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PA199
Advanced Game Design
Lecture 12
Crowd Simulation
Dr. Fotis Liarokapis
12th May 2015
Path Planning
What is Path Planning
• Steer character from one point (or position) to
another one
Computer Games and Path Planning
• Fast and flexible
– Real-time planning for thousands of characters
– Flexibility to avoid other characters and local hazards
– Individuals and groups
• Natural Paths
– Smooth
– Collision-free
– Short
– Keep a preferred amount of clearance from obstacles
– Flexible
Typical Algorithms
• Dijkstra's Algorithm
• Bellman-Ford Algorithm
• Johnson's Algorithm
• Greedy Best-First-Search Algorithm
• A* Algorithms
Dijkstra's Algorithm
• Finding the shortest paths between nodes in a
graph, which may represent, for example, road
networks
– The algorithm exists in many variants
• Dijkstra's original variant found the shortest path
between two nodes
• A more common variant fixes a single node as
the "source" node and finds shortest paths from
the source to all other nodes in the graph
– Producing a shortest path tree
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Dijkstra's Algorithm Graph
• For a graph: G = (V,E)
– V is a set of vertices and
– E is a set of edges
• Dijkstra's algorithm keeps two sets of vertices:
– S the set of vertices whose shortest paths from the
source have already been determined
– V-S the remaining vertices
• The other data structures needed are:
– d array of best estimates of shortest path to each
vertex
– pi an array of predecessors for each vertex
Dijkstra's Mode of Operation
• 1. Initialise d and pi,
• 2. Set S to empty,
• 3. While there are still vertices in V-S
– i. Sort the vertices in V-S according to the current
best estimate of their distance from the source,
– ii. Add u, the closest vertex in V-S, to S,
– iii. Relax all the vertices still in V-S connected to u
Dijkstra's Algorithm Unity Video
https://www.youtube.com/watch?v=dhvf9KCAsVg
Xlent Games - Pathfinding Test
https://www.youtube.com/watch?v=rIQ8-7k_kek
Bellman-Ford Algorithm
• Computes shortest paths from a single source
vertex to all of the other vertices in a weighted
digraph
• Disadvantage is that it is slower than Dijkstra's
algorithm
• Advantage is that it is more versatile
– Capable of handling graphs in which some of the
edge weights are negative numbers
Bellman-Ford Algorithm .
• Negative edge weights are found in various
applications of graphs
– Hence the usefulness of this algorithm
• If a graph contains a "negative cycle" (i.e. a cycle
whose edges sum to a negative value) that is
reachable from the source, then there is no
cheapest path
– Any path can be made cheaper by one more walk
around the negative cycle
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Bellman-Ford Algorithm ..
• It uses d[u] as an upper bound on the distance
d[u, v] from u to v
• The algorithm progressively decreases an
estimate d[v] on the weight of the shortest path
from the source vertex s to each vertex v in V
until it achieve the actual shortest-path
• Returns Boolean
– TRUE if the given digraph contains no negative cycles
that are reachable from source vertex s
– Otherwise it returns FALSE
Bellman-Ford Algorithm …
• INITIALIZE-SINGLE-SOURCE (G, s)
• 2.for each vertex i = 1 to V[G] - 1 do
• 3. for each edge (u, v) in E[G] do
• 4. RELAX (u, v, w)
• 5.For each edge (u, v) in E[G] do
• 6. if d[u] + w(u, v) < d[v] then
• 7. return FALSE
• 8.return TRUE
Johnson's Algorithm
• Johnson's algorithm is a way to find the shortest
paths between all pairs of vertices in a sparse, edge
weighted, directed graph
• It allows some of the edge weights to be negative
numbers
– But no negative-weight cycles may exist
• It works by
– Using the Bellman-Ford algorithm to compute a
transformation of the input graph that removes all
negative weights
– Allowing Dijkstra's algorithm to be used on the
transformed graph
Greedy Best-First-Search Algorithm
• Greedy Best-First-Search algorithm works in a
similar way to Dijkstra's, except that it has some
estimate (called a heuristic) of how far from the
goal any vertex is
• Instead of selecting the vertex closest to the
starting point, it selects the vertex closest to the
goal
• Greedy Best-First-Search is not guaranteed to
find a shortest path
– However, it runs much quicker than Dijkstra’s
algorithm
A* Algorithm
• A* is the most popular choice for pathfinding,
because it’s fairly flexible and can be used in a
wide range of contexts
• A* is like Dijkstra’s algorithm in that it can be
used to find a shortest path
• A* is like Greedy Best-First-Search in that it can
use a heuristic to guide itself
• In the simple case, it is as fast as Greedy Best-
First-Search
A* Algorithm
• Combines the pieces of information that
Dijkstra’s algorithm uses and information that
Greedy Best-First-Search uses
– g(n) represents the exact cost of the path from the
starting point to any vertex n
– h(n) represents the heuristic estimated cost from
vertex n to the goal
• A* balances the two as it moves from the
starting point to the goal
• Each time through the main loop, it examines the
vertex n that has the lowest f(n) = g(n) + h(n)
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A* Algorithm with Python-Pygame
