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GeoGridDirectionDifference
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GeoGridDirectionDifference

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gives the difference between the angle from north to direction β on the geo grid obtained with projection proj and the actual angle from north to direction β at location loc.

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GeoGridDirectionDifference[proj,loc,αβ]

gives the difference between projected and unprojected angles from direction α to direction β.

Details and Options

  • Geo grid direction difference is a measure of how much angles between geo directions get expanded or contracted during map projection.
  • GeoGridDirectionDifference[proj,loc,αβ] computes the difference angle (-)-(β-α) where α, β are azimuths defined on the Earth at the given location loc, and , are the respective projected bearings on the map.
  • GeoGridDirectionDifference[proj,loc,α] is equivalent to GeoGridDirectionDifference[proj,loc,0α].
  • GeoGridDirectionDifference[proj,loc] computes the largest absolute value of GeoGridDirectionDifference[proj,loc,αα+90] for any value of α.
  • A geo projection can be given as a named projection "proj" with default parameters or as {"proj",params}, where "proj" is any of the entities of GeoProjectionData and params are parameter rules like "StandardParallels"->{33,60}. GeoProjectionData["proj"] gives the default values of the parameters for the projection "proj".
  • The location loc can be given as a coordinate pair {lat,lon} in degrees, a geo position object like GeoPosition[…] or GeoGridPosition[…] or as a geo entity Entity[…].
  • The bearing or azimuthal direction α is an angle measured clockwise from true north. It can be given as a Quantity angle, as a number in degrees or as a named compass direction like "North", "NE" or "NEbE".
  • GeoGridDirectionDifference threads over its location and direction arguments.
  • Possible options of GeoGridDirectionDifference include:
  • GeoModel Automaticmodel of Earth or a celestial body

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Compute the angular difference induced by the Mollweide projection in the eastward direction at New York:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-xvzf6f
Out[1]=1

The angle between the projected north and east directions is about 27.7° smaller than the original 90°:

In[2]:=2
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-zlnrsd
Out[2]=2

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

Compute the geo grid direction difference along the northeast direction for a geo projection at your current geo location:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-7o46v8
Out[1]=1

These are the default values of the parameters of the "Albers" projection:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-ijio5v
Out[2]=2

Specify other values for the parameters of the projection:

In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-casj5h
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0d4li4c2dna8k4wi-jhoi12
Out[4]=4

Compare any two initial directions with their projected versions:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-ylxz4r
Out[1]=1

Specify the azimuth as a number of degrees:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-scuzy8
Out[1]=1

Specify the azimuth as a Quantity angle:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-eghlel
Out[2]=2

Use any other angular unit:

In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-z6kxia
Out[3]=3

Specify a location using a pair {lat,lon} in degrees:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-oblue2
Out[1]=1

Use locations with geo position heads:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-mxtpox
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-mv5nny
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0d4li4c2dna8k4wi-g9eq9s
Out[4]=4

Specify a location using a geo Entity object:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-h5tq64
Out[1]=1

Compute the geo grid direction difference for a list of different azimuths at the same location:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-ims07
Out[1]=1

The input can also be given as a QuantityArray object:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-mgw46x
Out[2]=2

Find the maximum absolute value of the angular difference of perpendicular directions:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-b99j04
Out[1]=1

Check the result graphically:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-gjevjv
Out[2]=2

Return the projected angular difference of a list of locations in different formats:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-bimnz1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-09463y
Out[2]=2

GeoGridDirectionDifference can efficiently process values for large numbers of locations:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-pcm2kl
In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-faqg5p
In[3]:=3
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-k3gk85
Out[3]=3

Options  (1)Common values & functionality for each option

GeoModel  (1)

By default, GeoGridDirectionDifference returns values for a spherical geo model:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-pmybot
Out[1]=1

Using an ellipsoidal model of Earth produces a slightly different value:

In[2]:=2
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-zxprhn
Out[2]=2

The global scale of the reference model does not affect geo direction distortion:

