Map Projections of Alternative Structures: Torus, Hyperboloid, Paraboloid, Onion Shape and Others - Map Projections: Cartographic Information Systems - page 617

(ii) equiareal:

(1 + 4 V 2 ) 3 / 2

− 1

x =

cos ( nU )

6 n

(1 + 4 V 2 ) 3 / 2

− 1

y = sin ( nU )

6 n

(1 + 4 V 2 ) 3 / 2 (1 + 4 V 2 ) 3 / 2

Λ 1 = n

− 1

,Λ 2 = V

− 1

V

6 n

n

6 n

(iii) equidistant:

2 V √ 1+4 V 2 + 1

x =( 1

4 arcsinh 2 V )cos( nU )

2 V √ 1+4 V 2 + 1

y=( 1

4 arcsinh 2 V ) sin ( nU )

2 n √ 1+4 V 2 +

Λ 1 = 1

n
4 V arcsinh (2 V ) ,Λ 2 =1

P 2 onto a developed cylinder C 1

Fig. 23.16. Conformal mapping of