Exact collision detection of two moving ellipsoids under rational motions

In this paper, we describe an exact method for detecting collision between two moving ellipsoids under pre-specified rational motions. Our method is based on an algebraic condition that determines the separation status of two static ellipsoids - the condition itself is described by the signs of roots of the characteristic equation of the two ellipsoids. To deal with moving ellipsoids, we derive a bivariate function whose zero-set possesses a special topological structure. By analyzing the zero-set of this function, we are able to tell whether or not two moving ellipsoids under pre-specified rational motions are collision-free; and if not, we can determine the intervals in which they overlap.