Geography Reference
In-Depth Information
metric units should be kept in metric units. If a transformation is made
between metric and standard units, be sure that all geographic information
was converted using the same constants. The transformations can also alter
geographic representations and cartographic representations, leading to
geographic information that is not only inaccurate but also incorrect. A com-
mon example is scaling small-scale maps to match large-scale maps of the
same area. Because the small-scale maps lack accuracy in comparison to a
large scale map, differences between the two maps can be the results of
changes made during the generalization process—for example, when a road
is displaced to fit the railroad track symbol in next to a bend in a river.
A Sample Scale Transformation
The simplest type of sale transformation is an affine transformation. Even
an affine transformation makes it possible to scale, rotate, skew, and trans-
late geographic information coordinates.
Affine transformations use two equations for the
x
and
y
coordinates of
two-dimensional geographic information.
x
′
=A
x
+B
y
+C
y
′
=D
x
+E
y
+F
The values
x
and
y
stand for the coordinates of the input geographic
information;
x
stand for the coordinate values of the transformed
geographic information. A, B, C, D, E, and F are the six geometric parame-
ters for transforming the geographic information coordinate values. Some
GIS require the entry of these parameters; others will calculate them for you
based on common reference points in the input geographic information and
in the output geographic information. A linear transformation simply multi-
′
and
y
′
Affine scale transformation operations
(generalized).
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