GeoGraphics
GeoArea
GeoReposition
GeoProjection
GeoStyling
GeoRange
GeoPath
CountryData

Geography
Visualization & Graphics

Remove Map Projection Distortions

Reposition Russia over Africa and compare their geodesic areas to quantify how projection distortions affect perceived size

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Map projections such as Mercator can significantly distort the apparent size of regions, especially at higher latitudes. In this example, we reposition Russia over Africa to remove location-based visual bias, and then compute their geodesic surface areas to determine (i) what percentage of Africa's area equals Russia's area and (ii) how many Russia-sized areas fit into Africa.

Select the two regions:

In[1]:=

russia=

Russia

COUNTRY

;africa=

Africa

GEOGRAPHIC REGION

;

Reposition the first region over the second with

GeoReposition

In[2]:=

repositionedRussia=GeoReposition[russia["Polygon"],russiaafrica]

Out[2]=

PolygonGeoPosition

Number of points: 4449

Points per list: {4310,139}



Create a

GeoGraphics

showing the country in its original location and repositioned to the new region. The default map projection is Equirectangular:

In[3]:=

GeoGraphics[{GeoStyling[Blue],russia["Polygon"],repositionedRussia,Thickness[0.005],Arrow[GeoPath[{russia,africa}]]},GeoRangeAll]

Out[3]=

Notice how the distortion is even larger for different projections, such as Mercator:

In[4]:=

GeoGraphics[{GeoStyling[Blue],russia["Polygon"],repositionedRussia,Thickness[0.005],Arrow[GeoPath[{russia,africa}]]},GeoRangeAll,GeoProjection"Mercator"]

Out[4]=

Verify that repositioning preserves area (up to numerical tolerance):

In[5]:=

Abs[GeoArea[russia]-GeoArea[repositionedRussia]]/GeoArea[russia]

Out[5]=

0.00915894

Quantify the true size relationship by comparing geodesic areas. Report (i) what percent of Africa is covered by Russia's area and (ii) how many Russias fit into Africa by area:

In[6]:=

aRussia=GeoArea[russia];aAfrica=GeoArea[africa];Dataset[{"quantity""Russia as % of Africa (by area)","value"PercentForm[N[aRussia/aAfrica]],"quantity""How many Russias fit in Africa?","value"NumberForm[N[aAfrica/aRussia],{Infinity,2}]}]

Out[6]=

quantity	value
Russia as % of Africa (by area)	55.71%
How many Russias fit in Africa?	1.80

Related Symbols

GeoGraphics
GeoArea
GeoReposition
GeoProjection
GeoStyling
GeoRange
GeoPath
CountryData

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Contributed by: Wolfram Staff

Wolfram Language Example Repository

Remove Map Projection Distortions

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