An algebraic approach to continuous collision detection for ellipsoids

We present algebraic expressions for characterizing three configurations formed by two ellipsoids in R3R3 that are 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 of two moving ellipsoids under arbitrary motions.

Research highlights
► A symbolic approach is presented to determine the configuration formed by two ellipsoids.
► The symbolic approach requires only the evaluation of five explicit formulae.
► The symbolic approach is then applied to the continuous collision detection of two moving ellipsoids under arbitrary continuous motions.
► Examples and comparisons with existed methods are provided.