Elliptic Coordinates
Parabolic Coordinates
Bipolar Coordinates
Confocal
Ellipsoidal Coordinates in 3D space
Ellipsoids (white),
Hyperboloids of one sheet
(orange) and
Hyperboloids of two sheets
(yellow)
References:
The first three figures are
scanned from
“Mathematical Methods for
Physicists” by Arfken
The color figure is my
coloring of a figure from one of my “Desert Island Books”:
“Geometry
and the Imagination” by Hilbert and Cohn-Vossen.
The ultimate reference for
this kind of stuff is
“Methods of
Theoretical Physics” by Morse and Feshbach.