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Crowd Simulations

Crowd Simulations. Guest Instructor - Stephen J. Guy. Outline. Animation basics Key framing Simulation Loop How to move one man Walk Cycle IK How to move one thousand Crowd Models Collision Avoidance Data Structures Rendering. Outline. Animation basics Key framing Simulation Loop

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Crowd Simulations

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  1. Crowd Simulations Guest Instructor - Stephen J. Guy

  2. Outline • Animation basics • Key framing • Simulation Loop • How to move one man • Walk Cycle • IK • How to move one thousand • Crowd Models • Collision Avoidance • Data Structures • Rendering

  3. Outline • Animation basics • Key framing • Simulation Loop • How to move one man • Walk Cycle • IK • How to move one thousand • Crowd Models • Collision Avoidance • Rendering

  4. Animation - Basics • Comp 768 Preview… • Goal: Illusion of continuous motion • Divide into several small time-steps (length T) • Show new image at each time-step • Needs to happened at least ~12/second (more is better) Advance T Draw Picture Update State

  5. Outline • Animation basics • Key framing • Simulation Loop • How to move one man • Walk Cycle • IK • How to move one thousand • Crowd Models • Collision Avoidance • Data Structures • Rendering

  6. Walk Cycle • Simply Translating a character to its goal is unrealistic • Walk Cycle: A looping series of positionswhich represent a character walking (or running or galloping) • Shifting the animation provides the illusion of walking Inplace Shifted w/ Time

  7. Digression - Eadweard Muybridge • 19th Century English Photograyher • Used multiple cameras to capture motion • Invented Zoopraxiscope (spinning wheel of still images) to animate images

  8. Walk Cycle - Analysis • Pros: • Simple to implement • Captures the basics of human movement • Cons: • Walks must cycle • Can’t handle changes in stride length • Can’t handle jumps • Must be animated by hand

  9. Walk Cycle - Alternatives • Inverse Kinematics • Using math to figure out where to place the rest of the body to get the feet moving forward • Motion Capture • Record data of real humans walking • Motion Clips • FSM of different motions 

  10. Outline • Animation basics • Key framing • Simulation Loop • How to move one man • Walk Cycle • IK • How to move one thousand • Crowd Models • Collision Avoidance • Data Structures • Rendering

  11. Crowd Simulation Models • Simplest model – Agent Based: • Capture Global Behavior w/ many interacting autonomous agents • Each person is represented by one agent • Chooses next state based on goal and neighbors • Pioneered by Craig Reynolds • Won 1998 (Technical) Academy Award Advance T For Each Agent s Draw Agent Update State Gather Neighbors

  12. Agent Based Simulations • Flocking • Craig Reylonds • SIGGRAPH1987 • Social Forces Model • Dirk Helbing • Physics Review B 1995 • Nature 2000 • Reciprocal Velocity Obstacles • Van den Berg • I3D 2008

  13. Agent Based Simulations • Flocking • Craig Reylonds • SIGGRAPH1987 • Social Forces Model • Dirk Helbing • Physics Review B 1995 • Nature 2000 • Reciprocal Velocity Obstacles • Van den Berg • I3D 2008

  14. Flocking • Seminal work in multi-agent movement • Assign simple force to each agent • Used in • Lion King • Batman Returns Separation Alignment Cohesion

  15. Boids - Continued • New forces can be added to incorporate more behaviors • Avoiding Obstacles • Collision Avoidance • Be Creative!

  16. Boids Online • Visit: http://www.red3d.com/cwr/boids/ • And: http://www.red3d.com/cwr/steer/Unaligned.html

  17. Agent Based Simulations • Flocking • Craig Reylonds • SIGGRAPH1987 • Social Forces Model • Dirk Helbing • Physics Review B 1995 • Nature 2000 • Reciprocal Velocity Obstacles • Van den Berg • I3D 2008

  18. Helbing’s Social Force Model • Very similar to boid model • Treats all agents as physical obstacles • Solves a = F/m where F is “social force”: • Fij – Pedestrian Avoidance • FiW – Obstacle (Wall) Avoidance Desired Velocity Current Velocity Avoiding Other Pedestrians Avoiding Walls

  19. Social Force Model – Pedestrian Avoidance • rij – dijEdge-to-edge distance • nij – Vector pointing away from agent • Ai*e[(rij-dij)/Bi] Repulsive force which is exponential increasing with distance • g(x)  x if agents are colliding, 0 otherwise • tij – Vector pointing tangential to agent • Vtji – Tangential velocity difference • FiW is very similar Collision Avoidance Non-penetration Sliding Force

  20. Helbing - Continued • Noticed arching • Also observed in real crowds • Killed or injured people whoexperienced too much force (1,600 N/m) – became unresponsive obstacles • Noticed Faster-is-slower effect

  21. Agent Based Simulations • Flocking • Craig Reylonds • SIGGRAPH1987 • Social Forces Model • Dirk Helbing • Physics Review B 1995 • Nature 2000 • Reciprocal Velocity Obstacles • Van den Berg • I3D 2008

  22. Reciprocal Velocity Obstacles • Applied ideas from robotics to crowd simulations • Basic idea: • Given n agents with velocities, find velocities will cause collisions • Avoid them! • Planning is performed in velocity space • RVOAB(vB, vA) = {v’A | 2v’A – vA VOAB(vB)}

  23. RVO: Planning In Velocity Space ?

  24. RVO: Planning In Velocity Space ?

  25. RVO: Planning In Velocity Space RA+ RB ?

  26. RVO: Planning In Velocity Space (VA + VB)/2 ?

  27. RVO: Planning In Velocity Space ?

  28. RVO: Planning In Velocity Space

  29. RVO: Planning In Velocity Space

  30. RVO: Planning In Velocity Space

  31. RVO: Planning In Velocity Space

  32. RVO: Planning In Velocity Space

  33. Videos • 12 Agents in a Circle

  34. Videos • 1,000 agent’s in a circle

  35. Related data-structures • KD-trees • Allowing efficient gathering of nearby neighbors O(log n) • Roadmaps & A* • Allows global navigation around obstacles

  36. Roadmaps • Create roadmap in free space • Find visible source nodes • Graph Search to find path to Destination • A* is very popular graph search algorithm

  37. Video • 1,000 people leaving Sitterson Hall • Uses RVO, Roadmaps, A* and Kd-Trees

  38. Outline • Animation basics • Key framing • Simulation Loop • How to move one man • Walk Cycle • IK • How to move one thousand • Crowd Models • Collision Avoidance • Data Structures • Rendering

  39. Rendering Crowds • Traditional OpenGL pipeline can be too slow for 1000s of agents • View Culling helps, but often not enough • Need Level-of-Detail techniques • Use models with more polygons up close, less when far away

  40. Imposters • Replace Far off agents with an oriented texture • Several Issues • “Popping” • Uniformity • Lighting • Shadows • Many issues addressed in recent works

  41. Questions ?

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