Hair Simulation Model for Real-Time Environments

1. Hair Simulation Model for Real-Time Environments Petr Kmoch1, Ugo Bonanni2, Nadia Magnenat-Thalmann2 Faculty of Mathematics and Physics, Charles University in Prague MIRALab, University of Geneva Computer Graphics International 2009

2. Introduction Related work Physical model Twisting Head collision Results Conclusion Introduction Related work Physical model Twisting Head collision Results Conclusion Presentation Outline Hair Simulation Model for Real-Time Environments

3. 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 Introduction Related work Physical model Twisting Head collision Results Conclusion Hairstyle Modelling Hair Simulation Model for Real-Time Environments

4. Virtual hairstyling • Explicit, strand-based representation • Real-time performance desired Mechanical model • Elastic rods • Hair-specific optimizations Introduction Related work Physical model Twisting Head collision Results Conclusion Our Approach Hair Simulation Model for Real-Time Environments

5. 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] Introduction Related work Physical model Twisting Head collision Results Conclusion Related Work Hair Simulation Model for Real-Time Environments

6. Based on [Bergou et al. 08] Polyline • Nodes xi, segments ej Material frame • Adapted tangent tj • Cross-section m1j, m2j Mechanical properties • Bending stiffness matrix Bj • Twist stiffness β Introduction Related work Physical model Twisting Head collision Results Conclusion Discrete Rod Model xi ej m1j m2j tj Hair Simulation Model for Real-Time Environments

7. Material frame • Scalar rotation θj of twist-free reference frame Instantaneous propagation • Not part of dynamic equations • Quasistatic update Introduction Related work Physical model Twisting Head collision Results Conclusion Twist Formulation Hair Simulation Model for Real-Time Environments

8. 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 Introduction Related work Physical model Twisting Head collision Results Conclusion Hair Mechanical Properties Hair Simulation Model for Real-Time Environments

9. Introduction Related work Physical model Twisting Head collision Results Conclusion 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 Hair Simulation Model for Real-Time Environments

10. Introduction Related work Physical model Twisting Head collision Results Conclusion 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 ηj θj ηj+1 Hair Simulation Model for Real-Time Environments

11. Introduction Related work Physical model Twisting Head collision Results Conclusion Computing Twist (2) • Find orientation • ? • Root-to-tip, segment j • Elastic energies • Simple criteria • Use θwith minimal E • Major axis orientation θj+π θj θj-π Hair Simulation Model for Real-Time Environments

12. 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 Introduction Related work Physical model Twisting Head collision Results Conclusion Constraints Hair Simulation Model for Real-Time Environments

13. Extra constraints Set P of nodes penetrating head • Fixed for one step • Constraint value: penetration depth Very little overhead Robust solution Introduction Related work Physical model Twisting Head collision Results Conclusion Hair-Head Collisions Hair Simulation Model for Real-Time Environments

14. Introduction Related work Physical model Twisting Head collision Results Conclusion Results Hair Simulation Model for Real-Time Environments

15. 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 Introduction Related work Physical model Twisting Head collision Results Conclusion Conclusion Hair Simulation Model for Real-Time Environments

16. Introduction Related work Physical model Twisting Head collision Results Conclusion Thank You For your attention For your questions • Supported by • Grant Agency of the Charles University, project #100209 • Swiss National Science Foundation Hair Simulation Model for Real-Time Environments