Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
Discrete geometric mechanics for variational time integrators
ACM SIGGRAPH 2006 Courses
Volume conserving finite element simulations of deformable models
ACM SIGGRAPH 2007 papers
Backward steps in rigid body simulation
ACM SIGGRAPH 2008 papers
Lie group integrators for animation and control of vehicles
ACM Transactions on Graphics (TOG)
Asynchronous contact mechanics
ACM SIGGRAPH 2009 papers
Energy stability and fracture for frame rate rigid body simulations
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
ACM SIGGRAPH 2010 papers
Element-wise mixed implicit-explicit integration for stable dynamic simulation of deformable objects
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Simulation of deformable solids in interactive virtual reality applications
Proceedings of the 18th ACM symposium on Virtual reality software and technology
Energetically consistent invertible elasticity
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Energetically consistent invertible elasticity
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Fast simulation of mass-spring systems
ACM Transactions on Graphics (TOG)
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We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems---an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details.