ellipsoid

ellipse +‎ -oid

ellipsoid (plural ellipsoids)

1. (mathematics, geometry) A surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x²/a² + y²/b² + z²/c² = 0.
   • 2002, John Michael Hollas, Basic Atomic and Molecular Spectroscopy, page 133,

     Polarizability can be imagined as a three-dimensional ellipsoid centred on the centre of the molecule, as shown in Figure 10.4.

   • 2004, Alfred Leick, GPS Satellite Surveying, 3rd Edition, page 367,

     Because only ellipsoids of rotation have been adopted in practical geodesy and surveying and triaxial ellipsoids have been limited to theoretical studies, we will use the term ellipsoid for brevity to mean ellipsoid of rotation.

   • 2010, Jan Van Sickle, Basic GIS Coordinates, 2nd Edition, page 73,

     As mentioned before, modern geodetic datums rely on the surfaces of geocentric ellipsoids to approximate the surface of the earth.

2. (geography) Such a surface used as a model of the shape of the earth.

   Here the geoid is thirty meters below the ellipsoid.

The general case, with semiaxes a, b and c all different, is a triaxial ellipsoid (more rarely, scalene ellipsoid). If two are the same, say b = c, the result is an ellipsoid of revolution, which may be oblate (if a < b) or prolate (a > b). The degenerate case a = b = c is a sphere. An ellipsoid of revolution is also called a spheroid.

• ellipsoid of revolution
• ellipsoid geodesic
• ellipsoid method
• ellipsoid packing
• scalene ellipsoid (rare)
• triaxial ellipsoid

• ellipsoidal
• subellipsoid

• geoid

ellipsoid (comparative more ellipsoid, superlative most ellipsoid)

1. Shaped like an ellipse; elliptical.
2. (mathematics) Of or pertaining to an ellipse; elliptic.
3. (botany) Having the tridimensional shape of an ellipse rotated on its long axis.

• ellipsoidal
• globoid
• ovoid

• globose
• oblong

ellipsoid c

1. (mathematics) ellipsoid