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152 Cha pte r F i v e

projection. If conformally projected, an area has an identical shape on
the projected map to its 3D shape on the Earth’s surface. Conformal
projection is accomplishable by exact transformation of angles around
points. Equivalence, equidistance, and true direction are less impor-
tant than conformality in thematic mapping from satellite imagery.
They are not covered here.
There are many ground coordinate systems in existence. Some
systems are suitable for one part of the globe while others are designed
for the entire Earth’s surface. Two coordinate systems, UTM and
New Zealand Map Grid (NZGM), are introduced in this section.

5.2.1 UTM Projection
The Universal Transverse Mercator (UTM) projection is a common
cylindrical projection with meridians as lines of tangency, and parallels
as lines of secancy. After the projection cylinder is rotated 90° from the
vertical axis, the Earth’s surface is placed in such a way that the cylin-
der intersects with it at the desired central meridian. All parallels are
projected to the cylindrical surface mathematically. Graticular angles
of 90° are obtained after the cylinder is “cut.” Lines of tangency run
north and south, along which there is no scale distortion. Lines of
secancy represent scale variation, even though it is possible to preserve
the scale along one or two parallels. In order to minimize the amount
of distortion, the Earth’s surface is divided into dozens of small zones.
Each zone is projected individually but identically, with the central
meridian varying from zone to zone. The smaller a zone is, the smaller
the error in approximating its surface as a flat one.
The UTM coordinate system is an international plane system
commonly adopted for medium- and large-scale maps. It ranges from
84°N to 80°S in latitude, outside which there is a significant geometric
distortion. Such a large geographic area is divided into 60 nonover-
lapping quadrangles in order to minimize distortion. These zones are
numbered 1 to 60 eastward, beginning at 180°W (Fig. 5.6). Each zone
covers 6° of longitude. Within each zone, the central meridian is used
as the line of tangency. It extends 3° eastward and 3° westward. Each
zone is divided into horizontal bands spanning 8° of latitude. These
bands are lettered, south to north, beginning at 80°S with the letter C
and ending at 84°N with the letter X. The letters I and O are skipped
to avoid confusion with the numbers one and zero. In total, there are
21 zones in the north-south direction. With the exception of band X
that covers 12° of latitude, all bands cover a latitude of 8°. Each UTM
band is projected independently using formulas for a transverse ver-
sion of the Mercator projection.
This projection is conformal and displays true direction along
straight lines. In order to reduce the distortion within each zone, scale
along the central meridian is reduced to 0.9996. Thus, two parallel
lines approximately 180 km away from the central meridian do not
2
have any distortion. Each zone is divided into 100,000 m , within