We use a finite element model to predict the vibration response of objects in a rigid body simulation, such that rigid objects are augmented to provide a plausible elastic collision response between distant objects due to vibration. We start with a generalized eigenvalue decomposition of the elastic model to precompute a response to an impact at any point on an elastic object with fixed boundary conditions. Then, given a collision between objects, we generate an approximate response impulse to distribute to other objects already in contact with the colliding bodies. This can lead to distant impacts causing an object to slip, or a delicate stack of objects to fall. We also use a geodesic distance based spatial attenuation approximation for travelling waves in objects to respond to an impact at one contact with an impulse at other locations. This response ultimately allows a long distance relationship between contacts, both across a single object being struck, but also traversing the contact graph of a larger collection of objects. We qualitatively validate our approach with a ground truth simulation, and demonstrate a number of scenarios where a long distance relationship between contacts is valuable.

中文翻译：

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刚体仿真中的远距离碰撞响应

我们使用有限元模型来预测刚体模拟中物体的振动响应，从而增强刚性物体以在远处物体之间由于振动而提供合理的弹性碰撞响应。我们从弹性模型的广义特征值分解开始，以预先计算对具有固定边界条件的弹性物体上任何点的冲击的响应。然后，给定物体之间的碰撞，我们生成一个近似的响应脉冲，以分配给已经与碰撞体接触的其他物体。这可能会导致远距离撞击，导致物体滑倒，或一堆精致的物体掉落。我们还对物体中的行波使用基于测地距离的空间衰减近似，以响应一个接触处的冲击与其他位置的脉冲。这种响应最终允许接触之间的长距离关系，既可以跨越被击中的单个对象，也可以遍历更大对象集合的接触图。我们通过地面实况模拟定性地验证了我们的方法，并展示了许多联系人之间的长距离关系很有价值的场景。