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 f left + f bottom = f right + f top 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 = S x,y-.5 – S x,y+.5 y = S x-.5,y – S x+.5,y

7. Flow Tiles Creation: 1. Set corner stream values S -.5,-.5 = 0 S nx+.5,-.5 = S -.5,-.5 + f bottom S -.5,ny+.5 = S -.5,-.5 - f left S nx+.5,ny+.5 = S -.5,-.5 + f top

8. Flow Tiles Creation: 2. For each corner determine stream values around it S.5,-.5 = S -.5,-.5 + y 0,0 S -.5,.5 = S -.5,-.5 - x 0,0 S.5,.5 = S -.5,-.5 + y 0,0 3. Fit Bezier patch that interpolates the values around the corners 4. 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