Flow Tiles

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 = 0Snx+.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