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1月31日 · 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 lengths a, b, and c.

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.

Ellipsoid. An ellipsoid is a 3D geometric figure that has an elliptical shape. It can be viewed as a stretched sphere. An ellipsoid gets its name from an ellipse. Any plane that cuts through an ellipsoid forms an ellipse. Two ellipsoids are shown in the figure below. Real life examples of an ellipsoid include an egg or a blimp. Ellipsoid equation

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. As you can verify below, all of the cross sections of an ellipsoid are ellipses.

An ellipsoid is a shape like a sphere, but prolate (longer in one or more directions) like a rugby ball, or like an egg. It is the 3 dimensional analogue of an ellipse. The Earth is shaped slightly like an ellipsoid. Its shape is called an oblate spheroid.

Let us refer the ellipsoid \(\ref{4.3.4}\) to a set of axes \(\text{O}x^\prime y^\prime z^\prime\) such that the angles \(z^\prime \text{O} z\) and \(x^\prime \text{O} x\) are each \(θ\), and the \(y^\prime\)- and \(y\)-axes are identical.

An ellipsoid is a three-dimensional shape for which all plane cross-sections are either ellipses or circles. The ellipsoid has three axes which intersect at the centre of the ellipsoid. Each axis is perpendicular to the other two, and the ellipsoid is symmetrical around all three axes.

An ellipsoid is a three-dimensional geometric shape that can be visualized as a stretched or flattened version of a sphere. In other words, it's a smooth, closed surface similar to a sphere but with different proportions along its x, y, and z axes.

An ellipsoid is a three-dimensional geometric shape that resembles a stretched or compressed sphere. It is a type of quadric surface, which means it is defined by a second-degree equation in three variables. Mathematically, an ellipsoid is described by the equation: x …