“Sphere to Cylinder”: Pseudo-Cylindrical Projections - Map Projections: Cartographic Information Systems - page 333

C l =J l G r J l =

π 2

,

4cos 2 t

= 2 R 2

πΛ tan t cos Φ
−πΛ tan t cos Φ π 2 cos 2 Φ ( π 2 +4 Λ 2 tan 2 t )
16 cos 2 t

−

(13.24)

det(C l − Λ S G l )=

= R 2

8 2

π 2 cos 2 t − Λ S cos 2 Φ

−

π Λ tan t cos Φ

2cos 2 t Λ 2 tan 2 t + π 4

= (13.25)

cos 2 Φ 2

−

π Λ tan t cos Φ

− Λ S

=0 .

13-23 Parabolic Pseudo-Cylindrical Mapping (J. E. E. Craster),
Compare with Fig. 13.3

This mapping is defined in such a way that the meridians except the central meridian, which is a
straight line, are equally spaced parabolas. Parallels are unequally spaced straight lines, farthest
apart near the equator. The mapping equations are defined by ( 13.26 ). The left Jacobi matrix is
given by ( 13.27 ) and the left Cauchy-Green matrix is given by ( 13.28 )(G r =I 2 ). As can be seen
from Fig. 13.3 , map distortion is severe near outer meridians at high latitudes.

x =

= 3

π RΛ 2cos 2 Φ 3 − 1 ,

(13.26)

y =
= √ 3 πR sin Φ

3 ,

J l =

= R 3
π

2cos 2 3 − ,

4

3 Λ sin 2 3

1 −

(13.27)

π

3 cos 3

0

C l =J l G r J l =

.

2cos 2 3
12 Λ sin 2 3 1 − 2cos 2 3 16 Λ 2 sin 2 2 3 + π 2 cos 2 3

9 1 2cos 2 3 2 12 Λ sin 2 3 1 − −

= R 2
3 π

(13.28)