SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Simulation of clothing with folds and wrinkles
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Convex Optimization
A Versatile and Robust Model for Geometrically Complex Deformable Solids
CGI '04 Proceedings of the Computer Graphics International
Discrete geometric mechanics for variational time integrators
ACM SIGGRAPH 2006 Courses
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Geometric, variational integrators for computer animation
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Journal of Visual Communication and Image Representation
Efficient simulation of inextensible cloth
ACM SIGGRAPH 2007 papers
TRACKS: toward directable thin shells
ACM SIGGRAPH 2007 papers
As-rigid-as-possible surface modeling
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Robust treatment of simultaneous collisions
ACM SIGGRAPH 2008 papers
A mass spring model for hair simulation
ACM SIGGRAPH 2008 papers
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Fast continuous collision detection using deforming non-penetration filters
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Multi-resolution isotropic strain limiting
ACM SIGGRAPH Asia 2010 papers
Example-based elastic materials
ACM SIGGRAPH 2011 papers
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Updated sparse cholesky factors for corotational elastodynamics
ACM Transactions on Graphics (TOG)
Adaptive anisotropic remeshing for cloth simulation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Energy Conservation for the Simulation of Deformable Bodies
IEEE Transactions on Visualization and Computer Graphics
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We 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.