represents a three-dimensional vector of Cartesian components vX, vY, vZ in an orthonormal frame parallel to the geocentric frame, at location loc.


represents a collection of vectors veci at respective geo locations loci.


represents the same collection of vectors.


represents a geo vector whose associated location has been implicitly specified.


  • GeoVectorXYZ[] can represent any vectorial magnitude on the surface of the Earth or any other celestial globe, like wind speed, magnetic field, scalar gradients, etc.
  • GeoVectorXYZ describes data using an orthonormal frame of fixed orientation with respect to the ambient 3D space, but origin at the given location.
  • GeoVectorXYZ acts both as a vector data container and as a converter from other types of geo vector data, like GeoVector or GeoGridVector.
  • In GeoVectorXYZ[locvec], the components of the vector vec can be quantities, but their units must be compatible.
  • In GeoVectorXYZ[locvec], the location loc can be given as a {lat,lon} pair in degrees, a geo Entity object or any geo location object with head GeoPosition or similar.
  • GeoVectorXYZ[][prop] gives the specified property of a geo vector.
  • Possible properties include:
  • "Count"number of vectors in the GeoVectorXYZ object
    "Data"first argument of the GeoVectorXYZ object
    "Depth"vector depth: 0 for a single vector, 1 for a list of them,
    "Location"location data of the GeoVectorXYZ object
    "LocationDimension"number of coordinates for each position
    "LocationPackingType"Integer or Real if positions are packed; None otherwise
    "Vector"vector data of the GeoVectorXYZ object
    "VectorDimension"number of components for each vector
    "VectorPackingType"Integer or Real if vectors are packed; None otherwise


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Basic Examples  (2)

Construct two north-pointing vectors at different locations:

Their GeoVectorXYZ forms have different components, due to their different orientations in 3D space:

This is the angle in degrees formed by those two vectors in 3D space:

Take 50 random locations in the world:

Compute the magnetic field at those locations and convert it into GeoVectorXYZ form:

Extract the 3D coordinates of the locations and the 3D components of the vectors, in numeric form:

Draw 3D arrows for those vectors:

Scope  (7)

Data Specification  (4)

Specify the location of a geo vector as a {lat,lon} pair in degrees:

Construct a 3D velocity vector with three identical components at Chicago:

Rewrite the location as a geo position object with any head:

Anything that can be interpreted by GeoPosition can be used as a location:

Work with 3D vectors of any unit dimension:

Geo Vector Arrays  (2)

Specify gravitational field data simultaneously for several locations:

Rewrite as a single geo vector array with XYZ components:

Represent the very small horizontal components in a map:

Generate a million random 3D Cartesian vectors at respective random locations:

Convert them into polar form:

Use GeoVectorXYZ to transform them back to their 3D Cartesian form:

Check that the difference is just numerical error:

Data Extraction  (1)

A wind velocity vector at Chicago, expressed in XYZ components:

Extract the location of the geo vector:

Extract the vector data from the geo vector:

Extract the locvec rule:

Extract all properties:

Properties & Relations  (3)

Convert a GeoVectorXYZ expression into other types of geo vectors:

Convert back to GeoVectorXYZ form:

Converting a geo vector into GeoVectorXYZ form does not convert its location into GeoPositionXYZ form:

Use GeoPositionXYZ explicitly to convert the location:

GeoPositionXYZ[{x,y,z}] represents a positional vector from the center of the Earth, in meters:

You can have a tangent vector with the same components at the same location:

Transforming to ENU geo vector form shows that the vector is almost vertical, except for a south component due to the oblateness of the Earth:

Those components can also be computed (modulo sign) using GeoPositionENU:

Wolfram Research (2019), GeoVectorXYZ, Wolfram Language function,


Wolfram Research (2019), GeoVectorXYZ, Wolfram Language function,


Wolfram Language. 2019. "GeoVectorXYZ." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2019). GeoVectorXYZ. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_geovectorxyz, author="Wolfram Research", title="{GeoVectorXYZ}", year="2019", howpublished="\url{}", note=[Accessed: 15-July-2024 ]}


@online{reference.wolfram_2024_geovectorxyz, organization={Wolfram Research}, title={GeoVectorXYZ}, year={2019}, url={}, note=[Accessed: 15-July-2024 ]}