GeoGridDirectionDifference
✖
GeoGridDirectionDifference
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.
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 Automatic model of Earth or a celestial body
Examples
open allclose allBasic 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:

https://wolfram.com/xid/0d4li4c2dna8k4wi-xvzf6f

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-zlnrsd

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:

https://wolfram.com/xid/0d4li4c2dna8k4wi-7o46v8

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-ijio5v

Specify other values for the parameters of the projection:

https://wolfram.com/xid/0d4li4c2dna8k4wi-casj5h


https://wolfram.com/xid/0d4li4c2dna8k4wi-jhoi12

Compare any two initial directions with their projected versions:

https://wolfram.com/xid/0d4li4c2dna8k4wi-ylxz4r

Specify the azimuth as a number of degrees:

https://wolfram.com/xid/0d4li4c2dna8k4wi-scuzy8

Specify the azimuth as a Quantity angle:

https://wolfram.com/xid/0d4li4c2dna8k4wi-eghlel


https://wolfram.com/xid/0d4li4c2dna8k4wi-z6kxia

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-oblue2

Use locations with geo position heads:

https://wolfram.com/xid/0d4li4c2dna8k4wi-mxtpox


https://wolfram.com/xid/0d4li4c2dna8k4wi-mv5nny


https://wolfram.com/xid/0d4li4c2dna8k4wi-g9eq9s

Specify a location using a geo Entity object:

https://wolfram.com/xid/0d4li4c2dna8k4wi-h5tq64

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-ims07

The input can also be given as a QuantityArray object:

https://wolfram.com/xid/0d4li4c2dna8k4wi-mgw46x

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-b99j04


https://wolfram.com/xid/0d4li4c2dna8k4wi-gjevjv

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-bimnz1


https://wolfram.com/xid/0d4li4c2dna8k4wi-09463y

GeoGridDirectionDifference can efficiently process values for large numbers of locations:

https://wolfram.com/xid/0d4li4c2dna8k4wi-pcm2kl

https://wolfram.com/xid/0d4li4c2dna8k4wi-faqg5p

https://wolfram.com/xid/0d4li4c2dna8k4wi-k3gk85

Options (1)Common values & functionality for each option
GeoModel (1)
By default, GeoGridDirectionDifference returns values for a spherical geo model:

https://wolfram.com/xid/0d4li4c2dna8k4wi-pmybot

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-zxprhn

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-enbf18

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:

https://wolfram.com/xid/0d4li4c2dna8k4wi-cvpon0


https://wolfram.com/xid/0d4li4c2dna8k4wi-h5hlv9

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-b4y1g5

https://wolfram.com/xid/0d4li4c2dna8k4wi-e6ay7d


https://wolfram.com/xid/0d4li4c2dna8k4wi-xqk4xi

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-ndknqv

https://wolfram.com/xid/0d4li4c2dna8k4wi-693jpg

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-lnfrdl

https://wolfram.com/xid/0d4li4c2dna8k4wi-y3yyl9


https://wolfram.com/xid/0d4li4c2dna8k4wi-zvtbk7

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-cxssj1

Choose 100 random geo locations:

https://wolfram.com/xid/0d4li4c2dna8k4wi-dgvh09

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-c8fdr4


https://wolfram.com/xid/0d4li4c2dna8k4wi-9p26gp

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-y1t3hk

Choose 100 random geo locations:

https://wolfram.com/xid/0d4li4c2dna8k4wi-4m0zyr

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-1oewp7


https://wolfram.com/xid/0d4li4c2dna8k4wi-4vy39f

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-dbj986


https://wolfram.com/xid/0d4li4c2dna8k4wi-3vvl4a


https://wolfram.com/xid/0d4li4c2dna8k4wi-y7t0xw


https://wolfram.com/xid/0d4li4c2dna8k4wi-qzs391

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:

https://wolfram.com/xid/0d4li4c2dna8k4wi-fjgf9


https://wolfram.com/xid/0d4li4c2dna8k4wi-uf0hbg

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

https://wolfram.com/xid/0d4li4c2dna8k4wi-bqunkz

Neat Examples (1)Surprising or curious use cases
Make a density plot of angular distortion along the eastward direction for the island of Madagascar:

https://wolfram.com/xid/0d4li4c2dna8k4wi-znan6j


https://wolfram.com/xid/0d4li4c2dna8k4wi-r6l3rl

https://wolfram.com/xid/0d4li4c2dna8k4wi-kcx4wj

https://wolfram.com/xid/0d4li4c2dna8k4wi-l6xlql

https://wolfram.com/xid/0d4li4c2dna8k4wi-c0dkwv

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
]}
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
]}