Bipolar coordinates are a 2-D system of coordinates. There are two commonly defined types of bipolar coordinates, the first of
which is defined by
(1) | |||
(2) |
(3) |
(4) |
(5) | |||
(6) |
(7) |
Two-center bipolar coordinates are two coordinates giving the distances from two fixed centers and , sometimes
denoted and . For two-center bipolar coordinates with centers at ,
(8) | |||
(9) |
(10) |
(11) | |||
(12) |
(13) | |||
(14) |
References
Lockwood, E. H. ``Bipolar Coordinates.'' Ch. 25 in A Book of Curves. Cambridge, England: Cambridge University Press,
pp. 186-190, 1967.
© 1996-9 Eric W. Weisstein