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An algebraic condition for the separation of two ellipsoids

✍ Scribed by Wenping Wang; Jiaye Wang; Myung-Soo Kim

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
80 KB
Volume
18
Category
Article
ISSN
0167-8396

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✦ Synopsis

Given two ellipsoids, we show that their characteristic equation has at least two negative roots and that the ellipsoids are separated by a plane if and only if their characteristic equation has two distinct positive roots. Furthermore, the ellipsoids touch each other externally if and only if the characteristic equation has a positive double root. An advantage of this characterization is that only the signs of the roots matter.

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