https://www.youtube.com/watch?v=FNRfSQDF7TA
Snake Game AI with A* algorithm
https://www.youtube.com/watch?v=DnyltgX2ACo
Crowds Crowd Simulation
• Crowd simulation is
the process of
populating a virtual
scene with a large
number of intelligent
agents that display
distinct collective
behaviours
A simulation with large crowds of intelligent agents
Crowds In Computer Games
• Crowds are very popular
• Games offer technically
advanced visual and
interactive simulation
• Not specific to a single genre
– In Hitman crowds are utilised
for blending into the game
world to assassinate targets or
hide from pursuers
– In Grand Theft Auto, crowds are
a living part of the city,
simulated to act as normal
pedestrians
Grand Theft Auto 4
China Town level of
Hitman: Absolution
Crowds and Sociology
• Crowd simulation can also refer to simulations based
on group dynamics and crowd psychology
– Often in public safety planning
• In this case, the focus is just the behavior of the
crowd, and not the visual realism of the simulation
– Crowds have been studied as a scientific interest since the
end of the 19th Century
• A lot of research has focused on the collective social
behavior of people at:
– Social gatherings, assemblies, protests, rebellions,
concerts, sporting events and religious ceremonies
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Social Simulation Approaches
• Two different approaches, with totally
different results
• Macroscopic
– i.e. fluid dynamics
• Microscopic
– i.e. Multi-agent based simulation
Microscopic Simulation
• Also know as agent-based simulation
• Motion is computed separately for each
individual member
• Some well known approaches:
– Particle motion
– Steering Behaviors For Autonomous Characters
– Social force model
– Crowd AI
– Reciprocal Velocity Obstacles
Microscopic Simulation - Advantages
• Each individual character makes independent
decisions
• Capture each character’s unique situation:
visibility, proximity of other pedestrians, and
local factors
• Simulation parameters may be defined for each
character -> yield complex heterogeneous
motion
Microscopic Simulation - Drawbacks
• Not easy to develop behavioral rules that
consistently produce realistic motion
• Global path planning for each agent is
computationally expensive
– Particularly in simulating a large amount of agents
• Most agent models separate local collision
avoidance from global path planning and conflicts
inevitably arise between these two competing goals
• Local path planning often results in less realistic
crowd behavior
• The problems tend to be exacerbated in areas of
high congestion or rapidly changing environments
Particle Methods
• The characters are attached to point particles,
which are then animated by simulating
wind, gravity, attractions, and collisions
• The particle method is usually inexpensive to
implement, and can be done in most 3D software
packages
• The method is not very realistic because it is
difficult to direct individual entities when
necessary, and because motion is generally
limited to a flat surface
Steering Behaviors For Autonomous
Characters
• In games, autonomous characters are sometimes
called non-player characters
• The behavior of an autonomous character can be
better understood by dividing it into several
layers
http://www.red3d.com/cwr/steer/gdc99/
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Obstacle Avoidance
• Obstacle avoidance behavior
gives a character the ability to
maneuver in a cluttered
environment by dodging around
obstacles
• The implementation of obstacle
avoidance behavior assumes
that both the character and
obstacle can be reasonably
approximated as spheres
• Considers each obstacle in turn
(perhaps using a spatial
portioning scheme to cull out
distance obstacles) and
determines if they intersect with
the cylinder http://www.red3d.com/cwr/steer/gdc99/
Wander
• Type of random steering
• Easy implementation
generates a random steering
force each frame
– Produces rather uninteresting
motion
• Better approach retains
steering direction state
– Make small random
displacements to it each frame
• Another way is to use coherent
Perlin noise to generate the
steering direction http://www.red3d.com/cwr/steer/gdc99/
Path Following
• Path following behavior enables a
character to steer along a
predetermined path
– i.e. a roadway, corridor or tunnel
• The individual paths remain near,
and often parallel to, the centerline
of the corridor
– But are free to deviate from it
• To compute steering for path
following, a velocity-based
prediction is made of the character’s
future position
• The predicted future position is
projected onto the nearest point on
the path spine
http://www.red3d.com/cwr/steer/gdc99/
Wall Following and Containment
• Variations on path
following include ‘wall
following’ and
‘containment’
• Wall following means to
approach a wall (or other
surface or path) and then
to maintain a certain offset
from it
• Containment refers to
motion which is restricted
to remain within a certain
region
http://www.red3d.com/cwr/steer/gdc99/
Social Forces
• A social force model is a microscopic,
continuous time, continuous space,
phenomenological computer simulation
model of the movement of pedestrians
• Many models exist!
