From Riemann Manifolds to Euclidean Manifolds - Map Projections: Cartographic Information Systems - page 123

Fig. 2.1. Mollweide projection of an ellipsoid-of-revolution, Grafarend et al. ( 1995a )

Box 2.3 (The Mollweide projection of E A 1 ,A 1 ,A 2 ; the pseudo-cylindric, equiareal, equidistant

mapping of the circular equator).

Mapping equations:
x ( Λ, Φ )= aΛ cos t ( Φ ) ,

(2.53)

y ( Λ, Φ )= b sin t ( Φ ) .
Generalized Kepler equations:

ln 1+ E sin Φ

2 E sin Φ
1 −E 2 sin 2 Φ 1 −E sin φ +

2 t + sin 2 t = π . (2.54)

ln 1+ E

1 −E +ln 2 E

1 −E 2

Scales:
a = A 1 ,

ln 1+ E
1 E 2 .

E 2 )

b = A 1 (1

− 2 E

E +

(2.55)

πE − 1 −

Box 2.4 ([The left principal stretches, the left eigenvalues, and the generalized Mollweide
projection of the ellipsoid-of-revolution).

Characteristic equation of the left general eigenvalue problem:
Λ 4 tr[C l G − l ] Λ 2 +det[C l G − l ] = 0 subject to det [C l G − l ] = 1 − (2.56)