A model for the expected running time of collision detection using AABBs trees

In this paper, we propose a model to estimate the expected running time of hierarchical collision detection that utilizes AABB trees, which are a frequently used type of bounding volume (BV). We show that the average running time for the simultaneous traversal of two binary AABB trees depends on two characteristic parameters: the overlap of the root BVs and the BV diminishing factor within the hierarchies. With this model, we show that the average running time is in O(n) or even in O(logn) for realistic cases. Finally, we present some experiments that confirm our theoretical considerations. We believe that our results are interesting not only from a theoretical point of view, but also for practical applications, e. g., in time-critical collision detection scenarios where our running time prediction could help to make the best use of CPU time available.