Random Geo Locations and Geo Projections

Many computations involve (or can be approximated by) the use of randomly generated locations on a given region of the Earth. A set of geo locations that is uniform in a given geo projection may not be uniform in a map with a different geo projection. This example shows the relevance of appropriately choosing the geo projection.

Generate 1000 random geo positions uniform in area:

In[1]:=

ps=RandomGeoPosition["World",1000]

Out[1]=

GeoPosition

Number of points: 1000

Lat bounds: {-87.4,87.8}

Lon bounds: {-180.,180.}



They will look uniform in equal-area projections:

In[2]:=

Multicolumn[Labeled[GeoGraphics[Point[ps],GeoProjection#],#]&/@{"LambertAzimuthal","Hatano","EckertII","Balthasart","Bottomley","Shield","Werner","Mollweide","TissotConicEqualArea"},3]

Out[2]=

LambertAzimuthal

Balthasart

Werner

Hatano

Bottomley

Mollweide

EckertII

Shield

TissotConicEqualArea

The same locations will not look uniform in non-equal-area projections:

In[3]:=

Multicolumn[Labeled[GeoGraphics[Point[ps],GeoProjection#],#]&/@{"Mercator","Armadillo","Lagrange","AmericanPolyconic","ArdenClose","GinzburgI","TransverseMercator","LambertConicConformal","Orthographic"},3]

Out[3]=