Helbing’s Social Force 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
• 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
Crowd AI
• Agents are given artificial intelligence, which guides
the entities based on one or more functions
– i.e. sight, hearing, basic emotion, energy level,
aggressiveness level, etc
• The entities are given goals and then interact with
each other as members of a real crowd would
• They are often programmed to respond to changes
in environment enabling them to climb hills, jump
over holes, scale ladders, etc
• This is much more realistic than particle motion
– But is very expensive to program and implement
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
Macroscopic Simulation
• Simulate a large amount of crowd
• Treat motion as a per particle energy
minimization
• Adopt a continuum perspective on the system
• This formulation yields a set of dynamic potential
and velocity fields over the domain that guide all
individual motion simultaneously
Methods
Continuum Crowds, ACM Transactions on Graphics, Volume 25 Issue 3, July 2006,
[Adrien Treuille et al.]
Examples
Continuum Crowds, ACM Transactions on Graphics, Volume 25 Issue 3, July 2006,
[Adrien Treuille et al.]
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Interactive Manipulation of LargeScale
Crowd Animation
https://www.youtube.com/watch?v=DYLfFa6CNRU
Simulating Dynamic Features of Escape
Panic Case Study
Aim
• A model of pedestrian behaviour to
investigate the mechanisms of panic and
jamming by uncoordinated motion in crowds
http://angel.elte.hu/panic/
Features of Escape Panic
• People move or try to move considerable faster
than normal
• Individuals start to pushing, and interactions
become physical
• Moving becomes uncoordinated
• At exist, arching and clogging are observed
• Jams build up
• Pressure on walls and steel barriers increase
• Escape is further slowed by fallen or injured people
acting as ‘obstacles’
http://angel.elte.hu/panic/
The Problem & Solution
Crowd stampedescan be deadly
People act in uncoordinated and dangerousways when panicking
It is difficult to obtain real data on crowd panics
Model people as self-driven particles
Model physical and socio-psychologicalinfluences
on people’s movement as forces
Simulate crowd panics and see what happens
http://angel.elte.hu/panic/
Acceleration of Simulated People
• vi
0(t) = desired speed
• ei
0(t) = desired direction
• vi(t) = actual velocity
• τi = characteristic time
• mi = mass
http://angel.elte.hu/panic/
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Forces from Other People
• Force from other people’s bodies being in the
way
• Force of friction preventing people from sliding
• Psychological “force” of tendency to avoid each
other
• Sum of forces of person j on person i is fij
http://angel.elte.hu/panic/
Total Force of Other People
• Aiexp[(rij – dij)/Bi]nij is psychological “force”
• Ai and Bi are constants
psychologicalforce
sum of the people’s radii distance between people`s centers of mass
normalized vector from j to i
http://angel.elte.hu/panic/
Physical Forces
• g(x) is 0 if the people don’t touch and x if they
do touch
• k and κ are constants
http://angel.elte.hu/panic/
force from other bodies force of sliding friction
tangentialdirectiontangentialvelocity difference
Forces from Walls
• Forces from walls are calculated in basically
the same way as forces from other people
http://angel.elte.hu/panic/
Values Used for Constants and
Parameters
• Insufficient data on actual panic situations to
analyze the algorithm quantitatively
• Values chosen to match flows of people
through an opening under non-panic
conditions
http://angel.elte.hu/panic/
Simulation of Clogging
http://angel.elte.hu/panic/
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Simulation of Clogging .
• As desired speed increases beyond 1.5m s-1, it
takes more time for people to leave
• As desired speed increases, the outflow of
people becomes irregular
• Arch shaped clogging occurs around the
doorway
http://angel.elte.hu/panic/
Widening Can Create Crowding
• The danger can be
minimized by avoiding
bottlenecks in the
construction of buildings
• However, that jamming
can also occur at
widenings of escape
routes
http://angel.elte.hu/panic/
Mass Behavior
• Panicking people tend to exhibit either
herding behavior or individual behavior, or try
to mixture of both
• Herding simulated using “panic parameter” pi
http://angel.elte.hu/panic/
Individual direction Average direction
of neighbors
Effects of Herding
http://angel.elte.hu/panic/
Effects of Herding .
