“Sphere to Tangential Plane”: Oblique Aspect - Map Projections: Cartographic Information Systems - page 245

Fig. 7.2. Mapping the sphere to a tangential plane: oblique aspect, equidistant mapping. Point-of-contact:
meta-North Pole at Stuttgart/Germany ( Λ 0 =9 ◦ 11 ,Φ 0 =48 ◦ 46 )

7-22 Conformal Mapping (Oblique Stereographic Projection,
Oblique UPS)

The oblique conformal mapping of the sphere to a tangential plane is the generalization of equa-
tions derived earlier. The results are stated more precisely in Box 7.2 . Figure 7.3 gives an impres-
sion of the famous oblique conformal mapping of the sphere to a tangential plane with the meta-
North Pole located at Rio de Janeiro ( Λ 0 = 43 ◦ 12 ,Φ 0 = 22 ◦ 54 ).

− −

Box 7.2 (Oblique conformal mapping of the sphere to a plane at the meta-North Pole Λ 0 ∈
[0 ◦ , 360 ◦ ] ,Φ

90 ◦ , 90 ◦ ]) .

∈ [ −

Parameterized mapping:

α = A, r = f ( B )=2 R tan π

,

B
2 4 −

(7.9)

x =2 R tan π

cos A, y =2 R tan π sin A,

B
2

B
2

4 − 4 −

(7.10)

cos Φ sin( Λ − Λ 0 )

tan A =

sin Φ cos Φ 0 ,

cos Φ sin Φ 0 cos( Λ − Λ 0 ) −