Flow Tiles

1. Flow Tiles A paper by Stephen Chenney

2. Outline • Flows • Flow tiles • Applications • Assessment • Conclusion

3. 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

4. Flows Problems: • Hard to design (especially with specific boundary conditions) • Expensive to store => Flow Tiles

5. Flow Tiles Characterisation: • 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)

6. Flow Tiles Representation: • Instead of velocities store 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

7. Flow Tiles Creation: • 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

8. Flow Tiles Creation: • 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 • Fit Bezier patch that interpolates the values around the corners • Evaluate patch to determine missing values Result: Smooth continuous flow

9. 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

10. Applications Three example applications are presented: • A river • A crowd in a city • Swirling fog

11. Assessment General comments about the paper: • 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

12. Assessment Flow tiles and crowd simulation Advantages: • Easy to design the flow • Fast to compute • No collision detection necessary

13. Assessment Flow tiles and crowd simulation Disadvantages: • 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

14. Assessment Flow tiles and crowd simulation Disadvantages: • Because of flow properties: • Agents cannot cross each other at intersection • No interaction between agents

15. Assessment Flow 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

16. Assessment Flow tiles and crowd simulation Disadvantages: • Flows have to be designed by hand • Allows detailed control of crowd flow but very expensive for large environments • Design might not be realistic

17. 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