Download ppt - Hair Simulation COMP 768 Qi Mo. Motivation Cosmetic prototyping Entertainment industry - Feature animation - Interactive systems

Hair Simulation

COMP 768 Qi Mo

Motivation

• Cosmetic prototyping

• Entertainment industry

- Feature animation

- Interactive systems

Motivation



- Feature animation


Motivation



- Feature animation


Motivation



- Feature animation


Motivation



- Feature animation


Motivation



- Feature animation


Motivation



- Feature animation


Challenges

• Over 100,000 hair strands

• Real hair properties still under research

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

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

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

Hair styling

• Attaching hair to the scalp

• Global hair shape

• Fine details

Attaching hair to the scalp

• 2D Placement

• 3D Placement

• Distribution of hair strands on the scalp

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
























• Generation of hairstyles from images

Finer Details

Finer Details

Finer Details

Hair Mechanics• Difficult to shear and stretch

• Easy to bend and twist

• Anisotropic friction

• Hair geometry also affects motion

Dynamics of Individual Strand

• Mass-spring systems

• One dimensional projective equations

• Rigid multi-body serial chain

• Dynamic super-helices

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

One-dimensional Projective Equations

• Hair strand as a chain of rigid sticks

Easy to implementEfficientNon-stretchingBending

No tortional stiffnessDifficult to handle

external punctual forces

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

Super-Helices

• Accurate Mechanical Model

Kirchhoff Equation and Cosserat Curves

Super-Helices Model for Strands

• Cosserat curve: a one-dimensional rod

• A material frame defined at each point on the centerline

Kinematics

r (s, t) – centerline

s – curvilinear abscissa along r

t – time ni(s, t) – axis of material frame

Kinematics

Ω(s, t) – Darboux Vector

τ(s, t) – twist

κi (s, t) - curvatures

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

Dynamic Equations• Solve equations of motion using

Lagrangian mechanicsq (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

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

Equation of Motion• Symbolic Integrations

– inertia matrix

– stiffness matrix

qn – rest position

A – all remaining terms

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

Parameters of Model

• Chosen based on physical measurements

- Hair mass

- Mean radius and ellipticity

- Natural curliness:

- Internal friction γ

Results and Validation

Dynamics of a Full Hairstyle

• Hair as a Continuous Medium

• Hair as Disjoint Groups

• Collision detection and response

• Hair-hair and hair-object interaction

Hair as a Continuous Medium

• Fluid Dynamics

• Loosely Connected Particles

• Interpolation between Guide Hair Strands

• Free Form Deformation

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 strandsCannot capture the dynamic clustering effectsComputationally expensive

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

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

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

Hair as Disjoint Groups

• Group nearby hair strands, simulate groups as independent, interacting entities

Account for discontinuities during fast motionSave computation time

• Simulation of

- Hair strips

- Wisps

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 hairsLimited in the types of hairstyle and motion

Simulation of Wisps

• Group neighboring strands into wisps

• Wisp representations - Trigonal prism-based wisp

- Typical strand and

random displacements

- Layered wisp model

Multi-resolution Methods

• Tradeoff: performance and realism

• Level-of-detail representations

• Adaptive clustering

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

Adaptive Clustering

• Continuously adjustment with Adaptive Wisp Tree (AWT)

• Dynamically splits or groups wisps while preserving tree-like structure

• Implicitly models hair interactions

Hair Rendering

• Representation

• Light scattering in hair

• Hair self-shadowing

• Acceleration

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

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

Light scattering

• One-dimensional reformulation of BRDF

• Reflection and refraction in cylinders

• Physical measurement of scattering

Light Scattering Model

• Kay and Kajiya’s model

• Marschner’s model

Self-shadowing

• Challenges - complex geometry - strong forward scattering properties

• Ray-casting through a volumetric representation• Shadow maps

Rendering Acceleration

• Approximating Hair Geometry

• Interactive Volumetric Rendering

• Graphics Hardware

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

Open Challenges

• Physically-based realism

• Visual realism with high user control

• Computations acceleration

Reference

1. Anjyo, Usami & Kurihara (1992): A simple method for extracting the natural beauty of hair

2. Bertails, Kim, Cani & Neumann (2003): Adaptive wisp tree – a multiresolution control structure for simulating dynamic clustering in hair motion

3. Chang, Jin & Yu (2002): A practical model for hair mutual interactions

4. Hadap & Magnenat-Thalmann (2001): Modeling dynamic hair as a continuum

5. Koh & Huang (2000): Real-time animation of human hair modeled in strips

6. Kurihara, Anjyo & Thalmann (1993): Hair animation with collision detection

7. L'Oréal (2005): Hair Science www.hair-science.com8. Magnenat-Thalmann & Hadap (2000): State of the art in

hair simulation9. Petrovic, Henne & Anderson (2007): Volumetric methods

for simulation and rendering of hair10. Plante, Cani & Poulin (2001): A layered wisp model for

simulating interactions inside long hair11. Rosenblum, Carlson & Tripp (1991): Simulating the

structure and dynamics of human hair: Modeling, rendering, and animation

http://www.hair-science.com/

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