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, conicalor planar ●Projections by type of geometric distortions: conformal, equivalent, equidistantor compromise●Projections allow us to transfer the Earth’s curved surface onto a flat surface. However, geometric distortions always occurin 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: theUniversal Transverse Mercator (UTM) Coordinate Systemand the State Plane Coordinate (SPC) System. Table of Contents ●1. Cartesian Coordinate System●2. Universal Transverse Mercator (UTM) CoordinateSystem○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-up1. 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.