### Flow Tiles

```Outline
 Flows
 Flow tiles
 Applications
 Assessment
 Conclusion
Flows
 Using flows for steering already seen in paper by
Reynolds => flow following behaviour
 Flow modelled by
velocity field which assigns
a velocity to every point
in the plane
Flows
Problems:
 Hard to design (especially with specific
boundary conditions)
 Expensive to store
=> Flow Tiles
Flow Tiles
Characterisation:
 Divergence free tiles
f left + f bottom = 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 Tiles
Representation:
stream function values
v(x,y) = x (S(x,y)z)
 Reduces data storage from
2n(n+1) to (n+1)2
 Velocities easily computed
by interpolation
x = Sx,y-.5 – Sx,y+.5
y = Sx-.5,y – Sx+.5,y
Flow Tiles
Creation:
1. Set corner stream values
S-.5,-.5
Snx+.5,-.5
S-.5,ny+.5
Snx+.5,ny+.5
=0
= S-.5,-.5 + f bottom
= S-.5,-.5 - f left
= S-.5,-.5 + ftop
Flow Tiles
Creation:
2. For each corner determine stream values around it
S.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 values
Result:
Smooth continuous flow
Flow Tiles
Usage:
 Not trivial to create valid
tiling
 Determine corner
velocity based on
neighbours
 Set up two integer
programmes to solve
each edge flux
 Can be done efficiently
using hot-start solutions
Applications
Three example applications are presented:
 A river
 A crowd in a city
 Swirling fog
Assessment
 Generally well written and structured
 Clearly states its relevance and contributions to related
work
 Not all steps are clearly explained and not all decisions
motivated
 No evaluation of results
 General knowledge of fluid-dynamics assumed
Assessment
Flow tiles and crowd simulation
 Easy to design the flow
 Fast to compute
 No collision detection necessary
Assessment
Flow tiles and crowd simulation
 Flow principles based on homogenous fluids, a crowd
is not homogenous
 Not possible to set different goals
for individuals
 Not possible to set different
characteristics for individuals
Assessment
Flow tiles and crowd simulation
 Because of flow properties:
 Agents cannot cross each other
at intersection
 No interaction between agents
Assessment
Flow tiles and crowd simulation
 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
Assessment
Flow tiles and crowd simulation
 Flows have to be designed by hand
 Allows detailed control of crowd
flow but very expensive for large
environments
 Design might not be realistic
Conclusion
 Flow 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
```