An algebraic approach to continuous collision detection for ellipsoids (Q543838)

This paper is focused on continuous collision detection of two general free-from moving objects which are approximated by bounding volumes ellipsoids. Minimum bounding ellipsoid has low algebraic degree and suitable bounding approximation properties for a wide class of objects. The authors introduce a symbolic approach to determine the relative position of two ellipsoids which can be used to detect possible collisions of two continuously moving ellipsoids under arbitrary motion. The separation, external touching and overlapping are mentioned as the three important relative positions of the two ellipsoids. The distinguishing of the ellipsoids configuration is based on the number of positive roots of the characteristic polynomial. In the paper, examples of the suggested approach when moving two ellipsoids by rational and helical motion are given.