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 surface that may be defined as the zero set of a polynomial of degree two in three variables.

2025年3月5日 · The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by. where the semi-axes are of lengths , , and . In spherical coordinates, this becomes. Tietze (1965, p. 28) calls the general ellipsoid with a "triaxial ellipsoid."

Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal coordinate system is based on confocal quadrics.

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. If a, b, and c are the principal semiaxes, the general equation of such an ellipsoid is x2/a2 + y2/b2 + z2/c2.

Ellipsoids are often classified based on the lengths of their semi-axes, a, b, and c. 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 meaning of ELLIPSOID is a surface all plane sections of which are ellipses or circles.

Calculates ellipsoid and spheroid volume and surface area. Ellipsoid is a sphere-like surface for which all cross-sections are ellipses. where a - radius along x axis, b - radius along y axis, c - radius along z axis. The surface area of a general ellipsoid cannot be expressed exactly by an elementary function.

Description of the ellipsoid with interactive graphics that illustrate cross sections and the effect of changing parameters.

Define ellipsoidal. ellipsoidal synonyms, ellipsoidal pronunciation, ellipsoidal translation, English dictionary definition of ellipsoidal. ellipsoid The equation for an ellipsoid is x2/a2 + y2/b2 + z2/c2 = 1. n. A geometric surface, all of whose plane sections are either ellipses or circles....

In this article, we will discuss the mathematical properties of ellipsoids, their applications, and examples of how they are used in various fields. Body Paragraphs: Definition: An ellipsoid is a three-dimensional shape that is symmetrical along three axes.