition Algorithm with realtime constraints Optimal graph partition for Assignments to graphic processors

6 Graph Partition Algorithm - Overview of Spectral Bisection A Workload Graph expresses as a Laplacian Matrix. Rayleigh quotient of Assignment Vector and laplacian matrix represents sum of cutting edge cost between two partitions. Laplacian Matrix L ij 1 if ( v i, v j ) = d i if i = j 0 else E Discrete Optimization x t Lx = 4 {# edges connecting nodes in N - to nodes in N + } x i = ± 1 Continues Relaxation F ( x ) = x t Lx x x = ( i, j) E ( x i x j ) 2

7 Graph Partition Algorithm - Overview of Spectral Bisection Spectral analysis of laplacianl matrix; Second smallest eigenvector minimizes Rayleigh Quotient. Optimal assignment vector is a good approximation to load balanced graph partition problem with minimal communication edges between partitions. Spectral Analysis L = n t λi ziz λ i 1 = 0, z1 = e and λi < λi+ 1 i= 1 Optimal Assignment Vector minimize x 0 t e x= 0 t x Lx x x over x x = z 2, t x Lx x x = λ 2

8 Graph Partition Algorithm Algorithm Selection Avoidance of computing full spectral analysis; just need is second smallest Eigen vector. Modification of conventional optimization method; Conjugate Gradient Method Shows High convergence speed to second smallest Eigen vector of Laplacian matrix Meets Load balance constraint Requires Low memory

9 Conjugate gradient method for the spectral partitioning of graphs F( x) t x Lx 2 =, F( x) = ( L x F( x) x) x x x x Step 1: Initialize x 0 and gradient vector g ( h = g 0 = F x0), 0 0 Step 2: Step 3: Fletch-Reeves Conjugate gradient method α x g h k k k k = min F( xk 1 + αhk 1) α = x k 1 + α h = F( x ) k 1 gk gk = gk + hk g g k k k 1 k 1 Check for convergence. If convergence has not been reached go to Step 2. 1 Step 4: Accept optimal vector x = x k

10 Experiment for feasibility study Visibility Culling Graph Modeling Graph Partitioning View frustum Culling with 3D 6 Grid Vertex Graph User Specific Hazard and Hierarchical Structure for problem set Load balance thresholds Visible iibl Octree cell set per each image frame Rendering Primitive Cost Modeling via Weighted Laplacian Fast, Efficient i and Scalable Graph Partition Algorithm with realtime constraints Optimal graph partition for Assignments to graphic processors

11 Load Balanced Partition Generation Urban Scene (Digital Media City) Positive Set Negative Set triangles [262 visible octree cells] [49] [213] Imbalance 5185 / = 1.60%

12 Optimal Bisection for a image frame Objective imbalance 182 iteration for partitioning weighted graph of 262 octree cells

13 Optimal Bisection for animation frames Camera Closing to urban ground and Partitions

14 Dynamic Workload by camera movement Graph Size and Imbalance VertexCount imbalance With Objective function threshold , Imbalance threshold 2%

15 Time Complexity and Execution Time 1000 Graph Size and Iteration Count VertexCount IterCount Graph Size and Execution Time Intel Pentium 2.4Ghz 3Giga Memory VertexCount MilliSec

16 Conclusion Optimal partition i could be solved in realtime for parallel graphics and simulations. Future works Graphics Hazards Modeling for reducing parallel graphics hazards Valley Constraint Optimization for partition s frame coherency Recursive partitioning for K-way processors

17 Thanks a lot.