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Map Projections Problem: Project a sphere onto a flat surface. Scale

Maps - Resource A. Map Projections Problem: Project a sphere onto a flat surface. Scale Alternative projection methods Distortions Terminology of map projections. Map Projections - Resource A. Properties of the Globe Grid.

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Map Projections Problem: Project a sphere onto a flat surface. Scale

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  1. Maps - Resource A • Map Projections • Problem: Project a sphere onto a flat surface. • Scale • Alternative projection methods • Distortions • Terminology of map projections

  2. Map Projections - Resource A Properties of the Globe Grid • All meridians are of equal length; each is one-half the length of the equator. • All meridians converge at the poles and are true north-south lines. • All lines of latitude (parallels) are parallel to the equator and to each other. • Parallels decrease in length as one nears the poles. • Meridians and parallels intersect at right angles. • The scale on the surface of the globe is the same in every direction.

  3. Map Projections - Resource A • Geometrical (Perspective) Projections • Graticule transferred to geometric shape and then the shape is cut and flattened. • Developable surfaces

  4. Map Projections - Resource A • Projection Classes • Cylindrical • Conic • Planar (Azimuthal) • Oval or Elliptical

  5. Map Projections - Resource A • Orthographic • light source at infinity • Gnomonic • light source at center • Stereographic • light source at antipode.

  6. Map Projections - Resource A • Mathematical Projections • Emphasize and preserve elements of globe grid that perspective projections cannot. • Map Distortions of the Globe Grid Properties • Equal Area (equivalent) - Preserves proportionate size but distorts shape. • Shape (conformal) - Preserves true shape and directionality for small areas. • Only maps for small areas can preserve both conformality and equivalence.

  7. Map Projections - Resource A • Map Distortions of the Globe Grid Properties (cont.) • Distance (equidistant) - Correctly represent true great arc distances for one or two points on map. Distances between other points are distorted. • Direction (azimuthal) - Preserve directionality radiating from one central point. Gnomonic projection centered on Washington, DC. Great circle arcs are straight lines. Gnomonic

  8. Map Projections - Resource A Examples Equal area sinusoidal Azimuthal equidistant Mercator (conformal)

  9. Map Projections - Resource A Examples Azimuthal Equidistant (planar) Miller (cylindrical) Robinson Projection (oval) Albers equal area (conic)

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