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Flow TilesA paper by Stephen Chenney
Outline
FlowsFlow tilesApplicationsAssessmentConclusion
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
Flows
Problems:Hard to design (especially with
specific boundary conditions)Expensive to store
=> Flow Tiles
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)
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
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
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
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
ApplicationsThree example applications are presented:A river A crowd in a citySwirling fog
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
AssessmentFlow tiles and crowd simulation
Advantages:Easy to design the flowFast to computeNo collision detection necessary
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
AssessmentFlow tiles and crowd simulation
Disadvantages: Because of flow properties:
Agents cannot cross each otherat intersection
No interaction between agents
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
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
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
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