Minimum distance between two ellipses
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Maltepe Üniversitesi
Erişim Hakkı
CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
We 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.
Açıklama
Anahtar Kelimeler
Ellipses, Distance, Euclidean space
Kaynak
International Conference of Mathematical Sciences (ICMS 2019)
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Tounchev, I. (2019). Minimum distance between two ellipses. International Conference of Mathematical Sciences (ICMS 2019). s. 199.
