WOLFRAM

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.

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:

Out[1]=1

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

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:

Out[1]=1

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

Out[2]=2

Specify other values for the parameters of the projection:

Out[3]=3
Out[4]=4

Compare any two initial directions with their projected versions:

Out[1]=1

Specify the azimuth as a number of degrees:

Out[1]=1

Specify the azimuth as a Quantity angle:

Out[2]=2

Use any other angular unit:

Out[3]=3

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

Out[1]=1

Use locations with geo position heads:

Out[2]=2
Out[3]=3
Out[4]=4

Specify a location using a geo Entity object:

Out[1]=1

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

Out[1]=1

The input can also be given as a QuantityArray object:

Out[2]=2

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

Out[1]=1

Check the result graphically:

Out[2]=2

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

Out[1]=1
Out[2]=2

GeoGridDirectionDifference can efficiently process values for large numbers of locations:

Out[3]=3

Options  (1)Common values & functionality for each option

GeoModel  (1)

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

Out[1]=1

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

Out[2]=2

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

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:

Out[1]=1
Out[2]=2

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

Out[2]=2
Out[3]=3

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

Out[2]=2

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

Out[4]=4
Out[5]=5

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

Out[1]=1

Choose 100 random geo locations:

Out[2]=2

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

Out[3]=3
Out[4]=4

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

Out[1]=1

Choose 100 random geo locations:

Out[2]=2

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

Out[3]=3
Out[4]=4

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

Out[1]=1
Out[2]=2
Out[3]=3
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:

Out[1]=1
Out[2]=2

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

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:

Out[1]=1
Out[7]=7
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.

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.

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

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 ]}

@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 ]}

@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 ]}