Introduction

•  Importance of Coordinate Systems
•  Map Projections and Coordinate Systems

Importance of Coordinate Systems

Coordinate systems serve as the framework by which geographic data are referenced to the earth's surface. As such, coordinate systems are vital to mapping, surveying, and engineering. Coordinate systems are especially important in geographic and land information systems because they provide a common reference for all information.

This handbook describes coordinate systems used in the state of Wisconsin. The remainder of this section introduces the basics of map projections, along with a discussion of geographic and rectangular coordinate systems. The section on Regional Coordinate Systems describes and lists the parameters for the State Plan (SPC, Universal Transverse Mercator (UTM), and Wisconsin Transverse Mercator (WTM) coordinate systems. The last portion of this handbook discusses local coordinate systems and the Wisconsin County Coordinate System, and provides an alphabetical listing of Wisconsin County Coordinate System parameters.

Map Projections and Coordinate Systems
The most common and perhaps best known earth coordinate system, which is not rectangular, is the geographic. This system of latitude and longitude is spherical, and uses angular units of degrees, minutes, and seconds.

Unfortunately, measurements, computations, and the computer storage of geographic data are difficult to manage and manipulate using angular units. In contrast, rectangular coordinate systems allow easier storage and less intensive computations of positions, area, and distance.

Rectangular coordinate systems are mathematically based on the principles of map projections. A map projection transforms points from the ellipsoid of a datum (a mathematically defined model of the size and shape of the earth) to a plane. The projection process transforms the spherical surface of the earth to a flat (map) surface onto which a rectangular coordinate grid can be overlaid.

The three dimensional earth's surface cannot be transformed and portrayed on a flat map without introducing some distortion. Distortion caused by stretching or compressing the surface can affect shape, area, scale (distance), or direction, depending upon the projection used. Many map projections may have been devised to minimize particular distortions, but no single projection gives an exact representation of the surface of the earth.

The two most common projections used as reference surfaces for rectangular coordinate systems are the Lambert conformal conic (Figure1) and the transverse Mercator (Figure 2). Both of these projections have varying scale but retain the correct shape of the mapped surface. Scale variation is greatest in north-south directions for Lambert projections and the east-west directions for transverse Mercator projections (Figure 3).

It is important to note the difference between a map projection and a rectangular coordinate system. A map projection simply defines how the surface of the earth is transformed to a flat surface. A horizontal rectangular coordinate system is then superimposed on this projected surface and referenced to a horizontal datum.

A rectangular coordinate system is defined by four things: a map projection (referenced to a datum), an orientation, a point of origin, and a unit of measurement. Note that a map projection makes up only part of the definition of a rectangular coordinate system. For example, the State Plane Coordinate System (SPC) is a rectangular coordinate system that, by its definition, uses a specific set of transverse Mercator and Lambert conformal conic maps projections. SPC is a coordinate system, not a projection.

Coordinate systems are designed to meet the needs of a particular application or user. Thus, Wisconsin has several coordinate systems in common use. This handbook is a compilation of those coordinate systems in one reference publication

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