• Neither individuals nor herding behaviors
performs well
• Pure individualistic behavior:
– Each pedestrian finds an exit only accidentally
• Pure herding behavior:
– Entire crowd will eventually move into the same and
probably blocked direction
http://angel.elte.hu/panic/
Injured People Block Exit
http://angel.elte.hu/panic/
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A Column Can Increase Outflow
http://angel.elte.hu/panic/
Scalable Crowd Simulation Case Study
http://angel.elte.hu/panic/
Scalable Crowd Simulation
• Large Crowds
– Scalable performance
• Large Complex Environments
– Scalable Authoring
• Rich, Complex Behaviors
– Scalable Behaviors
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Conflicting Goals
• Large, Complex World
• Rich Behaviors
• But…
• Fast performance (simple agents)
• Reasonable authoring
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
An Environment
• Example:
– Model of Street
• Simulation:
– Real time, Reactive
• Rendering:
– Unreal Game Engine
for playback
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Scalability: Complex Environments
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Store Window
In front of Store Window
Friends Together
Doorway
In front of Doorway
In a hurryIn Crosswalk
Use crosswalk
Sidewalk
Street
Bench
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Observation: Behavior Depends on
Situation
Store Window
In front of Store Window
Possibly:
stop to window shop
Friends Together:
Possibly: Stop to talk
Probably: Have same goal
Doorway
In front of Doorway
Possibly: open door, enter
Unlikely: stand blocking door
In a hurry:
Check for traffic
Run across street
In Crosswalk:
Walk across street once
you’ve started
Use crosswalk:
Wait for green light
Start crossing
Sidewalk:
Walk here
Street:
Generally, Don’t walk here
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Managing Environmental Complexity:
Situation-Based Approach
• Many different situations
• Each has a different set of local behaviors
• An agent only needs a few at a time
• Blend situations/behaviors together
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Store Window
In front of Store Window
Possibly:
stop to window shop
Friends Together:
Possibly: Stop to talk
Probably: Have same goal
Doorway
In front of Doorway
Possibly: open door, enter
Unlikely: stand blocking door
Use crosswalk:
Wait for green light
Start crossing
Sidewalk:
Walk here
Observation: Crowds are Crowds
• Individuals are anonymous
– Doesn’t matter what any
one does
– At any given time, do
something reasonable
– Aggregate behavior
• Stochastic Control
• Short term view of agent
An Individual
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Key Ideas
• Situation-Based Approach
– Breaks behavior into small pieces
– Extensible agents kept simple
• Situation Composition
– Probabilistic scheme to compose behaviors
• Painting Interface
– Place behaviors in world, not agents
• Use Motion-Graph-based runtime
– Based on Gleicher et al 2003
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Situation-Based Approach: Agent
Architecture
• Agents:
– Discrete set of actions
– Randomly choose from distribution
– Behavior functions provide distributions
• All aspects of agents can be updated
dynamically
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Situation-Based Approach: Simple
Default Agents
• Default agents very simple
– Wander, don’t bump into things, …
• Extend agents as necessary to achieve
complex behaviors
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
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Situation-Based Approach: Extensible
Agent
• Situations extend agents
– Add Actions
– Add Behavior Functions
– Add Sensors and Rules that inform Behavior
Functions
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Simple Example
• Default agent can’t cross the street
• How an agent crosses the street…
– Enters a Crosswalk Situation
– Crosswalk situation extends agent
• Sensor to see traffic light
• Behavior Functions to cross street
• Behavior Functions to stop
• Rules to wait for light to change
– Remove extensions when done
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Composing Behaviors: Action Selection
Agent
Left
Right
Straight
?
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Composing Behaviors: Probability
Scheme
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Behavior
Function A
Agent
Left
Right
Straight
.5
.3
.2
Composing Behaviors: Probability
Scheme
Behavior
Function A
Agent
Left
Right
Straight
.5
.3
.2
Behavior
Function B
.1
.1
.2
.4
.25
.33
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Composing Behaviors: Extending
Agents
Agent
Left
Right
Straight
Behav
Func A
.5
.3
.2
Jump
Behav
Func B
.1
.1
.2
Behav
Func J
.5
.5
.5
.2
.41
.24
.33
.03
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
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Video
http://research.cs.wisc.edu/graphics/Gallery/Crowds/
Character Modeling
3D Animation
• Rendering
– 3D Scene and Motion
– Sequence of Frames
• Rates: Video 30fps, Film 24fps
– Persistence of Vision
• Animator must create
– Illusion of Life
– Weight
Animation
• Almost every property of every object in
the scene can be animated changed
through time
–Models, cameras
–Transformations (Move, Rotate, Scale)
• Modifications/Deformation:
– Edits, bends, twists, manipulating a skeleton
• Materials, colors, textures
Animation .
