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GeoDisk

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GeoDisk[loc,r]

is a two-dimensional GeoGraphics primitive that represents a filled disk of radius r centered at the location loc on the surface of the Earth.

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GeoDisk[loc,r,{α1,α2}]

gives a sector of a disk from bearing α1 to bearing α2.

Details and Options

  • A geo disk with center loc and radius r is defined as the area covered by all geodesics of length r starting from loc. Specifying bearings α1 and α2 restricts the set of geodesics.
  • The location loc can be specified either as latitude and longitude coordinates {lat,lon} in degrees, GeoPosition[…], or as a named geographical Entity[…].
  • The radius r can be given as a Quantity length or as a number in meters.
  • Bearings α1 and α2 are measured clockwise from true north and can be given as Quantity angles, as numbers in degrees, as DMS strings, or as named compass points like "N" or "SouthWest".
  • By default, GeoDisk is drawn partially transparent to allow the background map to show through.
  • FaceForm, EdgeForm, and GeoStyling can be used to give directives specifying how the interiors and boundaries of geographic regions should be rendered. The opacity of the interior can only be modified using GeoStyling.
  • GeoDisk[loc] represents a geo disk centered at loc, with an automatic choice of radius.
  • GeoDisk[] is equivalent to GeoDisk[$GeoLocation].

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

A disk of 2000 kilometers around a geo location:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-ksy9cx
Out[1]=1

A sector of a disk centered at Paris:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-bqf6kt
Out[1]=1

Scope  (6)Survey of the scope of standard use cases

The center location of the geo disk can be specified in several ways:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-8fh7rr
Out[1]=1

The default location is the local geo position:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-5kh819
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-z9s0ni
Out[2]=2

The geo disk radius can be specified as a Quantity object, or directly in meters:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyujv-zgak94
Out[1]=1

Plot a disk with default size around Madrid:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-4l8yop
Out[1]=1

Bearings are given in degrees, clockwise with respect to true north:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyujv-56far4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-nhacni
Out[2]=2

Use different stylings for geo disks:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-e8suiu
Out[1]=1

Applications  (3)Sample problems that can be solved with this function

The Mercator projection is conformal because it preserves shapes, though not areas or distances:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-cw8u7m
Out[1]=1

Compare with the default equirectangular projection:

In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-v5vpa4
Out[2]=2

Plot sectors to find overlap:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-h2e9k4
Out[1]=1

Plot various distances from the epicenter of the 1992 Landers earthquake:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-us772q
Out[1]=1

Properties & Relations  (11)Properties of the function, and connections to other functions

A geo disk is the set of points whose distance to the center is at most its radius:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-1oa0pq
In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-mkuypz
Out[2]=2

The boundary of a geo disk is a geo circle:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-ydlvuh
In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-hlspt4
Out[2]=2

A GeoDisk object is described using coordinates and distances on the Earth, irrespective of the coordinates used in the final map. A Disk object is described using the coordinates of the final map:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyujv-bez1gv
Out[1]=1

It is possible to use a GeoPosition object to specify the center of the Disk object. Its radius, however, cannot be specified as a length on the surface of the Earth:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyujv-nsyr1b
Out[2]=2

As we get closer to the poles, geo disks look more distorted in the equirectangular projection:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-9lv2p0
Out[1]=1

A geo disk containing a pole spans all values of longitude:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-rf04q
In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-7w9hnp
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bdpsyujv-1ez9mj
Out[3]=3

Progressive distortion of concentric geo disks of increasing radius:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-vj2g64
Out[1]=1

Same disks (still concentric) in the Mercator projection:

In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-50gwsi
Out[2]=2

The complement of a geo disk is approximately another geo disk centered in the antipodal location:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-pf05w2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-c45tq2
Out[2]=2

A large geo disk covers most of the Earth, including both poles. Only a small area is left uncovered:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-34ukac
Out[1]=1

All three sides of a geo disk sector are generically curved in most projections. The radii spanning from the center are geodesics:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyujv-jubcxx
Out[1]=1

Even starting from bearings and , the sides are curved:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyujv-8lshic
Out[2]=2

A geo disk sector centered at a pole may be projected onto a rectangle:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyujv-nuy1vc
Out[1]=1

Bearing at the South Pole coincides with longitude. Bearing α at the North Pole is related to longitude by the relation , taking both angles in degrees:

In[2]:=2
✖
https://wolfram.com/xid/0bdpsyujv-7yfv6m
Out[2]=2

Large disks accumulating around the antipodal point, using a spherical model of the Earth:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-t438io
Out[1]=1

The default reference model is an ellipsoid:

In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-rx6dh5
Out[2]=2

Interactive Examples  (2)Examples with interactive outputs

Interactively place a geo disk of fixed radius and observe how its form changes as a function of latitude:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-o5e2h7
Out[1]=1

Explore the arguments of GeoDisk:

In[1]:=1
✖
https://wolfram.com/xid/0bdpsyujv-bhue5w
Out[1]=1

Neat Examples  (1)Surprising or curious use cases

Show that the cities in the US farthest from the US boundary are in Kansas. Take the US polygon:

In[1]:=1
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https://wolfram.com/xid/0bdpsyujv-b6vxcd

Compute the distances in miles between consecutive points and accumulate them:

In[2]:=2
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https://wolfram.com/xid/0bdpsyujv-3ep8ui

This is the total estimated length of the boundary, in miles:

In[3]:=3
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https://wolfram.com/xid/0bdpsyujv-mi6u4w
Out[3]=3

Construct a parametrization of the boundary:

In[4]:=4
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https://wolfram.com/xid/0bdpsyujv-09ehal
Out[4]=4

Draw 300 geo disks of 650 miles of radius along equidistant points of the boundary. There is a small space left uncovered—the region of the US farther than such distance from the boundary—and it is in Kansas:

In[5]:=5
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https://wolfram.com/xid/0bdpsyujv-h1bvzu
Out[5]=5
Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.
✖
Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.

Text

Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.

✖
Wolfram Research (2014), GeoDisk, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisk.html.

CMS

Wolfram Language. 2014. "GeoDisk." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoDisk.html.

✖
Wolfram Language. 2014. "GeoDisk." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoDisk.html.

APA

Wolfram Language. (2014). GeoDisk. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoDisk.html

✖
Wolfram Language. (2014). GeoDisk. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoDisk.html

BibTeX

@misc{reference.wolfram_2025_geodisk, author="Wolfram Research", title="{GeoDisk}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/GeoDisk.html}", note=[Accessed: 09-July-2025 ]}

✖
@misc{reference.wolfram_2025_geodisk, author="Wolfram Research", title="{GeoDisk}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/GeoDisk.html}", note=[Accessed: 09-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geodisk, organization={Wolfram Research}, title={GeoDisk}, year={2014}, url={https://reference.wolfram.com/language/ref/GeoDisk.html}, note=[Accessed: 09-July-2025 ]}

✖
@online{reference.wolfram_2025_geodisk, organization={Wolfram Research}, title={GeoDisk}, year={2014}, url={https://reference.wolfram.com/language/ref/GeoDisk.html}, note=[Accessed: 09-July-2025 ]}