THE GENERALIZED MOLLWEIDE PROJECTION OF THE BIAXIAL ELLIPSOID

The standard Mollweide projection of the sphere S-R(2) which is of type pseudocylindrical - equiareal is generalized to the biaxial ellipsoid E(A,B)(2). Within the class of pseudocylindrical mapping equations (1.8) of E(A,B)(2) (semimajor axis A, semiminor axis B) it is shown by solving the general eigenvalue problem (Tissot analysis) that only equiareal mappings, no conformal mappings exist. The mapping equations (2.1) which generalize those from S-R(2) to E(A,B)(2) lead under the equiareal postulate to a generalized Kepler equation (2.21) which is solved by Newton iteration, for instance (Table 1). Two variants of the ellipsoidal Mollweide projection in particular (2.16), (2.17) versus (2.19), (2.20) are presented which guarantee that parallel circles (coordinate lines of constant ellipsoidal latitude) are mapped onto straight lines in the plane while meridians (coordinate lines of constant ellipsoidal longitude) are mapped onto ellipses of variable axes. The theorem collects the basic results. Sixd computer graphical examples illustrate the first pseudocylindrical map projection of E(A,B)(2) of generalized Mollweide type.