“Sphere to Tangential Plane”: Oblique Aspect - Map Projections: Cartographic Information Systems - page 246

sin B =cos Φ cos Φ 0 cos( Λ − Λ 0 )+sin Φ sin Φ 0 .

Left principal stretches:

1

cos 2 4 −

2 .

Λ 1 = Λ 2 = (7.11)

B

Left eigenvectors:

1 1

cos 2 4 −

2 , C 2 Λ 2 = E B

cos 2 4 −

2 .

C 1 Λ 1 = E A (7.12)

B B

Parameterized inverse mapping:
tan A = y

x , tan π

=

2 R x 2 + y 2 ,

B
2

1

4 −

(7.13)

sin A
tan B cos Φ 0 +cos A sin Φ 0 ,

tan( Λ − Λ 0 )=

sin Φ = − cos B cos A cos Φ 0 +sin B sin Φ 0 .

Fig. 7.3. Mapping the sphere to a tangential plane: oblique aspect, conformal mapping. Point-of-contact: meta-
North Pole at Rio de Janeiro ( Λ 0 = − 43 ◦ 12 ,Φ 0 = − 22 ◦ 54 )