Hair Simulation Model for RealTime Environments Computer Graphics

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

Introduction Related work Physical model Twisting Head collision Results Conclusion Presentation Outline § § § § Introduction Related work Physical model Twisting Head collision Results Conclusion 27. 5. 2009 Hair Simulation Model for Real-Time Environments 2

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 (100 k-150 k) § Solutions: LOD, interpolation, volume 27. 5. 2009 Hair Simulation Model for Real-Time Environments 3

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 27. 5. 2009 Hair Simulation Model for Real-Time Environments 4

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] 27. 5. 2009 Hair Simulation Model for Real-Time Environments 5

Introduction Related work Physical model Twisting Head collision Results Conclusion Discrete Rod Model § Based on [Bergou et al. 08] § Polyline xi ej § Nodes xi, segments ej m 1 j § Material frame § Adapted tangent tj § Cross-section m 1 j, m 2 j tj m 2 j § Mechanical properties § Bending stiffness matrix Bj § Twist stiffness β 27. 5. 2009 Hair Simulation Model for Real-Time Environments 6

Introduction Related work Physical model Twisting Head collision Results Conclusion Twist Formulation § Material frame § Scalar rotation θj of twist-free reference frame § Instantaneous propagation § Not part of dynamic equations § Quasistatic update 27. 5. 2009 Hair Simulation Model for Real-Time Environments 7

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 § 27. 5. 2009 “Infinite” bending stiffness over minor axis Hair Simulation Model for Real-Time Environments 8

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 27. 5. 2009 Hair Simulation Model for Real-Time Environments 9

Introduction Related work Physical model Twisting Head collision Results Conclusion Computing Twist (1) § Bending axes given ηj § Co-planar § Compute angles ηj, ηj+1 θj § Oriented § Compute initial θj § Both bent: § One bent: η ηj+1 § Unbent: § Major axis direction 27. 5. 2009 Hair Simulation Model for Real-Time Environments 10

Introduction Related work Physical model Twisting Head collision Results Conclusion Computing Twist (2) § Find orientation ? § θj+π § Root-to-tip, segment j § Elastic energies § Simple criteria θj θj-π § Use θ with minimal E § Major axis orientation 27. 5. 2009 Hair Simulation Model for Real-Time Environments 11

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

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 27. 5. 2009 Hair Simulation Model for Real-Time Environments 13

Introduction Related work Physical model Twisting Head collision Results Conclusion Results 27. 5. 2009 Hair Simulation Model for Real-Time Environments 14

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

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 27. 5. 2009 Hair Simulation Model for Real-Time Environments 16