SMB: Collision detection based on temporal coherence

Abstract

The paper presents a novel collision detection algorithm, termed the sort moving boxes (SMB) for large number of moving 2D/3D objects which are represented by their axis-aligned bounding boxes (AABBs). The main feature of the algorithm is the full exploitation of the temporal coherence of the objects exhibited in a dynamic environment. In the algorithm, the AABBs are first projected to each Cartesian axis. The projected intervals on the axes are separately sorted by the diminishing increment sort (DIS) and further divided into subsections. By processing all the intervals within the subsections to check if they overlap, a complete contact list can be built. The SMB is a fast and robust collision detection algorithm, particularly for systems involving a large number of moving AABBs, and also supports for the dynamic insertion and deletion of objects. Its performance in terms of both expected total detection time and memory requirements is proportional to the total number of AABBs, N, and is not influenced by size differences of AABBs, the space size and packing density over a large range up to ten times difference. The only assumption made is that the sorted list at one time step will remain an almost sorted list at the next time step, which is valid for most applications whose movement and deformation of each AABB and the dynamic change of the total number N are approximately continuous.