Crowd Simulations

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Crowd Simulations

• Guest Instructor - Stephen J. Guy

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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

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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

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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)

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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

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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
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Digression - Eadweard Muybridge

• 19th Century English Photograyher
• Used multiple cameras to capture motion
• Invented Zoopraxiscope (spinning wheel of still
  images) to animate images

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Walk Cycle - Analysis

• Pros
• Simple to implement
• Captures the basics of human movement
• Cons
• Walks must cycle
• Cant handle changes in stride length
• Cant handle jumps
• Must be animated by hand

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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

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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

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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

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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

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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

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Flocking

• Seminal work in multi-agent movement
• Assign simple force to each agent
• Used in
• Lion King
• Batman Returns

Separation
Alignment
Cohesion
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Boids - Continued

• New forces can be added to incorporate more
  behaviors
• Avoiding Obstacles
• Collision Avoidance
• Be Creative!

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Boids Online

• Visit http//www.red3d.com/cwr/boids/
• And http//www.red3d.com/cwr/steer/Unaligned.html
  

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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

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Helbings 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
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Social Force Model Pedestrian Avoidance
Collision Avoidance
Non-penetration
Sliding Force

• rij dij ?Edge-to-edge distance
• nij Vector pointing away from agent
• Aie(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

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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

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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

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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) vA 2vA vA ? VOAB(vB)

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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
RA RB
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RVO Planning In Velocity Space
(VA VB)/2
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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
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RVO Planning In Velocity Space
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Videos

• 12 Agents in a Circle

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Videos

• 1,000 agents in a circle

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Related data-structures

• KD-trees
• Allowing efficient gathering of nearby neighbors
  O(log n)
• Roadmaps A
• Allows global navigation around obstacles

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Roadmaps

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

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Video

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

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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

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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

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Imposters

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

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Questions

• ?