Function Repository Resource:

RhumbLineDistanceList

Successive pairwise rhumbline distances between a list of geodetic positions

Contributed by: Peter Cullen Burbery

ResourceFunction["RhumbLineDistanceList"][{loc₁,loc₂,…,loc_n}]

returns the list of loxodromic distances between consecutive pairs of locations.

Details and Options

The locations loc_i in ResourceFunction["RhumbLineDistanceList"][{loc₁,…,loc_n}] can be given as pairs {lat,lon} in degrees, GeoPosition objects, geographic Entity objects, or any other specification of a location.

The result is returned as a QuantityArray object with dimensions of length. The unit used can be chosen with the option UnitSystem, which has "Metric" as its default value.

If the input list of locations has length n, the resulting list of distances has length n-1.

Examples

Basic Examples (3)

List of consecutive loxodromic distances between cities:

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Convert the QuantityArray object to its normal form:

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Draw the three rhumbline segments on a map:

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GeoGraphics[{Red, Thick, GeoPath[{Entity[
"City", {"BuenosAires", "BuenosAires", "Argentina"}], Entity["City", {"RioDeJaneiro", "RioDeJaneiro", "Brazil"}], Entity["City", {"MexicoCity", "DistritoFederal", "Mexico"}], Entity["City", {"NewYork", "NewYork", "UnitedStates"}]}, "RhumbLine"]}]

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Scope (3)

Specify locations as pairs {lat,lon} in degrees:

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Latitude and longitude can also be given as DMS strings:

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Or as Quantity angles:

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Use GeoPosition objects:

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Use other forms of geodetic position:

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$ResourceFunction[ "RhumbLineDistanceList"][{GeoPosition[{0, 0}], GeoPositionXYZ[{5.19*^6, 3.00*^6, 2.20*^6}], GeoGridPosition[{1, 1}, "Albers"]}] // Normal$

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Use Entity objects:

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Options (2)

UnitSystem (2)

The default unit of the result is "Metric":

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Change to a different system:

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Properties and Relations (3)

RhumbLineDistanceList is basically equivalent to a combination of Subsequences and RhumbLineDistance:

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RhumbLineDistanceList[{loc}] returns an empty list:

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RhumbLineDistanceList reports distances along the rhumb line. GeoSpatialDistanceList reports straight-line distances through space. GeoDistanceList reports geodesic distance. TravelDistanceList reports distance by road:

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Neat Examples (1)

Compute the distances between the capitals of members of NATO:

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Publisher

Peter Burbery

Requirements

Wolfram Language 13.3 (June 2023) or above

Version History

1.0.0 – 05 July 2023

Related Resources

Author Notes

Ideas for future research including adding support for different distance functions including “Boundary”, corresponding to minimum distance between any points in regions, and “SignedBoundary”, corresponding to distance to boundary, negative for interior points. I think “Center” is used by default, which corresponds to distance between centers of regions. I tried using RegionDistance which as of 13.3 supports region₁ and region₂, not just a region and a point, but the problem was what function it was using to compute the distance. I think it was using the geodesic distance over the ellipsoid. The problem was that it differed slightly from GeoDistance for some reason.

GeoDistance[,,DistanceFunction→"Boundary"] () should be equivalent to Quantity[RegionDistance[Region[["Polygon"]],Region[["Polygon"]]],"Meters"] (). The difference is . To make this work, I would need to first figure out why there is a difference here. Then I would need indicate to RegionDistance I am using not the geodesic distance but the loxodromic distance. The function SignedRegionDistance could be used for the option "SignedBoundary" once it supports two regions, and not just a region and a point. SignedRegionDistanceis effectivelyMinValue[{Norm[p-q],q∈reg},q∈reg]whenpis not inregand-MinValue[{Norm[p-q],q∉reg},q]otherwise. This could be used to compute the signed region distance while I wait for support for two regions to be introduced, but there's still the bug and the problem of using a loxodrome and not a geodesic. An example of where this could be useful is GeoDistance[,] () and GeoDistance[,,DistanceFunction→"SignedBoundary"] ().

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License