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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
◦
,Φ
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
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