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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
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
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

Examples and How To

Calculate Intersection of Rhumb Line Tracks

This example shows how to calculate the intersection of rhumb lines using the rhxrh function.

Calculate Intersections of Arbitrary Vector Data

This example shows how to calculate the intersections of arbitrary vector data, such as polylines or polygons, using the polyxpoly function.

Concepts

Great Circles

A great circle defines 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.

About Azimuths

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

Positions, Azimuths, Headings, Distances, Length, and Ranges

Several angular and linear quantities express the distance between two points on a sphere.

Reckoning — The Forward Problem

Reckoning is the determination of a destination given a starting point, an initial azimuth, and a distance.

Distance, Azimuth, and Back-Azimuth (the Inverse Problem)

Distance and azimuth are calculated from the position of two points in geometric space.

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