 The word "spheroid" originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape, and that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of the Earth).The equation of a tri-axial ellipsoid centred at the origin with semi-axes , and aligned along the coordinate axes is

The equation of a spheroid with as the symmetry axis is given by setting