Ellipsoïdale

Ellipsoïdale is the term used to describe things relating to an ellipsoid, the three-dimensional analogue of an ellipse.

In geometry, an ellipsoid is a closed quadric surface obtained by scaling a sphere along three perpendicular axes. It can be described by the equation x^2/a^2 + y^2/b^2 + z^2/c^2 = 1, with a, b, c > 0 being the semi-axes. The surface is convex and has elliptical cross-sections in all coordinate planes.

Special cases include the sphere a = b = c; oblate spheroid a = b ≠ c with c < a; and prolate spheroid a = b ≠ c with c > a. A common parametrization is x = a sinφ cosθ, y = b sinφ sinθ, z = c cosφ, with φ ∈ [0, π] and θ ∈ [0, 2π].

Ellipsoïdale shapes arise in applications across science and engineering. Geodesy uses reference ellipsoids to model Earth's shape for map projections and positioning, with models such as WGS84 and GRS80. In astronomy, planetary bodies are often approximated as ellipsoids. In computer graphics, ellipsoids serve as bounding volumes and for collision detection. In mathematics, ellipsoidal coordinates and ellipsoidal harmonics provide tools for problems with ellipsoidal symmetry.

The term is common in Dutch and related languages to describe anything with an ellipsoidal form, and it appears across disciplines whenever a three-dimensional ellipsoid is involved. See also: ellipsoid, reference ellipsoid, quadric surface.