• 3D Scene does not have
– Gravity
– Weight
– Force
– Complete interactions between objects
• Sometimes it has…
• You must make it seem so
Preproduction Phases
• Screen-play
• Storyboards
• Character
development
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3D Characters
• Digital actor
– Tin can
– Sack of flower
– Butterfly, beetle
– Bird
– Flower
– Robot
– Humanoid
– Etc…
Typical Character
• Mechanics of movement must be
convincing
• Skin and clothing moves & bends
appropriately
• This process of preparing character controls
is called rigging (see next slides)
–Fully rigged character has:
• Skeleton joints, surfaces, deformers, expressions,
Set Driven Key, constraints, etc
Typical Character . Facial Animation Video
https://www.youtube.com/watch?v=z86YsS-pVsQ
Character Resolution
• Use low resolution character that has
surfaces ‘parented’ to skeleton
– Allows interactive animations
– Switch to full resolution character later
Typical Character Animation Workflow
• Character Design
• Model
• Skeleton Rigging
• Binding
• Animation
• Integration
• Rendering
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Rigging
• Rigging refers to the construction and
setup of an animatable character
– Similar to the idea of building a puppet
• A ‘rig’ has numerous degrees of freedom
(DOFs) that can be used to control various
properties
Primary Methods of Animation
• Keyframe
• Procedural
–Expressions
–Scripting
• Dynamics/Simulation
–Physics
• Motion Capture
• Combinations of the above
Keyframe Workflow
• Set Keys
– Usually extreme positions
– Less is more: Keys only the properties being
animated
• Set Interpolation
– Specify how to get from one key to another
– Secondary, but a necessary step
• Scrub Time slider and refine motion curve
Setting Keys
• Start with extreme positions
• Add intermediate positions
– Secondary motion
• Less is more
– Don’t add keys for properties that you are not
animating
– Easier to manage/edit fewer keys
Skeletal Hierarchy
• The Skeleton is a tree of bones
– Often flattened to an array in practice
• Top bone in tree is the “root bone”
– May have multiple trees, so multiple roots
• Each bone has a transform
– Stored relative to its parent’s transform
• Transforms are animated over time
• Tree structure is often called a “rig”
Bone Masks
• Some animations only affect some bones
– Wave animation only affects arm
– Walk affects legs strongly, arms weakly
• Arms swing unless waving or holding something
• Bone mask stores weight for each bone
– Multiplied by animation’s overall weight
– Each bone has a different effective weight
– Each bone must be blended separately
• Bone weights are usually static
– Overall weight changes as character changes
animations
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Variable Delta Extraction
• Uses root bone motion directly
• Sample root bone motion each frame
• Find delta from last frame
• Apply to instance pos+orn
– Instance pos+orn is the root bone!
• Root bone is ignored when rendering
Animation Storage Problem
• 4x3 matrices, 60 per second is huge
–200 bone character = 0.5Mb/sec
• Consoles have around 32-64Mb
• Animation system gets maybe 25%
• PC has more memory
–But also higher quality requirements
Decomposition
• Decompose 4x3 into components
– Translation (3 values)
– Rotation (4 values - quaternion)
–Scale (3 values)
– Skew (3 values)
• Most bones never scale & shear
• Many only have constant translation
• Don’t store constant values every frame
Interpolation
• Specify how to get from one key to the
other (in between)
• Common types
–Step: stay at the same value, then suddenly
switch
–Linear: change at constant rate
–Spline/Smooth: make it smooth
• All of these (and more) are useful and
appropriate in the right circumstance
Mesh Deformation
• Find Bones in World Space
• Find Delta from Rest Pose
• Deform Vertex Positions
• Deform Vertex Normals
Find Bones in World Space
• Animation generates a “local pose”
– Hierarchy of bones
– Each relative to immediate parent
• Start at root
• Transform each bone by parent bone’s worldspace
transform
• Descend tree recursively
• Now all bones have transforms in world space
– “World pose”
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Find Delta from Rest Pose
• Mesh is created in a pose
– Called the “rest pose”
• Must un-transform by that pose first
• Then transform by new pose
– Multiply new pose transforms by inverse of rest pose
transforms
– Inverse of rest pose calculated at mesh load time
• Gives “delta” transform for each bone
Deform Vertex Positions
• Deformation usually performed on GPU
• Delta transforms fed to GPU
–Usually stored in “constant” space
• Vertices each have n bones
