Geography Reference
In-Depth Information
14
“Ellipsoid-of-Revolution to Cylinder”: Polar Aspect
Mapping the ellipsoid-of-revolution to a cylinder: polar aspect. Its generalization for general
rotationally symmetric surfaces. Normal equidistant, normal conformal, and normal equiareal
mappings. Cylindric mappings (equidistant) for a rotationally symmetric figure. Torus map-
ping.
At the beginning of this chapter, let us briefly refer to Chap.
8
, where the data of the best fitting
“ellipsoid-of-revolution to Earth” are derived in form of a table. Here, we specialize on the
mapping
equations
and the
distortion measures
for mapping an ellipsoid-of-revolution
A
1
,A
2
to a cylinder,
equidistant on the equator. Section
14-1
concentrates on the structure of the mapping equations,
while Sect.
14-2
gives special cylindric mappings of the ellipsoid-of-revolution, equidistant on the
equator. At the end, we shortly review in Sect.
14-3
the general mapping equations of a rotationally
symmetric figure different from an ellipsoid-of-revolution, namely the torus.
E
14-1 General Mapping Equations
General mapping equations of an ellipsoid-of-revolution to a cylinder: the polar aspect. Appli-
cations. Deformation tensor. Principal stretches.
The first postulate fixes the image coordinate
y
by the assumption of an exclusive dependence on
the ellipsoidal latitude
Φ
. In contrast, the image coordinate
x
is only dependent on the longitude
Λ
, especially assuming that the equator is mapped equidistantly.
Postulate.
x
=A
1
Λ, y
=
f
(
Φ
)
.
(14.1)
End of Postulate.
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