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Map Projections

Map projections are an important aspect of all maps, as all maps require the transformation of the spherical earth to a flat surface

Flatten out Orange Peel, Springbok, and Toad

PROP) Globe

• on a globe: distance, direction, shape, and areas are not distorted

• Google Earth and other virtual globes

• problems with globes

"Near Globes" and Globe Gores

Map projection process always introduces some kind of distortion

• distortion of area, shape, angles, etc.

• a few have tears and rips in them, but most stretch geography to fill these gaps

• more 'white lies'!

The Power of Maps: maps shape the way we see the world: map projections do this!

Example...

Children's Mental Maps of World: Looks like the Mercator Projection, which greatly exaggerates areas in the North.

From: T. Saarinen. "The Eurocentric Nature of Mental Maps of the World." Research in Geographic Education 1:2, 1999.





Kids Mental Maps of World







Mercator Map Projection







Peters Map Projection

Mercator map projection as good example of how we have become naturalized (used to) a view of the world that is very distorted and abstract from reality

• it looks normal to us

• but it has greatly modified, stretched, and distorted the earth

Tissot's Indidicatrix: perfect circles of equal size on the globe; reveal patterns of distortion on projected maps.

Mercator Projection: Distortion of areas but not shapes...

Equal Area Rectangular Projection (close to Peters): Distortion of shapes but not areas...

Dynamic Map Projections (Mike Rostock) & with distortion circles added (Ningchuan Xiao)

There are an infinite number of ways to flatten out (project) the earth and thousands of named map projections

DEMO) Map Projections in ArcGIS

Further understanding of how map projections transform our earth: Map Projections of other 3D Objects

Three Dimensional Full Body Scanner







Isis and Venus Scanned in 3 Dimensions

Scan a human body in 3D in a Full Body Scanner and Flatten using Map Projections:

• Lilla Locurto and Bill Outcault

  
  

  

  Mercator Projection of Body

  
  
  

  

  Robinson Projection of Body

  
  
  

  

  Amulet Projection of Body

  
  
  

  WWW) Locurto/Outcault

Several issues are of fundamental importance

1. What are the basic characteristics of the map projection process?

• how does map projection work?

2. What kind of flat surface to we project the spherical earth on to?

• flat paper, a cone, and a cylinder

3. How do map projections not distort aspects of our 3D Earth?

• some basic categories of what map projetions preserve.

• How does map projection work?
  

Map projection involves a series of mathematical transformations:

• Earth: geoid
  • transformed mathematically to a simpler shape

  
  

• Called a reference ellipsoid:
  • geodesy

  • further transformed (mathematically) into an actual sphere or spheroid

  
  

• Called nominal, reference, or generating globe
  • further transformed (mathematically) into a flat (plane) surface

  • this is where much of the distortion gets added to the map

This is Map Projection: transformation of the spherical surface into a plane surface

Three Overlapping Map Projections (Source)


all meridians and parallels are transformed in this process: the graticule
all human and physical earth features (coasts, rivers, lakes, boundaries, etc.) are also transformed in this process

2. What kind of flat surface to we project the spherical earth on to?

called "developable surfaces"

PROP) globe and developable surfaces

imagine a light source at the center of the globe
imagine the lines (continents, boundaries) as they are projected onto the paper

Three basic manipulations of our flat surface

• results in different look and distortions

Developable Surfaces for map projections

• also called projection families

• Projection onto a flat surface: a "plane"
  official name: azimuthal projection families

  
  

  Azimuthal Map Projections (Source)

  
  
  

  Projection onto a cylindrical flattenable surface

  • official name: cylindrical projection families
    
    
    Cylindrical Map Projections (Source)

  
  
  

  Projection onto a conical flattenable surface

  • official name: conic projection families
    
    
    Conic Map Projections (Source)

Adjust where the plane, cylinder, or cone touches the globe: Projection Case

• Tangent: touch the globe along one line (or at one point)

• pattern of less and more distortion: where?

  
  

  

• Map users and makers should select a map projection with the least distortion given the phenomena being mapped

• Voyager Map Example: which is best map projection?

• US Census Data Example: which is best map projection?

3. How do map projections not distort aspects of our 3D Earth?

Preservation of areas, shapes, distances, and directions

World projected into apple shape

Again: Tissot's Indicatrix: common way to visualize map projection distortion

Circles on the map: on the globe they are

• all equal in area (size)
  
• all equal in shape (a circle)
  
• when projected: see the distortions on the projection

Review five major categories of map projections based on the characteristics they preserve from the spherical earth

3a. Preserving Area: Equal Area or Equivalent Projections

• Area relationships are preserved
  ArcGIS) GeoCart: Mollweide

  Area representing square mile on map is a square mile everywhere on map

Equal area projections are very important to thematic mapping

• why

• equal area: a good general default for all thematic maps, small or large scale

• best for world map of data in areas: vegetation cover, bedrock types, etc.

WWW) Peters Projection: Equal Area

• when to use Peters

WWW) Lambert Azimuthal projection

if mapping out any data in geographic areas: use equal area projection
if focused on continent, such as US: use Lambert Azimuthal or Albers Equal Area
usually 'zoom' in on region or continent

Important: You give up shape (conformality) to preserve area (equivalence)

• cannot have both!

3b. Preserving Shape: Conformal Projections

Angular relationships are preserved from points

• and shape is preserved for small areas around a given point
  

  
  

  ex) Four Corners boundary of AZ, NM, CO and UT

  on the globe, these are 90 degree angles

  on a conformal projection, these are 90 degree angles

  alas, areas will be distorted

Important: can never preserve areas (equivalence) and shape (conformality) at the same time

WWW) Mercator map projection is conformal

Mercator Map Projection


Mercator: useful for navigation: straight lines on the map are lines of constant compass bearing (north, south, east, west) in the real world

3c. Preserving Distance: Equidistance Projections

WWW) Azimuthal Equidistant Projection

centered on one point (Ohio, in this case)
distance from that point to all other points is correct
useful for plotting the distance for direct air routes from the point

Important: a map cannot preserve distances and preserve area

3d. Preserving Direction: Azimuthal Projections

WWW) Orthographic

this example looks like a little globe: orthographic
such a projection is usually centered on one point (Pacific Ocean, in this case)
from that point, direction can be correct to all other points
useful for plotting the direction of some phenomena from a point
mostly used as inset/locator map

Important: direction can be preserved on equal area (equivalent), conformal (shape preserving), and equidistant projections

3e. Compromise Projections

WWW) Robinson: National Geographic

Courtesy of Hayden "Crash" Knisley

A compromise which attempts to preserve enough of area, shape, distance, and direction so that the earth looks right - but actually preserves none of them.

Summary: Map Projections

1. What are the basic characteristics of the map projection process?

• how does map projection work?
  
• from the lumpy earth to a sphere to a flat surface

2. What kind of flat surface to we project the spherical earth on to?

• flat surface, a cone, and a cylinder: projection families
  
• distinctive looks for each

3. What are the basic kinds of map projection distortions?

• some basic categories

• preserving area: equivalent projections

• preserving shape: conformal projections
  
• cannot preserve both area and shape

• preserving distance: equidistant projections
  
• cannot preserve both area and distance

• preserving direction: azimuthal projections
  
• can preserve direction and area OR shape OR distance

• compromise: don't preserve area, shape, distance, or direction
  
• but minimize distortion of all of these
  
• good default for world maps

E-mail: jbkrygier@owu.edu

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