“Ellipsoid-of-Revolution to Cylinder”: Transverse Aspect - Map Projections: Cartographic Information Systems - page 399

L 02 ) 2 cos B 0 sin B 0 (1 E 2 sin 2 B 0 ) 5 / 2

t 20 = ( L 01

− −

A 1 (1 − E 2 ) 2

E 2 sin 2 B 0 ) 1 / 2 5

L 02 ) 4 tan B 0 (1 E 2 28 sin 2 B 0

− ( L 01 − − − −

16 E 2 sin 2 B 0 +24sin 4 B 0 +
+86 E 2 sin 4 B 0 +26 E 4 sin 4 B 0 −

−

72 E 2 sin 6 B 0 − 100 E 4 sin 6 B 0

− 12 E 6 sin 6 B 0 +
+77 E 4 sin 8 B 0 +39 E 6 sin 8 B 0 28 E 6 sin 10 B 0 [48 A 1 (1

E 2 ) 3 ] − 1 ,

− −

t 11 = ( L 01 − L 02 )cos B 0 (1 − E 2 sin 2 B 0 ) 3 / 2
A 1 (1

+

− E 2 )

+( L 01 − L 02 ) 3 cos B 0 (1 − E 2 sin 2 B 0 ) 3 / 2 5 − E 2

− 18 sin 2 B 0 − 18 E 2 sin 2 B 0

+45 E 2 sin 4 B 0 +
+15 E 4 sin 4 B 0 − 28 E 4 sin 6 B 0 [6 A 1 (1

E 2 ) 3 ] − 1 ,

−

E 2 sin 2 B 0 ) 5 / 2 L 02 ) 2 cos B 0 sin B 0 (1 ( L 01 − −

t 02 = − −

A 1 (1 − E 2 ) 2

E 2 sin 2 B 0 ) 1 / 2 5 L 02 ) 4 E 2 cos B 0 sin B 0 (1 E 2 28 sin 2 B 0 − ( L 01 − − − −

16 E 2 sin 2 B 0 +24sin 4 B 0 +
+86 E 2 sin 4 B 0 +26 E 4 sin 4 B 0 − 72 E 2 sin 6 B 0 − 100 E 4 sin 6 B 0
− 12 E 6 sin 6 B 0 +
+77 E 4 sin 8 B 0 +39 E 6 sin 8 B 0

−

28 E 6 sin 10 B 0 [16 A 1 (1 E 2 ) 4 ] − 1 . − −

15-62 Two Examples of Strip Transformations

Let us consider two examples of a strip transformation of conformal coordinates of Gauss-
Krueger type with a dilatation factor ρ =1( Schoedlbauer 1981a , b , 1982a , b) and a strip trans-
formation of conformal coordinates of UTM type with p =0 . 999578. Due to Example 15.8 ,
we start from the coordinates ellipsoidal longitude/latitude of TP I.O. Bonstetten ( =

{ 10 ◦ 42 59 . 3215 , 48 ◦ 26 45 . 4355 } ) on the Bessel ellipsoid of semi-major axis A = 377,397.155m and
reciprocal flattening f − 1 = 299 . 15281285. The first and second strip has been fixed with L 01 =9 ◦
and L 02 =12 ◦ , respectively. The ellipsoidal latitude of the reference point was chosen to B 0 =48 ◦ .
In addition, we compared the direct transformation {L, B}→{x 1 ,y 1 } and {L, B}→{x 2 ,y 2 } as
illustrated by the commutative diagram of Fig. 15.17 , leading to differences in the submillimeter
range. By contrast, Example 15.9 gives the strip transformation of a point

{ L, B }

12 . 01 ◦ , 49 ◦ }
on the ellipsoid referring to WGS84 ( A =6 , 378 , 137 m ,f − 1 = 298 . 257223563) with a first refer-
ence meridian of L 01 =9 ◦ and a second of L 01 =15 ◦ . The differences again in the comparison of
both ways of calculating the UTM coordinates have been in the submillimeter range the closer
B 0 is chosen to the point

{ L, B } = {

{ L, B } .