Ellipsoid-of-Revolution to Tangential Plane - Map Projections: Cartographic Information Systems - page 272

East coordinates:

y ∗ = y ∗ ( p )=
= H 0

(8.77)

− N cos Φ sin( Λ − Λ 0 )

H 0 . N 0 + N 0 E 2 sin 2 Φ 0

N cos Φ cos Φ 0 cos( Λ − Λ 0 )+ N (1 − E 2 )sin Φ sin Φ 0 − −

A 1 A 1

N := 1 , N 0 := 1 . (8.78)

E 2 sin 2 Φ E 2 sin 2 Φ − −

Alternatives .

East coordinates:

x ∗∗ = y ∗ .

(8.79)

North coordinates:
y ∗∗ = x ∗ . − (8.80)

Polar coordinates (South azimuth α, radial coordinate r ):

tan α ∗ =

N cos Φ sin( Λ − Λ 0 )

=

N 0 E 2 sin Φ 0 cos Φ 0 ,

(8.81)

N cos Φ sin Φ 0 cos( Λ − Λ 0 ) − N (1 − E 2 )sin Φ cos Φ 0 −

r = x ∗ 2 + y ∗ 2 = x ∗∗ 2 + y ∗∗ 2 .

Alternative coordinates:

α ∗∗ =90 ◦ −

α ∗ (East azimuth) . (8.82)

At this point, you may enjoy our examples. Our first example, see Fig. 8.9 ,usesa tilted perspec-
tive , also called Space Photo projection: the eastern seaboard viewed from a point about 160km
above Newburgh, New York ( Φ 0 =41 ◦ 30 northern latitude, Λ 0 =74 ◦ Western longitude, 1 ◦
graticule). Our second example, see Fig. 8.10 ,usesa tilted perspective , also called Space Photo
projection: France and Central Europe viewed from a point about 640km above central Spain
( Φ 0 =40 ◦ northern latitude, Λ 0 =5 ◦ western longitude, 2 ◦ graticule).