Dufferin Peel by mikeholy

VIEWS: 3 PAGES: 30

									http://www.colorado.edu/geography/gcraft/
notes/mapproj/mapproj_f.html
                     Introduction
• Map projections are attempts to portray the surface of
  the earth or a portion of the earth on a flat surface. Some
  distortions of conformality, distance, direction, scale, and
  area always result from this process. Some projections
  minimize distortions in some of these properties at the
  expense of maximizing errors in others. Some projection
  are attempts to only moderately distort all of these
  properties.
Globes versus maps
Advantages of a globe
1. Shapes of things are true
2. Areas are true
3. Scale is constant
4. Directions are true
In a map, one or more of these is
lost
It is difficult to accurately “flatten”
a sphere
Example of map “problem”
 A
          A is true shape and size on a globe




                 A and B are same shape but
  B              different in area




      C                  A and C have same area but
                         are different in shape
Map projections: methods for
  “flattening” the sphere
                             Projections
•   Shape (Conformality)
     – When the scale of a map at any point on the map is the same in any direction,
       the projection is conformal. Meridians (lines of longitude) and parallels (lines of
       latitude) intersect at right angles. Shape is preserved locally on conformal maps.
•   Distance
     – A map is equidistant when it portrays distances from the center of the projection
       to any other place on the map.
•   Direction
     – A map preserves direction when azimuths (angles from a point on a line to
       another point) are portrayed correctly in all directions.
•   Scale
     – Scale is the relationship between a distance portrayed on a map and the same
       distance on the Earth.
•   Area
     – When a map portrays areas over the entire map so that all mapped areas have
       the same proportional relationship to the areas on the Earth that they represent,
       the map is an equal-area map.
Map projections fall into four
     general classes
      •   Cylindrical
      •   Conic
      •   Azimuthal
      •   Miscellaneous
          Cylindrical Projection
• Cylindrical projections
  result from projecting a
  spherical surface onto a
  cylinder.
• When the cylinder is
  tangent to the sphere
  contact is along a great
  circle (the circle formed
  on the surface of the
  Earth by a plane passing
  through the center of the
  Earth)..
Cylindrical projections




        Least distortion along line of tangency,
        where projection surface touches globe
            Conic Projection
• Conic projections
  result from projecting
  a spherical surface
  onto a cone.
• When the cone is
  tangent to the sphere
  contact is along a
  small circle.
Conic projections




      Least distortion along line of tangency,
      where projection surface touches globe
      along standard parallel.
         Azimuthal Projection
• Azimuthal projections
  result from projecting
  a spherical surface
  onto a plane.
• When the plane is
  tangent to the sphere
  contact is at a single
  point on the surface
  of the Earth.
              Planar projection


Least distortion at
point of tangency,         In a polar
where projection           projection, the
surface touches            point of tangency
globe                      is the pole.
    Miscellaneous Projections
• Miscellaneous projections include
  unprojected ones such as rectangular
  latitude and longitude grids and other
  examples of that do not fall into the
  cylindrical, conic, or azimuthal categories
          Cylindrical Projections
Mercator
• The Mercator
  projection has straight
  meridians and parallels
  that intersect at right
  angles. Scale is true at
  the equator or at two
  standard parallels
  equidistant from the
  equator. The projection
  is often used for marine
  navigation because all
  straight lines on the
  map are lines of
  constant azimuth.
            Peters Projection
The Peters
projection is a
cylindrical equal-
area projection
that de-
emphasizes
area
exaggerations in
high latitudes by
shifting the
standard
parallels to 45 or
47 degrees.
Comparing Mercators to Peters
         Projection
The Peters Map vs The Mercator
             Map
The Greenland Problem
Greenland: 0.8 million sq. miles




                   Africa: 11.6 million sq. miles
The North compared to the South
             The North is 18.9 million square miles.
             The South is 38.6 million square miles.
Europe compared to South
        America
            Europe is 3.8 million square miles.
         South America is 6.9 million square miles.
Africa compared to the Former
         Soviet Union




        The former Soviet Union is 8.7 million square miles.
                Africa is 11.6 million square miles.
Greenland Compared to China
             Greenland is 0.8 million square miles.
               China is 3.7 million square miles.
    Important characteristics of the Peters Map
•    The Peters Map is an equal area map.
•    This new map shows all areas -
     whether countries, continents or
     oceans - according to their actual size.
     Accurate comparisons become
     possible.
•    The Peters Map is an equal axis map.
•    All North-South lines run vertical on
     this map. Thus, geographic points can
     be seen in their precise directional
     relationship.
•    The Peters Map shows equal
     positions.
•    All East-West Lines run parallel. Thus
     the relationship of any point on the
     map to its distance from the equator or
     the angle of the sun can readily be
     determined. Fairness to All Peoples
•    In the complex and interdependent
     world in which nations now live, the
     people of the world deserve and need
     an accurate portrayal of the world.
•    The Peters Map is the map for our
     day.
                    Conclusion
• Why is Europe at the top half of maps and Africa at the
  bottom? Although we are accustomed to that convention,
  it is, in fact, a politically motivated, almost entirely
  subjective way of depicting a ball spinning in space.
  Maps do not portray reality, only interpretations of it. To
  begin with, they are two-dimensional projections of a
  three-dimensional, spherical Earth. Add to that the fact
  that every map is made for a purpose and its design
  tends to reflect that purpose. Finally, a map is often a
  psychological projection of the historical, political, and
  cultural values of the cartographer--or of the nation,
  person or organization for which the map was created.

								
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