Visualize Distortions in the Mercator Projection

Use a grid of disks to illustrate size and shape distortions in the Mercator projection

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Generate a number of disks at different latitudes longitudes and and form their union:

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disks=RegionUnion@@Flatten[Table[Disk[{long,lat},5],{long,-180,180,30},{lat,-80,80,20}]];

Superimpose the disks on a map of the world with an equirectangular projection:

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Show[GeoGraphics[GeoRange"World",GeoProjection"Equirectangular"],RegionPlot[disks,PlotStyleDirective[Gray,Opacity[0.3]],BoundaryStyleGray],AspectRatio1/2,ImageSizeLarge]

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Specify the displacement from the equirectangular projection to a Mercator projection:

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displacement={long,180/πLog[Abs[Sec[π/180lat]+Tan[π/180lat]]]}-{long,lat};

Show the deformed disks on a map with the Mercator projection:

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Show[GeoGraphics[GeoRange"World",GeoProjection"Mercator"],VectorDisplacementPlot[displacement,{long,lat}∈disks,PlotPoints50,VectorSizesFull,RegionBoundaryStyleNone,RegionFillingStyleNone],ImageSizeLarge]

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Related Symbols

VectorDisplacementPlot
GeoGraphics

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Contributed by: Wolfram Staff

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Visualize Distortions in the Mercator Projection

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