A Quadratic Surface which is given in Cartesian Coordinates by

(1) |

(2) |

(3) | |||

(4) | |||

(5) |

The Surface Area (Bowman 1961, pp. 31-32) is

(6) |

(7) | |||

(8) | |||

(9) |

and is given by inverting the expression

(10) |

(11) |

A different parameterization of the ellipsoid is the so-called stereographic ellipsoid, given by the parametric equations

(12) | |||

(13) | |||

(14) |

A third parameterization is the Mercator parameterization

(15) | |||

(16) | |||

(17) |

(Gray 1993).

The Support Function of the ellipsoid is

(18) |

(19) |

**References**

Beyer, W. H. *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, p. 131, 1987.

Bowman, F. *Introduction to Elliptic Functions, with Applications.* New York: Dover, 1961.

Fischer, G. (Ed.). Plate 65 in *Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume.*
Braunschweig, Germany: Vieweg, p. 60, 1986.

Gray, A. ``The Ellipsoid'' and ``The Stereographic Ellipsoid.'' §11.2 and 11.3 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 215-217, and 296, 1993.

© 1996-9

1999-05-25