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Motivation

Motivation. Articulated bodies in Computer Graphics Humans, hair, animals Trees, forests, grass Deformable bodies Molecular graphics … . Motivation. Forward dynamics Optimal solutions are linear Production constraints

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Motivation

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  1. Motivation • Articulated bodies in Computer Graphics • Humans, hair, animals • Trees, forests, grass • Deformable bodies • Molecular graphics • …

  2. Motivation • Forward dynamics • Optimal solutions are linear • Production constraints “Dynamics computations should take less than 10-20 seconds per frame to make animators’ lives easy”Sunil Hadap, PDI/DreamWorks • Optimal forward dynamics methods are too slow for numerous or complex articulated bodies

  3. Contributions • Forward dynamics • Adaptive forward dynamics • Specify the number of degrees of freedom • Only this number of degrees of freedom is simulated • The most relevant degrees of freedom are automatically found

  4. Contributions • Hybrid bodies • Novel articulated-body representation • To reduce the number of degrees of freedom • Adaptive joint selection • Novel customizable motion metrics • To determine the most relevant degrees of freedom • Adaptive update mechanisms

  5. Outline • Related work • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Results

  6. Outline • Related work • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Results

  7. Related work Forward dynamics of articulated bodies • Optimal algorithms • [Hollerbach 1980] • [Featherstone 1987] • [McMillan and Orin 1995] • [Baraff 1996] • Parallel algorithms • [Fijany et al. 1995] • [Featherstone 1999] Divide and Conquer Algorithm (DCA) • [Yamane and Nakamura 2002]

  8. Related work Simulation levels of detail • Human motion • [Carlson and Hodgins 1997] • [Popovic and Witkin 1999] • Plant motion • [Perbet and Cani 2001] • [Beaudoin and Keyser 2004] • Hair modeling • [Bertails et al. 2003] • [Ward et al. 2003]

  9. Related work Simulation levels of detail • View-dependent dynamics • [Chenney and Forsyth 1997] • [Chenney et al. 1999] • [Chenney et al. 2001] • Articulated-body motion simplification • [Faure 1999] • [Redon and Lin 2005] – Adaptive quasi-statics

  10. Outline • Related work • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Results

  11. Hybrid bodies Featherstone’s DCA • Recursive definition An articulated body is formed by assembling two articulated bodies

  12. Hybrid bodies Featherstone’s DCA • Recursive definition An articulated body is formed by assembling two articulated bodies

  13. The complete articulated body Pairs of rigid bodies Rigid bodies Hybrid bodies Featherstone’s DCA • Recursive definition The assembly tree of an articulated body

  14. Hybrid bodies Featherstone’s DCA • Recursive definition • Articulated-body equation Body Accelerations Inverse inertias and cross-inertias Applied Forces Bias accelerations

  15. Hybrid bodies Featherstone’s DCA • Recursive definition • Articulated-body equation The cross-coupling inverse inertia describes the effect of a force applied to body 2, on the acceleration of body 1

  16. Hybrid bodies Featherstone’s DCA • Recursive definition • Articulated-body equation The bias acceleration is the acceleration of body 1 when no forces are applied

  17. Hybrid bodies Featherstone’s DCA • Recursive definition • Articulated-body equation • Two main steps • Compute the articulated-body coefficients () Inverse inertias Bias accelerations

  18. Hybrid bodies Featherstone’s DCA • Recursive definition • Articulated-body equation • Two main steps • Compute the joint accelerations and forces () Joint acceleration Kinematic constraint forces

  19. Hybrid bodies Definitions • Active region The active region contains the mobile joints

  20. Hybrid bodies Definitions • Active region • Hybrid-body coefficients Articulated-body coefficients Rigidify joint Hybrid-body coefficients

  21. Hybrid bodies Definitions • Active region • Hybrid-body coefficients • Hybrid-body simulation • Same steps as articulated-body simulation • Computations restricted to a sub-tree (cf. paper)

  22. Outline • Related work • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Results

  23. Adaptive joint selection Motion metrics • Acceleration metric • Velocity metric

  24. Adaptive joint selection Motion metrics • TheoremThe acceleration metric value of an articulated body can be computed before computing its joint accelerations

  25. =3 =-6 =6 =-3 =2 =-1 =1 Adaptive joint selection Motion metrics • Example = 96

  26. Adaptive joint selection Acceleration simplification = 96 Compute the acceleration metric value of the root

  27. Adaptive joint selection Acceleration simplification = 96 -3 Compute the joint acceleration of the root

  28. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 Compute the acceleration metric values of the two children

  29. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 Select the node with the highest acceleration metric value

  30. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 Compute its joint acceleration

  31. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 = 9 = 36 Compute the acceleration metric values of its two children

  32. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 = 9 = 36 = 36 Select the node with the highest acceleration metric value

  33. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 = 9 = 36 6 Compute its joint acceleration

  34. Adaptive joint selection Acceleration simplification = 96 -3 = 6 -6 = 9 6 Stop because a user-defined sufficient precision has been reached

  35. Adaptive joint selection Acceleration simplification = 96 -3 = 6 -6 = 9 6 Four subassemblies with joint accelerations implicitly set to zero

  36. Outline • Related work • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Results

  37. Adaptive update mechanisms • Position-dependent coefficients • Hierarchical state representation [Redon and Lin 2005]

  38. Adaptive update mechanisms • Velocity-dependent coefficients • Linear coefficients tensors (Implementation sketch tomorrow 11:20am 515B)

  39. Outline • Related work • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Results

  40. Results Adaptive selection MOVIE Adaptive joint selection example (10x speed-up)

  41. Results Adaptive joint selection Adaptive joint selection example (10x speed-up)

  42. Results Time-dependent simplification One color per sub-assembly

  43. Results Time-dependent simplification One color per sub-assembly

  44. Results Adaptive selection MOVIE Time-dependent simplification

  45. Results Progressive dynamics Progressive dynamics of a 300-link pendulum

  46. Results Progressive dynamics Number of active joints N=300 N=100 N=50 N=20 N=1 Progressive dynamics of a 300-link pendulum

  47. Results Progressive dynamics Average cost per time step N=300 5ms N=100 1.7ms N=50 0.7ms N=20 0.25ms N=1 0.02ms Progressive dynamics of a 300-link pendulum

  48. Results Test application MOVIE

  49. Conclusion Summary • A new adaptive dynamics algorithm • Hybrid bodies • Adaptive joint selection • Adaptive update mechanisms • Precision / Performance trade-off

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