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

Dec 3, 2025 · The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/ (a^2)+ (y^2)/ (b^2)+ (z^2)/ (c^2)=1, (1) where the semi-axes are of …

An ellipsoid has three axes of rotational symmetry. If an ellipsoid is rotated 180° (half a turn) about its axes, it will look the same as the original shape. The three axes are perpendicular to each other and …

Ellipsoid, closed surface of which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the centre.

An ellipsoid is a three-dimensional geometric figure that resembles a sphere, but whose equatorial axis (a in Figure 2.15.1, above) is slightly longer than its polar axis (b).

Apr 24, 2012 · The section of an ellipsoid by any plane is an ellipse. If two semi-axes of an ellipsoid are equal, the ellipsoid is called an ellipsoid of revolution, and the sections of an ellipsoid of revolution by …

Just as an ellipse is a generalization of a circle, an ellipsoid is a generalization of a sphere. In fact, our planet Earth is not a true sphere; it's an ellipsoid, because it's a little wider than it is tall.

Aug 4, 2025 · Unlike a perfect sphere, which has a single radius, an ellipsoid is characterized by three distinct, mutually perpendicular semi-axes that determine its length, width, and depth.

An ellipsoid is a three-dimensional surface that is a 3D analogue of an ellipse. It can be visualized as a sphere that has been stretched or compressed along its three perpendicular axes.

When the ellipsoid is not of revolution, there exist two directions of planes for which these sections are circular, which proves that the ellipsoid is a doubly circled surface (see the 5th parametrization above).