DISTORTION PROPERTIES IN MAP PROJECTIONS


Hi all, i read this somewhere and i found it good to share with you, especially my classmates. Hope you'll benefit.


DISTORTION PROPERTIES IN MAP PROJECTIONS
  • angles, areas, directions, shapes and distances become distorted when transformed from a curved surface to a plane
  • all these properties cannot be kept undistorted in a single projection
    • usually the distortion in one property will be kept to a minimum while other properties become very distorted
1. TISSOT'S INDICATRIX
  • is a convenient way of showing distortion
  • imagine a tiny circle drawn on the surface of the globe
  • on the distorted map the circle will become an ellipse, squashed or stretched by the projection
  • the size and shape of the Indicatrix will vary from one part of the map to another
  • we use the Indicatrix to display the distorting effects of projections
2. CONFORMAL (ORTHOMORPHIC)

  • a projection is conformal if the angles in the original features are preserved
    • over small areas the shapes of objects will be preserved
    • preservation of shape does not hold with large regions (i.e. Greenland in Mercator projection)
    • a line drawn with constant orientation (e.g. with respect to north) will be straight on a conformal projection, is termed a rhumb line or loxodrome
  • parallels and meridians cross each other at right angles (note: not all projections with this appearance are conformal)
  • the Tissot Indicatrix is a circle everywhere, but its size varies
  • conformal projections cannot have equal area properties, so some areas are enlarged
    • generally, areas near margins have a larger scale than areas near the center
3. EQUAL AREA (EQUIVALENT)


  • the representation of areas is preserved so that all regions on the projection will be represented in correct relative size
  • equal area maps cannot be conformal, so most earth angles are deformed and shapes are strongly distorted
  • the Indicatrix has the same area everywhere, but is always elliptical, never a circle (except at the standard parallel)
4. EQUIDISTANT


  • cannot make a single projection over which all distances are maintained
  • thus, equidistant projections maintain relative distances from one or two points only
    • i.e., in a conic projection all distances from the center are represented at the same scale


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