共焦二次曲面[Confocal Quadrics] - 达人(其实～我是卧底，来自外星)

2005/02/01 | 共焦二次曲面[Confocal Quadrics]
类别(∑〖数学〗) | 评论(0) | 阅读(32) | 发表于 13:41: A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an orthogonal coordinate system known as confocal ellipsoidal coordinates (Hilbert and Cohn-Vossen 1991, pp. 22-23).

The planes of symmetry of the tangent cone from any point P in space to any surface of the confocal system which does not enclose P are the tangent planes at P to the three surfaces of the system that pass through P. As a limiting case, this result means that every surface of the confocal system when viewed from a point lying on a focal curve and not enclosed by the surface looks like a circle with its center on the line of sight, provided that the line of sight is tangent to the focal curve (Hilbert and Cohn-Vossen 1999, p. 24).; 0