Geography Reference
In-Depth Information
x = R cos Φ cos Λ = X,
(5.90)
y = R cos Φ sin Λ = Y,
subject to the left Cauchy-Green eigenspace
left CG eigenspace = E Λ , E Φ
.
1
sin Φ
(5.91)
End of Lemma.
Note that the northern orthographic projection covers all points of the northern hemisphere, while
the southern orthographic projection covers all points of the southern hemisphere. Accordingly,
the union of the two charts generated by a northern and a southern orthographic projection
constitutes a minimal atlas of the sphere. Additionally, let us here emphasize that the left maximal
angular shear of the gnomonic projection and the orthographic projection coincide.
Question: “What makes the orthographic projection (par-
allel projection, orthogonal projection) particularly useful
in Geographic Information Systems?” Answer: “It is the
property, which is called concircular , that parallel circles of
the sphere
2
2
2
S
R are mapped onto circles of T N
S
R ,T S S
R ,or
2
O
P
.Bymeansof r = R cos Φ ,theyare radius preserving -
an essential characteristic!”
S 2 R
T N S 2 R
Fig. 5.22. The orthographic projection of the sphere:
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