Frictional contact between deformable elastic objects remains a difficult simulation problem in computer graphics. Traditionally, contact has been resolved using sophisticated collision detection schemes and methods that build on the assumption that contact happens between polygons. While polygonal surfaces are an efficient representation for solids, they lack some intrinsic properties that are important for contact resolution. Generally, polygonal surfaces are not equipped with an intrinsic inside and outside partitioning or a smooth distance field close to the surface. Here we propose a new method for resolving frictional contacts against deforming implicit surface representations that addresses these problems. We augment a moving least squares (MLS) implicit surface formulation with a local kernel for resolving contacts, and develop a simple parallel transport approximation to enable transfer of frictional impulses. Our variational formulation of dynamics and elasticity enables us to naturally include contact constraints, which are resolved as one Newton-Raphson solve with linear inequality constraints. We extend this formulation by forwarding friction impulses from one time step to the next, used as external forces in the elasticity solve. This maintains the decoupling of friction from elasticity thus allowing for different solvers to be used in each step. In addition, we develop a variation of staggered projections, that relies solely on a non-linear optimization without constraints and does not require a discretization of the friction cone. Our results compare favorably to a popular industrial elasticity solver (used for visual effects), as well as recent academic work in frictional contact, both of which rely on polygons for contact resolution. We present examples of coupling between rigid bodies, cloth and elastic solids.

中文翻译：

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光滑弹性固体上的摩擦接触

可变形弹性物体之间的摩擦接触仍然是计算机图形学中一个困难的模拟问题。传统上，接触已经使用复杂的碰撞检测方案和方法来解决，这些碰撞检测方案和方法建立在多边形之间发生接触的假设之上。虽然多边形表面是实体的有效表示，但它们缺乏一些对接触分辨率很重要的内在属性。通常，多边形表面不具备内在的内外分隔或靠近表面的平滑距离场。在这里，我们提出了一种新的方法来解决摩擦接触，以解决这些问题的变形隐式表面表示。我们使用局部核来增加移动最小二乘 (MLS) 隐式曲面公式，以解决接触问题，并开发一个简单的平行传输近似，以实现摩擦脉冲的传递。我们对动力学和弹性的变分公式使我们能够自然地包含接触约束，这些约束被解决为具有线性不等式约束的 Newton-Raphson 求解。我们通过将摩擦脉冲从一个时间步向前传递到下一个时间步来扩展这个公式，用作弹性求解中的外力。这保持了摩擦与弹性的分离，从而允许在每个步骤中使用不同的求解器。此外，我们开发了一种交错投影的变体，它仅依赖于没有约束的非线性优化，并且不需要对摩擦锥进行离散化。我们的结果优于流行的工业弹性求解器（用于视觉效果），以及最近在摩擦接触方面的学术工作，两者都依赖于多边形来解决接触问题。我们展示了刚体、布料和弹性固体之间的耦合示例。