# GeoPath

GeoPath[{loc1,loc2},pathtype]

is a GeoGraphics primitive that represents a path of type pathtype between locations loc1 and loc2.

GeoPath[{loc1,loc2,},pathtype]

represents a path formed by joining paths of type pathtype between consecutive locations loci.

GeoPath[{loc1,d,α},pathtype]

represents a path moving from location loc1 a distance d with initial bearing α.

GeoPath[{{loc11,loc12,},{loc21,},},pathtype]

represents a disjoint collection of paths of type pathtype.

# Details and Options

• The locations loci can be specified as latitude and longitude coordinates {lat,lon} in degrees, as GeoPosition[{lat,lon}], or as named entities Entity[].
• Entities will be interpreted as the position determined by their "Position" property.
• GeoPath supports the geographic path types:
•  "Geodesic" geodesic path between points "Rhumb","RhumbLine","Loxodrome" path of constant bearing between points "GreatEllipse","GreatCircle" path on a plane through Earth's center
• GeoPath[{loc1,}] represents a path of type "Geodesic".
• For multiple locations loci in a "Geodesic" path, each pair of consecutive locations is joined by a geodesic, but the complete path will not be a geodesic in general. The same can be said of other path types.
• A combination of multiple steps of distances di with respective initial bearings αi can be represented using GeoPath[{loc1,GeoDisplacement[{d1,α1}],GeoDisplacement[{d2,α2}],},pathtype].
• Long paths will generically not appear straight in the map.
• Special named geo paths include:
•  GeoPath[{"Parallel",lat}] parallel of latitude lat, extending 360° in longitude GeoPath[{"Meridian",lon}] meridian of longitude lon, extending 180° in latitude GeoPath[{"Parallel",lat,{lon1,lon2}}] parallel of latitude lat, from longitude lon1 to lon2 GeoPath[{"Meridian",lon,{lat1,lat2}}] meridian of longitude lon, from latitude lat1 to lat2 GeoPath["Equator"] parallel of latitude 0° GeoPath["NorthernTropic"] parallel of latitude 23.43703° GeoPath["SouthernTropic"] parallel of latitude -23.43703° GeoPath["ArcticCircle"] parallel of latitude 66.56297° GeoPath["AntarcticCircle"] parallel of latitude -66.56297° GeoPath["GreenwichMeridian"] meridian of longitude 0° GeoPath["DateLineMeridian"] meridian of longitude 180° GeoPath["DateLine"] international date line
• Line thickness can be specified using Thickness or AbsoluteThickness, as well as Thick and Thin.
• Line dashing can be specified using Dashing or AbsoluteDashing, as well as Dashed, Dotted, etc.
• Line shading or coloring can be specified using CMYKColor, GrayLevel, Hue, Opacity, or RGBColor.
• The option VertexColors->{c1,c2,} can be used to specify that the color of the line should interpolate between colors ci specified for each point.
• Joining of line segments can be specified using JoinForm.
• Line caps can be specified using CapForm.

# Examples

open allclose all

## Basic Examples(5)

Shortest path (geodesic) between two locations:

Line of constant rhumb (loxodrome) between two locations:

Move 500 kilometers along a geodesic from New York:

Draw a curve of constant bearing between two cities:

Draw the shortest route between several cities:

## Scope(8)

Locations can be specified in various forms:

A geodesic specified by relative displacement from an initial location:

A sequence of displacements along rhumb lines from an initial position:

Draw several parallels:

Draw meridians, from pole to pole:

Draw parts of parallels, from west to east or from east to west:

Important named geo lines:

Draw the international date line:

## Options(3)

### VertexColors(2)

A geo path with vertex colors:

A random walk of 100 geodesic steps of 5000 kilometers on the Earth:

### CurveClosed(1)

A geo path is not a closed curve in general:

Close the path by joining the first and last points with a curve of the same type, a geodesic in this case:

## Applications(4)

A geo triangle, with geodesic sides, in the "LambertAzimuthal" projection:

The same geo triangle in the "Equirectangular" projection:

Or in the "Bonne" projection:

A geo polygon with holes:

Several paths with the same displacement data but with different initial positions. Use Arrow:

Create tooltips to allow coordinates to be read off geo grid lines drawn as geo paths:

## Properties & Relations(7)

A line of constant rhumb (constant angle with respect to all meridians) eventually spirals around a pole:

Take two locations:

Neither the rhumb line (red) nor the geodesic (green) is a straight line (given for comparison in black), using the default equirectangular geo projection:

The rhumb line is straight in the Mercator projection, and now it is superimposed on the black line:

The geodesic is straight in an azimuthal projection centered at one of the points, and now it is superimposed on the black line:

Take a polyhedron:

Get the latitude and longitude of the vertices on a sphere:

Draw the geodesics among those vertices on a world map:

Use an azimuthal projection:

A geo disk or a geo circle is constructed using the endpoints of geodesics starting from its center:

The endpoint of a geodesic path may be computed using GeoDestination:

Check the displacement data of the path using GeoDistance and GeoDirection:

Or directly with GeoDisplacement:

Construct a geodesic path that leaves London with NE direction and goes around the Earth three times:

Computations are performed on an ellipsoidal Earth by default. Hence geodesic paths do not close:

Use a spherical model for the Earth. Then the geodesic is closed:

Or use a great ellipse, which is always closed:

Take two geo positions:

For the low eccentricity of the Earth, geodesics are close to great ellipses:

For larger eccentricities, they may differ substantially:

## Interactive Examples(1)

Compare the geodesic (green line) and the loxodrome (red line) between any two points:

## Neat Examples(3)

Show an effect of the Earth's curvature using four path segments:

Draw the four geodesic segments:

Move from the Temple of Zeus along a path given by the first 3141 terms of the continued fraction of :

The path ends just a few miles east of Kossuth, Mississippi:

Visualize the journey:

Study a candidate hexagonal tiling on the Earth. Recursively move from Denver in steps of 100 miles:

For each geodesic of initial bearing , draw two new ones with bearings and :

The resulting set of geodesics does not overlap, due to the curvature of the Earth's surface:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_geopath, author="Wolfram Research", title="{GeoPath}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/GeoPath.html}", note=[Accessed: 18-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_geopath, organization={Wolfram Research}, title={GeoPath}, year={2014}, url={https://reference.wolfram.com/language/ref/GeoPath.html}, note=[Accessed: 18-September-2024 ]}