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:

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:

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

The same geo triangle in the "Equirectangular" projection:

Or in the "Bonne" projection:

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:

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 Rome 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:

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

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: