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GeoAntipode
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GeoAntipode

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gives the antipodal position of location loc.

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gives the antipodal primitive of the geo primitive g.

Details

  • The location loc in GeoAntipode[loc] can be a GeoPosition, GeoGridPosition or other position object. It can also be a geo Entity object.
  • For a geo primitive g, GeoAntipode[g] returns the antipodal primitive, with locations in g being replaced by their antipodal locations.

Examples

open allclose all

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

Find out the antipode of your location:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-0u6j9q
Out[1]=1

Find out the antipode of the capital of Spain:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-lrplyq
Out[1]=1

That location is in New Zealand:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-ps1r4p
Out[2]=2

The antipode of a geo disk centered at loc is another geo disk centered at the antipode of loc:

In[1]:=1
✖
https://wolfram.com/xid/0bniola6y2fy2-m1ueho
Out[1]=1

Show the antipodal polygon of Brazil:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-vtwr1a
Out[1]=1

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

Find the antipode of a GeoPosition object:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-ym4aej
Out[1]=1

Elevation is left unchanged:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-wdimc2
Out[2]=2

Find the antipode of a GeoPositionXYZ object:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-wxsi4h
Out[1]=1

All three coordinates change sign:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-rkcsxn
Out[2]=2

Find the antipode of a GeoPositionENU object:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-iib4m4
Out[1]=1

The East and Up components are preserved, but the North component changes sign:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-nibwt5
Out[2]=2

Find the antipode of a GeoGridPosition object:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-ku6aai
Out[1]=1

For general projections, the relation is highly nonlinear:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-7kdcm1
Out[2]=2

The antipodal position of a geo Entity location is returned as a GeoPosition object:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-y2gri7
Out[1]=1

Find the antipodes of a GeoPosition array:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-n5edma
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-9kkltf
Out[2]=2

Find out the antipode of a geo path:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-xv7a7t
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Take the polygon of South America:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-k96hh2
Out[1]=1

Compute the antipodal polygon:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-dirq5c
Out[2]=2

Draw a map of the antipodal polygon of South America:

In[3]:=3
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https://wolfram.com/xid/0bniola6y2fy2-tcihu6
Out[3]=3

Draw the antipode of Antarctica around the North Pole:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-rt8u64
In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-w9goit
Out[2]=2

Properties & Relations  (4)Properties of the function, and connections to other functions

The antipode of the antipode of a location is the original location:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-lq0ges
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-7bm6ts
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bniola6y2fy2-c9uh3c
Out[3]=3

If location p is east of location q, then the antipode of p is also east of the antipode of q:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-b95gnh
In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-1ly0qt
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bniola6y2fy2-24e4dv
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0bniola6y2fy2-ty93ny
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0bniola6y2fy2-px0aix
Out[5]=5

However, if p is north of q, then the antipode of p is south of the antipode of q:

In[6]:=6
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https://wolfram.com/xid/0bniola6y2fy2-oq1aig
Out[6]=6
In[7]:=7
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https://wolfram.com/xid/0bniola6y2fy2-43vtrz
Out[7]=7

The day and night hemispheres for a given date are antipodal:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-c2dy3
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-hc5n8g
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bniola6y2fy2-oz5o0f
Out[3]=3

The day-night terminator is its own antipode:

In[4]:=4
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https://wolfram.com/xid/0bniola6y2fy2-3koqx4
Out[4]=4

The geo hemispheres of two antipodal locations are complementary:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-ng06bs
Out[1]=1

They are related by this simple identity:

In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-e3b0ol
Out[2]=2

Neat Examples  (1)Surprising or curious use cases

Overlay the polygons of the world and their antipodal polygons:

In[1]:=1
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https://wolfram.com/xid/0bniola6y2fy2-haopwo
In[2]:=2
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https://wolfram.com/xid/0bniola6y2fy2-3uecvm
Out[2]=2
Wolfram Research (2017), GeoAntipode, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoAntipode.html.
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Wolfram Research (2017), GeoAntipode, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoAntipode.html.

Text

Wolfram Research (2017), GeoAntipode, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoAntipode.html.

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Wolfram Research (2017), GeoAntipode, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoAntipode.html.

CMS

Wolfram Language. 2017. "GeoAntipode." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoAntipode.html.

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Wolfram Language. 2017. "GeoAntipode." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoAntipode.html.

APA

Wolfram Language. (2017). GeoAntipode. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoAntipode.html

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Wolfram Language. (2017). GeoAntipode. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoAntipode.html

BibTeX

@misc{reference.wolfram_2025_geoantipode, author="Wolfram Research", title="{GeoAntipode}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/GeoAntipode.html}", note=[Accessed: 29-May-2025 ]}

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@misc{reference.wolfram_2025_geoantipode, author="Wolfram Research", title="{GeoAntipode}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/GeoAntipode.html}", note=[Accessed: 29-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geoantipode, organization={Wolfram Research}, title={GeoAntipode}, year={2017}, url={https://reference.wolfram.com/language/ref/GeoAntipode.html}, note=[Accessed: 29-May-2025 ]}

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@online{reference.wolfram_2025_geoantipode, organization={Wolfram Research}, title={GeoAntipode}, year={2017}, url={https://reference.wolfram.com/language/ref/GeoAntipode.html}, note=[Accessed: 29-May-2025 ]}