“Ellipsoid-of-Revolution to Cylinder”: Transverse Aspect - Map Projections: Cartographic Information Systems - page 369

−A 1 sin B 0

x 31 =

E 2 sin 2 B 0 ) 3 / 2 ×

6(1 − E 2 )(1 −

E 2 6sin 2 B 0 (1 + E 2 )+3 E 2 sin 4 B 0 (3 + E 2 ) 4 E 4 sin 6 B 0 ] ,

× [5 − − −

E 2 )sin B 0

x 13 = A 1 (1

−

E 2 B 0 ) 7 / 2 × 6(1 −

9 E 2 +2 E 2 sin 2 B 0 (5 3 E 2 )+4 E 4 sin 4 B 0 ] , × [1 − − (15.89)

A 1 cos B 0

x 30 =

E 2 sin 2 B 0 ) 1 / 2 × 120(1 − E 2 ) 3 (1 −

− 4sin 2 B 0 (7 + 4 E 2 )+2sin 4 B 0 (12 + 43 E 2 +13 E 4 ) −
− 4 E 2 sin 6 B 0 (18 + 25 E 2 +3 E 4 )+ E 4 sin(77 + 39 E 2 ) − 28 E 6 sin 10 B 0 ] ,

× [5 − E 2

A 1 cos B 0
120(1 − E 2 )(1 − E 2 sin 2 B 0 ) 5 / 2 ×

−

x 32 =

× [5 − E 2 − 2sin 2 B 0 (9 + 4 E 2 + E 4 )+15 E 2 sin 4 B 0 (3 + E 2 ) −

− 2 E 4 sin 6 B 0 (23 + 3 E 2 )+16 E 6 sin 8 B 0 ] ,

A 1 (1 − E 2 )cos B 0
24(1

x 14 =

E 2 sin 2 B 0 ) 9 / 2 × −

2 E 2 )+
+12 E 4 sin 4 B 0 (5 − 2 E 2 )+8 E 6 sin 6 B 0 ] .

9 E 2 +36 E 2 sin 2 B 0 (1

× [1 − −

Box 15.5 (A representation of the non-vanishing coecients in a polynomial setup of a
conformal mapping of type Gauss-Krueger or UTM).

y ( l,b )=
= y 01 b + y 20 l 2 + y 02 b 2 + y 21 l 2 b + y 03 b 3 + y 40 l 4 + y 22 l 2 b 2 + y 04 b 4
+ y 41 l 4 b + y 23 l 2 b 3 +

(15.90)

+ y 05 b 5 +O(6) ,

E 2 ) A 1 (1 −

E 2 sin 2 B 0 ) 3 / 2 ,
y 20 = A 1 cos B 0 sin B 0

y 01 =

(1 −

2(1 − E 2 sin 2 B 0 ) 1 / 2 ,
y 02 = 3 A 1 E 2 (1

E 2 )cos B 0 sin B 0

−

E 2 sin 2 B 0 ) 5 / 2

2(1 −