12 “Sphere to cylinder”: oblique aspect
Mapping the sphere to a cylinder: meta-cylindrical projections in the oblique aspect. Equidistant, conformal, and equal area mappings.
Cylindrical projections in the oblique aspect are mainly used to display regions which have a predominant extent in the oblique direction, neither East-West nor North-South. In addition, they form the
most general cylindrical projections because mapping equations for projections in the polar and the
transverse aspect can easily be derived from it. This is done by setting the corresponding latitude of
the meta-North Pole Φ 0 to a specific value: Φ 0 = 90
◦ generates cylindrical projections in the polar
aspect, Φ 0 = 0
◦ result in cylindrical projections in the transverse aspect. As an introductory part, we
present the equations for general cylindrical mappings together with the equations for the principal
stretches, before derivations for specific cylindrical map projections of the sphere (oblique equidistant projection, oblique conformal projection and oblique equal area projection) are given. For a first
impression, have a look at Fig. 12.1.
Fig. 12.1. Mapping the sphere to a (tangent) cylinder. Oblique aspect.
Mapping the sphere to a cylinder: meta-cylindrical projections in the oblique aspect. Equidistant, conformal, and equal area mappings.
Cylindrical projections in the oblique aspect are mainly used to display regions which have a predominant extent in the oblique direction, neither East-West nor North-South. In addition, they form the
most general cylindrical projections because mapping equations for projections in the polar and the
transverse aspect can easily be derived from it. This is done by setting the corresponding latitude of
the meta-North Pole Φ 0 to a specific value: Φ 0 = 90
◦ generates cylindrical projections in the polar
aspect, Φ 0 = 0
◦ result in cylindrical projections in the transverse aspect. As an introductory part, we
present the equations for general cylindrical mappings together with the equations for the principal
stretches, before derivations for specific cylindrical map projections of the sphere (oblique equidistant projection, oblique conformal projection and oblique equal area projection) are given. For a first
impression, have a look at Fig. 12.1.
Fig. 12.1. Mapping the sphere to a (tangent) cylinder. Oblique aspect.