GeoGridPosition
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GeoGridPosition
represents a point {x,y} in a planimetric cartographic grid using the projection proj.
represents a point {x,y,h} in a cartographic grid with height h with respect to the reference ellipsoid.
represents a point in a cartographic grid obtained by projection from data in the given datum.
returns the cartographic grid position of the specified geographical entity.
Details



- Coordinates x, y in GeoGridPosition[{x,y},proj] must be given as numeric values, whose meaning is determined by the projection proj.
- Height h in GeoGridPosition[{x,y,h},proj] can be given as a numeric object in meters or as a Quantity length.
- Height h in GeoGridPosition[{x,y,h},proj] is geodetic height, measured with respect to the reference ellipsoid.
- GeoGridPosition[{x,y,h,t},proj] includes a time t measured in seconds since the beginning of January 1, 1900 in the GMT time zone.
- A GeoGridPosition object with no explicit height assumes height zero with respect to the reference ellipsoid. A GeoGridPosition object with no explicit time assumes the current date.
- GeoGridPosition[pos,proj] converts from any geographic position to a grid point, essentially computing a cartographic projection. Any of the following coordinate types can be given: GeoPosition, GeoPositionXYZ, GeoPositionENU, GeoGridPosition.
- GeoGridPosition[GeoPosition[{lat,lon}],proj] performs the direct projection from geodetic coordinates to the projected map.
- Conversely, GeoPosition[GeoGridPosition[{x,y},proj]] performs the inverse projection from the map to geodetic coordinates.
- Projections can be specified in the following forms:
-
"proj" named projection with default parameter values {"proj","param1"->val1,"param2"->val2,…} projection with detailed parameters specified - Names of possible projections are given by GeoProjectionData[].
- Default values of parameters for a particular named projection are given by GeoProjectionData[proj].
- Values of height h and time t are preserved in projection computations.
- GeoPosition[…][prop] gives the specified property of a geo grid position.
- Possible properties include:
-
"AbsoluteTime" date as number of seconds since Jan 1, 1900, 00:00 GMT "Count" number of positions in the GeoGridPosition object "Data" first argument of the GeoGridPosition object "DateList" date list {y,m,d,h,m,s} in GMT time "DateObject" full date object "Datum" datum of the GeoGridPosition object "Depth" point depth: 0 for a single position, 1 for a list of them, … "Dimension" number of coordinates for each position "Elevation" numeric elevation in meters, with respect to the ellipsoid "GeoProjection" geo projection of the GeoGridPosition object "GridX" numeric x coordinate "GridY" numeric y coordinate "GridXY" numeric {x,y} pair "PackingType" Integer or Real if data is packed; None otherwise
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Convert a geodetic position to a grid point using a spherical Bonne projection:

https://wolfram.com/xid/0btn8dp4hzpu-lra52o

Convert back to a geodetic position:

https://wolfram.com/xid/0btn8dp4hzpu-097tru

Compute a spherical gnomonic projection using a custom setting for the central meridian:

https://wolfram.com/xid/0btn8dp4hzpu-vx8sgc

Compute a projection using explicitly specified projection parameters:

https://wolfram.com/xid/0btn8dp4hzpu-2oyqtx

Scope (7)Survey of the scope of standard use cases
Position Specification (3)
A geo grid position object specifying projected x, y coordinates:

https://wolfram.com/xid/0btn8dp4hzpu-pvcl8s


https://wolfram.com/xid/0btn8dp4hzpu-pv3q5w

Specify time as well, in seconds since 1900:

https://wolfram.com/xid/0btn8dp4hzpu-mgjqva

Projection from geodetic positions to a cartographic grid, using various geo projections:

https://wolfram.com/xid/0btn8dp4hzpu-oal5gc


https://wolfram.com/xid/0btn8dp4hzpu-ist21s


https://wolfram.com/xid/0btn8dp4hzpu-5ylkmc


https://wolfram.com/xid/0btn8dp4hzpu-vmf40k

Directly specify the geographic Entity object:

https://wolfram.com/xid/0btn8dp4hzpu-8vqyzs

Conversion to GeoGridPosition (2)
Projection from three-dimensional XYZ specifications:

https://wolfram.com/xid/0btn8dp4hzpu-5eokac


https://wolfram.com/xid/0btn8dp4hzpu-7s5wef


https://wolfram.com/xid/0btn8dp4hzpu-r53mhd


https://wolfram.com/xid/0btn8dp4hzpu-hxqa16

Start from a geodetic position in a nondefault datum:

https://wolfram.com/xid/0btn8dp4hzpu-t5qrcs

The projection keeps track of the datum information:

https://wolfram.com/xid/0btn8dp4hzpu-ozqq62

Recover the original specification:

