Map Projections Goal: translate places on the Earth (3D) to
Cartesian coordinates (2D)
Types of projections
Developable surface: (a) plane (b) cylinder (c) cone
Projections: (a) Azimuthal (b) Cylindrical (c) Conic
Projection Aspects
cylindrical
conical
planar
Views of projected surfaces
Tangent vs. Secant projections
Standard line
Standard lineStandard line
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.
Standard Lines or Point
Types of projections (based on distortion) Conformal projections: preserve shape
Equal area: preserve area
Simple conic projections: preserve distance
Miscellaneous (Robinson projection)
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)
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
Common Map Projections in GIS Lambert conformal conic projection
Transverse Mercator projection
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
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
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
Cartesian Coordinates
Computationally, it is much simpler to work with Cartesian coordinates than with spherical coordinates
x,y coordinatesreferred to as “eastings” & “northings”defined units, e.g. meters, feet
Common Examples:Universal Transverse Mercator:
applicable nearly world-wideMany countries have Cartesian systems…
U.S. - State PlaneU.K. - Ordnance Survey National Grid
The Universal Transverse Mercator Coordinate System
Starting at longitude 180 degrees West60 zones, each 6° longitude wide, easterly directionzones run from 80° S to 84° N latitude poles covered by Universal Polar System (UPS)
USA In The UTM Zones
Transverse Mercator Projection applied to each 6o zone to minimize distortion
UTM Zone Projection
UTM Coordinate Parameters
Unit: meters
N and S zones: separate coord
X-origin: 500,000 m west of central meridian
Y-origin: equator
Advantage of UTM Simple coordinate system Easy for analysis – distance measure
DisadvantageCoordinates are discontinuous across UTM zone
boundaries, analysis are difficult across these boundaries.
Georgia – UTM 16 and 17
