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
How to move one man Walk Cycle IK
How to move one thousand Crowd Models Collision Avoidance
Rendering
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
Update StateDraw Picture
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
Walk Cycle 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 19th Century English Photograyher
Used multiple cameras to capture motion Invented Zoopraxiscope (spinning wheel of still
images) to animate images
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
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
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
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
Gather Neighbor
s
Draw Agent
Update State
s
For Each Agent
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
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
Flocking Seminal work in multi-agent movement Assign simple force to each agent Used in
Lion King Batman Returns
Separation Alignment Cohesion
Boids - Continued New forces can be added to incorporate more
behaviors Avoiding Obstacles
Collision Avoidance
Be Creative!
Boids Online Visit: http://www.red3d.com/cwr/boids/
And: http://www.red3d.com/cwr/steer/Unaligned.html
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
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
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 Vt
ji – Tangential velocity difference
FiW is very similar
Collision Avoidance
Non-penetration Sliding Force
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
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
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
RA + RB
25
RVO: Planning In Velocity Space
(VA +
VB)/2
RVO: Planning In Velocity Space
26
27
RVO: Planning In Velocity Space
28
RVO: Planning In Velocity Space
RVO: Planning In Velocity Space
29
30
RVO: Planning In Velocity Space
RVO: Planning In Velocity Space
31
RVO: Planning In Velocity Space
32
Videos 12 Agents in a Circle
Videos 1,000 agent’s in a circle
Related data-structures KD-trees
Allowing efficient gathering of nearby neighbors O(log n)
Roadmaps & A* Allows global navigation around obstacles
Roadmaps
1. Create roadmap in free space
2. Find visible source nodes
3. Graph Search to find path to Destination
A* is very popular graph search algorithm
36
Video 1,000 people leaving Sitterson Hall
Uses RVO, Roadmaps, A* and Kd-Trees
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
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
Imposters
40
Replace Far off agents with an oriented texture
Several Issues “Popping” Uniformity Lighting Shadows
Many issues addressed in recent works
Questions
?