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CartographyCS444
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Why draw a map?
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The world is not flat!
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What do the internal angles of a triangle sum to?
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The world is not flat!
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If you walked your way out of Tucson, forever going east, would you be walking in a straight line?
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The world is not flat!
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https://bost.ocks.org/mike/map/
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Map Projections
https://www.jasondavies.com/maps/transition/
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What properties do we want projections to preserve?
• Shape
• Bearing
• Area
• Distance
Can we preserve all of these at once?
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Cylindrical Projections
http://www.progonos.com/furuti/MapProj/
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Equirectangular Projection
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Equirectangular Projection
• y = lat
• x = long
• Preserves lat and long
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Mercator Projection• Preserves local shape
• “conformal”: angles are preserved
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• Bearing: following a compass direction makes a straight line in the Mercator projection
https://www.jasondavies.com/maps/loxodrome/
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Mercator Projection
• y = log (tan (45 + lat/2))
• x = long
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Lambert’s Cylindrical Equal-Area Projection
• y = sin (lat)
• x = long
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Lambert’s Cylindrical Equal-Area Projection
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Azimuthal Projections(“Directional” Projections)
Directions from center point are preserved
http://bl.ocks.org/mbostock/
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More complex projectionsAlbers: Conic, equal-area
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More complex projectionsComposite Albers projection
used by the USGS and Census Bureau
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More complex projections
Hammer
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More complex projectionsWinkel-Tripel
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Many, many, many more…
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How do we compare projections?
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Tissot’s Indicatrixhttps://www.jasondavies.com/maps/tissot/
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Tissot’s Indicatrix
https://en.wikipedia.org/wiki/Tissot%27s_indicatrix
https://en.wikipedia.org/wiki/Mollweide_projection
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Cartograms
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Distort maps explicitly to use area as channel
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http://www.pnas.org/content/101/20/7499.full.pdf
Gastner & Newman: Diffusion-based method for producing density-equalizing maps
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Dorling Cartograms: Turn shapes into Circles
# Starbucks per state in the US
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Let’s implement Dorling Cartograms
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Limitations
• What can we encode with area?
• What do we want to preserve?
• What happens with extreme distortions?
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Limitations
http://www-personal.umich.edu/~mejn/election/2016/
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Limitations