18-2 Special pseudo-conic projections based upon the sphere 399
Mapping equations (Stab–Werner):
x = r cos α =
= R
π
2
− Φ
cos
cos Φ
π
2 − Φ
Λ
,
y = r sin α =
= R
π
2
− Φ
sin
cos Φ
π
2 − Φ
Λ
.
(18.25)
Principal stretches (Stab–Werner):
Λ
2
S
1
=
1
2
2+
+Λ
2
cos ∆ −
sin ∆
∆
2 +
4Λ 2
cos ∆ −
sin ∆
∆
2 + Λ 4
cos ∆ −
sin ∆
∆
4
,
Λ
2
S
2
=
1
2
2+
+Λ
2
cos ∆ −
sin ∆
∆
2 −
4Λ 2
cos ∆ −
sin ∆
∆
2 + Λ 4
cos ∆ −
sin ∆
∆
4
.
(18.26)
Fig. 18.1. Stab–Werner mapping, pseudo-conic projection, Tissot ellipses of distortion.