We present a novel approach to enrich arbitrary rig animations with elastodynamic secondary effects. Unlike previous methods which pit rig displacements and physical forces as adversaries against each other, we advocate that physics should complement artists' intentions. We propose optimizing for elastodynamic displacements in the subspace orthogonal to displacements that can be created by the rig. This ensures that the additional dynamic motions do not undo the rig animation. The complementary space is high-dimensional, algebraically constructed without manual oversight, and capable of rich high-frequency dynamics. Unlike prior tracking methods, we do not require extra painted weights, segmentation into fixed and free regions or tracking clusters. Our method is agnostic to the physical model and plugs into non-linear FEM simulations, geometric as-rigid-as-possible energies, or mass-spring models. Our method does not require a particular type of rig and adds secondary effects to skeletal animations, cage-based deformations, wire deformers, motion capture data, and rigid-body simulations.

中文翻译：

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互补动力学

我们提出了一种新颖的方法来丰富具有弹性动力学辅助效果的任意绑定动画。与之前将钻机位移和物理力相互对抗的方法不同，我们主张物理学应该补充艺术家的意图。我们建议优化子空间中的弹性动力学位移，该位移正交于可由钻机创建的位移。这确保了额外的动态运动不会撤消钻机动画。互补空间是高维的，代数构造，无需人工监督，具有丰富的高频动态。与之前的跟踪方法不同，我们不需要额外的绘制权重、分割成固定和自由区域或跟踪集群。我们的方法与物理模型无关，并插入非线性 FEM 模拟、尽可能刚性的几何能量或质量弹簧模型。我们的方法不需要特定类型的绑定，并为骨骼动画、基于笼的变形、线变形器、运动捕捉数据和刚体模拟添加辅助效果。