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

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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:

Now follow four loxodrome segments instead:

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:

Introduced in 2014
 (10.0)