# ellipsoid

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## 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
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 It might be outdated or ideologically biased.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

## ellipsoid

[ə′lip‚sȯid]
(mathematics)
A surface whose intersection with every plane is an ellipse (or circle).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In this research, we focused on the kinematic evolution of the ore-bearing ductile shear zone in the Zagros Orogeny and applied strain ellipsoid shape as a vector to the interpretation of structure and intensity of deformation.
We choose 6 different ellipsoids (three of them are prolate and three are oblate).
Asada, "Dynamic analysis and design of robot manipulators using inertia ellipsoids," in Proceedings of the 1984 IEEE International Conference on Robotics and Automation, pp.
Section 3 provides two new approaches for the estimation and prediction of the debris dispersion due to the breakup during the reentry which is introduced by propagating the covariances of positional probabilistic ellipsoids. Section 4 shows performance comparisons of the proposed estimation approaches, that is, the statistical linear regression with the unscented transformation and the Gauss-Hermite cubature-based numerical approximation are demonstrated.
The inertia ellipsoid S is defined by the equation [mathematical expression not reproducible], or equivalently [mathematical expression not reproducible] where [mathematical expression not reproducible].
Generally, they are based on the fact that this chamber possesses a similar geometry to the ellipsoid of revolution, or, still, to a truncated prolate spheroid (TPS), implying that two of its axle shafts must have equal measures [4-9].
Both of the two shape families, ellipsoids as well as prisms, are represented with discrete number of similar particles characterised by an specific elongation factor [k.sub.elon], non-dimensional values of which are ranging between 10 and 0.1, i.e.
Ellipsoids are tighter fitting than spheres for elongated objects, chiefly arms and legs in humanoid modeling; they are not invariant to rotations; however, their calculation and the test between ellipsoids is more complex than spheres volumes (Arcila & Banon, 2005; Bing et al., 2009) (Figure 1 (f)).
The predominant type of phytoliths is "irregular ruminate" (57%), significantly few encountered phytoliths as "thinning rough parallelepiped with rounded edges" (10%) and "smooth ellipsoids" (9%).

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