• n is usually 4
–4 bone indices
–4 bone weights 0-1
–Weights must sum to 1
Deform Vertex Normals
• Normals are done similarly to positions but
use inverse transpose of delta transforms
– Translations are ignored
–For pure rotations, inverse(A)=transpose(A)
– So inverse(transpose(A)) = A
– For scale or shear, they are different
• Normals can use fewer bones per vertex
– Just one or two is common
Motion of characters
• Along with key frame animation we can use
kinematics
– Kinematics = study of motion without regard to the
forces that cause it
Specify fewer degrees of freedom
More intuitive control
FK & IK
• Most animation is “forward kinematics”
– Motion moves down skeletal hierarchy
• But there are feedback mechanisms
– Eyes track a fixed object while body moves
– Foot stays still on ground while walking
– Hand picks up cup from table
• This is “inverse kinematics”
– Motion moves back up skeletal hierarchy
Skeleton Puppet Game Video (FK & IK)
https://www.youtube.com/watch?v=QDwo9d8Fa5M
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User Control of Kinematic Characters
• Joint Space
– Position all joints
• Fine level of control
• Cartesian Space
– Specify environmental interactions easily
• Most DOF computed automatically
Inverse Kinematics
• Balance = keep center-of-mass over support
polygon
• Control
– i.e. position vaulter’s hands on line between
shoulder and vault
– i.e. Compute knee angles that will give runner the
right leg length
Inverse Kinematics is Hard
• Redundancy
Inverse Kinematics is Hard .
• Singularities
Momentum-based Inverse Kinematics
with Motion Capture Video
https://www.youtube.com/watch?v=FJTBMnP6oCM
Single Bone IK
• Orient a bone in given direction
–Eyeballs
–Cameras
• Find desired aim vector
• Find current aim vector
• Find rotation from one to the other
–Cross-product gives axis
–Dot-product gives angle
• Transform object by that rotation
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Multi-Bone IK
• One bone must get to a target position
– Bone is called the “end effector”
• Can move some or all of its parents
• May be told which it should move first
– Move elbow before moving shoulders
• May be given joint constraints
– Cannot bend elbow backwards
Cyclic Coordinate Descent
• Simple type of multi-bone IK
• Iterative
– Can be slow
• May not find best solution
– May not find any solution in complex cases
• But it is simple and versatile
– No pre-calculation or pre-processing needed
Cyclic Coordinate Descent .
• Start at end effector
• Go up skeleton to next joint
• Move (usually rotate) joint to minimize
distance between end effector and target
• Continue up skeleton one joint at a time
• If at root bone, start at end effector again
• Stop when end effector is “close enough”
• Or hit iteration count limit
Cyclic Coordinate Descent ..
• May take a lot of iterations
• Especially when joints are nearly straight
and solution needs them bent
–e.g. a walking leg bending to go up a step
–50 iterations is not uncommon!
• May not find the “right” answer
–Knee can try to bend in strange directions
Two-Bone IK
• Direct method, not iterative
• Always finds correct solution
– If one exists
• Allows simple constraints
– Knees, elbows
• Restricted to two rigid bones with a rotation
joint between them
– Knees, elbows!
• Can be used in a cyclic coordinate descent
Two-Bone IK .
• Three joints must stay in user-specified plane
– e.g. knee may not move sideways
• Reduces 3D problem to a 2D one
• Both bones must remain same length
• Therefore, middle joint is at intersection of two
circles
• Pick nearest solution to current pose
• Or one solution is disallowed
– Knees or elbows cannot bend backwards
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Two-Bone IK ..
Allowed
elbow
position
Shoulder
Wrist
Disallowed
elbow
position
IK by Interpolation
• Animator supplies multiple poses
• Each pose has a reference direction
– e.g. direction of aim of gun
• Game has a direction to aim in
• Blend poses together to achieve it
• Source poses can be realistic
– As long as interpolation makes sense
– Result looks far better than algorithmic IK with
simple joint limits
IK by Interpolation .
• Result aim point is inexact
– Blending two poses on complex skeletons
does not give linear blend result
• Can iterate towards correct aim
• Can tweak aim with algorithmic IK
– But then need to fix up hands, eyes, head
– Can get rifle moving through body
Attachments
• For example character holding a gun
• Gun is a separate mesh
• Attachment is bone in character’s skeleton
–Represents root bone of gun
• Animate character
• Transform attachment bone to world
space
–Move gun mesh to that pos+orn
Attachments .
