IEEE Trans Vis Comput Graph. 2017 Oct;23(10):2222-2234. doi: 10.1109/TVCG.2017.2730875. Epub 2017 Jul 24.
We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constitutive models and hard constraints while retaining the speed, parallelizability, and robustness of projective dynamics. We further extend the algorithm to improve the handling of dynamically changing constraints such as sliding and contact, while maintaining the benefits of a constant, prefactored system matrix. We demonstrate the benefits of our algorithm on several examples that include cloth, collisions, and volumetric deformable bodies with nonlinear elasticity and skin sliding effects.
我们将交替方向乘子法 (ADMM) 优化算法应用于弹性体的隐式时间积分，并表明所得到的方法与最近提出的投影动力学算法密切相关。然而，由于 ADMM 是一种通用的优化算法，适用于广泛的目标函数，因此它允许使用非线性本构模型和硬约束，同时保持投影动力学的速度、可并行性和鲁棒性。我们进一步扩展了算法，以改善对动态变化的约束（如滑动和接触）的处理，同时保持常系数、预因子化系统矩阵的优势。我们在几个示例中展示了我们算法的优势，包括布料、碰撞和具有非线性弹性和皮肤滑动效果的体积可变形体。
