WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

GeoPolygon
Copy to clipboard.
✖
GeoPolygon

Copy to clipboard.
✖
GeoPolygon[{loc1,…,locn}]

is a GeoGraphics primitive that represents a filled polygon whose boundary is formed by geodesic segments between locations loci and loci+1.

Copy to clipboard.
✖
GeoPolygon[{loc1,…,locn}{{q1,…,qm},…}]

represents a geo polygon with holes {q1,…,qm}, ….

Copy to clipboard.
✖
GeoPolygon[{poly1,poly2,…}]

represents a collection of polygons polyi.

Copy to clipboard.
✖
GeoPolygon[{poly1,poly2,…},sideness]

specifies which of the two sides of each boundary polyi is in the interior of the geo polygon.

Copy to clipboard.
✖
GeoPolygon[polys,sideness,pathtype]

represents a geo polygon whose boundary is formed by geo paths of type pathtype.

Details

  • GeoPolygon[…] describes a 2D geographic region on the Earth or another geo model. It can be used in geo visualization functions like GeoGraphics or in geo computations like GeoArea.
  • In GeoPolygon[{loc1,…,locn}], the boundary {loc1,…,locn} divides the world in two complementary regions, and by default GeoPolygon[{loc1,…,locn}] and GeoPolygon[{loc1,…,locn},Automatic] refer to the smaller one. Possible ways to specify the region are:
  • GeoPolygon[locs{intloc}]intloc is an interior location to the geo polygon
    GeoPolygon[locs,extloc]extloc is an exterior location to the geo polygon
    GeoPolygon[locs,"SmallerArea"]the interior of the geo polygon is the smaller region
    GeoPolygon[locs,"LargerArea"]the interior of the geo polygon is the larger region
    GeoPolygon[locs,"LeftArea"]the interior is to the left as locs are traversed
    GeoPolygon[locs,"RightArea"]the interior is to the right as locs are traversed
  • The locations loci can be specified as latitude and longitude coordinates {lat,lon} in degrees, as GeoPosition[{lat,lon}] or as named entities Entity[…].
  • Entities will be interpreted as the position determined by their "Position" property.
  • GeoPolygon supports the geographic path types:
  • "Geodesic"geodesic path between points
    "Rhumb","RhumbLine","Loxodrome"path of constant bearing between points
    "GreatEllipse","GreatCircle"path on a plane through Earth's center

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Draw a geodesic rectangle on the surface of the Earth:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-t6zczz
Direct link to example
Out[1]=1

Draw the complementary region of a geodesic rectangle on the surface of the Earth:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-1kea9x
Direct link to example
Out[1]=1

Draw a geodesic rectangle with a hole:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-opukkx
Direct link to example
Out[1]=1

Scope  (9)Survey of the scope of standard use cases

Data Specification  (3)

Specify the vertices of a geo polygon as latitude-longitude pairs in degrees:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-qw5huy
Direct link to example
Out[1]=1

Give the vertices of a geo polygon as a GeoPosition object:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-xnd8p4
Direct link to example
Out[1]=1

Use a list of individual GeoPosition objects instead:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-cgvxlb
Direct link to example
Out[2]=2

Use a geo entity to specify a region:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-g3qkai
Direct link to example
Out[1]=1

Specify holes in a geographic region using other geo entities:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-050suf
Direct link to example
Out[2]=2

Sideness Specification  (4)

Specify one of the two sides of the equator by giving an interior point, for example, a pole:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-l7muu6
Direct link to example
Out[1]=1
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-d3b60p
Direct link to example
Out[2]=2

Specify the opposite pole for the same boundary locations:

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0en0c0eqy-osihnq
Direct link to example
Out[3]=3
Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0en0c0eqy-fxrnm3
Direct link to example
Out[4]=4

Specify geo polygon sideness by giving an exterior point:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-9gfftx
Direct link to example
Out[1]=1

Choose the opposite side of the world by indicating that {0, 0} is an exterior point:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-f6my8n
Direct link to example
Out[2]=2

Indicate whether the region of interest is the smaller or the larger of the two sides of a closed boundary:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-29idou
Direct link to example
Out[1]=1

Take the polygon of Portugal as returned by EntityValue:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-nr1z0h
Direct link to example
Out[1]=1

The polygon boundary is followed clockwise:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-bcovkn
Direct link to example
Out[2]=2

Therefore, the interior of Portugal falls on the right of the curve:

