Map Projection

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• What?
  • A systematic representation of all or part of a spherical surface on a plane surface
  • Mapping a three-dimensional surface into two dimensions => distortion (four basic properties: area, shape, distance, direction)
  • Mathematical formulas are used to transform a 3-D location to a 2-D location
• Why?
  • For metric measurement and calculation of georaphic properties (distance and area) (degrees are not associated with a standard length)
  • Source of data in different projections => one single integrated GIS database
  • Output maps still need to be in a map projection

Real-world Coordiate Systems

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• Geographic coordinates (Latitude-Longitude)
  • Angular measurement (lampda, phi) from the center of the earth (in units of DMS)
  • Graticule (meridians and parallels)
  • The origin of lat and lon (The equator and Greenwich, England - Prime Meridian)
• Cartesian coordiate systems (UTM, State Plane, etc.)
  • Planar measurement (x, y) from a chosen origin (in units of meters or feet)
  • Measures of length, angle, and area are constant across the x, y directions
  • Based on a particular map projection

Categories of map projections

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• By projection properties (for different applications and purposes)
  • Equal-area (equivalent) projections (preserve areas of features)
  • Conformal projections (preserve shape for small areas)
  • Equidistant projections (preserve correct distances to places from one or two points)
  • Azimuthal projections (preserve correct directions from one point - map center)
• By the type of flat surface used in the projection
  • Cylindrical: earth projected onto a cylinder or tube
  • Conic: earth projected onto a cone
  • Azimuthal: earth projected onto a plane

Datums

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• A reference for horizontal and vertical measurements, specified as a set of numerical values.
• Horizontal datums (geodetic control based on a spheroid)
  • NAD27 (Clarke 1866, Meades Ranch, KS)
  • NAD83 (geoid, the center of the earth)
• Vertical datums - Mean sea level (MSL) - NAVD88

Universal Transverse Mercator (UTM) and State Plane (SPCS)

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• UTM
  • Zone-based (6 each starting from 180th meridian, total 60 zones)
  • secant projection (180 km to each side the the central meridian)
  • northing and false easting in meters (origin at equator and central meridian)
• SPCS
  • Zone-based (specified by law, 125 zones for the entire U.S., multiple zones for some states)
  • Three projections used depending on the shape of the state: Transverse Mercator, Lambert Conic Conformal, and Obilique Mercator
  • northing and easting in feet (origin varies from zone to zone)