Ellipsoidial

ellipsoidial refers to anything related to an ellipsoid. An ellipsoid is a quadric surface that is defined by the equation x²/a² + y²/b² + z²/c² = 1 in a Cartesian coordinate system. It is a three-dimensional generalization of an ellipse. Imagine taking an ellipse and stretching or squashing it along its axes to form a 3D shape. That shape is an ellipsoid.

The shape of an ellipsoid is determined by the lengths of its semi-axes, a, b, and c. If all three semi-axes are equal (a=b=c), the ellipsoid is a sphere. If two semi-axes are equal, the ellipsoid is an oblate spheroid (like a squashed ball) or a prolate spheroid (like a stretched ball), depending on which two axes are equal and how they relate to the third. For example, if a=b ≠ c, the ellipsoid is a spheroid.

In various fields, the term ellipsoidial appears. In geometry and calculus, it describes surfaces and volumes that are ellipsoidal in form. In physics and engineering, celestial bodies like planets and stars are often approximated as ellipsoids, and their gravitational fields are described using ellipsoidal coordinates. In computer graphics and image processing, ellipsoids are fundamental shapes used for modeling and analysis. The properties of an object that is ellipsoidial are those that can be described or are characteristic of an ellipsoid.