Exploiting Subdivision in Modeling and Animation

1. Exploiting Subdivision in Modeling and Animation David R. Forsey The University of British Columbia&Radical Entertainment Inc.

2. Topics • Multiresolution Animation • What it is. • How to use it.

3. Retrospective • “Hierarchical B-Spline Refinement”, SIGGRAPH’88Forsey/Bartels.

4. Motivations for H-Splines • H-Splines were developed specifically for animation. • Address problems with traditional B-splines • non-local knot insertion • the “degree-of-freedom” problem.

5. Local Refinement • Models rapidly become “heavy” • patches in locations they are not needed • extra rendering overhead • may affect previously defined animation • even more points to animate • Local refinement adds patches to a restricted area

6. Local Refinement

7. Local Refinement • Created using a multiresolution representation • Can dramatically reduce the storage requirements

8. Multiresolution Editing • Each resolution procedurally related to the next coarsest level • arbitrary procedure (offset operator) for each control point. • creates a “reactive surface”

9. H-Splines • Applicable to any surface formulation with: • Local support • Subdivision that does not alter the shape of the limit surface • polygons • other splines (including curves & deformation lattices) • various subdivision surface formulations • wavelets (depending upon basis used)

10. H-Splines • Advantages • Top-down modelling (more like sculpting) • details maintained during broad-scale editing • faster/easier to animate complex surfaces • Efficient representation (compression) • Refinement only where needed

11. Multiresolution Animation • Available in a limited form commercially: • MetaNURBs (Lightwave) • Meshsmooth (3DMax) • Symbolics L-surf (now Nicheman) • various polygon smoothing packages

12. Animating with H-Splines • Offset Operators: • tangent plane offset • “frame” offset (attaches a control vertex to a skeletal segment) • others described later

13. Simple Head

14. Low-Res Attachment

15. Effect on finer resolution

17. Example Animation

18. “Locking down” geometry

19. Locking Down Geometry, Part II • Full Detail Lowest Resolution

20. Locking Down Geometry, Part II • Level 1 Level 2

21. Locking Down Geometry, Part II • Full Resolution Bent Full Resolution Straight

22. Example Animation

23. Multiresolution Animation • Advantages • allows top-down approach to surface animation • easy to mix broad-scale and fine scale effects • faster to animate • low-res model always available (for interactive speed) • less worry about high-res model behaviour

24. Layered Animation • Low-res modification High-res effect

25. Layered Animation • Medium-res modification High-res effect

26. Layered Animation • Both modifications Both modifications, jaw open

27. Example Animation

28. Level of Detail • Because the animation occurs at multiple levels of detail, low-res models still animate when used as low resolution geometry

29. Layered Animation • Animation at each resolution layers deformations rather than blending them. • Makes it easy to combine vertex animation with shape interpolation. • Can combine relative (offset animation) with absolute (skeletal attachments) effects easily. • Provides LOD for animation as well as geometry

30. Editing Operations • Any spline-based tools can be used with H-Splines • Additional operations possible: • copy level, region (rubber stamp details) • non-hierarchical editing • modify offset: • move cv normal/tangent/along parent surface • move cv along offset • rotate offset • move offset origin

31. Secondary Motion using Offsets • Typical spring/mass simulations produce “jello” effects • Can provide more structure by treating each offsets as a rod/mass system. • prevents motion into surface • surface details preserved • fast, easy to calculate

32. Secondary Motion using Offsets

33. Secondary Motion using Offsets • Sample animation

34. Secondary Motion using Offsets • Wrinkles • Uses a “behaviour map” indicating location of wrinkle and dynamic properties (if combined with rod/mass simulation). • value from map used to determine how to alter the offset parameterized by change in distance to neighbour • low-res modifications to surface increase/decrease size of wrinkle

35. Secondary Motion using Offsets • Wrinkles

36. Secondary Motion using Offsets • Wrinkles

37. More Examples

38. Surface Approximation • Problem • Animators need to control placement of isoparms • Draw lines directly onto sculptures for digitization as a spline control mesh • Non-locality of knots creates heavier mesh, crowded lines • H-Spline Approach • Allows mesh to be drawn with areas of higher detail

39. Variations Link to paper • Surface Pasting • Diagonal features are difficult to model • Such features are modeled separately and “pasted” onto the low-res surface • Generalizes H-Splines, but are more computationally expensive. (Note: commercially available in the Houdini animation system)

40. Surface Pasting

41. Surface Pasting • Overlapping features Underlying parameter space

42. Grafting Surfaces • Arbitrary topology surfaces difficult with tensor-product splines • use Catmull-Clark subdivision surfaces to join spline surfaces • maintain compatibility with B-splines • minimizes the number of extraordinary points • maintains a simple U/V mapping for textures and attribute maps

43. Grafting • Two grafted cylinders Finger grafts

44. Grafting • Low-res hand with grafts Rendered hand

45. Multiresolution Simulation • Problem • simulations based on simple finite elements (spring/mass meshes) are difficult to control • unclear how to set the parameters for a particular behaviour • stiff systems suffer from numerical instability or small step sizes • very few formulations that deal with micro/macro effects in the same model

46. Multiresolution Simulation link to paper • Animator’s Solution: • use a multiresolution representation of surface • propagate a proportion of forces to each successive resolution • similar to multigrid methods, but different equation solved at each resolution • can retain surface details using an offset representation

47. Multiresolution Simulation 100 % of forces applied at lowest resolution 100 % of forces applied at highest resolution Forces applied at multiple resolutions

48. Multiresolution Deformations link to paper • Uses similar approach, but uses kinematics rather than dynamics

49. Multiresolution Deformations • Different behaviours are created by varying the amount each resolution accomodates the deformation

50. Multiresolution deformations Time varying effects are added by delaying the change to the position and orientation of the offsets Behaviour during insertion of sphere Behaviour during withdrawal of sphere