CMSC340 3D Character Design & Animation

1. Cloth CMSC340 3D Character Design & Animation

2. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

3. Motivation • Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

4. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

5. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

6. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

7. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

8. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

9. Challenges Over 100,000 hair strands Real hair properties still under research

10. Overview • Styling Geometry of hair Density, distribution, orientation of hair strands • Simulation Dynamic motion of hair Collision between hair and other objects Mutual hair interactions • Rendering Light scattering and shadows

11. Overview • Styling Geometry of hair Density, distribution, orientation of hair strands Simulation Dynamic motion of hair Collision between hair and other objects Mutual hair interactions Rendering Light scattering and shadows

12. Hair Geometry • Curliness: Straight, wavy, curly, etc. • Shape of cross-section - Asian hair strand: circular - African hair strand: very elliptical - Caucasian hair strand: between the two

13. Hair styling Attaching hair to the scalp Global hair shape Fine details

14. Attaching hair to the scalp 2D Placement 3D Placement Distribution of hair strands on the scalp

15. Global Hair Shape Generation • Geometry-based hairstyling - Parametric surface - Wisps and generalized cylinders • Physically-based hairstyling - Fluid flow - Styling vector and motion fields Generation of hairstyles from images

16. Global Hair Shape Generation • Geometry-based hairstyling - Parametric surface - Wisps and generalized cylinders

17. Global Hair Shape Generation Geometry-based hairstyling - Parametric surface - Wisps and generalized cylinders

18. Global Hair Shape Generation Geometry-based hairstyling - Parametric surface - Wisps and generalized cylinders

19. Global Hair Shape Generation • Physically-based hairstyling - Fluid flow - Styling vector and motion fields

20. Global Hair Shape Generation Physically-based hairstyling - Fluid flow - Styling vector and motion fields

21. Global Hair Shape Generation Physically-based hairstyling - Fluid flow - Styling vector and motion fields

22. Global Hair Shape Generation Geometry-based hairstyling - Parametric surface - Wisps and generalized cylinders Physically-based hairstyling - Fluid flow - Styling vector and motion fields Generation of hairstyles from images

23. Finer Details

24. Finer Details

25. Finer Details

26. Hair Mechanics Difficult to shear and stretch Easy to bend and twist Anisotropic friction Hair geometry also affects motion

27. Dynamics of Individual Strand Mass-spring systems One dimensional projective equations Rigid multi-body serial chain Dynamic super-helices

28. Mass-Spring Systems • Particles connected by stiff springs bending rigidity ensured by angular spring at each joint • Simple and easy to implement • But does not account for tortional rigidity or non-stretching of each strand

29. One-dimensional Projective Equations Hair strand as a chain of rigid sticks • Easy to implement • Efficient • Non-stretching • Bending • No tortional stiffness • Difficult to handle external punctual forces

30. Rigid Multi-body Serial Chain Hair strand as a rigid multi-body open chain • Bending and twisting DOFs only, stretching DOF removed Motion computed using forward dynamics

31. Super-Helices Accurate Mechanical Model Kirchhoff Equation and Cosserat Curves

32. Super-Helices Model for Strands Cosserat curve: a one-dimensional rod A material frame defined at each point on the centerline

33. Kinematics r (s, t) – centerline s – curvilinear abscissa alongr t – time ni(s, t) – axis of material frame

34. Kinematics Ω(s, t) – Darboux Vector τ(s, t) – twist κi (s, t) - curvatures

35. Spatial Discretization N –number of segments Q –index of segments1≤Q ≤ N qi,Q(t) – constant curvatures & twist χQ (s) – characteristic function of Q

36. Dynamic Equations Solve equations of motion using Lagrangian mechanics q (t) – generalized coordinates T (q, , t) – kinetic energy U (q, t)– internal energy D (q, , t) – dissipation potential F (s, t) – linenic density of forces JiQ (s, q, t) – Jacobian matrix

37. Energy Terms ρS – mass per unit length (EI)0 – torsional stiffness (EI)1,2 – bending stiffness κ0–natural twist κ1,2–natural curvatures γ –internal friction coefficient

38. Equation of Motion Symbolic Integrations –inertia matrix –stiffness matrix qn–rest position A–all remaining terms

39. Key Features Discrete model for Kirchhoff equations Space integrations performed symbolically • Stiff constraint of inextensibility incorporated into reconstruction process, therefore removed from the equations of motion • Stable simulation even for small N When N →∞, Kirchhoff Eq recovered

40. Parameters of Model Chosen based on physical measurements - Hair mass - Mean radius and ellipticity - Natural curliness: - Internal friction γ

41. Results and Validation

42. Dynamics of a Full Hairstyle Hair as a Continuous Medium Hair as Disjoint Groups Collision detection and response • Hair-hair and hair-object interaction

43. Hair as a Continuous Medium Fluid Dynamics Loosely Connected Particles Interpolation between Guide Hair Strands Free Form Deformation

44. Animating Hair with Fluid Dynamics Kinematically link each hair strand to fluid particles in their vicinity Hair-hair interactions modeled by pressure and viscosity forces between strands Hair-body interactions modeled by creating boundary particles around solid objects • Captures the complex interactions of hair strands • Cannot capture the dynamic clustering effects • Computationally expensive

45. Loosely Connected Particles Use a set of fluid particles that interact in an adaptive way • Neighboring particles with similar orientations are linked During motion particles interact with other particles in its local neighborhood through breakable links Allows separation and grouping while maintaining constant hair length

46. Interpolation between Guide Hair Strands Only simulate a sparse set of hair strands Remaining strands created by interpolation Only use the guide strands to detect and handle collisions - Might miss collisions

47. Free Form Deformation (FFD) Define a mechanical model for a lattice surrounding the head Lattice deformed using a global volumetric FFD scheme Good for simulating complex hairstyles when head motion has low magnitude Cannot reproduce discontinuities in hair

48. Hair as Disjoint Groups Group nearby hair strands, simulate groups as independent, interacting entities • Account for discontinuities during fast motion • Save computation time Simulation of - Hair strips - Wisps

49. Simulation of Hair Strips Model groups of strands using a thin flat patch, e.g. a NURBS surface • Achieves real time using a strip to represent tens or hundreds of hairs • Limited in the types of hairstyle and motion

50. Simulation of Wisps Group neighboring strands into wisps Wisp representations - Trigonal prism-based wisp - Typical strand and random displacements - Layered wisp model