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Ellipsoid

Ellipsoid El*lip"soid, n. [Ellipse + -oid: cf. F. ellipsoide.] (Geom.) A solid, all plane sections of which are ellipses or circles. See Conoid, n., 2 (a) . Note: The ellipsoid has three principal plane sections, a, b, and c, each at right angles to the other two, and each dividing the solid into two equal and symmetrical parts. The lines of meeting of these principal sections are the axes, or principal diameters of the ellipsoid. The point where the three planes meet is the center. Ellipsoid of revolution, a spheroid; a solid figure generated by the revolution of an ellipse about one of its axes. It is called a prolate spheroid, or prolatum, when the ellipse is revolved about the major axis, and an oblate spheroid, or oblatum, when it is revolved about the minor axis.

Ellipsoid El*lip"soid, n. [Ellipse + -oid: cf. F. ellipsoide.] (Geom.) A solid, all plane sections of which are ellipses or circles. See Conoid, n., 2 (a) . Note: The ellipsoid has three principal plane sections, a, b, and c, each at right angles to the other two, and each dividing the solid into two equal and symmetrical parts. The lines of meeting of these principal sections are the axes, or principal diameters of the ellipsoid. The point where the three planes meet is the center. Ellipsoid of revolution, a spheroid; a solid figure generated by the revolution of an ellipse about one of its axes. It is called a prolate spheroid, or prolatum, when the ellipse is revolved about the major axis, and an oblate spheroid, or oblatum, when it is revolved about the minor axis.

Ellipsoid

Ellipsoid El*lip"soid, Ellipsoidal El`lip*soi"dal, a. Pertaining to, or shaped like, an ellipsoid; as, ellipsoid or ellipsoidal form.

Ellipsoid El*lip"soid, Ellipsoidal El`lip*soi"dal, a. Pertaining to, or shaped like, an ellipsoid; as, ellipsoid or ellipsoidal form.

ellipsoid

Conoid Co"noid, n. [Gr. ? conical; ? cone + ? from: cf. F. cono["i]de.] 1. Anything that has a form resembling that of a cone. 2. (Geom.) (a) A solid formed by the revolution of a conic section about its axis; as, a parabolic conoid, elliptic conoid, etc.; -- more commonly called paraboloid, ellipsoid, etc. (b) A surface which may be generated by a straight line moving in such a manner as always to meet a given straight line and a given curve, and continue parallel to a given plane. --Math. Dict.

Conoid Co"noid, n. [Gr. ? conical; ? cone + ? from: cf. F. cono["i]de.] 1. Anything that has a form resembling that of a cone. 2. (Geom.) (a) A solid formed by the revolution of a conic section about its axis; as, a parabolic conoid, elliptic conoid, etc.; -- more commonly called paraboloid, ellipsoid, etc. (b) A surface which may be generated by a straight line moving in such a manner as always to meet a given straight line and a given curve, and continue parallel to a given plane. --Math. Dict.

- An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation...

- In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, which is the truer, imperfect figure of the Earth,...

- point is the angle formed by the vector perpendicular (or normal) to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six...

- An Earth ellipsoid is a mathematical figure approximating the Earth's form, used as a reference frame for com****tions in geodesy, astronomy, and the...

- or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its prin****l axes; in other words, an ellipsoid with...

- ellipsoid method is an algorithm which finds an optimal solution in a finite number of steps. The ellipsoid method generates a sequence of ellipsoids...

- The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth...

- John ellipsoid or Löwner-John ellipsoid E(K) ****ociated to a convex body K in n-dimensional Euclidean space Rn can refer to the n-dimensional ellipsoid of...

- is composed of: a standard reference ellipsoid model, named urn:ogc:def:ellipsoid:EPSG::7030; and this ellipsoid is located a standard datum, named...

- A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under equilibrium which arises when a self-gravitating fluid body of uniform density rotates...

- In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, which is the truer, imperfect figure of the Earth,...

- point is the angle formed by the vector perpendicular (or normal) to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six...

- An Earth ellipsoid is a mathematical figure approximating the Earth's form, used as a reference frame for com****tions in geodesy, astronomy, and the...

- or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its prin****l axes; in other words, an ellipsoid with...

- ellipsoid method is an algorithm which finds an optimal solution in a finite number of steps. The ellipsoid method generates a sequence of ellipsoids...

- The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth...

- John ellipsoid or Löwner-John ellipsoid E(K) ****ociated to a convex body K in n-dimensional Euclidean space Rn can refer to the n-dimensional ellipsoid of...

- is composed of: a standard reference ellipsoid model, named urn:ogc:def:ellipsoid:EPSG::7030; and this ellipsoid is located a standard datum, named...

- A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under equilibrium which arises when a self-gravitating fluid body of uniform density rotates...

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