“Sphere to Cylinder”: Transverse Aspect - Map Projections: Cartographic Information Systems - page 320

Fig. 11.3. Mapping the sphere to a cylinder: transverse aspect, conformal mapping, B 0 =0 ◦ , transverse Mer-
cator projection

11-22 Conformal Mapping (Transverse Mercator Projection),
Compare with Fig. 11.3

x
y

= R cos B 0 = R cos B 0 =

A A

ln cot 4 −

2

ln tan 4 + 2

B

= R cos B 0

=

A

(11.5)

1

2 ln 1+sin B

1 − sin B

= R cos B 0 A

,

artanh(sin B )

Λ 1 = Λ 2 = cos B 0

cos B .

(11.6)

11-23 Equal Area Mapping (Transverse Lambert Projection),
Compare with Fig. 11.4

x
y

= R A cos B 0 ,

(11.7) sin B

cos B 0