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Flow TilesA paper by Stephen Chenney
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Outline
FlowsFlow tilesApplicationsAssessmentConclusion
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FlowsUsing flows for steering already seen in
paper by Reynolds => flow following behaviour
Flow modelled by velocity field which assignsa velocity to every pointin the plane
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Flows
Problems:Hard to design (especially with
specific boundary conditions)Expensive to store
=> Flow Tiles
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Flow TilesCharacterisation:Divergence free tiles
fleft + fbottom = fright + ftop
Tile defined by 4 corner velocities and 4 edge fluxes
Tile set defined by set of corner and flux values (1,1,0,0)
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Flow TilesRepresentation:Instead of velocities store
stream function valuesv(x,y) = x (S(x,y)z)
Reduces data storage from 2n(n+1) to (n+1)2
Velocities easily computed by interpolationx = Sx,y-.5 – Sx,y+.5
y = Sx-.5,y – Sx+.5,y
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Flow TilesCreation:1. Set corner stream values
S-.5,-.5 = 0
Snx+.5,-.5 = S-.5,-.5 + fbottom
S-.5,ny+.5 = S-.5,-.5 - fleft
Snx+.5,ny+.5 = S-.5,-.5 + ftop
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Flow TilesCreation:2. For each corner determine stream values
around itS.5,-.5 = S-.5,-.5 + y0,0
S-.5,.5 = S-.5,-.5 - x0,0
S.5,.5 = S-.5,-.5 + y0,0
3. Fit Bezier patch that interpolates the values around the corners
4. Evaluate patch to determine missing valuesResult: Smooth continuous flow
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Flow TilesUsage:Not trivial to create
valid tilingDetermine corner
velocity based on neighbours
Set up two integer programmes to solve each edge flux
Can be done efficiently using hot-start solutions
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ApplicationsThree example applications are presented:A river A crowd in a citySwirling fog
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AssessmentGeneral comments about the paper:
Generally well written and structuredClearly states its relevance and contributions
to related workNot all steps are clearly explained and not all
decisions motivatedNo evaluation of resultsGeneral knowledge of fluid-dynamics
assumed
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AssessmentFlow tiles and crowd simulation
Advantages:Easy to design the flowFast to computeNo collision detection necessary
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AssessmentFlow tiles and crowd simulation
Disadvantages:Flow principles based on homogenous fluids,
a crowd is not homogenousNot possible to set different goals
for individualsNot possible to set different
characteristics for individuals
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AssessmentFlow tiles and crowd simulation
Disadvantages: Because of flow properties:
Agents cannot cross each otherat intersection
No interaction between agents
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AssessmentFlow tiles and crowd simulation
Disadvantages:Grid based
artefact will occur if not enough different tiles are used
Possible flows that can be designed is limited and depends on grid scale
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AssessmentFlow tiles and crowd simulation
Disadvantages:Flows have to be designed by hand
Allows detailed control of crowd flow but very expensive for largeenvironments
Design might not be realistic
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ConclusionFlow tiles provide in intuitive and efficient
procedural method for designing velocity fields
Useful for the simulation of fluids
Not enough to simulate a realistic crowd consisting of a agents with different goals and characteristics