Hair Simulation

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
• 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

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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

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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
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Hair Mechanics

• Difficult to shear and stretch
• Easy to bend and twist
• Anisotropic friction
• Hair geometry also affects motion

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Dynamics of Individual Strand

• Mass-spring systems
• One dimensional projective equations
• Rigid multi-body serial chain
• Dynamic super-helices

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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

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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

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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

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Super-Helices

• Accurate Mechanical Model
• Kirchhoff Equation and Cosserat Curves

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Super-Helices Model for Strands

• Cosserat curve a one-dimensional rod
• A material frame defined at each point on the
  centerline

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Kinematics

• r (s, t) centerline
• s curvilinear abscissa along r
• t time
• ni(s, t) axis of material frame

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Kinematics
O(s, t) Darboux Vector t(s, t) twist ?i (s,
t) - curvatures
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Spatial Discretization
N number of segments Q index of segments 1Q
N qi,Q(t) constant curvatures twist ?Q (s)
characteristic function of Q
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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
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Energy Terms
?S mass per unit length (EI)0 torsional
stiffness (EI)1,2 bending stiffness ?0
natural twist ?1,2 natural curvatures ?
internal friction coefficient
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Equation of Motion

• Symbolic Integrations

inertia matrix stiffness matrix qn
rest position A all remaining terms
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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 ?8, Kirchhoff Eq recovered

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Parameters of Model

• Chosen based on physical measurements
• - Hair mass
• - Mean radius and ellipticity
• - Natural curliness
• - Internal friction ?

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Results and Validation
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Dynamics of a Full Hairstyle

• Hair as a Continuous Medium
• Hair as Disjoint Groups
• Collision detection and response
• Hair-hair and hair-object interaction

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Hair as a Continuous Medium

• Fluid Dynamics
• Loosely Connected Particles
• Interpolation between Guide Hair Strands
• Free Form Deformation

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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

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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

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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

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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

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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

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Simulation of Wisps

• Group neighboring strands into wisps
• Wisp representations
• - Trigonal prism-based wisp
• - Typical strand and
• random displacements
• - Layered wisp model

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Multi-resolution Methods

• Tradeoff performance and realism
• Level-of-detail representations
• Adaptive clustering

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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

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Adaptive Clustering

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

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Hair Rendering

• Representation
• Light scattering in hair
• Hair self-shadowing
• Acceleration

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Representation

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

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Hair Optical Properties

• Hair composed of amorphous proteins as a
  transparent medium with an index of refraction ?
  1.55
• Contain pigments that absorb light in a
  wavelength-dependent way -gt color
• Circular/elliptical fibers treated as
  one-dimensional

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Light scattering

• One-dimensional reformulation of BRDF
• Reflection and refraction in cylinders
• Physical measurement of scattering

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Light Scattering Model

• Kay and Kajiyas model
• Marschners model

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Self-shadowing

• Challenges
• - complex geometry
• - strong forward scattering properties
• Ray-casting through a volumetric representation
• Shadow maps

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Rendering Acceleration

• Approximating Hair Geometry
• Interactive Volumetric Rendering
• Graphics Hardware

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Summary

• Styling
• 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

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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

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• 6. Kurihara, Anjyo Thalmann (1993) Hair
  animation with collision detection
• 7. L'Oréal (2005) Hair Science
  www.hair-science.com
• 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

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• 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