Hair Simulation Model for Real-Time Environments Petr Kmoch 1, Ugo Bonanni 2, Nadia Magnenat- Thalmann 2 1. Faculty of Mathematics and Physics, Charles University in Prague 2. MIRALab, University of Geneva Computer Graphics International 2009

Presentation Outline Introduction Related work Physical model Twisting Head collision Results Conclusion Hair Simulation Model for Real-Time Environments2 Introduction Related work Physical model Twisting Head collision Results Conclusion

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 Hair Simulation Model for Real-Time Environments3 Introduction Related work Physical model Twisting Head collision Results Conclusion

Our Approach Virtual hairstyling Explicit, strand-based representation Real-time performance desired Mechanical model Elastic rods Hair-specific optimizations Hair Simulation Model for Real-Time Environments4 Introduction Related work Physical model Twisting Head collision Results Conclusion

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] Hair Simulation Model for Real-Time Environments5 Introduction Related work Physical model Twisting Head collision Results Conclusion

Discrete Rod Model Based on [Bergou et al. 08] Polyline Nodes x i, segments e j Material frame Adapted tangent t j Cross-section m 1 j, m 2 j Mechanical properties Bending stiffness matrix B j Twist stiffness β Hair Simulation Model for Real-Time Environments6 Introduction Related work Physical model Twisting Head collision Results Conclusion xixi ejej tjtj m1jm1j m2jm2j

Twist Formulation Material frame Scalar rotation θ j of twist-free reference frame Instantaneous propagation Not part of dynamic equations Quasistatic update Hair Simulation Model for Real-Time Environments7 Introduction Related work Physical model Twisting Head collision Results Conclusion

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 over minor axis Hair Simulation Model for Real-Time Environments8 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 Environments9 Introduction Related work Physical model Twisting Head collision Results Conclusion

Computing Twist (1) Bending axes given Co-planar Compute angles η j, η j+1 Oriented Compute initial θ j Both bent: One bent: η Unbent: Major axis direction Hair Simulation Model for Real-Time Environments10 Introduction Related work Physical model Twisting Head collision Results Conclusion ηjηj η j+1 θjθj

Computing Twist (2) Find orientation ? Root-to-tip, segment j Elastic energies Simple criteria Use θ with minimal E Major axis orientation Hair Simulation Model for Real-Time Environments11 Introduction Related work Physical model Twisting Head collision Results Conclusion θjθj θj+πθj+π θj-πθj-π

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 Hair Simulation Model for Real-Time Environments12 Introduction Related work Physical model Twisting Head collision Results Conclusion

Hair-Head Collisions Extra constraints Set P of nodes penetrating head Fixed for one step Constraint value: penetration depth Very little overhead Robust solution Hair Simulation Model for Real-Time Environments13 Introduction Related work Physical model Twisting Head collision Results Conclusion

Results Hair Simulation Model for Real-Time Environments14 Introduction Related work Physical model Twisting Head collision Results Conclusion

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 Hair Simulation Model for Real-Time Environments15 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 # Swiss National Science Foundation Hair Simulation Model for Real-Time Environments16 Introduction Related work Physical model Twisting Head collision Results Conclusion