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GeoVectorXYZ
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GeoVectorXYZ

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GeoVectorXYZ[loc{vX,vY,vZ}]

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

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GeoVectorXYZ[{loc1,loc2,…}{vec1,vec2,…}]

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

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GeoVectorXYZ[{loc1vec1,loc2vec2,…}]

represents the same collection of vectors.

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

Details

  • 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

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Construct two north-pointing vectors at different locations:

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-3wlbq9
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-xyh8m5
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-8b24dr
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0v50m8jne23l0-ksd9vy
Out[4]=4

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

In[5]:=5
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https://wolfram.com/xid/0v50m8jne23l0-htym80
Out[5]=5

Take 50 random locations in the world:

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-zy1ndd
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-p204l8
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-jsonwo

Draw 3D arrows for those vectors:

In[4]:=4
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https://wolfram.com/xid/0v50m8jne23l0-806pp0
In[5]:=5
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https://wolfram.com/xid/0v50m8jne23l0-fcp2g
Out[5]=5

Scope  (7)Survey of the scope of standard use cases

Data Specification  (4)

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-13u4fo
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-069j5
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-9iitxm
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-nmj0q5
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0v50m8jne23l0-cijd7f
Out[4]=4

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-pg52d2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-f1vi9f
Out[2]=2

Work with 3D vectors of any unit dimension:

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-t75s6b
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-9ap3il
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-676bga
Out[3]=3

Geo Vector Arrays  (2)

Specify gravitational field data simultaneously for several locations:

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-dhkqdd
Out[1]=1

Rewrite as a single geo vector array with XYZ components:

In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-297ch6
Out[2]=2

Represent the very small horizontal components in a map:

In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-7iun6j
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-cgd9hy
Out[1]=1

Convert them into polar form:

In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-iq7k9p
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-4ik0xq
Out[3]=3

Check that the difference is just numerical error:

In[4]:=4
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https://wolfram.com/xid/0v50m8jne23l0-zuzias
Out[4]=4

Data Extraction  (1)

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-1yszhe
Out[1]=1

Extract the location of the geo vector:

In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-pve0te
Out[2]=2

Extract the vector data from the geo vector:

In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-m5q56t
Out[3]=3

Extract the locvec rule:

In[4]:=4
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https://wolfram.com/xid/0v50m8jne23l0-bpa56o
Out[4]=4

Extract all properties:

In[5]:=5
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https://wolfram.com/xid/0v50m8jne23l0-gzjluk
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0v50m8jne23l0-fhr1o5
Out[6]=6

Properties & Relations  (3)Properties of the function, and connections to other functions

Convert a GeoVectorXYZ expression into other types of geo vectors:

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-wbdkn
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-rs5mvp
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-zc8dr5
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0v50m8jne23l0-45rmd4
Out[4]=4

Convert back to GeoVectorXYZ form:

In[5]:=5
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https://wolfram.com/xid/0v50m8jne23l0-nty3rb
Out[5]=5

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-u9gx40
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-mzgilp
Out[2]=2

Use GeoPositionXYZ explicitly to convert the location:

In[3]:=3
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https://wolfram.com/xid/0v50m8jne23l0-oi9p2t
Out[3]=3

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

In[1]:=1
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https://wolfram.com/xid/0v50m8jne23l0-pmvpw8
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0v50m8jne23l0-p92gbv
Out[2]=2

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:

In[3]:=3
✖
https://wolfram.com/xid/0v50m8jne23l0-sefrz6
Out[3]=3

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

In[4]:=4
✖
https://wolfram.com/xid/0v50m8jne23l0-j4jpur
Out[4]=4
Wolfram Research (2019), GeoVectorXYZ, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoVectorXYZ.html.
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Wolfram Research (2019), GeoVectorXYZ, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoVectorXYZ.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_geovectorxyz, author="Wolfram Research", title="{GeoVectorXYZ}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoVectorXYZ.html}", note=[Accessed: 16-April-2025 ]}

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@misc{reference.wolfram_2025_geovectorxyz, author="Wolfram Research", title="{GeoVectorXYZ}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoVectorXYZ.html}", note=[Accessed: 16-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geovectorxyz, organization={Wolfram Research}, title={GeoVectorXYZ}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoVectorXYZ.html}, note=[Accessed: 16-April-2025 ]}

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@online{reference.wolfram_2025_geovectorxyz, organization={Wolfram Research}, title={GeoVectorXYZ}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoVectorXYZ.html}, note=[Accessed: 16-April-2025 ]}