# GeoDisplacement

GeoDisplacement[{dist,α}]

represents a geodesic displacement of length dist and initial bearing α from a geo location.

GeoDisplacement[{dist,α},pathtype]

represents a displacement of length dist and initial bearing α along a path of type pathtype.

GeoDisplacement[loc1,loc2,pathtype]

returns the displacement needed to reach loc2 from loc1 along a path of type pathtype.

# Details

• The distance dist can be given as a Quantity length or as a number in meters.
• The bearing α is measured clockwise from true north (geodetic north). It can be given as a Quantity angle, a number in degrees, a DMS string, or a named compass point like "N" or "SouthWest".
• Locations loci in GeoDisplacement[loc1,loc2,pathtype] can be given as geographic Entity objects, {lat,lon} pairs in degrees, GeoPosition objects, or any other geodetic position specification.
• GeoDisplacement[loc1,loc2] assumes a path of type "Geodesic".
• The list of possible path types is given in the documentation of GeoPath.
• GeoDisplacement can be used with GeoDestination to compute sequences of displacements and with GeoPath to draw them.

# Examples

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## Basic Examples(4)

Compute a destination location moving 10000 kilometers from another location:

Compute a list of intermediate destinations:

A random path of 100 geodesic steps of 5000 kilometers with random bearings:

Compute distance and direction along a rhumb line from Tokyo to Paris:

Compute distance and direction along a geodesic:

Compare the rhumb line (in red) with the geodesic (in blue) in a world map:

## Scope(9)

A relative displacement along a geodesic of initial bearing 40 degrees:

A relative displacement along a rhumb line:

A relative displacement along a great ellipse:

Distance can be given as a number in meters:

Or as a Quantity length with any unit:

Results are automatically converted into meters:

Bearing can be given as a number in degrees:

Or as a Quantity angle with any unit:

Results are automatically converted into degrees:

Bearing can also be specified as a DMS string:

Or using a named compass point:

Traditional names for the principal eight winds are also possible:

A GeoDisplacement specification of multiple relative displacements along the same geodesic:

The same specification using Quantity distances:

A GeoDisplacement specification of multiple destinations on a geo circle around a location:

The same specification using Quantity angles:

A grid of destinations:

Compute the geodesic needed to go from one location to another location:

Compute the great ellipse between the same two locations:

Compute the rhumb line between the same two locations:

Use GeoPosition specifications for the locations, or {lat,lon} pairs:

Use other types of geodetic positions:

## Applications(1)

The magnetic field of the Earth changes with time, in particular, the position of the North magnetic pole:

As of February 2019, the North magnetic pole is moving toward the west, about 118 meters per day:

## Properties & Relations(3)

GeoDisplacement is the inverse of GeoDestination:

The computation performed by GeoDisplacement combines GeoDistance and GeoDirection:

Take the geo displacement between two points:

The geo displacement between the antipodal points has the same distance but complementary bearing:

## Possible Issues(1)

When any of the locations in GeoDisplacement[loc1,loc2] are extended entities, the computation is performed using some average position:

Wolfram Research (2014), GeoDisplacement, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisplacement.html.

#### Text

Wolfram Research (2014), GeoDisplacement, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoDisplacement.html.

#### CMS

Wolfram Language. 2014. "GeoDisplacement." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoDisplacement.html.

#### APA

Wolfram Language. (2014). GeoDisplacement. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoDisplacement.html

#### BibTeX

@misc{reference.wolfram_2024_geodisplacement, author="Wolfram Research", title="{GeoDisplacement}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/GeoDisplacement.html}", note=[Accessed: 30-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_geodisplacement, organization={Wolfram Research}, title={GeoDisplacement}, year={2014}, url={https://reference.wolfram.com/language/ref/GeoDisplacement.html}, note=[Accessed: 30-May-2024 ]}