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Position based fluids

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A summary of the SIGGRAPH paper, "Position Based Fluids."

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Position based fluids

  1. 1. Position Based FluidsSIGGRAPH 20132013/06/11ked
  2. 2. Authors Miles Macklin, Matthias Muller
  3. 3. OverviewSmoothed particlehydrodynamics (SPH)Scalar density constraintPosition baseddynamics (PBD)Artificial pressure &Vorticity confinementPosition basedfluids
  4. 4. OverviewSmoothed particlehydrodynamics (SPH)Scalar density constraintPosition baseddynamics (PBD)Artificial pressure &Vorticity confinementPosition basedfluids
  5. 5. Smoothed particle hydrodynamics “Particle-Based Fluid Simulation forInteractive Applications” M. Muller, D. Charypar, M. Gross Symposium on Computer Animation 2003
  6. 6. Kernel functions
  7. 7. Surface tracking Marching cubes Point splatting upsampling
  8. 8. OverviewSmoothed particlehydrodynamics (SPH)Scalar density constraintPosition baseddynamics (PBD)Artificial pressure &Vorticity confinementPosition basedfluids
  9. 9. Traditional approaches to simulation1. All forces are accumulated2. Using the density, the forces aretransformed into accelerations3. Compute velocities from the accelerationsand then positions from the velocities
  10. 10. Differential equationtv
  11. 11. Euler’s method
  12. 12. Problems of Euler’s method
  13. 13. Stability “Position Based Dynamics” M. Muller, B. Heideberger, M. Hennix, J. Ratcliff Workshop in Virtual Reality Interactions andPHYsical Simulation (VRIPHYS) 2006
  14. 14. Framework
  15. 15. Framework
  16. 16. Implicit / explicit “The integration does not fall clearly into thecategory of implicit or explicit schemes.” 1 iteration: explicit More iteration: implicit
  17. 17. Advantages “The scheme is unconditionally stable.” Steps (13) and (14) do not extrapolate blindly intothe future as traditional explicit schemes do
  18. 18. Numerical computing The same as “Position Based Fluids”
  19. 19. OverviewSmoothed particlehydrodynamics (SPH)Scalar density constraintPosition baseddynamics (PBD)Artificial pressure &Vorticity confinementPosition basedfluids
  20. 20. Density constraint : target density “Constraint Fluids” K. Bodin, C. Lacoursiere, M. Servin TVCG 2011
  21. 21. Comparison
  22. 22. OverviewSmoothed particlehydrodynamics (SPH)Scalar density constraintPosition baseddynamics (PBD)Artificial pressure &Vorticity confinementPosition basedfluids
  23. 23. Density constraint : : target density
  24. 24. Taylor approximation
  25. 25. Newton steps
  26. 26. Final equation
  27. 27. Results – convergence
  28. 28. Results – performance Frame time = 16ms
  29. 29. Surface tracking Anisotropic kernel “Reconstructing Surfaces of Particle-Based FluidsUsing Anisotropic Kernels” J. Yu, G. Truk TOG 2013
  30. 30. OverviewSmoothed particlehydrodynamics (SPH)Scalar density constraintPosition baseddynamics (PBD)Artificial pressure &Vorticity confinementPosition basedfluids
  31. 31. Artificial pressure
  32. 32. Vorticity confinement
  33. 33. Demo 128k particles, 2 steps/frame, 3 iters/step
  34. 34. Thx.

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