• For example person is hanging off bridge
• Attachment point is a bone in hand
– As with the gun example
• But here the person moves, not the bridge
• Find delta from root bone to attachment
bone
• Find world transform of grip point on bridge
• Multiply by inverse of delta
–Finds position of root to keep hand gripping
Collision Detection
• Most games just use bounding volume
• Some need perfect triangle collision
–Slow to test every triangle every frame
• Pre-calculate bounding box of each bone
–Transform by world pose transform
–Finds world-space bounding box
• Test to see if bounding box was hit
–If it did, test the this bone influences
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NCCA Video 1 NCCA Video 2
Case Study For Crowd Modeling Aim
• Aim
– Feedback into improving the development
processes of simulations and video games,
implementing virtual crowds, especially those
within urban environments
• Research Question
– What Features of Behaviour Positively Influence the
Perceived Realism of Agents Within a Virtual Urban
Environment, and to What Degree?
Complexity Fallacy
• Over complex AI’s do not necessarily produce
better behaviour
• There have been cases where over complex
AI’s have not produced good results whereas
simple techniques have
• To quantify the effectiveness of crowd
behaviour within a simulation, a method
other than the judging the complexity is
required
Types of Realism
• Realism is an important aspect in the majority of
crowd simulations, however the type of realism
required depends upon a simulations purpose
• Several definitions of realism within the context
of crowd simulation relating to specific aspects
– i.e. Graphical fidelity
• Two important types
– Virtual Realism
– Perceived Realism
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Virtual Realism
• Virtual Realism is how
close a simulation or
specific feature is to
reality
• This type of realism is
important for serious
simulations
– Evacuation procedures
– Urban planning
The HiDAC system showing high density crowds
Perceived Realism
• Perceived Realism is how realistic
a simulation or specific feature is
perceived to be by human
viewers
• Important for entertainment
based simulations
– i.e. Video games
• Perceptual Experiments can be
utilised to gauge the Perceived
Realism of a simulation or feature
• This is the primary realism type
investigated in this research
Virtual crowds in the Assassin’s Creed 3
video game published by Ubisoft
Methodology
• Analysis: Identify a feature and inform
algorithm construction, by analysing real-world
and similar instances of crowd behaviour
• Synthesis: Synthesise a new generation
simulation with further refinement and the
behaviour impacting feature that was identified
in analysis
• Perception: Conduct the psychophysical
experiment for gauging the perceived realism
values of the implemented feature
Urban Crowd Simulation
• The primary purpose for developing the urban
crowd simulation was to create a platform with
alterable parameters capable of customising
agent behaviour for the purposes of perceptual
evaluation
• Due to the perceptual aspect, the standard
modelling and behaviour approaches had to be
altered to accommodate the fact that more
stimuli were needed than just the configuration
that appeared most realistic to the developer
Procedural City Generation
• A procedural approach
was selected to
generate the virtual
urban city
– Allows for the
possibility of multiple
layouts and setups
– Produces complex
geometry without
having to manually
model and place object
A procedurally generated city in the urban crowd simulation
Core AI Components
• Four core components
implemented for the
agents in the urban crowd
simulation:
– Decision making utilising
finite-state machines
– Pathfinding with the A*
algorithm
– Steering with the crowd
path-following mechanic
– Perception utilising radial
local neighbourhoods
The urban crowd simulation displaying crowds of agents
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Social Forces Model
• The realistic motion of
pedestrians would be
subject to social forces
• An additional social forces
component has been
implemented for the
altering the behaviour of
agents
• The model consists several
distinct forces that when
presented together help to
produce realistic behaviour
with regards to pedestrians
A scene from the urban crowd simulation with initial social
forces implemented
Social Forces Model
A) Repulsive force between the individual pedestrian
and other pedestrians that are close by
B) Repulsive force between the individual pedestrian
and obstructions such as buildings, close by
C) Attractive force between the individual pedestrian
and other pedestrians nearby
– However this has an element of randomness
D) Attractive forces between the individual
pedestrian and objects, such as a store window or
parked car
Quantitative Evaluation
• Along with the core components, other behaviour
orientated features are identified in analysis,
implemented in synthesis and then perceptually
tested in perception
• These features require parameter space and
customisability for perceptual evaluation
