A shrunken edge algorithm for contact detection between convex polyhedral blocks

The detection of contacts between interacting blocks is an important but time-consuming calculation in discontinuity-based numerical methods. This paper presents a new algorithm for the detection of contacts between arbitrary convex polyhedra with planar boundaries. In this algorithm, a pair of contacting blocks is identified as a main block and a target block. The concept of a shrunken edge is introduced in this paper. First, each vertex of the main block is shrunk toward the centre of the neighbouring faces. The shrinkage is infinitesimal yet useful for contact detection. Shrunken edges parallel to the original edges on the main block are established by connecting the shrunken points. Contact detection is then performed by determining the geometric relationship between a shrunken edge and its approaching face on the target block. From the three possible geometric relationships, all six contact types in three dimensions can be identified precisely, which allows for an easy and efficient detection process. Finally, the accuracy and effectiveness of the new contact algorithm are demonstrated through several examples in which two or more blocks collide in a three-dimensional domain.