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Stephen Wolfram
An Elementary Introduction to the Wolfram Language
Second Edition (2017)
18Geocomputation
The Wolfram Language has extensive built-in knowledge of geography. For example, it knows where New York City is, and it can compute how far it is from there to Los Angeles.
Compute the distance between the centers of New York and Los Angeles:
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You can also plot locations on a map, using GeoListPlot.
Plot New York and Los Angeles on a map:
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Plot countries on a map:
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You can do things at a much smaller scale too.
Plot two famous locations in Paris:
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GeoListPlot is the analog for geography of ListPlot. GeoGraphics is the analog of Graphics.
Generate a map of New York City:
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GeoPath represents a path on the surface of the Earth.
Show the shortest path from New York to Tokyo:
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Styling works just like in other graphics:
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GeoDisk is the analog of Disk; you specify its center and its radius.
Show a 1-mile-radius disk around the Eiffel Tower:
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Generate a table of maps, with disks whose sizes go up as powers of 10:
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GeoPosition gives a position on the Earth. The numbers it contains are longitude and latitude—the standard coordinates on the surface of the Earth.
Find the geo position of the Eiffel Tower:
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Draw a 4000-mile-radius disk around 0 latitude, 0 longitude:
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Notice that the disk isn’t quite circular. That’s because we have to use a projection to draw the surface of the Earth on a flat map. It’s one of the many subtleties in doing geocomputation.
GeoNearest finds what’s nearest to a given place on the Earth. You tell it what type of thing to look for, and how many you want it to find.
Find the nearest 5 countries to 0 longitude, 0 latitude:
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Find the nearest cities instead:
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It’s often nice to know your own geo position. So long as your computer, phone, etc. knows, Here will give you that.
Find where your computer (or phone, etc.) thinks it is:
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You can do computations with Here.
Compute how far it is to the Eiffel Tower:
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Find the nearest 5 volcanoes to my position:
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Plot volcanoes on a map:
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Vocabulary
GeoDistance[entity1,entity2] geo distance between entities
GeoListPlot[{entity1,entity2, ...}] plot a list of entities on a map
GeoGraphics[...] map constructed from primitives
GeoPath[{entity1,entity2}] path between entities
GeoDisk[entity,r] disk with radius r around an entity
Here where your computer, phone, etc. thinks it is
GeoPosition[entity] geo position of an entity
GeoNearest["type",location,n] nearest n objects of a certain type to a location
18.1Find the distance from New York to London. »
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18.2Divide the distance from New York to London by the distance from New York to San Francisco. »
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18.3Find the distance from Sydney to Moscow in kilometers. »
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18.4Generate a map of the United States. »
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18.5Plot on a map Brazil, Russia, India and China. »
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18.6Plot on a map the path from New York City to Beijing. »
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18.7Plot a disk centered on the Great Pyramid, with radius 10 miles. »
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18.8Plot a disk centered on New York with a radius large enough to just reach San Francisco. »
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18.9Find the nearest 5 countries to the North Pole (GeoPosition["NorthPole"]). »
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18.10Find the flags of the 3 countries nearest to latitude 45°, longitude 0°. »
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18.11Plot the 25 volcanoes closest to Rome. »
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18.12Find the difference in latitude between New York and Los Angeles. »
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+18.1Plot on a map the countries in NATO. »
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+18.2Plot on a map a thick red line from Moscow to Beijing and a thick blue line from Washington, DC to London. »
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+18.3Find the distance from 0 latitude, 0 longitude to the Eiffel Tower. »
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+18.4Plot a disk styled red of radius 100 miles centered on Los Angeles. »
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+18.5Make a list of plots showing disks with radii 1, 2 and 3 miles around the Empire State Building. »
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+18.6Find the 5 countries nearest to New York City. »
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+18.7Find the nearest ocean to Chicago. »
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Q&A
Can I get different projections for maps?
Yes. Just use the GeoProjection option. There are more than 300 built-in projections to choose from. The default projection used in any particular case depends on the scale and location of the map.
How detailed are the maps in the Wolfram Language?
They go down to the level of individual streets. Most streets in the world are included.
How does the Wolfram Language find my geo position?
It uses the function FindGeoLocation. On a mobile device, this will normally ask for your GPS position. On a computer, it’ll normally try to deduce your location from your internet address—this won’t always work correctly. You can always explicitly set your geo location by assigning a value to $GeoLocation.
How can I specify the range of a map?
Use the option GeoRangedistance (e.g. GeoRange) or GeoRangeplace (e.g. GeoRange), as discussed in Section 20.
Can the Wolfram Language compute driving directions?
Yes. Use TravelDirections. GeoDistance gives the direct shortest path; TravelDistance gives the path following roads, etc. TravelTime gives estimated travel time.
Is the Wolfram Language restricted to maps of the Earth?
No. For example, the moon and Mars also work. Use the option GeoModel"Moon", etc.
Tech Notes
More to Explore
Guide to Maps & Cartography in the Wolfram Language »
Guide to Geographic Data & Entities in the Wolfram Language »
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