Continuum Crowds Adrien Treuille, Siggraph 2006 9557550 王上文.
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Transcript of Continuum Crowds Adrien Treuille, Siggraph 2006 9557550 王上文.
Continuum Crowds
Adrien Treuille, Siggraph 2006
9557550王上文
Outline
Introduction Related work Approach
The Governing Equations Optimal Path Computation Speed & Density Dynamic Potential Field Approximation & approximation
Result & Demo Video Conclusion
Introduction
What is Crowds? Large groups of people. Enormous complexity and subtlety.
Introduction
Crowds’ difficulty Computation
Environmental constraints. Dynamic interactions between people. Intelligent path planning.
The characteristic of dense crowds Real-time crowd simulation is difficult due to large
computation.
Related work
Most previous work has been “agent-based” Motion is computed separately for each individual. It can capture each person’s unique situation.
Visibility Proximity of other pedestrians Other local factors
Different simulation parameters may be defined for each member.
But…
Related work (continue)
The agent-based approach has some drawbacks. Difficult to consistently produce realistic motion. Global path planning for each agent expensive.
Most models separate local collision avoidance from global path planning.
Conflicts arise.
Approach - Overview
A dynamic potential field model Optimal Path Computation Density & Speed Computation The Governing Equations
Maximum Speed Field Discomfort Field Unit Cost Field
Discretized grid structure Density conversion Unit cost computation Dynamic Potential Field Construction
Approach - Overview
Program flowchart
Approach – The Governing Equations Maximum Speed Field f
People move at the maximum speed possible.
Approach – The Governing Equations Discomfort Field
People generally follow trodden paths when they exist.
People do not cross a street until they reach a crosswalk
Achieving these by assuming a “discomfort field”.
Approach – The Governing Equations Unit Cost Field
Choose paths as to minimize a linear combination of the following three terms. The length of the path The amount of time to the destination The discomfort felt, per unit time, along the path
Approach – The Governing Equations Unit Cost Field (Continued)
Equation (2) can be rewritten as Eq(3)
Then Eq(3) can be simplified to Eq(4)
Approach – Optimal Path Computation A Dynamic Potential Function
For any person, the optimal strategy is to move opposite the gradient of the this function
Else satifies the equation:
So every person moves with the scaled speed
Approach – Optimal Path Computation It need to calculate the potential function for
the group only once With the same identical speed field, discomfort,
and goal. Calculate potential function is the slowest aspect
of simulation. As few groups as possible.
Approach – Speed & Density
Speed is a density-dependent variable. A crowd density field Slow speed with high density High speed with low density
Approach – Speed
Speed is a density-dependent variable. Convert each person into an individual density
field. The average velocity field
Approach – Speed
Low density The terrain is bounded to lie within the minimum
and maximum slopes & is the slope of the height field h in
direction Topographical speed
Approach – Speed
High density Flow speed is average velocity field.
Approach – Speed
Medium density Interpolate between the topographical and flow sp
eeds.
Approach - Density
How to get density to compute the speed field? Splat the crowd particles onto a density grid
Approach - Density
two requirements of the density conversion function The density field must be continuous.
Could be satisfied by any number of splatting technique, including Bilinear and Gaussian
Each person should contribute no less than to their own grid cell and no more than to any neighboring grid cell.
is a threshold.
Approach - Density
In order to satisfy the second requirement The density is then added to the grid as
The density exponent determines the speed of density falloff.
Then each person contributes at least to their grid cell, but no more than to neighboring cells, with
Approach – Density & Speed
With the density field, we can compute maximum speed field f.
So we can calculate the unit cost field C
Approach – The Algorithm
Approach – Dynamic Potential Field Approximation Dynamic Potential Field Approximation
Solve Equation (5) to get potential field is expensive
Approach – Dynamic Potential Field Approximation First find the less costly adjacent grid cell
along the both x- and y-axes
Then use these upwind directions to calculate a finite difference approximation to Equation (5)
Approach – Dynamic Potential Field Construction Algorithm
1. Assigning 0 inside the goal and marked as KNOWN.
2. Assigning all other cells and marked as UNKNOWN.
3. Those UNKNWON cells adjacent to KNOWN cells are included in the list of CANDIDATE cells and approximate by solving Eq. (11)
4. The CANDIDATE cell with the lowest potential is marked as KNOWN and its neighbors are marked as CANDIDATE and re-approximating the potential.
5. Repeat 4
Approach
Then we can get each person’s position and speed. Maximum speed field f
From density field Potential field
From unit cost field C From maximum speed field f
Result
Demo
Demo Video
Conclusion
Advantages The individuals do not face conflicting. Smoother motion than previous methods. It’s possible to integrate this model with agent
models. The moving cars and the UFO in demo are all agents.
Conclusion
Advantages Can capture a number of emergent phenomena.
Lane formation Short lived vortices during turbulent congestion.
Conclusion
Disadvantage Not feasible for real crowds in unknown
environment. It assume people really know the dynamic properties of
the environment. It change direction without respect to inertia.
Can be solved, but it would not be real-time. Without the flexibility and individual variability of
the full agent-based approach. Can be solved by adding some agents.
Q&A
Any Question?