The Incremental Potential Contact (IPC) method enables robust complex simulations of deformable objects with contact and friction. The key to IPC's robustness is its strict adherence to geometric constraints, avoiding intersections, which are a common cause of robustness issues in contact mechanics. A key element of the IPC approach to contact is a geometric barrier function, which is defined directly in the discrete setting. While IPC achieves its main goal of providing guarantees for contact constraints, its parameters need to be chosen carefully to avoid significant simulation artifacts and inaccuracies. We present a systematic derivation of an IPC-like continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence of shape, and absence of forces in rest configurations, based on the idea of candidate sets. Our potential is formulated in a way independent of surface discretization. This new potential is suitable for piecewise-linear surfaces and its efficiency is similar to standard IPC. We demonstrate its behavior and compare it to IPC on a range of challenging contact examples.

翻译：增量势能接触（IPC）方法能够对具有接触和摩擦的可变形物体进行鲁棒的复杂模拟。IPC方法鲁棒性的关键在于其严格遵守几何约束，避免相交——这是接触力学中鲁棒性问题的常见诱因。IPC接触方法的一个关键要素是几何势垒函数，该函数直接在离散设定中定义。虽然IPC实现了为接触约束提供保证的主要目标，但其参数需要谨慎选择以避免显著的模拟伪影和不准确性。我们基于候选集思想，从识别接触势能的一组自然要求（包括势垒特性、局部性、形状的可微依赖性以及静止构型中无作用力）出发，系统性地推导了一种适用于光滑及分段光滑表面的类IPC连续势能。我们的势能公式独立于表面离散化方式。这一新势能适用于分段线性表面，其计算效率与标准IPC方法相当。我们通过一系列具有挑战性的接触算例展示了其特性，并与IPC方法进行了比较。