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0en0c0eqy-5zbbeo
Direct link to example
Out[3]=3
Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0en0c0eqy-xvjmvr
Direct link to example
Out[4]=4

Use "LeftArea" to select the left side of the boundary:

Copy to clipboard.
In[5]:=5
✖
https://wolfram.com/xid/0en0c0eqy-v4q9
Direct link to example
Out[5]=5
Copy to clipboard.
In[6]:=6
✖
https://wolfram.com/xid/0en0c0eqy-8m1la4
Direct link to example
Out[6]=6

Geo Path Types  (2)

By default, the edges of a GeoPolygon object are geodesic segments:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-o51lym
Direct link to example
Out[1]=1

Use loxodromes as edges for a different GeoPolygon object with the same vertices:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-gfiyh9
Direct link to example
Out[2]=2

Geodesics and great ellipses are similar but not identical on the ellipsoid:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-5sm8k3
Direct link to example
Out[1]=1

Zoom in around a location in northern Italy to see deviations of the order of a kilometer:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-mv3xw3
Direct link to example
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

The boundary of a GeoPolygon[locs] object is a closed GeoPath[locs] object:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-ddxqj3
Direct link to example
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-w3fhmj
Direct link to example
Out[2]=2

The same holds for other path types:

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0en0c0eqy-8a3t7x
Direct link to example
Out[3]=3

GeoPolygon[locs] uniquely defines the positions of all boundary points, both vertices and edges:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-5fo8y5
Direct link to example
Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-081s4a
Direct link to example
Out[2]=2

Polygon[GeoPosition[locs]] defines the position of the vertices, using straight lines between them:

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0en0c0eqy-saskax
Direct link to example
Out[3]=3

In other projections, the red GeoPolygon area stays constant, but not the blue area:

Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0en0c0eqy-o3y3w
Direct link to example
Out[4]=4

Possible Issues  (1)Common pitfalls and unexpected behavior

GeoPolygon boundary segments joining antipodal points may be ambiguous:

Copy to clipboard.
In[1]:=1
✖
https://wolfram.com/xid/0en0c0eqy-jmoqer
Direct link to example
Out[1]=1

That geo polygon was empty because the geodesic joining points and goes through the North Pole, as shown by a small change in the longitude of the first point:

Copy to clipboard.
In[2]:=2
✖
https://wolfram.com/xid/0en0c0eqy-4cbmrq
Direct link to example
Out[2]=2

To close the geo polygon through the equator, add an intermediate point on the equator:

Copy to clipboard.
In[3]:=3
✖
https://wolfram.com/xid/0en0c0eqy-2q47w8
Direct link to example
Out[3]=3

To close the geo polygon through the South Pole, add the South Pole as an intermediate point:

Copy to clipboard.
In[4]:=4
✖
https://wolfram.com/xid/0en0c0eqy-4oubs7
Direct link to example
Out[4]=4
Wolfram Research (2020), GeoPolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoPolygon.html.
Copy to clipboard.
✖
Wolfram Research (2020), GeoPolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoPolygon.html.

Text

Wolfram Research (2020), GeoPolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoPolygon.html.

Copy to clipboard.
✖
Wolfram Research (2020), GeoPolygon, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoPolygon.html.

CMS

Wolfram Language. 2020. "GeoPolygon." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoPolygon.html.

Copy to clipboard.
✖
Wolfram Language. 2020. "GeoPolygon." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoPolygon.html.

APA

Wolfram Language. (2020). GeoPolygon. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoPolygon.html

Copy to clipboard.
✖
Wolfram Language. (2020). GeoPolygon. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoPolygon.html

BibTeX

@misc{reference.wolfram_2025_geopolygon, author="Wolfram Research", title="{GeoPolygon}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GeoPolygon.html}", note=[Accessed: 16-April-2025 ]}

Copy to clipboard.
✖
@misc{reference.wolfram_2025_geopolygon, author="Wolfram Research", title="{GeoPolygon}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/GeoPolygon.html}", note=[Accessed: 16-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geopolygon, organization={Wolfram Research}, title={GeoPolygon}, year={2020}, url={https://reference.wolfram.com/language/ref/GeoPolygon.html}, note=[Accessed: 16-April-2025 ]}

Copy to clipboard.
✖
@online{reference.wolfram_2025_geopolygon, organization={Wolfram Research}, title={GeoPolygon}, year={2020}, url={https://reference.wolfram.com/language/ref/GeoPolygon.html}, note=[Accessed: 16-April-2025 ]}