1. Hair Simulation
COMP 768 Qi Mo

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 Simulation Dynamic motion 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 Simulation Dynamic motion 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 along r
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 segments 1≤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 qn – rest position
– 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

51. Multi-resolution Methods
Tradeoff: performance and realism
Level-of-detail representations
Adaptive clustering

52. Level-of-Detail Representations
Three discrete levels of detail
- strands, clusters, and strips
Common representation by subdivided curves and surfaces
Collision detection using Swept Sphere Volumes
Dynamic level transition based on visibility, viewing distance, and motion

53. Adaptive Clustering
Continuously adjustment with Adaptive Wisp Tree (AWT)
Dynamically splits or groups wisps while preserving tree-like structure
Implicitly models hair interactions

54. Hair Rendering Representation Light scattering in hair
Hair self-shadowing
Acceleration

55. Representation Explicit representation
curved cylinder, trigonal prism, triangle strips
thin -> undersampling -> blending techniques
Implicit representation
volumetric textures, cluster model with density
avoid aliasing, but traversal may be expensive

56. Hair Optical Properties
Hair composed of amorphous proteins as a transparent medium with an index of refraction η= 1.55
Contain pigments that absorb light in a wavelength-dependent way -> color
Circular/elliptical fibers treated as one-dimensional

57. Light scattering One-dimensional reformulation of BRDF
Reflection and refraction in cylinders
Physical measurement of scattering

58. Light Scattering Model
Kay and Kajiya’s model
Marschner’s model

59. Self-shadowing Challenges - complex geometry
- strong forward scattering properties
Ray-casting through a volumetric representation
Shadow maps

60. Rendering Acceleration
Approximating Hair Geometry
Interactive Volumetric Rendering
Graphics Hardware

61. Summary Styling Simulation Rendering
Hair geometry
Attaching hair to scalp, generate global shape, capture finer details
Simulation
Hair mechanics
Mass-spring systems, One dimensional projective equations, Rigid multi-body serial chain, Dynamic super-helices
Continuous medium, disjoint groups
Multi-resolution methods
Rendering
Hair optics
Representation, light scattering, self-shadowing, acceleration techniques

62. Open Challenges Physically-based realism
Visual realism with high user control
Computations acceleration

63. Reference
Anjyo, Usami & Kurihara (1992): A simple method for extracting the natural beauty of hair
Bertails, Kim, Cani & Neumann (2003): Adaptive wisp tree – a multiresolution control structure for simulating dynamic clustering in hair motion
Chang, Jin & Yu (2002): A practical model for hair mutual interactions
Hadap & Magnenat-Thalmann (2001): Modeling dynamic hair as a continuum
Koh & Huang (2000): Real-time animation of human hair modeled in strips

64. 6. Kurihara, Anjyo & Thalmann (1993): Hair animation with collision detection
7. L'Oréal (2005): Hair Science
8. Magnenat-Thalmann & Hadap (2000): State of the art in hair simulation
9. Petrovic, Henne & Anderson (2007): Volumetric methods for simulation and rendering of hair
10. Plante, Cani & Poulin (2001): A layered wisp model for simulating interactions inside long hair
11. Rosenblum, Carlson & Tripp (1991): Simulating the structure and dynamics of human hair: Modeling, rendering, and animation

65. 12. Volino & Magnenat-Thalmann (1999): Animating complex hairstyles in real-time
13. Watanbe & Suenaga (1992): A trigonal prism-based method for hair image generation
14. Ward, Bertails, Kim, Marschner, Cani & Lin (2007): A survey on hair modeling: styling, simulation and rendering
15. Ward & Lin (2003): Adaptive grouping and subdivision for simulating hair dynamics
16. Ward, Lin, Lee, Fisher & Macri (2003): Modeling hair using level-of-detail representations