“Sphere to Cylinder”: Pseudo-Cylindrical Projections - Map Projections: Cartographic Information Systems - page 332

Fig. 13.2. Equal area pseudo-cylindrical mapping. Mollweide projection

Table 13.1 The solution of the special Kepler equation

Φ t Φ t Φ t Φ t

0 ◦ 30 ◦ 60 ◦ 90 ◦

0 0.41585 0.86698 π/ 2

10 ◦ 40 ◦ 70 ◦

0.13724 0.55974 1.03900

20 ◦ 50 ◦ 80 ◦ 0.27548 0.70910 1.23877

The solution of the special Kepler equation is shown in Table 13.1 . Thus, the final mapping equa-
tions are provided by ( 13.22 ). The left principal stretches are best determined by the numerical
solution of the biquadratic characteristic equation based on the left Jacobi matrix ( 13.23 )aswell
as the left Cauchy-Green deformation matrix ( 13.24 )(G r =I 2 ).

x = 2 √ 2
π

RΛ cos t, y = R √ 2sin t,

(13.22)

2 t + sin 2 t = π sin Φ,

J l =

= R √ 2
π

2cos t ,

πΛ tan t cos Φ
2cos t

−

(13.23)

π 2 cos Φ
4cos t

0