Cartography CS444 Why draw a map? The world is not flat! What do - - PowerPoint PPT Presentation

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Cartography CS444 Why draw a map? The world is not flat! What do - - PowerPoint PPT Presentation

Feb 24, 2023 508 likes •964 views

Cartography CS444 Why draw a map? The world is not flat! What do the internal angles of a triangle sum to? The world is not flat! If you walked your way out of Tucson, forever going east, would you be walking in a straight line? The

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Cartography

CS444

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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

  • f 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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Sizes?

http://thetruesize.com/

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Mercator Projection

http://thetruesize.com/

Sizes?

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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 projections

Albers: Conic, equal-area

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More complex projections

Composite Albers projection used by the USGS and Census Bureau

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More complex projections

Hammer

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More complex projections

Winkel- Tripel

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Many, many, many more…

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How do we compare projections?

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Tissot’s Indicatrix

https://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