Plausible motion simulation for computer graphics animation
Proceedings of the Eurographics workshop on Computer animation and simulation '96
Computer animation: algorithms and techniques
Computer animation: algorithms and techniques
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Geometric, variational integrators for computer animation
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Lie group integrators for animation and control of vehicles
ACM Transactions on Graphics (TOG)
Energy-preserving integrators for fluid animation
ACM SIGGRAPH 2009 papers
Fast simulation of skeleton-driven deformable body characters
ACM Transactions on Graphics (TOG)
Fast simulation of mass-spring systems
ACM Transactions on Graphics (TOG)
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In this chapter, we present a geometric--instead of a traditional numerical-analytic--approach to the problem of time integration. Geometry at its most abstract is the study of symmetries and their associated invariants. Variational approaches based on such notions are commonly used in geometric modeling and discrete differential geometry. Here we will treat mechanics in a similar way. Indeed, the very essence of a mechanical system is characterized by its symmetries and invariants. Thus preserving these symmetries and invariants (e.g., certain momenta) into the discrete computational setting is of paramount importance if one wants discrete time integration to properly capture the underlying continuous motion. Motivated by the well-known variational and geometric nature of most dynamical systems, we review the use of discrete variational principles as a way to derive robust, and accurate time integrators.