Tounchev, Ivaylo2024-07-122024-07-122019Tounchev, I. (2019). Minimum distance between two ellipses. International Conference of Mathematical Sciences (ICMS 2019). s. 199.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2099We consider the distance problem between two ellipses in R 3 . This problem arises in widely disparate fields as celestial mechanics [1], computer animation, computer vision, CAD/CAM [2] and so on. We proof that in the general case, the complex critical points of the square of the distance between two ellipses are at most sixteen and they correspond to the roots of sixteenth degree polynomial which coefficients are real and depend explicitly of the ellipses equations. We prove that the real critical points are between four and sixteen. We give as example the distance between Neptune and Pluto. Then both ellipses have the Sun as a common focus; the critical points are six: one maximum, three saddle points and two local minima. We prove that the global minimum is about 2.52 astronomical units.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessEllipsesDistanceEuclidean spaceArticle200199