Wouter G. van Toll Atlas F. Cook IV Roland Geraerts Realistic Crowd Simulation with Density-Based Path Planning ICT.OPEN / ASCI October 22nd, 2012

Realistic Crowd Simulation with Density-Based Path Planning Introduction Path planning in virtual environments (e.g. games) Global planning: find a main route Local planning: variety, collision avoidance Many characters at once: crowd simulation Problem: in a crowd, short routes are not always good Collision avoidance cannot solve everything Other routes are unused 2

Realistic Crowd Simulation with Density-Based Path Planning Overview 3 We use crowd density information for global planning Stored in a navigation mesh (Explicit Corridor Map) Planning algorithm: time-based A* Periodic replanning Results Characters take detours around congested areas Crowd spreads over different routes Efficient: tens of thousands of characters in real-time

Realistic Crowd Simulation with Density-Based Path Planning Sneak preview Before:After: 4

Realistic Crowd Simulation with Density-Based Path Planning Preliminaries Navigation Meshes / Crowd Density 5

Realistic Crowd Simulation with Density-Based Path Planning Navigation meshes Characters need to find paths through an environment Navigation graph: 1D edges Not flexible enough for crowds Navigation mesh: 2D polygons Global path: sequence of polygons Local planning during movement Common in modern games / simulations “Crowd simulation has been solved!” Assumptions in the navigation mesh / crowd General framework? 6

Realistic Crowd Simulation with Density-Based Path Planning An exact and flexible navigation mesh Medial axis Closest-obstacle annotations A* on the medial axis  path + corridor Shortest paths with clearance Collision avoidance Multi-layered environments Dynamic updates Explicit Corridor Map 7

Realistic Crowd Simulation with Density-Based Path Planning Fraction of a region R i that is occupied by characters Often in persons per m² Often in levels and colors For us: value ρ i between 0 and 1 (allows multiple character sizes) Practical studies When the density is high, people walk more slowly Density-speed function v(ρ) : [0,1]  [0, v max ] Time-based path planning? crowd density avg. walking speed Crowd density 8 F D E C B A

Realistic Crowd Simulation with Density-Based Path Planning Method Density Map / Density-Based Path Planning 9

Realistic Crowd Simulation with Density-Based Path Planning ECM divides the environment into non-overlapping regions Each region maps to an ECM edge Each region stores its local density Updated in real-time Density of a region  Expected walking speed within the region  Expected traversal time of the edge  Expected delay Density map 10

Realistic Crowd Simulation with Density-Based Path Planning Density-based path planning A* search on the medial axis A character wants a “fast path”, not necessarily the shortest Each ECM edge e i has a density ρ i t min (e i ): traversal time at speed v(0) = v max t dens (e i ): traversal time at speed v(ρ i ) t delay (e i ) = t min (e i ) - t dens (e i ) cost(e i ) = t min (e i ) + w t delay (e i ) Controlling the sensitivity to delays w = 0: shortest path w = 1: “fastest path” (Höcker et al., 2010) w > 1: more eager to take detours 11

Realistic Crowd Simulation with Density-Based Path Planning Replanning Densities change all the time Characters should re-check their paths “We cannot see crowds that are far away” Density viewing distance D along the medial axis A*: if the path length > D, assume ρ = 0  Path has a visible and an invisible part Partial replanning: re-use invisible parts Character has moved More points are visible At a mutually invisible point, A* can stop  Speed vs. knowledge 12

Realistic Crowd Simulation with Density-Based Path Planning Results Realistic Crowds in Real-Time 13

Realistic Crowd Simulation with Density-Based Path Planning Experimental results Varying the cost weight w w = 0  congestions w = 1, no replanning  periodic effect w = 1, replanning  realistic crowd flow  longer but faster paths w > 1  larger detours, indecisive crowd  Useful in other environments? Varying the viewing distance ms in a large city Real-time periodic replanning Multi-threading: steering 50K characters in 30 ms/frame 70 ms/frame left for e.g. replanning 14 # path vertices replanning time D = ∞D = 350 mD = 0 m

Realistic Crowd Simulation with Density-Based Path Planning Closing Comments Conclusions / Future work 15

Realistic Crowd Simulation with Density-Based Path Planning Conclusions The ECM navigation mesh serves as a density map Non-overlapping, exact, always defined Region densities map to “edge speeds” Updated in real-time Characters use density-based A* Short paths with little expected delay Sensitivity to delay can be set (Partial) replanning Result: More realistic crowds Characters spread over routes Characters avoid congestions Emergent: global effects due to individual choices (Still) real-time performance for large crowds 16

Realistic Crowd Simulation with Density-Based Path Planning Future work New questions Use flow information? (speed + direction) Use actual visibility? Event-based vs. periodic replanning Plan with terrain information? 17

Realistic Crowd Simulation with Density-Based Path Planning More information Poster Contact us Questions? 18