Mapping and Projections

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Mapping and Projections

• Web resources
• Geographers Craft, Department of Geography,
  University of Colorado at Boulder - particularly
  Peter H. Danas part
• http//www.colorado.edu/geography/gcraft/contents.
  html
• Laurie Garo, Map Projections module, in Virtual
  Geography Department, U. of Texas at Austin
  (hosted at U. of Colorado)
• http//www.colorado.edu/geography/virtdept/content
  s.html

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Map Projections

• Basic problem
• Earth is round
• Paper is flat

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Conformal
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Equivalent or Equal Area
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Equidistant
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Equidistant CylindricalMap from Carlo Futuri
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Solving the Problem

• How do you represent a curved surface on a flat
  surface?
• Bonehead way - just plot latitude vs. longitude
  as cartesian rectangular coordinates
• Projection - fit a flat surface around (or
  through) a sphere, and trace the pertinent
  information on it

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Unprojected map
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Types of projections

• Three main families
• Cylindrical - wrap sheet of paper around globe in
  cylinder shape
• Also pseudocylindrical - like cylindrical but the
  sheet of paper bends inward at the poles
• Conic - form sheet of paper into a cone and
  insert globe
• Also polyconic - multiple cones
• Azimuthal - place flat sheet of paper next to
  globe project features out onto it

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Cylindrical Projection
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Cylindrical Projection

• Formed by wrapping a large, flat plane around the
  globe to form a cylinder.
• Transfer latitude, longitude, shapes onto
  cylinder, then unfolded into a flat plane.
• Typically used to represent the entire world
  often projected from center of globe with equator
  as tangent line
• Most types show parallels and meridians forming
  straight perpendicular lines.

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Cylindrical Projection
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Pseudocylindrical Projection

• Projection surface is not rectangular
• Instead, it curves inwards at the poles.
• Latitude lines are straight central meridian is
  straight, but other meridians are curved (concave
  toward the central meridian).
• Often used for world maps

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Pseudocylindrical Projection
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Pseudocylindrical Projection
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Pseudocylindrical Projection
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Conic Projection
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Conic Projection

• Points from the globe are transferred to a cone
  fit around the sphere.
• Usually, the pointy end of the cone is directly
  over the north or south pole, but you can do it
  anywhere.
• Can represent both hemispheres, but distortion
  increases the farther along the cone you go

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Conic Projection

• Often used to project areas that have a greater
  east-west extent than north-south, e.g., the
  United States.
• When projected from the center of the globe,
  conic projections typically show parallels
  forming arcs concave toward the North or South
  pole, and meridians are either straight or curved
  and radiate outwards from the direction of the
  point of the cone.

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Conic Projection
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Equidistant Conic Projection
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Albers Equal Area Conic
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Polyconic Projection

• Complex projection, used originally by USGS for
  quadrangle maps of U.S.
• Uses an infinite number of cones applied to an
  infinite number of tangents across a given
  hemisphere
• Reduces distortion, but harder to conceptualize
  and produce

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Polyconic Projection
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Polyconic Projection(centered at equator, 90ºW)
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Azimuthal (Planar) Projection
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Azimuthal or Planar Projection

• Globe grid is projected onto a flat plane
• Plane is normally placed above the north or south
  pole, so normally only one hemisphere, or a
  portion of it, is represented
• When projected from the center of the globe, a
  typical polar azimuthal projection shows circular
  latitude lines with radiating longitude lines

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Azimuthal Projection
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Azimuthal Projection
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Oblique Azimuthal Projection
Orthographic sort of means viewed from infinite
distance
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Types of projections

• Tangent
• Flat surface only touches globe along one
  circular line (or at one point for Azimuthal)
• Secant
• Flat surface passes through globe touches
  surface at two circular lines (or in one circle
  for Azimuthal)
• Some projection is inward rather than outward
• Reduces distortion of large areas

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Tangent Projection
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Secant Projection
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Secant Projection
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Robinson Projection
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Goodes Interrupted Homolosine Projection
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Tissot indicators

• Tissots idea - to see the effects of distortion,
  show what shape small circles on the surface of
  the globe take after projection
• This shows shape, scale, area, and other
  distortions

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Tissot Indicators Mercator (Conformal)
Image from http//quantdec.com/tissot
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Tissot Indicators Peters Equal Area
Image from http//quantdec.com/tissot
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Tissot Indicators Azimuthal Equidistant
Image from http//quantdec.com/tissot
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Tissot Indicators
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Silly Projections
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Web sites to visit

• http//www.guilford.edu/geology/Geo340.html