A physically based approach to the accurate simulation of stiff fibers and stiff fiber meshes.pdf

Computers Graphics 53 (2015) 136–146Contents lists available at ScienceDirectComputers Graphicshttp://d 0097-84 ☆This n Corr E-mjournal homepage: /locate/cagTechnical SectionA physically based approach to the accurate simulation of stiff fibers and stiff fiber meshes$ Dominik L. Michels n, J. Paul T. Mueller, Gerrit A. Sobottka Computer Science Department, Stanford University, 353 Serra Mall, Stanford, CA 94305, USAa r t i c l e i n f o Article history: Received 23 March 2015 Received in revised form 27 September 2015 Accepted 2 October 2015 Available online 22 October 2015 Keywords: Cosserat rods Exponential integrators Fibers and fiber meshes Hair /10.1016/j.cag.2015.10.001 93/ 2015 Elsevier Ltd. All rights reserved. article was recommended for publication by esponding author. ail address: michels@ (D.L. Mica b s t r a c t We devise a physically based approach to the accurate simulation of stiff fibers like human hair, wool, or yarn. For that we describe fibers as three-dimensional coupled oscillator networks. The application of special analytical mapping expressions allows us to mimic the existence of Youngs and shear modulus in the oscillator network so that real material parameters can be used. For the efficient numerical treatment of the stiff equations of motion of the system a Damped Exponential Time Integrator (DETI) is introduced. This type of integrator is able to take large time steps during the solution process of the stiff systemwhile sustaining stability. It also handles Rayleigh damping analytically by employing the closed-form solution of the fully damped harmonic oscillator. We validate the fiber model against the outcome obtained by solving the special Cosserat theory of rods. Moreover, we demonstrate the efficiency of our approach on some complex fiber assemblies like human hair and fiber meshes. Compared to established methods we reach a significant speed up and at the same time achieve highly accurate results. 2015 Elsevier Ltd. All rights r