Introduction to Cartography GEOG 2016 E

1. Introduction to CartographyGEOG 2016 E Lecture-3 Scale, Reference and Coordinate Systems

2. What is Scale • Ratio between distances on a map and the corresponding distances on the earth’s surface. • Example: • 1:100,000 means that 1 cm on the map corresponds to 100,000 cm (or 1 km) on earth. • 1:50,000 means that 1 cm on the map corresponds to 50,000 cm (or 0.5 km) on earth.

3. Scale and Features • Showing features on a map depends on the scale chosen. • The larger the scale of the map, the more details it shows. • A map with a scale of 1:10,000 will show a lot more details than a map with a scale of 1:100,000. • The scale of 1:10,000 is larger than the scale of 1:100,000.

4. Scale and Features • A map with a scale of 1:10,000 can be used to show individual houses or buildings. • However, a map with a scale of 1:100,000 can show those houses or buildings only as points. • Choosing the right scale is very important in cartography. • The choice depends on the area to be covered and the features to be shown.

5. Reference Systems • A reference system is needed to locate a point on earth’s surface. • Latitude and longitude comprise a reference system. • A coordinate system is needed for referencing.

6. Coordinate Systems • A coordinate system is needed for positioning and navigation. • For example, global positioning systems use coordinate system for precise location of points in space. • Different coordinate systems have been constructed and are used in cartography. • Cartesian, polar and spherical are three most commonly used coordinate systems.

7. Cartesian Plane Coordinate System • A plane or two-dimensional coordinate system can be defined with respect to a single plane.

8. Plane Polar Coordinate System • Points on a two-dimensional surface can also be represented by radius-angle pairs.

9. Polar - Cartesian Conversion • Plane polar coordinates can be converted into plane Cartesian coordinates.

10. Exercise • Convert the following Cartesian coordinates into their polar equivalents: • (1.245, -2.769) • (0.673, 1.999) • (-9.999, 4.531) • Convert the following polar coordinates into their Cartesian equivalents: • (1.296, 36.7) • (4.555, 0) • (6.782, 173.8)

11. Answers • Cartesian to polar: • (1.245, -2.769)  (3.04, -65.79) • (0.673, 1.999)  (2.109, 71.39) • (-9.999, 4.531)  (10.98, 155.6) • Polar to Cartesian: • (1.296, 36.7)  (1.039, 0.774) • (4.555, 0)  (4.555, 0) • (6.782, 173.8)  (-6.742, 0.732)

12. Three-Dimensional Cartesian System

13. Longitude, Latitude, Height • Most commonly used global coordinate system in cartography • Reference planes for latitude and longitude are defined by prime meridian and equator

14. Geodetic Latitude • Angle from the equatorial plane to vertical direction of a line normal to the reference ellipsoid.

15. Geodetic Longitude • Angle between the reference plane and a plane passing through the point. Both planes must be perpendicular to the equatorial plane.

16. Geodetic Height • Distance from the reference ellipsoid to the point in the direction normal to the ellipsoid.

17. Earth-Centered Earth-Fixed X,Y,Z • Generally called ECEF XYZ • Three-dimensional Cartesian coordinate system • Centered at the center of mass of reference ellipsoid

18. Universal Transverse Mercator (UTM) • Recall that Mercator is a cylindrical projection. • UTM coordinates define two-dimensional positions. • Dimensions are defined by zone numbers and zone characters. • Zone numbers designate 6-degree longitudinal strips. Extend from 80 degrees South latitude to 84 degrees North latitude • Zone characters designate 8-degree zones. Extend North and South from equator.

19. UTM

20. World Geographic Reference System Index (GEOREF) • Based on latitude and longitude • Earth’s sphere is divided into: • 12 bands of latitude • 24 zones of longitude • Used in aircraft navigation