Contact Detection Algorithm for Convex NURBS Particles

Abstract

The present work proposes a contact detection algorithm for convex particles whose boundaries are mathematically defined by non-uniform B-splines (NURBS). This algorithm involves a hierarchy of contact searches, including both global and local steps. The focus is on the formulation of the local contact problem (LCP) using a master-to-master approach. It is based on computer graphics and optimization techniques. Besides the algorithm, the paper also discusses strategies for modeling particle geometry and their implications in contact detection. The use of multiple parameterizations (patches) assembled in space, for instance, provides more flexibility in the construction of particles and avoids numerical singularities. However, it leads to local geometric imperfections at the connection between patches. The LCP formulation proposed herein can deal with such imperfections through a contact degeneration technique. An example shows the robustness of the method.