different between ellipsoid vs indicatrix

English

Etymology

ellipse +? -oid

Noun

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.

Usage notes

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.

Hypernyms

• quadric surface, quadric

Derived terms

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

Related terms

• ellipsoidal
• subellipsoid

Translations

See also

• geoid

Adjective

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.

Related terms

• ellipsoidal
• globoid
• ovoid

Translations

See also

• globose
• oblong

Swedish

Noun

ellipsoid c

1. (mathematics) ellipsoid

Declension

English

Noun

indicatrix (plural indicatrices)

1. (mathematics, crystallography) An ellipsoid whose three axes represent the refractive indices of an anisotropic crystal for light following different directions with respect to the crystal axes