https://wolfram.com/xid/0btn8dp4hzpu-1hgbf5

Geo Grid Position Arrays (1)
Use an array of points as the first argument:

https://wolfram.com/xid/0btn8dp4hzpu-depk8f
All points are transformed at once:

https://wolfram.com/xid/0btn8dp4hzpu-4vh4r2

Here each point is transformed individually:

https://wolfram.com/xid/0btn8dp4hzpu-3jzrdl

Results coincide up to numerical error:

https://wolfram.com/xid/0btn8dp4hzpu-te122p

Coordinate Extraction (1)
Use properties to extract information from a GeoPosition object:

https://wolfram.com/xid/0btn8dp4hzpu-01t9q0


https://wolfram.com/xid/0btn8dp4hzpu-gzjluk


https://wolfram.com/xid/0btn8dp4hzpu-fhr1o5

Applications (1)Sample problems that can be solved with this function
Get latitude, longitude lists for the main boundaries of a country:

https://wolfram.com/xid/0btn8dp4hzpu-p11f33
Convert geodetic coordinates to grid positions using the spherical Mercator projection:

https://wolfram.com/xid/0btn8dp4hzpu-kybi8g

Use the Cassini projection with a particular center:

https://wolfram.com/xid/0btn8dp4hzpu-smp1tc


https://wolfram.com/xid/0btn8dp4hzpu-xxsr2g

Properties & Relations (3)Properties of the function, and connections to other functions
Gudermannian implements the inverse Mercator projection for the latitude coordinate:

https://wolfram.com/xid/0btn8dp4hzpu-lsl2hl


https://wolfram.com/xid/0btn8dp4hzpu-xz2zui


https://wolfram.com/xid/0btn8dp4hzpu-6b4v3g
Parameters of the default reference ellipsoid:

https://wolfram.com/xid/0btn8dp4hzpu-thltmw


https://wolfram.com/xid/0btn8dp4hzpu-chclns

Project that location on the ellipsoid using the cylindrical-aspect Mercator projection:

https://wolfram.com/xid/0btn8dp4hzpu-smgn5

The result can also be obtained as:

https://wolfram.com/xid/0btn8dp4hzpu-j7nf72


https://wolfram.com/xid/0btn8dp4hzpu-qtq5ed

Project the same location using the transverse-aspect Mercator projection:

https://wolfram.com/xid/0btn8dp4hzpu-3lhjl2

The result can also be obtained by solving this equation:

https://wolfram.com/xid/0btn8dp4hzpu-n0bdhr


https://wolfram.com/xid/0btn8dp4hzpu-1qsnv3


https://wolfram.com/xid/0btn8dp4hzpu-m3olot


https://wolfram.com/xid/0btn8dp4hzpu-l5pmdq

There is no simple relation between the projected coordinates of a point and those of its antipode:

https://wolfram.com/xid/0btn8dp4hzpu-ms7s12


https://wolfram.com/xid/0btn8dp4hzpu-1j9hzi

Possible Issues (1)Common pitfalls and unexpected behavior
In actual applications, the "ReferenceModel" parameter of the projection will usually coincide with the datum in the third argument of GeoGridPosition, but this is not needed. For example, the standard webMercator projection uses the spherical Mercator projection, with some radius r, even though the locations are associated with a datum based on a standard reference ellipsoid. This is represented by:

https://wolfram.com/xid/0btn8dp4hzpu-1j6swu


https://wolfram.com/xid/0btn8dp4hzpu-5yvhev


https://wolfram.com/xid/0btn8dp4hzpu-jh89yt

Using the ellipsoidal Mercator projection gives slightly different results:

https://wolfram.com/xid/0btn8dp4hzpu-de8vxs

Wolfram Research (2008), GeoGridPosition, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridPosition.html (updated 2019).
Text
Wolfram Research (2008), GeoGridPosition, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridPosition.html (updated 2019).
Wolfram Research (2008), GeoGridPosition, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridPosition.html (updated 2019).
CMS
Wolfram Language. 2008. "GeoGridPosition." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/GeoGridPosition.html.
Wolfram Language. 2008. "GeoGridPosition." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/GeoGridPosition.html.
APA
Wolfram Language. (2008). GeoGridPosition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoGridPosition.html
Wolfram Language. (2008). GeoGridPosition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoGridPosition.html
BibTeX
@misc{reference.wolfram_2025_geogridposition, author="Wolfram Research", title="{GeoGridPosition}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoGridPosition.html}", note=[Accessed: 08-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_geogridposition, organization={Wolfram Research}, title={GeoGridPosition}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoGridPosition.html}, note=[Accessed: 08-July-2025
]}