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© Donald Boyes, Department of Geography and Planning, University of Toronto 1
Purpose of map projections
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© Donald Boyes, Department of Geography and Planning, University of Toronto 2
Selecting a coordinate system
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© Donald Boyes, Department of Geography and Planning, University of Toronto 3
Globe:
Three‐dimensional (3D)
Expensive, cumbersome, no detail, but no distortion
Map:
Two‐dimensional (2D)
Easier to measure distance, area, direction
Can show more detail
Easy to work with, portable, cheaper
Distortion.
Globe vs. Map
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© Donald Boyes, Department of Geography and Planning, University of Toronto 4
http://thetruesize.com
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© Donald Boyes, Department of Geography and Planning, University of Toronto 5
How projections work
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What is a map projection?
Transformation of 3D Earth to a 2D map
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© Donald Boyes, Department of Geography and Planning, University of Toronto 7
Goal: Flat map with scale of 1:100,000,000
1:100,000,000
Principal scale
Full‐sized Earth
First, imagine that the Earth
has been shrunk to the desired scale
Can use either
sphere or ellipsoid
Reference
Globe
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© Donald Boyes, Department of Geography and Planning, University of Toronto 8
Hypothetical
Still 3D
Principal scale =
6.378 cm
Reference globe
1:100,000,000
Reference globe radius
Earth’s radius
637813700 cm
or 1:100,000,000
= 0.00000001
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© Donald Boyes, Department of Geography and Planning, University of Toronto 9
Transfer all points from 3D globe to 2D map...
1:100,000,000 1:100,000,000
Reference Globe (3D) Flat Map (2D)
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© Donald Boyes, Department of Geography and Planning, University of Toronto 10
Distances are distorted
1:100,000,000 1:100,000,000
Reference Globe (3D) Flat Map (2D)
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© Donald Boyes, Department of Geography and Planning, University of Toronto 11
From curved surface to flat
To flatten globe, must stretch, tear, or distort...
reference
globe
paper
Map distance
(shrunk, or distorted)
Actual distance
(based on Melita and Kopp, 2004)
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© Donald Boyes, Department of Geography and Planning, University of Toronto 12
"Not only is it easy to lie with maps, it's
essential. To portray meaningful relationships
for a complex, three‐dimensional world on a flat
sheet of paper or video screen, a map must
distort reality"
Mark Monmonier, How to Lie with Maps, 1996
How to lie with maps...
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Associating points from 3D to 2D
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Associating points
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Equator
Draw a line from the equator to the pole...
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Equirectangular projection
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Graticule: indicates how projections work
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Variable scale bar
http://en.wikipedia.org/wiki/Mercator_projection
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1:500,000
Representative fraction
(absolute scale)
Bar scale
“one inch to one mile”
Verbal scale
0 50 100 200 300 400 Km
> 1:250,000
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© Donald Boyes, Department of Geography and Planning, University of Toronto 33
Projection case
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© Donald Boyes, Department of Geography and Planning, University of Toronto 36
Scale factor with two standard lines
Scale factor > 1
Scale factor = 1
Scale factor < 1