Hair Simulation Model for Real-Time Environments

Petr Kmoch1, Ugo Bonanni2, Nadia Magnenat-Thalmann2

1. Faculty of Mathematics and Physics, Charles University in Prague2. MIRALab, University of Geneva

Computer Graphics International 2009

Hair Simulation Model for Real-Time Environments 2

Presentation Outline Introduction Related work Physical model Twisting Head collision Results Conclusion

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 3

Hairstyle Modelling Unintuitive, tedious Solution: simulate real hairstyling

Physical simulation of hair Difficulties

Anisotropic character of hair Complex interaction Sheer numbers (100k-150k)

Solutions: LOD, interpolation, volume

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 4

Our Approach Virtual hairstyling

Explicit, strand-based representation Real-time performance desired

Mechanical model Elastic rods Hair-specific optimizations

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 5

Related Work Hair animation

[Hadap 06], [Selle et al. 08], [Ward and Lin 03], [Volino and Magnenat-Thalmann 04], [Bertails et al. 06]

Elastic rods [Pai 02], [Spillmann and Teschner 07], [Bergou et al. 08]

Hairstyling [Ward et al. 06], [Magnenat-Thalmann et al. 06] , [Bonanni

and Kmoch 08]

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 6

Discrete Rod Model Based on [Bergou et al. 08] Polyline

Nodes xi, segments ej

Material frame Adapted tangent tj

Cross-section m1j, m2

j

Mechanical properties Bending stiffness matrix Bj

Twist stiffness β27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

xi

ej

tj

m1j

m2j

Hair Simulation Model for Real-Time Environments 7

Twist Formulation Material frame

Scalar rotation θj of twist-free reference frame Instantaneous propagation

Not part of dynamic equations Quasistatic update

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 8

Hair Mechanical Properties Elliptical cross section

Varies with ethnicity Only bends over major axis

Coupled with twisting Twists to bend over major axis only Dictates bending stiffness matrix

“Infinite” bending stiffness overminor axis

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 9

Hair Twisting Ideal: eliminate bending

over minor axes Prescribes major axis at

node Frames assigned to

segments Conflicting requirements

Solution Minimize minor-axis

bending instead Optimal twist is directly

computable

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 10

Computing Twist (1) Bending axes given

Co-planar Compute angles ηj, ηj+1

Oriented Compute initial θj

Both bent: One bent: η Unbent:

Major axis direction

1jj ηη2

1

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

θ̂

ηj

ηj+1

θj

Hair Simulation Model for Real-Time Environments 11

Computing Twist (2) Find orientation

? Root-to-tip, segment j

Elastic energies Simple criteria

Use θ with minimal E Major axis orientation

π-θ ,πθ ,θ jjj

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

EEE ,,0

20

20

βπ)θ̂βπ(θ2ˆ2

βπ)θ̂βπ(θ2ˆ2

θ̂θ

jjjj

j

jjjj

j

jj

BEE

BEE

EE

ω

ω

θj

θj+π

θj-π

Hair Simulation Model for Real-Time Environments 12

Constraints Post-integration step

Removes equation stiffness Constraints

Inextensibility, rigid body (head) coupling Projection to nearest constrained state

Metric ~ kinetic energy of change Iterative manifold projection

Efficient, stable

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 13

Hair-Head Collisions Extra constraints Set P of nodes penetrating head

Fixed for one step Constraint value: penetration depth

Very little overhead Robust solution

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 14

Results

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 15

Conclusion Hair animation method based on rods

Suitable for real-time Hair-specific twist computation

Fast, stable, non-iterative Efficient hair-head collision treatment

Future work Haptic interaction GPU implementation

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair Simulation Model for Real-Time Environments 16

Thank You

For your attentionFor your questions

Supported by Grant Agency of the Charles University, project #100209 Swiss National Science Foundation

27.5.2009

Introduction Related work Physical model Twisting Head collision Results Conclusion