Geography 222 The Power of Maps

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Geog 222 Lecture Outline: Map Projections
Update: 10/6/17

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



PROP) Globe





"Near Globes" and Globe Gores





Map projection process always introduces some kind of distortion


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

Example...



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


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



Cool Free Map Projection Software (Download): G.Projector



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




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



Several issues are of fundamental importance

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

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

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




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


Map projection involves a series of mathematical transformations:



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




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




PROP) globe and developable surfaces



Three basic manipulations of our flat surface


Developable Surfaces for map projections




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




We get different distortions from these different surfaces (projection families)




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

Preservation of areas, shapes, distances, and directions


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

Circles on the map: on the globe they are



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



Equal area projections are very important to thematic mapping


WWW) Peters Projection: Equal Area



WWW) Lambert Azimuthal projection


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



3b. Preserving Shape: Conformal Projections

Angular relationships are preserved from points




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

WWW) Mercator map projection is conformal





3c. Preserving Distance: Equidistance Projections

WWW) Azimuthal Equidistant Projection




Important: a map cannot preserve distances and preserve area



3d. Preserving Direction: Azimuthal Projections

WWW) Orthographic



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




3e. Compromise Projections

WWW) Robinson: National Geographic

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?


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


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



E-mail: jbkrygier@owu.edu

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