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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