Numerical Integration Methods for Simulation of Mass-Spring-Damper Systems

  • Mete Özgüz
  • M. Taner Eskil
Conference paper


The dynamics of a face are often implemented as a system of connected particles with various forces acting upon them. Animation of such a system requires the approximation of velocity and position of each particle through numerical integration. There are many numerical integrators that are commonly used in the literature. We conducted experiments to determine the suitability of numerical integration methods in approximating the particular dynamics of mass-spring-damper systems. Among Euler, semi-implicit Euler, Runge-Kutta and Leapfrog, we found that simulation with Leapfrog numerical integration characterizes a mass-spring-damper system best in terms of the energy loss of the overall system.


Numerical integration methods Physically-based facial modeling Animation Semi-implicit Euler Runge-Kutta Leapfrog 



This research is part of project “Expression Recognition based on Facial Anatomy", grant number 109E061, supported by The Support Programme for Scientific and Technological Research Projects (1001) of The Scientific and Technological Research Council of Turkey (TÜB\(\dot{\hbox{I}}\)TAK).


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Copyright information

© Springer-Verlag London Limited  2011

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, Pattern Recognition and Machine Intelligence LaboratoryISIK UniversityIstanbulTurkey

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