Geography Reference
In-Depth Information
A sample of the polar orthographic projection (parallel projection, orthogonal projection) of the
sphere is finally presented to you in Fig.
5.24
.
S
2
R
→
P
2
O
Fig. 5.23.
The orthographic projection of the sphere:
Box 5.16 (Orthographic projection).
Parameterized orthographic mapping (polar coordinates):
α
=
Λ, r
=
R
cos
Φ.
(5.92)
Parameterized orthographic mapping (Cartesian coordinates):
x
y
=
R
cos
Φ
cos
Λ
=
X
.
(5.93)
sin
Λ
Y
Left principal stretches:
Λ
1
=1
,
2
=sin
Φ.
(5.94)
Left eigenvectors:
C
1
Λ
1
=
E
Λ
(Easting)
,C
2
Λ
2
=
E
Φ
sin
Φ
(Northing)
.
(5.95)
Left maximal angular distortion:
Ω
l
=2 arcsin
=2 arcsin
Λ
1
−
Λ
2
Λ
1
+
Λ
2
1
sin
Φ
1+sin
Φ
−
.
(5.96)
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