Contact detection is one of the most important steps to be handled during numerical simulations of particle systems. It is extremely dependent on particle geometry, which governs the mechanical behavior of systems and the computational cost of simulations. NURBS are an option to model the boundary of particles with nonstandard geometries, here called “NURBS particles”. The contact between NURBS particles, however, is not trivial. The present paper presents a complete contact detection algorithm for convex NURBS particles, which automatically performs a hierarchy of contact searches. It is based on computer graphics and optimization techniques to address local contact. For robustness, specific strategies are implemented to model closed NURBS geometries, indicating the occurrence of local geometric imperfections when using multiple NURBS parameterizations. The main novelty of the work is related to a degeneration of the local contact problem to deal with such imperfections, which allows using general particle geometries. Numerical examples demonstrate the robustness of the proposed algorithm.

接触检测是粒子系统数值模拟期间要处理的最重要步骤之一。它极其依赖于粒子几何形状，粒子几何形状控制着系统的机械行为和模拟的计算成本。NURBS 是对具有非标准几何形状的粒子（此处称为“NURBS 粒子”）边界进行建模的选项。然而，NURBS 粒子之间的接触并非微不足道。本文提出了一种完整的凸 NURBS 粒子接触检测算法，该算法自动执行接触搜索的层次结构。它基于计算机图形学和优化技术来解决局部接触问题。为了鲁棒性，实施了特定策略来对闭合 NURBS 几何进行建模，表明使用多个 NURBS 参数化时会出现局部几何缺陷。这项工作的主要新颖性与处理此类缺陷的局部接触问题的退化有关，这允许使用一般的粒子几何形状。数值例子证明了所提出算法的鲁棒性。