RandomGeoPosition

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`RandomGeoPosition`

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RandomGeoPosition[]

gives a pseudorandom geo position uniformly distributed on the surface of the Earth.

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RandomGeoPosition[{{latmin,lonmin},{latmax,lonmax}}]

gives a pseudorandom geo position uniformly distributed in the given geo bounding box.

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RandomGeoPosition[g]

gives a pseudorandom geo position uniformly distributed in the geo region g.

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RandomGeoPosition[g,n]

gives a list of n pseudorandom geo positions uniformly distributed in the geo region g.

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RandomGeoPosition[g,{n₁,n₂,…}]

gives an n₁× n₂×… pseudorandom geo position array.

Details and Options

The geo region g in RandomPosition[g,…] can be given as a geo primitive like GeoDisk[…] or GeoBoundsRegion[…] or as an extended geo Entity object.
Possible options for RandomGeoPosition include:
GeoModel Automatic model of the generated geo positions

GeoProjection None projection in which locations are uniform
RandomGeoPosition[] is equivalent to RandomGeoPosition["World"] and RandomGeoPosition[{{-90,-180},{90,180}}].
RandomGeoPosition gives a different sequence of pseudorandom geo positions whenever you run the Wolfram Language. You can start with a particular seed using SeedRandom.

Examples

open allclose all

Basic Examples (4)Summary of the most common use cases

Generate a pseudorandom geo position on the Earth:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-9lcxgo

Out[1]=1

Restrict the generated geo position to a given bounding box:

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-ilc2zo

Out[2]=2

Generate a pseudorandom point on Mars:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-y7izch

Out[1]=1

Generate a list of pseudorandom geo positions in the US:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-vm8dby

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-go99wa

Out[2]=2

Generate geo locations uniformly distributed in the Mercator projection:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-9nf221

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-br41rl

Out[2]=2

They are not uniformly distributed in an equal-area projection like Mollweide:

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-kqq208

Out[3]=3

Scope (7)Survey of the scope of standard use cases

Generate a random geo position on the Earth:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-uvahgw

Out[1]=1

Generate 100 random geo positions uniformly distributed on the Earth:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-r60ubv

Out[1]=1

Generate a random geo position in a given bounding box:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-w9qyi2

Out[1]=1

Generate random geo positions in France:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-g7q5t8

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-b4c7d7

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-qtwidq

Out[3]=3

Generate random geo positions in different geo variants of a country:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-nc5l3q

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-b0vk62

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-zkef0u

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0mldc8qyy4eq-gdvm0i

Out[4]=4

Generate random geo positions in the interior of a geo primitive:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-mprdgq

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-kd1gb8

Out[2]=2

Generate a random geo position array:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-3berp8

Out[1]=1

Options (2)Common values & functionality for each option

GeoModel (1)

By default, RandomGeoPosition generates locations on the Earth using the "ITRF00" datum:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-5pyam2

Out[1]=1

Use the GeoModel option to specify other models of the Earth or other celestial globes:

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-c9vcrt

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-rvogb9

Out[3]=3

GeoProjection (1)

Generate random geo positions uniformly distributed in the Albers projection:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-qso82m

Out[1]=1

Check that they are homogeneously distributed in that projection:

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-bn3s2f

Out[2]=2

They are not homogeneously distributed in other projections:

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-86nc83

Out[3]=3

Properties & Relations (5)Properties of the function, and connections to other functions

Use SeedRandom to get repeatable random values:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-1k87ey

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-ouigj4

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-gdzh1y

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0mldc8qyy4eq-zsfu8q

Out[6]=6

Use BlockRandom to block one use of RandomGeoPosition from affecting others:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-sfco5m

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-vptj4y

Out[2]=2

Take 200 geo locations uniformly distributed in a geo bounding box:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-i3erh7

Out[1]=1

The central feature and spatial median locations are close to the center of that bounding box:

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-52wi46

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-s82e3i

Out[3]=3

Take 2000 geo locations uniformly distributed on the surface of the Earth:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-rrgp0o

Select those geo locations in Africa:

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-ud7vro

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-pundyy

Out[3]=3

Compute the relative fraction and compare with the relative area of Africa with respect to the world:

In[4]:=4

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https://wolfram.com/xid/0mldc8qyy4eq-l4cq8s

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0mldc8qyy4eq-0pgqki

Out[5]=5

Geo locations uniformly distributed in an area look uniform in equal-area projections:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-xh7noy

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-kw60bw

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-isgjl8

Out[3]=3

They do not look uniform in other types of geo projections, like conformal projections:

In[4]:=4

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https://wolfram.com/xid/0mldc8qyy4eq-4fpsjt

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0mldc8qyy4eq-788j0q

Out[5]=5

Possible Issues (1)Common pitfalls and unexpected behavior

Take 1000 pseudorandom geo positions uniformly distributed over the world in a given projection:

In[1]:=1

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https://wolfram.com/xid/0mldc8qyy4eq-21ft4

Out[1]=1

The geo positions look uniform in a GeoGraphics map if the same geo range is chosen:

In[2]:=2

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https://wolfram.com/xid/0mldc8qyy4eq-heyop9

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0mldc8qyy4eq-v22ok9

Out[3]=3

They may not look uniform in other geo ranges, including the default choice in GeoGraphics:

In[4]:=4

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https://wolfram.com/xid/0mldc8qyy4eq-06gg3b

Out[4]=4

In[5]:=5

✖

https://wolfram.com/xid/0mldc8qyy4eq-53bwwe

Out[5]=5

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