1. Map Projections
Goal: translate places on the Earth (3D) to Cartesian coordinates (2D)

2. Types of projections
Developable surface: (a) plane (b) cylinder (c) cone
Projections: (a) Azimuthal (b) Cylindrical (c) Conic

3. Projection Aspects
cylindrical
conical
planar

4. Views of projected surfaces

5. Tangent vs. Secant projections
Standard line
Standard line
Standard line

6. Standard Lines or Point
standard point/lines: on a projected map, the location(s) free of all distortion at the exact point or lines where the surface (cylinder, cone, plane) touches the globe.

7. Types of projections (based on distortion)
Conformal projections: preserve shape
Equal area: preserve area
Simple conic projections: preserve distance
Miscellaneous (Robinson projection)

8. Map projections distortion
The Mercator projection maintains shape. The Sinusoidal and Equal-Area Cylindrical projections both maintain area, but look quite different from each other. The Robinson projection does not enforce any specific properties but is widely used because it makes the earth’s surface and its features "look right.“ (ESRI Press)
                                                                                                                                                     

9. Preservation of Properties
Map projections always introduce some sort of distortion. How to deal with it?
Choose a map projection that preserves the globe properties appropriate for the application

10. Common Map Projections in GIS
Lambert conformal conic projection
Transverse Mercator projection

11. Lambert conformal conic projection
A cone intersecting the surface of the Earth along two arcs, typically parallels of latitude
(standard parallels)
Distortion:
1. Smallest near the standard parallels
2. Show similar distortion properties in an east-west direction  may be used for areas that extend in an east-west direction

12. Transverse Mercator Projection
Envelop the Earth in a horizontal cylinder, intersects the Earth ellipsoid along a single north-south tangent, or along two secant lines
Distortion
1. smaller nearer the line of intersection
2. show similar distortion properties in an north-south direction  may be used for areas that extend in an north-south direction

13. Coordinate Systems
Coordinates in GIS: absolute location with respect to an origin.
Geographic Coordinate System,
Universal Transverse Mercator (UTM) Coordinate System
State Plate Coordinate System

14. Cartesian Coordinates
Computationally, it is much simpler to work with Cartesian coordinates than with spherical coordinates
x,y coordinates
referred to as “eastings” & “northings”
defined units, e.g. meters, feet
Common Examples:
Universal Transverse Mercator:
applicable nearly world-wide
Many countries have Cartesian systems…
U.S. - State Plane
U.K. - Ordnance Survey National Grid

15. The Universal Transverse Mercator Coordinate System
Starting at longitude 180 degrees West
60 zones, each 6° longitude wide, easterly direction
zones run from 80° S to 84° N latitude
poles covered by Universal Polar System (UPS)

16. USA In The UTM Zones

17. UTM Zone Projection
Transverse Mercator Projection
applied to each 6o zone to
minimize distortion

18. UTM Coordinate Parameters
Unit:
meters
N and S zones:
separate coord
X-origin:
500,000 m west
of central meridian
Y-origin:
equator

19. Advantage of UTM Simple coordinate system
Easy for analysis – distance measure
Disadvantage
Coordinates are discontinuous across UTM zone boundaries, analysis are difficult across these boundaries.
Georgia – UTM 16 and 17