We propose a fast and robust solver to simulate continuum-based deformable models with constraints, in particular, rigid-body and joint constraints useful for soft articulated characters. Our method embeds the degrees of freedom of both articulated rigid bodies and deformable bodies in one unified constrained optimization problem, thus coupling the deformable and rigid bodies. Inspired by Projective Dynamics which is a fast numerical solver to simulate deformable objects, we also propose a novel local/global solver that takes full advantage of the pre-factorized system matrices to accelerate the solve of our constrained optimization problem. Therefore, our method can efficiently simulate character models, with rigid-body parts (bones) being correctly coupled with deformable parts (flesh). Our method is stable because backward Euler time integration is applied to both rigid and deformable degrees of freedom. Our unified optimization problem is rigorously derived from constrained Newtonian mechanics. When simulating only articulated rigid bodies as a special case, our method converges to the state-of-the-art rigid body simulators.

中文翻译：

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射影动力学中的软关节特征

我们提出了一种快速而强大的求解器来模拟具有约束的基于连续体的可变形模型，特别是对软关节角色有用的刚体和关节约束。我们的方法将铰接刚体和可变形体的自由度嵌入到一个统一的约束优化问题中，从而耦合了可变形体和刚体。受 Projective Dynamics（一种模拟可变形物体的快速数值求解器）的启发，我们还提出了一种新颖的局部/全局求解器，它充分利用了预分解系统矩阵来加速约束优化问题的求解。因此，我们的方法可以有效地模拟角色模型，刚体部分（骨骼）与可变形部分（肉体）正确耦合。我们的方法是稳定的，因为向后欧拉时间积分适用于刚性和可变形自由度。我们的统一优化问题严格源自受约束的牛顿力学。当仅模拟铰接刚体作为特殊情况时，我们的方法收敛于最先进的刚体模拟器。