Generalized Hammer Projection - Map Projections: Cartographic Information Systems - page 805

⎡ ⎤ ⎡ ⎤ ⎡ ⎤

1 b 13 b 15
01 b 35
00 1

1 a 13 a 15
01 a 35
00 1

100
010
001

⎣ ⎦ ⎣ ⎦ = ⎣ ⎦ .

R A R B =I 3 , (H.126)

Finally, we obtain( H.127 ) and thus ( H.128 ) .
b 13 = a 13 ,b 15 =3 a 13 −

− a 15 , 35 = − 3 a 13 , (H.127)

2

3 E 2 , 15 = 11 15 E 4 .

b 13 = − (H.128)

Using the first row of R B , row arrive at ( H.129 ) .

x = y + b 13 y 3 + b 15 y 5 +O( y 7 ) .

(H.129)

The powers of y are computed according to ( H.130 ), leading to ( H.131 ).

5 E 4 sin 5 Φ +O( E 6 ) ,
y 3 = c 4 sin 3 Φ +2 E 2 sin 5 Φ + 47

y = c 4 sin Φ + 2

3 E 2 sin 3 Φ + 3

15 E 4 sin 7 Φ +O( E 6 ) ,

(H.130)

y 5 = c 4 sin 5 Φ + 10

9 E 4 sin 9 Φ +O( E 6 ) , 3 E 2 sin 7 Φ + 67

sin Φ ∗ = c 4 sin Φ 1+ 2

c 4 )+ 1

3 E 2 sin 2 Φ (1 15 E 4 sin 4 Φ (9

20 c 4 +11 c 4 )

− −

+O( E 6 ) . (H.131)

With our students of Stuttgart University has been the vote
that the Hammer projection was in the list of the two most
popular map projections.

Note that the original contribution “mapping the sphere” is due to Hammer ( 1892 ). Here, we
use the works of Grafarend and Syffus ( 1997e ), Hoschek ( 1984 ), and Wagner ( 1962 ). We used
Abramowitz and Stegun ( 1965 ) as well as E. Grafarend, T. Krarup, and R. Syffus for the math-
ematical details. Special reference is also Grafarend ( 1995 ).