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GeoGridVector
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GeoGridVector

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GeoGridVector[loc{vx,vy},proj]

represents a horizontal two-dimensional vector of components vx, vy in the orthonormal frame of the coordinates of the geo projection proj, at geo location loc.

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GeoGridVector[loc{vx,vy,vz},proj]

represents a three-dimensional vector of horizontal components vx, vy and vertical component vz at geo location loc.

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GeoGridVector[{loc1,loc2,…}{vec1,vec2,…},proj]

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

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GeoGridVector[{loc1vec1,loc2vec2,…},proj]

represents the same collection of vectors.

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GeoGridVector[vec,proj]

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

Details

  • GeoGridVector[…] can represent any vectorial magnitude on the surface of the Earth or any other celestial globe, like wind speed, magnetic field, scalar gradients, etc.
  • GeoGridVector describes data using an orthonormal frame tangent to the reference ellipsoid at the given location.
  • GeoGridVector acts both as a vector data container and as a converter from other types of geo vector data, like GeoVectorENU or GeoVector.
  • In GeoGridVector[locvec], the components of the vector vec can be quantities, but their units must be compatible.
  • In GeoGridVector[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.
  • In GeoGridVector[locvec,proj], the geo projection proj 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].
  • GeoGridVector[…][prop] gives the specified property of a geo grid vector.
  • Possible properties include:
  		• "Count"number of vectors in the GeoGridVector object
    		"Data"first argument of the GeoGridVector object
    		"Depth"vector depth: 0 for a single vector, 1 for a list of them, …
    		"GeoProjection"geo projection of the GeoGridVector object
    		"Location"location data of the GeoGridVector object
    		"LocationDimension"number of coordinates for each position
    		"LocationPackingType"Integer or Real if positions are packed; None otherwise
    		"Vector"vector data of the GeoGridVector 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

Take a geo vector aligned with the vertical axis of the Albers coordinates at your location:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-ngkiun
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-p5aitt
Out[2]=2

That vector does not point northward in the local Mercator projection:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-friqt4
Out[3]=3

Take two orthogonal geo vectors at New York:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-58rf4x
Out[1]=1

They are not orthogonal in the Mollweide projection with default centering:

In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-br4xrq
Out[2]=2

Show the geo grid vectors as darts in a GeoGraphics map with that projection:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-5uxbom
Out[3]=3

Scope  (10)Survey of the scope of standard use cases

Data Specification  (4)

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

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-13u4fo
Out[1]=1

Construct a horizontal velocity vector crossing the Bonne frame axes at 45 degrees at Chicago:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-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/0dqwnz0xb0q-9iitxm
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-nmj0q5
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0dqwnz0xb0q-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/0dqwnz0xb0q-pg52d2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-f1vi9f
Out[2]=2

Work with horizontal 2D or 3D vectors of any unit dimension:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-zzxuas
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-9rxgbb
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-bxde4
Out[3]=3

Geo Projection Conversion  (2)

Convert geo grid vector data in the Mercator projection to different geo projections:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-9j9wje
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-q5n5ud
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-zjyic4
Out[3]=3

Convert back to the original projection:

In[4]:=4
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https://wolfram.com/xid/0dqwnz0xb0q-uanxcy
Out[4]=4

Use projections with default parameters, as given by GeoProjectionData:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-n15fna
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-qvwb7h
Out[2]=2

Convert the geo grid vector to the Albers projection with nondefault parameters:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-e4sgdm
Out[3]=3

Convert back to the Albers projection with default parameters:

In[4]:=4
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https://wolfram.com/xid/0dqwnz0xb0q-dupj93
Out[4]=4

Geo Vector Arrays  (3)

Compute gravitational field data simultaneously for several locations:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-5gq5x1
Out[1]=1

Convert it to a single geo grid vector array in the Mercator projection:

In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-7bdnvx
Out[2]=2

Represent the relative sizes and directions of the small horizontal components:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-7iun6j
Out[3]=3

Generate a million random geo grid vectors at respective random locations:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-cgd9hy
Out[1]=1

Convert them into geo vector form:

In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-iq7k9p
Out[2]=2

Use GeoGridVector to transform them back to their projected form in the Albers projection:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-4ik0xq
Out[3]=3

Check that the difference is just numerical error:

In[4]:=4
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https://wolfram.com/xid/0dqwnz0xb0q-zuzias
Out[4]=4

Generate a million random geo grid vectors at respective random locations:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-ecdhnm
Out[1]=1

Convert the geo grid vectors from the Albers to the Mollweide projection:

In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-w2djia
Out[2]=2

Use GeoGridVector to transform them back to the Albers projection:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-ydcdbp
Out[3]=3

Check that the difference is just numerical error:

In[4]:=4
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https://wolfram.com/xid/0dqwnz0xb0q-nep8ud
Out[4]=4

Data Extraction  (1)

A horizontal velocity vector at Chicago:

In[1]:=1
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https://wolfram.com/xid/0dqwnz0xb0q-1yszhe
Out[1]=1

Extract the location of the geo vector:

In[2]:=2
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https://wolfram.com/xid/0dqwnz0xb0q-pve0te
Out[2]=2

Extract the vector data from the geo vector:

In[3]:=3
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https://wolfram.com/xid/0dqwnz0xb0q-m5q56t
Out[3]=3

Extract the locvec rule:

In[4]:=4
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https://wolfram.com/xid/0dqwnz0xb0q-bpa56o
Out[4]=4

Extract all properties:

In[5]:=5
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https://wolfram.com/xid/0dqwnz0xb0q-gzjluk
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0dqwnz0xb0q-fhr1o5
Out[6]=6

Properties & Relations  (1)Properties of the function, and connections to other functions

GeoGridVector components in the Mercator projection coincide with GeoVectorENU components:

In[1]:=1
✖
https://wolfram.com/xid/0dqwnz0xb0q-d8wg91
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0dqwnz0xb0q-dnb13u
Out[2]=2

Components are different in other projections, due to angular distortion or tilting of latitude, longitude lines:

In[3]:=3
✖
https://wolfram.com/xid/0dqwnz0xb0q-fkoa52
Out[3]=3
Wolfram Research (2019), GeoGridVector, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridVector.html.
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Wolfram Research (2019), GeoGridVector, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridVector.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_geogridvector, author="Wolfram Research", title="{GeoGridVector}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoGridVector.html}", note=[Accessed: 24-March-2025 ]}

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@misc{reference.wolfram_2025_geogridvector, author="Wolfram Research", title="{GeoGridVector}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/GeoGridVector.html}", note=[Accessed: 24-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_geogridvector, organization={Wolfram Research}, title={GeoGridVector}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoGridVector.html}, note=[Accessed: 24-March-2025 ]}

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@online{reference.wolfram_2025_geogridvector, organization={Wolfram Research}, title={GeoGridVector}, year={2019}, url={https://reference.wolfram.com/language/ref/GeoGridVector.html}, note=[Accessed: 24-March-2025 ]}