In[3]:=3
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-enbf18
Out[3]=3

Properties & Relations  (6)Properties of the function, and connections to other functions

The geo grid direction difference varies periodically with the azimuth, with a period of 180 degrees:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-cvpon0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-h5hlv9
Out[2]=2

Compute the azimuths of the minimal and maximal geo grid direction differences:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-b4y1g5
In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-e6ay7d
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-xqk4xi
Out[3]=3

Compute the maximum value of the geo grid direction difference for perpendicular directions:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-ndknqv
In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-693jpg
Out[2]=2

Check explicitly that the values agree when you compute them numerically:

In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-lnfrdl
In[4]:=4
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https://wolfram.com/xid/0d4li4c2dna8k4wi-y3yyl9
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0d4li4c2dna8k4wi-zvtbk7
Out[5]=5

Take the cylindrical projections, except for those requiring additional parameters or not given in normal aspect:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-cxssj1
Out[1]=1

Choose 100 random geo locations:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-dgvh09
Out[2]=2

Check that cylindrical projections do not distort the perpendicularity of the north and east directions:

In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-c8fdr4
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-9p26gp
Out[4]=4

Take the conformal projections, except for those requiring additional parameters:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-y1t3hk
Out[1]=1

Choose 100 random geo locations:

In[2]:=2
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https://wolfram.com/xid/0d4li4c2dna8k4wi-4m0zyr
Out[2]=2

Check that the geo grid direction difference is zero at all the chosen points:

In[3]:=3
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https://wolfram.com/xid/0d4li4c2dna8k4wi-1oewp7
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-4vy39f
Out[4]=4

Flat polar projections have maximal geo grid angle difference at the poles if the azimuths define a meridian:

In[1]:=1
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-dbj986
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-3vvl4a
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-y7t0xw
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-qzs391
Out[4]=4

Possible Issues  (1)Common pitfalls and unexpected behavior

If a geo location cannot be projected, then the geo grid direction difference cannot be computed either:

In[1]:=1
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-fjgf9
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-uf0hbg
Out[2]=2

This location is not on the half-Earth covered by the "Orthographic" projection with default center:

In[3]:=3
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-bqunkz
Out[3]=3

Neat Examples  (1)Surprising or curious use cases

Make a density plot of angular distortion along the eastward direction for the island of Madagascar:

In[1]:=1
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https://wolfram.com/xid/0d4li4c2dna8k4wi-znan6j
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-r6l3rl
Out[2]=2
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-kcx4wj
In[3]:=3
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-l6xlql
In[7]:=7
✖
https://wolfram.com/xid/0d4li4c2dna8k4wi-c0dkwv
Out[7]=7
Wolfram Research (2019), GeoGridDirectionDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.
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Wolfram Research (2019), GeoGridDirectionDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.

Text

Wolfram Research (2019), GeoGridDirectionDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.

✖
Wolfram Research (2019), GeoGridDirectionDifference, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.

CMS

Wolfram Language. 2019. "GeoGridDirectionDifference." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.

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Wolfram Language. 2019. "GeoGridDirectionDifference." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html.

APA

Wolfram Language. (2019). GeoGridDirectionDifference. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html

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Wolfram Language. (2019). GeoGridDirectionDifference. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html

BibTeX

@misc{reference.wolfram_2025_geogriddirectiondifference, author="Wolfram Research", title="{GeoGridDirectionDifference}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html}", note=[Accessed: 08-July-2025 ]}

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@misc{reference.wolfram_2025_geogriddirectiondifference, author="Wolfram Research", title="{GeoGridDirectionDifference}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html}", note=[Accessed: 08-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geogriddirectiondifference, organization={Wolfram Research}, title={GeoGridDirectionDifference}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html}, note=[Accessed: 08-July-2025 ]}

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@online{reference.wolfram_2025_geogriddirectiondifference, organization={Wolfram Research}, title={GeoGridDirectionDifference}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoGridDirectionDifference.html}, note=[Accessed: 08-July-2025 ]}