“Sphere to Cone”: Pseudo-Conic Projections - Map Projections: Cartographic Information Systems - page 446

Fig. 18.1. Stab-Werner mapping, pseudo-conic projection, Tissot ellipses of distortion

b = R (tan Δ 0 − Δ 0 ) . (18.29)
Next, we summarize the mapping equations of type Bonne, the inverse mapping equations, and
the principal stretches. Note that r ( Δ =0)= R (tan Δ 0 − Δ 0 ): “Pointwise mapping of the North
Pole, but not at the coordinate origin ”! Note that Rigobert Bonne's work can be

read in “Ptolemaeus Geographia” (Francesco Berlinghieri, Florenz 1482). Furthermore, note that
very often Φ 0 =50 ◦ Nischosen(Fig. 18.3 ).

{ x =0 ,y =0 }

Mapping equations:

sin Δ cos Φ

α = α ( Λ, Δ )=

Δ 0 +tan Δ 0 Λ = Φ +cot Φ 0 Λ,

(18.30)

Δ − Φ 0 −

r = r ( Δ )= R ( Δ − Δ 0 )+ R tan Δ 0 = R ( Φ 0 − Φ )+ R cot Φ 0 .

Direct mapping equations:

⎡

cos Λ

⎤

x
y

= R ( Φ 0 cos Φ

Φ 0 −Φ +cot Φ 0

⎣

sin cos Φ
Φ 0 −Φ +cot Φ 0

Λ

⎦ .

− Φ +cot Φ 0 ) (18.31)