Fast simulation of mass-spring systems

dc.contributor.authorLiu, Tiantian
dc.contributor.authorBargteil, Adam W.
dc.contributor.authorO'Brien, James F.
dc.contributor.authorKavan, Ladislav
dc.description.abstractWe describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton's method. Although the asymptotic convergence of Newton's method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton's. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton's iteration.en_US
dc.description.sponsorshipThis work was supported in part by funding from the Intel Science and Technology Center for Visual Computing, gifts from Pixar Animation Studios, Adobe Systems Incorporated, and National Science Foundation Awards IIS-1249756 and CNS-0855167.en_US
dc.format.extent7 pagesen_US
dc.genrejournal articles preprintsen_US
dc.identifier.citationTiantian Liu, Adam W. Bargteil,, Fast simulation of mass-spring systems, ACM Transactions on Graphics (TOG) TOG Homepage archive Volume 32 Issue 6, November 2013 Article No. 214, DOI:
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Computer Science and Electrical Engineering Department Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subjecttime integrationen_US
dc.subjectimplicit Euler methoden_US
dc.subjectmass-spring systemsen_US
dc.titleFast simulation of mass-spring systemsen_US


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