Optimization Integrator for Large Time Steps.
IEEE Transactions on Visualization and Computer Graphics(2015)
摘要
Practical time steps in todayu0027s state-of-the-art simulators typically rely on Newtonu0027s method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. We show that recasting backward Euler as a minimization problem allows Newtonu0027s method to be stabilized by standard optimization techniques with some novel improvements of our own. The resulting solver is capable of solving even the toughest simulations at the 24Hz frame rate and beyond. We show how simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. We also present novel penalty collision formulations for self collisions and collisions against scripted bodies designed for the unique demands of this solver.
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关键词
animation,optimization,minimization,newton method,robustness,computer graphics,digital tv,mathematical model,nonlinear systems
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