We present a method for the efficient processing of contact and collision in volumetric elastic models simulated using the Projective Dynamics paradigm. Our approach enables interactive simulation of tetrahedral meshes with more than half a million elements, provided that the model satisfies two fundamental properties: the region of the model's surface that is susceptible to collision events needs to be known in advance, and the simulation degrees of freedom associated with that surface region should be limited to a small fraction (e.g. 5%) of the total simulation nodes. In such scenarios, a partial Cholesky factorization can abstract away the behaviour of the collision-safe subset of the face model into the Schur Complement matrix with respect to the collision-prone region. We demonstrate how fast and accurate updates of bilateral penalty-based collision terms can be incorporated into this representation, and solved with high efficiency on the GPU. We also demonstrate iterating a partial update of the element rotations, akin to a selective application of the local step, specifically on the smaller collision-prone region without explicitly paying the cost associated with the rest of the simulation mesh. We demonstrate efficient and robust interactive simulation in detailed models from animation and medical applications.

中文翻译：

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射影动力学中局部碰撞的优化处理

我们提出了一种在使用投影动力学范式模拟的体积弹性模型中有效处理接触和碰撞的方法。我们的方法可以对具有超过 50 万个元素的四面体网格进行交互式仿真，前提是模型满足两个基本属性：需要提前知道模型表面易受碰撞事件影响的区域，以及仿真自由度与该表面区域相关联的应限制为总模拟节点的一小部分（例如 5%）。在这种情况下，部分 Cholesky 分解可以将人脸模型的碰撞安全子集的行为抽象为关于易碰撞区域的 Schur Complement 矩阵。我们展示了如何将基于双边惩罚的碰撞项的快速和准确更新合并到这种表示中，并在 GPU 上高效解决。我们还演示了迭代元素旋转的部分更新，类似于局部步骤的选择性应用，特别是在较小的易碰撞区域上，而无需明确支付与模拟网格其余部分相关的成本。我们在来自动画和医疗应用的详细模型中展示了高效且稳健的交互式模拟。特别是在较小的易碰撞区域，而无需明确支付与仿真网格其余部分相关的成本。我们在来自动画和医疗应用的详细模型中展示了高效且稳健的交互式模拟。特别是在较小的易碰撞区域，而无需明确支付与仿真网格其余部分相关的成本。我们在来自动画和医疗应用的详细模型中展示了高效且稳健的交互式模拟。