Browsing by Subject "physics simulation"
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Item Early Termination of Conjugate Gradients for Corotated Finite Elements(Association for Computing Machinery, 2019-10-28) Dahl, Alex; Bargteil, AdamSince the introduction of the conjugate gradient method to computer graphics, researchers have largely treated it as a black box. In particular, an arbitrary small value is chosen for the tolerance and the method is run to convergence. In the context of soft body animation, this approach results in significant wasted computation and has led researchers to consider alternative, more complex, and less versatile approaches. In this paper we argue that in the context of corotational finite elements, less than 10 iterations can give a good enough solution and substantial savings of computational cost. We examine the use of different preconditioners for conjugate gradient including the mass and Jacobi matrices, as well as the use of different initial guesses. We show that for our examples an initial guess of the previous velocity and the Jacobi preconditioner works best.Item Energized Rigid Body Fracture(Association for Computing Machinery (ACM), 2018-07) Li, Xiaokai; Jones, Ben; Andrews, Sheldon; Bargteil, AdamCompelling animation of fracture is a vital challenge for computer graphics. Methods based on continuum mechanics are physically accurate, but computationally expensive since they require computing elastic deformation. In many applications, this elastic deformation is imperceptible, so simulation methods based on rigid body dynamic with breakable constraints are popular in practice. Simply deleting constraints when thresholds on force or displacement are reached ignores the elastic energy that is stored just before fracture, which is captured by continuum mechanics based methods. Our approach computes the energy stored in these constraints when they are broken, and reintroduces it to the system as kinetic energy. As a result, our method is able to animate energetic fracture scenarios with results comparable to continuum mechanics approaches, but with the computational efficiency of rigid body simulation.Item Global Momentum Preservation for Position-based Dynamics(Association for Computing Machinery, 2019-10-28) Dahl, Alex; Bargteil, Adam W.Position-based dynamics has emerged as an exceedingly popular approach for animating soft body dynamics. Unfortunately, the basic approach suffers from artificial loss of angular momentum. We propose a simple approach to preserve global linear and angular momenta of bodies by directly tracking these quantities and adjusting velocities to ensure they are preserved. This approach entails negligible computational cost, requires less than 25 lines of code, and exactly preserves global linear and angular momenta.