Sfäroid

Sfäroid is a geometric solid of revolution formed by rotating an ellipse about one of its principal axes. When rotated about the ellipse’s minor axis, the result is an oblate sfäroid, flattened at the poles; when rotated about the major axis, the result is a prolate sfäroid, elongated along the symmetry axis.

The term is commonly used as the Swedish equivalent of spheroid; in English literature the shape is called a spheroid or spheroidal ellipsoid. A sfäroid with equatorial radius a and polar radius c satisfies the equation x^2/a^2 + y^2/a^2 + z^2/c^2 = 1. If a = c, the sfäroid reduces to a sphere.

Oblate sfäroids describe many natural bodies with rotation, such as planets and stars. Earth is approximately an oblate spheroid with an equatorial radius of about 6378 km and a polar radius of about 6357 km. In geodesy and astronomy, the spheroidal model is used to improve the accuracy of measurements and maps.

In computer graphics and engineering, sfäroids are used to model rounded objects and to simplify volume calculations. The volume of a sfäroid with radii a and c is V = 4/3 π a^2 c. Surface area has a closed form only in special cases; in general it involves elliptic integrals.