Geography Reference
In-Depth Information
subject to the principal stretches
1
cos 2 4
2
Λ 1 = Λ 2 =
(6.11)
B
and the left Cauchy-Green eigenspace
left CG eigenspace = E A
.
1
1
cos 2 4
2 , E B
cos 2 4
2
(6.12)
B
B
End of Lemma.
An idea of the appearance of the transverse conformal mapping to be considered here can be
obtained from Fig. 6.3 .
Fig. 6.3. Mapping the sphere to a tangential plane: transverse aspect, conformal mapping. Point-of-contact:
meta-North Pole at Λ 0 =90 0 =0
6-23 Equal Area Mapping (Transverse Lambert Projection)
For displaying eastern and western hemispheres in atlas maps, the equatorial aspect of the well-
known Lambert projection is widely used. In order to derive the mapping equations, we imme-
diately start from ( 5.35 ) of Lemma 5.3 again substituting spherical longitude Λ and spherical
latitude Φ by their counterparts meta-longitude A and meta-latitude B . We end up with the
parameterization in Lemma 6.2 . An illustration is given by Fig. 6.4 . It is easily observed from
Search WWH ::




Custom Search