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In collision detection involving multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number of required comparisons grows rapidly: for <math>n</math> objects, <math display="">{n(n-1)}/{2}</math> intersection tests are needed with a naive approach. This quadratic growth makes such an approach computationally expensive as <math>n</math> increases.<ref name=":col1" /><ref name=":0">{{Cite book |last1=Cohen |first1=Jonathan D. |last2=Lin |first2=Ming C. |last3=Manocha |first3=Dinesh |last4=Ponamgi |first4=Madhav |chapter=I-COLLIDE: An interactive and exact collision detection system for large-scale environments |date=1995 |title=Proceedings of the 1995 symposium on Interactive 3D graphics - SI3D '95 |chapter-url=http://portal.acm.org/citation.cfm?doid=199404.199437 |language=en |publisher=ACM Press |pages=189–ff |doi=10.1145/199404.199437 |isbn=978-0-89791-736-0}}</ref>
Due to the complexity mentioned above, collision detection is a computationally intensive process. Nevertheless, it is essential for interactive applications like video games, robotics, and real-time physics engines. To manage these computational demands, extensive efforts have gone into optimizing collision detection algorithms.
A commonly used approach towards accelerating the required computations is to divide the process into two phases: the '''broad phase''' and the '''narrow phase'''.<ref name=":col1" /><ref>{{Cite book |last1=Akenine-Möller |first1=Tomas |url=https://www.realtimerendering.com |title=Real-time rendering |last2=Haines |first2=Eric |last3=Hoffman |first3=Naty |last4=Pesce |first4=Angelo |last5=Iwanicki |first5=Michał |last6=Hillaire |first6=Sébastien |date=2018 |publisher=CRC Press, Taylor & Francis Group |isbn=978-1-138-62700-0 |edition=4th |series=An A K Peters book |___location=Boca Raton London New York}}</ref> The broad phase aims to answer the question of whether objects might collide, using a conservative but efficient approach to rule out pairs that clearly do not intersect, thus avoiding unnecessary calculations.
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