“Sphere to Tangential Plane”: Oblique Aspect - Map Projections: Cartographic Information Systems - page 242

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“Sphere to Tangential Plane”: Oblique Aspect
Mapping the sphere to a tangential plane: meta-azimuthal projections in the oblique aspect.
Equidistant, conformal (oblique UPS), and equal area (oblique Lambert) mappings.
In this chapter, we generalize the concept of azimuthal projections and present the class of widely
applied oblique azimuthal projection. The point-of-contact is not anymore restricted to be one of
the poles or lying on the equator, it can be any point on the reference sphere, i.e. Λ 0 ∈ [0 ◦ , 360 ◦ ],
Φ 0 ∈ [ − 90 ◦ , 90 ◦ ]. With this configuration, any region of interest can be mapped by an equidistant,
conformal, or equal area projection. The latter one is in particular appropriate for regions which
are approximately circular in extent. Figure 7.1 gives an impression of the geometrical situation
for mappings of meta-azimuthal projections in the oblique aspect.
Fig. 7.1. Mapping the sphere to a tangential plane: oblique aspect. Point-of-contact: meta-North Pole at Λ 0 =
330 ◦ ,Φ 0 =40 ◦