# Great Circles, Geodesics, and Rhumb Lines

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

## Functions

 `azimuth` Azimuth between points on sphere or ellipsoid `departure` Departure of longitudes at specified latitudes `distance` Distance between points on sphere or ellipsoid `gc2sc` Center and radius of great circle `gcxgc` Intersection points for pairs of great circles `gcxsc` Intersection points for great and small circle pairs `antipode` Point on opposite side of globe `meridianarc` Ellipsoidal distance along meridian `meridianfwd` Reckon position along meridian `reckon` Point at specified azimuth, range on sphere or ellipsoid `rhxrh` Intersection points for pairs of rhumb lines `surfdist` Interactive distance, azimuth, and reckoning calculations `track` Track segments to connect navigational waypoints `track1` Geographic tracks from starting point, azimuth, and range `track2` Geographic tracks from starting and ending points `trackg` Great circle or rhumb line defined via mouse input `trackui` GUI to display great circles and rhumb lines on map axes

## Topics

• 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

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

• Elevation

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.

• Reckoning

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.