ellipsoid

a geometric surface, symmetrical about the three coordinate axes, whose plane sections are ellipses or circles. Standard equation: x²/a² + y²/b² + z²/c² = 1, where ?a, ?b, ?c are the intercepts on the x-, y-, and z- axes

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

ellipsoid

(i-lip -soid) A surface or solid whose plane sections are circles or ellipses. An ellipse rotated about its major or minor axis is a particular type of ellipsoid, called a prolate spheroid (major axis) or an oblate spheroid (minor axis).

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

ellipsoid

[ə′lip‚sȯid]

(mathematics)

A surface whose intersection with every plane is an ellipse (or circle).

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Ellipsoid

a closed central quadric surface. An ellipsoid has a center of symmetry O (see Figure 1) and three axes of symmetry, which are called the axes of the ellipsoid. The plane sections of

Figure 1

ellipsoids are ellipses; in particular, one can always find a plane section that is a circle. In a suitable coordinate system the equation of an ellipsoid has the form

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References in periodicals archive

However, after searching along the ellipsoidal central path [??]([alpha]), the new generated point [mathematical expression not reproducible] is given by Lemma 1.

An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

On the other hand, the existence of the continuous two-dimensional distribution of images over a closed surface in the image system is a direct consequence of the three-dimensional character of the spheroidal or ellipsoidal geometry as it compares with the essentially one-dimensional character of the spherical geometry in which, as mentioned in Section 1, point and line images are enough to represent interior Neumann functions.

Image Theory for Neumann Functions in the Prolate Spheroidal Geometry

In Figures 20(a), 20(d), and 20(g), the figures suggest that, in Orientation 1, cylindrical, cuboidal, and ellipsoidal samples' PAE values have maximal values which are 0.74, 0.89, and 0.88, and the corresponding COV values are also located near the maximal values except ellipsoidal sample.

Shape Effect on the Temperature Field during Microwave Heating Process

Patera, "Space vehicle conflict probability for ellipsoidal conflict volumes," Journal of Guidance, Control, and Dynamics, vol.

A SVM Approach of Aircraft Conflict Detection in Free Flight

While forming local GPS/leveling geoid model, in the study area one makes use of the reference stations whose ellipsoidal (h) and Helmert orthometric (H) heights are known.

Geoid height computation in strip-area projects by using least-squares collocation

As we know that the illuminated ellipsoidal scattered region do not have the constant dimension a that's why rm is taken instead of a constant value a.

MITIGATING ISI IN CELLULAR NETWORKS FOR A 3D SCATTERRED MODEL

The ellipsoidal form of the Riemann path ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) is given in (13) as:

Other earths: search for life and the constant curvature

fernandezi 1'.--Spermatheca with atrium 2 undifferentiated 2.--Preanal pores ellipsoidal A.

A new species of Amblyseius (Acari: Phytoseiidae) in the state of Bahia, Brazil