Lecture 5 - Two Coordinate Systems
Last lecture covered map projection, the mathematical process to translate Earth's curved
surface to two-dimensional maps. There are a handful of projections in common use, and we
categorize them into two primary families:
●
Projections by shape of surface:
cylindrical
,
conical
or
planar
●
Projections by type of geometric distortions:
conformal
,
equivalent
,
equidistant
or
compromise
●
Projections allow us to transfer the Earth’s curved surface onto a flat surface. However,
geometric distortions
always occur
in the process of map projection. Depending on the
purpose of the map, some distortions are acceptable while others are not.
In this lecture you will become familiar with projected coordinate systems. We will cover
two projection systems that are commonly used in GIScience: the
Universal Transverse
Mercator (UTM) Coordinate System
and the
State Plane Coordinate (SPC) System
.
Table of Contents
●
1. Cartesian Coordinate System
●
2. Universal Transverse Mercator (UTM) Coordinate
System
○
2.1 UTM Basics
○
2.2 UTM Zone
○
2.3 UTM Eastings and Northings
■
2.3.1 Easting
■
2.3.2 Northing
○
2.4 UTM coordinate formatting
○
2.5 UTM limitations
●
3. State Plane Coordinate (SPC)
○
3.1 SPC Basics
○
3.2 SPC Origin
●
4. Coordinate Determination On Maps
●
Lecture Wrap-up
1. Cartesian Coordinate System
First, here's a general refresher on coordinate systems. Before being projected, locations on
Earth's surface are recorded in
Geographic Coordinates
of latitude and longitude and
expressed in degrees (Figure 1).

Figure 1. Geographic coodinate system to Cartesian coordinate system
Once map data are projected onto a two-dimensional surface (a plane), features must be
referenced by a planar coordinate system instead of a geographic coordinate system. The
geographic coordinate system (latitude-longitude), which is based on angles measured on a
sphere, is not valid for measurements on a plane. Because degrees of latitude and longitude
don't have a standard length, you can’t measure distances or areas accurately or display the
data easily on a flat map or computer screen.
Therefore, a
Cartesian coordinate system
is used. Cartesian coordinate system is defined by a
pair of orthogonal (x, y) axes drawn through an origin (Figure 1), where the origin (0, 0) is at
the lower left of the planar section. Geographic calculations and analysis are done in
Cartesian orPlanar coordinates (x, y).
Compared to the geographic coordinate system, the biggest
advantage
of the Cartesian
coordinate system is how it simplifies locating and measuring. Grid coordinate systems based
on the Cartesian coordinate system are especially handy for map analysis procedures such as
finding the distance or direction between locations or determining the area of a feature.