A global direct search method for high-fidelity contact detection between arbitrarily shaped three-dimensional convex polyhedral blocks

High-fidelity contact detection between arbitrarily shaped convex polyhedral blocks is an important problem. The common plane (CP) and GJK algorithms are fast but still have some drawbacks in identifying accurate contact points and planes. The Direct Search (DS) method can ascertain the contact points and planes accurately but is limited by its locality assumption. To be specific, irregular blocks with small angles or small edges can cause false contacts, and large penetration will induce vanishing contacts, which will destroy the simulation using the DS method. In this study, a novel Global Direct Search (GDS) method is proposed to search for meta (vertex-face or cross edge-edge in 3D) contacts globally. Without locality assumption, the GDS method can accurately detect contacts between arbitrarily shaped convex polyhedral blocks without suffering from false and vanishing contacts. The new method inherits the global search idea of Contact Theory. Several case studies are used to verify the method and show that the GDS successfully avoids false and vanishing contacts, as well as demonstrate its accuracy, robustness, and improved efficiency.