“Sphere to Tangential Plane”: Polar (Normal) Aspect - Map Projections: Cartographic Information Systems - page 206

D | cos Δ |− R H − R (1 −| sin Φ | )

Λ 2 =( D − R )

) 2 = H )] 2 . ( D − R | cos Δ | [ H + R (1 −| sin Φ |

Special isometry:

Δ → π ( | cos Δ |→ 1) or Φ →− π/ 2( | sin Φ |→ 1)

⇒ (5.75)

Λ 1 = Λ 2 =1 .

5-244 Line-of-Sight, Line-of-Contact, Minimal and Complete Atlas

The line-of-sight as well as the line-of-contact for both the general normal perspective mapping
to the tangential plane at the North Pole and to the tangential plane at the South Pole are
illustrated in Figs. 5.13 and 5.14 , respectively.

Fig. 5.13. Line-of-sight, normal perspective mapping of the sphere to the tangential plane at the North Pole,
projection plane at maximal distance