Geography Reference
In-Depth Information
I
Mercator Projection and Polycylindric Projection
Optimal Mercator projection and optimal polycylindric projection of conformal type. Case
study Indonesia. Universal Transverse Mercator Projection (UTM), Universal Polycylindric
Projection (UPC).
As a conformal mapping of the sphere
S
2
R
or as a conformal mapping of the ellipsoid-of-revolution
E
A
1
,A
2
, the Mercator projection maps the equator equidistantly while the transverse Merca-
tor projection maps the transverse meta-equator, the meridian-of-reference, with equidistance.
Accordingly, the Mercator projection is very well suited to geographic regions which extend East-
West along the equator. In contrast, the transverse Mercator projection is appropriate for those
regions which have a South-North extension. Like the optimal transverse Mercator projection,
which is also known as the
Universal Transverse Mercator Projection
(UTM) and which maps
the meridian-of-reference
Λ
0
with an optimal dilatation factor
ρ
=0
.
999 578 with respect to
the World Geodetic Reference System (WGS 84) and a strip [
Λ
0
−
Λ
W
,Λ
0
−
Λ
E
]
×
[
Φ
S
,Φ
N
]=
80
◦
,
+84
◦
], we construct an optimal dilatation factor
ρ
for the optimal Mercator
projection, summarized as the
Universal Mercator Projection
(UM), and an optimal dilatation
factor
ρ
0
for the optimal polycylindric projection for various strip widths which maps parallel
circles
Φ
0
equidistantly except for a dilatation factor
ρ
0
summarized as the
Universal Polycylin-
dric Projection
(UPC). It turns out that the optimal dilatation factors are independent of the
longitudinal extension of the strip and depend only on the latitude
Φ
0
of the parallel circle-of-
reference and the southern and northern extension, namely the latitudes
Φ
S
and
Φ
N
, of the strip.
For instance, for a strip [
Φ
S
,Φ
N
]=[
3
.
5
◦
,
+3
.
5
◦
]
[
−
×
[
−
1
.
5
◦
,
+1
.
5
◦
] along the equator
Φ
0
= 0, the optimal Mercator
projection with respect to WGS 84 is characterized by an optimal dilatation factor
ρ
=0
.
999 887
(strip width 3
◦
). For other strip widths and different choices of the parallel circle-of-reference
Φ
0
, precise optimal dilatation factors are given. Finally, the UPC for the geographic region of
Indonesia is presented as an example.
−
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