Crowd Simulations
Guest Instructor - Stephen J. Guy
Outline
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Animation basics
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How to move one man
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Walk Cycle
IK
How to move one thousand
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Key framing
Simulation Loop
Crowd Models
Collision Avoidance
Data Structures
Rendering
Outline
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Animation basics
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How to move one man
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Walk Cycle
IK
How to move one thousand
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Key framing
Simulation Loop
Crowd Models
Collision Avoidance
Rendering
Animation - Basics
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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
Outline
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Animation basics
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How to move one man
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Walk Cycle
IK
How to move one thousand
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Key framing
Simulation Loop
Crowd Models
Collision Avoidance
Data Structures
Rendering
Walk Cycle
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Simply Translating a character to its goal
is unrealistic
Walk Cycle: A looping series of positions
which represent a character walking (or running or
galloping)
Shifting the animation provides the illusion of walking
Inplace
Shifted w/ Time
Digression - Eadweard Muybridge
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19th Century English Photograyher
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Used multiple cameras to capture motion
Invented Zoopraxiscope (spinning wheel of still images) to
animate images
Walk Cycle - Analysis
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Pros:
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Simple to implement
Captures the basics of human movement
Cons:
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Walks must cycle
Can’t handle changes in stride length
Can’t handle jumps
Must be animated by hand
Walk Cycle - Alternatives
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Inverse Kinematics
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Motion Capture
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Using math to figure out where to place the
rest of the body to get the feet moving
forward
Record data of real humans walking
Motion Clips
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FSM of different motions
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Outline
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Animation basics
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How to move one man
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Walk Cycle
IK
How to move one thousand
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Key framing
Simulation Loop
Crowd Models
Collision Avoidance
Data Structures
Rendering
Crowd Simulation Models
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Simplest model – Agent Based:
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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
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Won 1998 (Technical) Academy Award
Advance T
For Each Agent
Draw
Agent
Update
s
State
Gather
Neighbors
Agent Based Simulations
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Flocking
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Social Forces Model
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Craig Reylonds
SIGGRAPH1987
Dirk Helbing
Physics Review B 1995
Nature 2000
Reciprocal Velocity Obstacles
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Van den Berg
I3D 2008
Agent Based Simulations
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Flocking
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Social Forces Model
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Craig Reylonds
SIGGRAPH1987
Dirk Helbing
Physics Review B 1995
Nature 2000
Reciprocal Velocity Obstacles
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Van den Berg
I3D 2008
Flocking
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Seminal work in multi-agent movement
Assign simple force to each agent
Used in
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Lion King
Batman Returns
Separation
Alignment
Cohesion
Boids - Continued
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New forces can be added to incorporate more behaviors
Avoiding Obstacles
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Collision Avoidance
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Be Creative!
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Boids Online
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Visit: http://www.red3d.com/cwr/boids/
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And: http://www.red3d.com/cwr/steer/Unaligned.html
Agent Based Simulations
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Flocking
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Social Forces Model
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Craig Reylonds
SIGGRAPH1987
Dirk Helbing
Physics Review B 1995
Nature 2000
Reciprocal Velocity Obstacles
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Van den Berg
I3D 2008
Helbing’s Social Force Model
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Very similar to boid model
Treats all agents as physical obstacles
Solves a = F/m where F is “social force”:
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Fij – Pedestrian Avoidance
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FiW – Obstacle (Wall) Avoidance
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Desired Velocity
Current Velocity
Avoiding Other
Pedestrians
Avoiding Walls
Social Force Model – Pedestrian Avoidance
Collision Avoidance
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Non-penetration
Sliding Force
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
Helbing - Continued
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Noticed arching
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Also observed in real crowds
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Killed or injured people who
experienced too much force (1,600 N/m) – became
unresponsive obstacles
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Noticed Faster-is-slower effect
Agent Based Simulations
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Flocking
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Social Forces Model
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Craig Reylonds
SIGGRAPH1987
Dirk Helbing
Physics Review B 1995
Nature 2000
Reciprocal Velocity Obstacles
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Van den Berg
I3D 2008
Reciprocal Velocity Obstacles
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Applied ideas from robotics to crowd simulations
Basic idea:
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Given n agents with velocities, find velocities will cause collisions
Avoid them!
Planning is performed in velocity space
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RVOAB(vB, vA) = {v’A | 2v’A – vA  VOAB(vB)}
RVO: Planning In Velocity Space
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RVO: Planning In Velocity Space
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RVO: Planning In Velocity Space
R A + RB
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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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RVO: Planning In Velocity Space
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Videos
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12 Agents in a Circle
Videos
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1,000 agent’s in a circle
Related data-structures
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KD-trees
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Allowing efficient gathering of nearby neighbors O(log n)
Roadmaps & A*
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Allows global navigation around obstacles
Roadmaps
Create roadmap in free
space
Find visible source
nodes
Graph Search to find
path to Destination
1.
2.
3.
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A* is very popular graph
search algorithm
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Video
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1,000 people leaving Sitterson Hall
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Uses RVO, Roadmaps, A* and Kd-Trees
Outline
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Animation basics
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How to move one man
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Walk Cycle
IK
How to move one thousand
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Key framing
Simulation Loop
Crowd Models
Collision Avoidance
Data Structures
Rendering
Rendering Crowds
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Traditional OpenGL pipeline can be too slow for 1000s of
agents
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View Culling helps, but often not enough
Need Level-of-Detail techniques
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Use models with more polygons up close, less when far away
Imposters
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Replace Far off agents with
an oriented texture
Several Issues
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“Popping”
Uniformity
Lighting
Shadows
Many issues addressed in
recent works
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Questions