An Algebraic Approach to Continuous Collision Detection for Ellipsoids

Xiaohong Jia 1 Yi-King Choi 1 Bernard Mourrain 2 Wenping Wang 1
1 Computer Graphics Group
Department of Computer Science [Hong Kong]
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We present algebraic conditions for characterizing three configurations of two ellipsoids in R3 that are the most relevant to collision detection: separation, external touching and overlapping. These conditions are given in terms of explicit formulae expressed by the subresultant sequence of the characteristic polynomial of the two ellipsoids and its derivative. For any two ellipsoids, the signs of these formulae can easily be evaluated to classify their configuration. Furthermore, based on these algebraic conditions, an efficient method is developed for continuous collision detection for two moving ellipsoids under arbitrary motion.
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Xiaohong Jia, Yi-King Choi, Bernard Mourrain, Wenping Wang. An Algebraic Approach to Continuous Collision Detection for Ellipsoids. Computer Aided Geometric Design, Elsevier, 2011, 28 (3), pp.164-176. ⟨10.1016/j.cagd.2011.01.004⟩. ⟨hal-00646511⟩

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