Crowd Simulation in Froblins

Jeremy Shopf, AMD GPG

Beyond Programmable Shading: In Action Outline

• Motivation • Global Navigation using the GPU • Local Navigation and Avoidance • Spatial Queries • Conclusions

• Global path finding along with local navigation and avoidance – Crowd dynamics similar to fluids – Agents “flow” towards the closest goal, along the path of least resistance – Froblins follow correct paths and do not “get stuck” • Implemented in DirectX® 10.1

• Continuum approach [Treuille et al. 2006] – Smooth flow-like crowd movement – Congestion avoidance – Emergent behavior

• Model environment as positive cost function Static Cost + Agent Density + Hazards = Total Cost

• Potential ( Φ ) = cost integrated along shortest path to goal. “Travel-time” • Φ=0 at goal, satisfies eikonal equation everywhere else: (x) = F

Cost Potential ∆ Potential • By following the negative gradient of the potential, agents are guaranteed to follow optimal path

• Initialization: Set goal cell Φ = 0. Mark goal cell as KNOWN. All else UNKNOWN.

UNKNOWN ∞ ∞ ∞ NEIGHBOR ∞ 0 ∞ KNOWN ∞ ∞ ∞

1. Mark UNKNOWN cells adjacent to KNOWN cells as NEIGHBOR

UNKNOWN ∞ ∞ ∞ NEIGHBOR ∞ 0 ∞ KNOWN ∞ ∞ ∞

2. Calculate Φ at each NEIGHBOR

UNKNOWN ∞ 2 ∞ NEIGHBOR 1 0 2 KNOWN ∞ 3 ∞

3. Mark NEIGHBOR cell with smallest Φ from step 2 as KNOWN

UNKNOWN ∞ 2 ∞ NEIGHBOR 1 0 2 KNOWN ∞ 3 ∞

1. Mark UNKNOWN cells adjacent to KNOWN cells as NEIGHBOR

UNKNOWN ∞ 2 ∞ NEIGHBOR 1 0 2 KNOWN ∞ 3 ∞

2. Calculate Φ at each NEIGHBOR

UNKNOWN 3 2 ∞ NEIGHBOR 1 0 2 KNOWN 4 3 ∞

3. Mark NEIGHBOR cell with smallest Φ from step 2 as KNOWN

UNKNOWN 3 2 ∞ NEIGHBOR 1 0 2 KNOWN 4 3 ∞

1. Mark UNKNOWN cells adjacent to KNOWN cells as NEIGHBOR

UNKNOWN 3 2 ∞ NEIGHBOR 1 0 2 KNOWN 4 3 ∞

2. Calculate Φ at each NEIGHBOR

UNKNOWN 3 2 4 NEIGHBOR 1 0 2 KNOWN 4 3 ∞

3. Mark NEIGHBOR cell with smallest Φ from step 2 as KNOWN

UNKNOWN 3 2 4 NEIGHBOR 1 0 2 KNOWN 4 3 ∞

3. Mark NEIGHBOR cell with smallest Φ from step 2 as KNOWN

UNKNOWN 3 2 4 .. And so on until the neighbor list is empty NEIGHBOR 1 0 2 KNOWN 4 3 ∞

• Worst-case complexity O(n lg n) • One cells’ potential calculated per iteration • Not fast enough for our application • Not readily parallelizable

• No ordered data structure • Iteratively update active cells in parallel • Active cells determined by convergence measure • Active cells updated and culled in tiles

• For smaller datasets, maintaining active tile list and testing convergence has negative performance impact • Conservative iteration # determined empirically • Solve 4 solutions simultaneously – 98% ALU utilization • 5-39x speedup over CPU FMM*

*Configuration: AMD reference platform with AMD Athlon™ 64 X2 Dual-Core Processor 4600+, 2.40GHz, 2GB RAM. GPU: ATI Radeon™ HD 4870 Graphics. Beyond Programmable Shading: In Action Motherboard: ASUSTek M2R32-MVP. Memory: DDR2-800 400 MHz. Operating 22 System: Windows Vista® SP1. All slides © 2008 Advanced Micro Devices, Inc. Used with permission. Global Navigation Direction Results

Results

• High API overhead – API calls and state changes – Compute API would provide quicker thread launch • Would benefit from shared memory – Perform several iterations for a tile in one launch [Jeong and Whitaker 2007] – Local Data Share (CAL/DX11/OpenCL) • Will map easily to DX11 Compute Shader

• Computed spatially • Scales well with number of agents • Motion fidelity dependent on resolution of solution

• “Sense” surroundings • Update velocity based on positions and velocities of nearby agents/obstacles • Based on Velocity Obstacle formulation [Fiorini and Shiller 1998]

Agent Positions Bin Counter Bin Array 3 0 1 0 0 3 1 5 1 0 0 1 1 5 2 0 0 0 1 2 6 4 0 0 0 2 4 6 • World space position mapped to 2D index • Bin Counter: color buffer, tracks bin loads • ID Array: depth array, stores binned IDs

• Translate position to 2D index • Fetch bin load from color buffer • Fetch binned agent IDs from depth array – IDs are stored in array in sorted order

• Binning is a multi-pass algorithm – A single agent can fall into a given bin per pass – Once binned, agents removed from working set – Algorithm repeats until working set is empty

• Rasterize agents as point primitives • Use depth-test unit to bin in sorted order • Additively blend binned points to maintain bin counts

• A naïve implementation requires n passes over m points • Use GS & stream-out to cull binned points • Use predicated rendering to terminate unnecessary draw calls once all agents are binned • Detailed description in course notes

• Evaluate a fixed set of possible directions relative to global navigation direction

• Calculate fitness of each discrete direction • Fitness based on minimum time to collision and angle relative to global navigation direction • Choose direction with greatest fitness

• Real-time frame rates (>20fps) on ATI Radeon™ HD 4870* – >65,000 agents simulated or – 3,000 highly detailed froblins rendered and simulated or – 16,384 simplified agents rendered and simulated

*Configuration: AMD reference platform with AMD Athlon™ 64 X2 Dual-Core Processor 4600+, 2.40GHz, 2GB RAM. GPU: ATI Radeon™ HD 4870 Grahpics. Beyond Programmable Shading: In Action Motherboard: ASUSTek M2R32-MVP. Memory: DDR2-800 400 MHz. Operating 37 System: Windows Vista® SP1. All slides © 2008 Advanced Micro Devices, Inc. Used with permission. Advantages/Disadvantages

Advantages Disadvantages

Smooth flow Group-based Computed spatially Global knowledge Global Avoids congestion Emergent phenomena

Fine-grained navigation and Small set of discrete avoidance directions may cause Local oscillations

Deadlock scenarios

• Massive crowd simulation entirely utilizing the GPU • Novel binning algorithm • See course notes for “Advances in Real- Time Rendering in 3D Graphics and Games” for more on Froblins

• Game Computing Applications Group – Natalya Tatarchuk, Chris Oat, Joshua Barczak, Abe Wiley • Dan Abrahams-Gessel • Won-Ki Jeong

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