Mixed cylindric map projections of the ellipsoid of revolution

Abstract.

The mixed spherical map projections of equiareal, cylindric type are based upon the Lambert projection and the sinusoidal Sanson–Flamsteed projection. These cylindric and pseudo-cylindric map projections of the sphere are generalized to the ellipsoid of revolution (biaxial ellipsoid). They are used in consequence by two lemmas to generate a horizontal and a vertical weighted mean of equiareal cylindric map projections of the ellipsoid of revolution. Its left–right deformation analysis via further results leads to the left–right principal stretches/eigenvalues and left–right eigenvectors/eigenspace, as well as the maximal left–right angular distortion for these new mixed cylindric map projections of ellipsoidal type. Detailed illustrations document the cartographic synergy of mixed cylindric map projections.