Geography Reference
In-Depth Information
Fig. 5.12. Spherical vertical section, the general normal perspective mapping of the sphere to the tangential
plane at the South Pole, projection plane at minimal distance. The geometrical details
Explicit spherical representation of the basic ratio:
r
R cos Φ =
R + D
R sin Φ + D
R + D
R sin Φ + D R cos Φ
r =
(5.47)
R + D
R cos Δ + D R sin Δ =: f ( Δ ) .
r =
Derivative of the function r = f ( Δ ) with respect to
colatitude (polar distance Δ ):
f ( Δ )= d f
d Δ =
R + D cos Δ
( R cos Δ + D ) 2 =
= R ( R + D )
(5.48)
R + D sin Φ
= R ( R + D )
( R sin Φ + D ) 2 .
 
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