“Sphere to Cone”: Pseudo-Conic Projections - Map Projections: Cartographic Information Systems - page 445

Mapping equations (Stab-Werner):
x = r cos α =

2 − Φ cos cos Φ

− Φ Λ ,

= R π

(18.25)

π
2

y = r sin α =

Φ sin cos Φ

Φ Λ .

= R π

2 −

π
2

−

Principal stretches (Stab-Werner):

⎡

A s 1 = 1

⎣ 2+

2

4 ⎤
⎦ ,

+ Λ 2 cos Δ

2

4 A 2 cos Δ

2

+ Λ 4 cos Δ

sin Δ
Δ

sin Δ
Δ

sin Δ
Δ

− + − − (18.26)

⎡

( Λ S ) 2 = 1

⎣ 2+

2

4 ⎤
⎦ .

+ Λ 2 cos Δ

2

4 Λ 2 cos Δ

2

+ Λ 4 cos Δ

sin Δ
Δ

sin Δ
Δ

sin Δ
Δ

− − − −

18-22 Bonne Mapping

We agree upon the postulate that the line-of-contact of the cone shall be mapped equidistantly.
We start the theory of the Bonne mapping from the following two postulates, from which fol-
lows ( 18.29 ). Compare with Fig. 18.2 .

Postulate.

r ( Δ )= aΔ + b. (18.27)

End of Postulate.

Postulate.

r ( Δ 0 )= R tan Δ 0 , a = R. (18.28)

End of Postulate.