Efficient collision detection for moving polyhedra
Proceedings of the eleventh annual symposium on Computational geometry
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Fast collision detection using QuOSPO trees
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Collision detection in aspect and scale bounded polyhedra
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Analysis of a bounding box heuristic for object intersection
Journal of the ACM (JACM)
Improved Computational Methods for Ray Tracing
ACM Transactions on Graphics (TOG)
Box-trees and R-trees with near-optimal query time
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Minimal hierarchical collision detection
VRST '02 Proceedings of the ACM symposium on Virtual reality software and technology
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Efficient collision detection of complex deformable models using AABB trees
Journal of Graphics Tools
Rapid Collision Detection by Dynamically Aligned DOP-Trees
VRAIS '98 Proceedings of the Virtual Reality Annual International Symposium
Time-critical collision detection using an average-case approach
Proceedings of the ACM symposium on Virtual reality software and technology
BD-tree: output-sensitive collision detection for reduced deformable models
ACM SIGGRAPH 2004 Papers
Development of real-time virtual environment with hierarchical construction
Proceedings of the 6th International Conference on Ubiquitous Information Management and Communication
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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.