Sphere

Spherical coordinates specify a point in three-dimensional space by its distance from an origin O and two angles λ and ϕ. Spherical coordinate systems represent a three-dimensional extension of the polar coordinate system and are therefore also called spatial polar coordinate systems. Spherical coordinate systems are often used simultaneously with Cartesian coordinate systems, and are then defined by the origin of the Cartesian coordinate system as center of the spherical coordinate system, the z-axis as polar axis, the x- and y-axis as equatorial plane, whereby the x-axis determines the reference direction for the spherical coordinate system. In the measuring technique spherical coordinates find various application. For example, spherical coordinates and the associated mathematical formulas are important for the calculation of surfaces or volumes of bodies with spherical boundaries, spherical surfaces and surfaces that have radial or angular symmetries. In particular, they can be useful in the calculation of integrals. In metrology, spherical coordinates play a role, for example, in the alignment of and measurement with the help of an interferometer as it occurs on laser trackers.