“Ellipsoid-of-Revolution to Cone”: Polar Aspect - Map Projections: Cartographic Information Systems - page 456

p 2 := X 2 + Y 2 , A 2 = A 1 (1 − E 2 ) , Z = (1 − E 2 ) A 1 sin Φ 1

(19.21)

E 2 sin 2 Φ

−

⇒

A 1 cos Φ

1

p = . (19.22)

E 2 sin 2 Φ −

We use the postulate of an equidistant mapping on the parallel circle-of-reference Φ 0 .

A 1 cos Φ 0

1

Λ = f ( Φ 0 ) α

E 2 sin 2 Φ 0

−

⇒

√ 1 − E 2 cos 2 Δ 0 Λ = c 1+ E cos Δ 0

n

E/ 2

A 1 sin Δ 0

tan Δ 0
2

cos Δ 0 Λ

1 − E cos Δ 0

⇒ (19.23)

1+ E cos Δ 0
1

−n

E/ 2

A 1 tan Δ 0

tan Δ 0
2

√ 1

c =

− E cos Δ 0

− E 2 cos 2 Δ 0

⇒

α
r

= nΛ ,

f ( Δ )

tan 2
tan Δ 2

E/ 2 n 1 − E cos Δ 0

1

A 1 tan Δ 0 1+ E cos Δ

1+ E cos Δ 0

f ( Δ )= √ 1 − E 2 cos 2 Δ 0 (19.24)

− E cos Δ

⎡

E ⎤
⎦

1+ E sin Φ
1+ E sin Φ 0

1

tan 4 −

2

n

Φ

E 2 sin 2 Φ 0 A 1 −

⎣

tan 4 −

Φ 2

=

tan Φ 0 1

.

E 2 sin 2 Φ 1 −

E 2 sin 2 Φ 0

−

19-222 Conformal Mapping: The Variant of Type Equidistant on Two Parallel Circles (Lambert
Conformal Mapping)

We then consider the variant of type equidistant on two parallel circles . In this context, the
projection constant n is determined by the postulate of an equidistant mapping on two parallel
circles fixed by Δ 1 = 2 − Φ 1 and Δ 2 = 2 − Φ 2 .