Geography Reference
In-Depth Information
development of WGS84—a worldwide, Earth-centered, latitude-longitude system—to correct or improve
or change the origin of those projected coordinate systems.
State plane coordinate systems are generally designed to have a scale error maximum of about 1 unit
in 10,000. Suppose you calculated the Cartesian distance (using the Pythagorean theorem) between
two points represented in a state plane coordinate system to be exactly 10,000 meters. Then, with a
perfect tape measure, pulled tightly across an idealized planet, you would be assured that the measured
result would differ by no more than 1 meter from the calculated one. The possible error with the UTM
coordinate system may be larger: 1 in 2500.
Coordinate Transformations
Coordinate transformation of a geographic data set is simply taking each coordinate pair of numbers
in that data set and changing it to another pair of numbers that indicates exactly the same spot on the
Earth's surface, but using a different system of assigning coordinates.
Let's make up a coordinate system for a garden delineated by lines between stakes. Suppose the origin
(0,0) is at the southwest corner. Now drive several stakes in the ground so that if you passed a string
around them it would outline a polygon. Suppose you use a surveyor's tape calibrated in survey feet to
measure the Cartesian coordinate for each stake. Stake 0 is at the origin (0.0). Stake 1 is 33 feet east and
0 feet north (i.e., 33,0). Stake 2 is at (33,10), and so on. See Figure 1-8.
Suppose the garden grows and then becomes overgrown. Next year someone locates the origin and
wants to find the original stakes. He also has a surveyors tape, but it is calibrated in meters instead of
feet. He asks you to provide the data on where the stakes are in meters. In this case, the transformation
of coordinate systems is easy: You simply multiply each number by a conversion factor (the number of
meters per survey foot, which is 0.3048). So Stake 1's coordinates are 10.06, 0). Those of Stake 2 are
(10.06, 3.05), and so on. See Figure 1-9.
(10,25)
(38,25)
(0,18)
(38,18)
(33,10)
(0,0)
(33,0)
FIGURE 1-8 Locations of garden stakes
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