• The agent velocity feature has been fully
implemented with parameter space for minimum
and maximum velocities, along with velocity
distribution
• An annotation mechanism has been implemented
for future features based on environmental factors
Urban Crowd Simulation Demo
Perceived Realism Experiments
• Three psychophysical experiments planned to
gauge perceived realism and identify successful
feature thresholds and parameter values
• Each experiment involves participants viewing
video clips of different simulation set-ups and
judging the realism
• Data is collected in the form of simulation
configuration ID’s with linked perceived realism
values
• A prototype survey platform has been used for a
pilot study
Prototype Survey Platform
• Platform developed using PHP
to act as a survey platform for
the psychophysical experiments
– Provides a slider for participants
to choose the realism level of a
given clip
– Orders the videos with regards to
the psychophysical methodology
employed
– As the platform was developed
using a language for server side
applications it can be extended
online to reach large numbers of
participants
The survey platform prototype displaying a
video clip
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Psychophysical Methodologies
• The type and order of video clips shown to participants
is dependant upon the psychophysical methodology and
the experiment
• The first and primary experiment utilises the adaptive
staircase procedure to establish the perceptual
thresholds and perceived realism levels of a feature
• The second experiment utilises the adjustment
procedure to rank features based on there perceptual
effectiveness
• The third experiment utilises the constant stimuli
procedure to determine the threshold and most effective
number of features required for perceptual plausibility
Pilot Study
• A pilot study was conducted with three participants
utilising the primary staircase methodology
• The feature perceptually tested was agent velocity
and the participants were shown different
configurations of velocity range and distribution
• Final results gave a velocity range of 0.3, based on a
perceived realism value of 0.82, with thresholds of
0.2 and 0.5
• Velocity distribution was 0.5, based on an average
perceived realism value of 0.85, with thresholds of
0.3 and 0.7
More Behavioural Features
Path-following steering
Radial perception
Social Forces Scenario
• The resultant steering force is calculated from
the three forces present in the algorithm
– SF = (ar * w) + (aa * w) + (or * w)
• where
– "SF" is the resultant calculated social force, which
acts as a steering modifier
– Agent repulsion is represented as "ar“
– agent attraction as "aa“
– object repulsion as "or“
– Parameter weight is represented as the modifier "w"
Social Forces Scenario .
• Calculated individually these forces are:
– ar = (a - aⁿ ) * n, (t, r)
– aa = (aⁿ - a) * n, (t, r)
– or = (a - oⁿ) * n, (t, r)
• where
– "aⁿ" is the position of all the agents within vision
– "oⁿ" is the position of all the objects within vision
– "a" is the current agents position
– "n" is the normalizing factor
– "t" is the time factor
– "f" is the behaviour fluctuation factor
Experiment
• 32 participants
• The experiment consists of two key variables
– One for each of the agent based social forces.
• These variables are tested at specific trials:
– Trials 01 to 09 for agent avoidance
– Trials 10 to 18 for agent attraction
• This accounts to a total of 18 trials
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Results
• 94% of participants found
that when the agent
avoidance social force is
present the behaviour of the
agents is more realistic
• 95% selected the videos with
the agent attraction social
force present to be more
realistic
• 95% of the participants find a
simulation with social forces
to be more realistic
Crowd Grouping Experiment
• A platform for testing
certain aspects of artificial
intelligence (AI) using
psychophysical
methodologies
• The current research is
looking into aspects
relating to crowd based AI,
most specifically for
pedestrians
http://psychophysicsforai.weebly.com/
Video Example References
• http://www.cs.cmu.edu/~jkh/
• https://www.cs.auckland.ac.nz/software/AlgAnim/dijks
tra.html
• http://www.personal.kent.edu/~rmuhamma/Algorithm
s/MyAlgorithms/GraphAlgor/bellFordAlgor.htm
• http://theory.stanford.edu/~amitp/GameProgramming
/AStarComparison.html
• http://www.red3d.com/cwr/steer/
• http://research.cs.wisc.edu/graphics/Gallery/Crowds/
• http://www.fi.muni.cz/~liarokap/publications/VSGAME
S2013b.pdf
Bibliography
• Social Force Model for Pedestrian Dynamics, 1998, [Dirk
Helbing and Peter Molnar]
• Real-time Navigation of Independent Agents Using
Adaptive Roadmaps, VRST, 2007 [Avneesh Sud et al.]
• Real-Time Multi-Agent Path Planning on Arbitrary
Surfaces, Proceedings of the 2010 ACM SIGGRAPH
symposium on Interactive 3D Graphics and Games, 2010
[Rafael P. Torchelsen et al.]
• Continuum Crowds, ACM Transactions on Graphics,
Volume 25 Issue 3, July 2006, [Adrien Treuille et al.]
• Space-time Group Motion Planning, Springer Tracts in
Advanced Robotics Volume 86, 2013, [Ioannis Karamouzas
et al.]
Questions