Main Content

Great Circles, Geodesics, and Rhumb Lines

Find the shortest path between two points; find the curve that crosses each meridian at the same angle


azimuthAzimuth between points on sphere or ellipsoid
departureDeparture of longitudes at specified latitudes
distanceDistance between points on sphere or ellipsoid
gc2scCenter and radius of great circle
gcxgcIntersection points for pairs of great circles
gcxscIntersection points for great and small circle pairs
antipodePoint on opposite side of globe
meridianarcEllipsoidal distance along meridian
meridianfwdReckon position along meridian
reckonPoint at specified azimuth, range on sphere or ellipsoid
rhxrhIntersection points for pairs of rhumb lines
surfdistInteractive distance, azimuth, and reckoning calculations
trackTrack segments to connect navigational waypoints
track1Geographic tracks from starting point, azimuth, and range
track2Geographic tracks from starting and ending points
trackgGreat circle or rhumb line defined via mouse input
trackuiGUI to display great circles and rhumb lines on map axes


Great Circles

A great circle is the shortest path between two points along the surface of a sphere.

Rhumb Lines

A rhumb line is a curve that crosses each meridian at the same angle.


Azimuth is the angle a line makes with a meridian, measured clockwise from north.


Elevation is the angle above the local horizontal of one point relative to another.

Relationship Between Points on Sphere

There are many ways to define the 2-D spatial relationship between two points on a perfect sphere, including azimuth, heading, spherical distance, linear distance, and range.

Generate Vector Data for Points Along Great Circle or Rhumb Line Tracks

You can generate vector data corresponding to points along great circle or rhumb line tracks by using two points on the track, or a point and an azimuth at that point.


You can determine the new position of an object along a sphere given a starting point, an initial azimuth, and a distance, following either a great circle or a rhumb line. This process is called reckoning.

Calculate Distance Between Two Points in Geographic Space

The measured distance between two points in geometric space depends on whether you specify a path along the great circle or the rhumb line.