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 …

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.

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 …

椭圆体是由平面椭圆绕其所在坐标系的x轴或y轴旋转一周所形成的三维几何体 [1-2]。其体积可通过公式V= (4/3)πabc计算，其中a、b、c分别为沿各轴的半轴长度。椭圆体具有独特的几何特性，如焦点到椭 …

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.

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).

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.