Mapping Toolbox

azimuth

Compute azimuth between two points on the globe

Syntax

• az = azimuth(pt1,pt2)
  az = azimuth(pt1,pt2,geoid)
  az = azimuth(pt1,pt2,units)
  az = azimuth(pt1,pt2,geoid,units)
  
  az = azimuth(track,pt1,...)
  
  az = azimuth(lat1,lon1,lat2,lon2)
  az = azimuth(lat1,lon1,lat2,lon2,geoid)
  az = azimuth(lat1,lon1,lat2,lon2,units)
  az = azimuth(lat1,lon1,lat2,lon2,geoid,units)
  
  az = azimuth(track,lat1,...)
  

Background

Azimuths are the bearings, or directions, between pairs of points. Azimuths are measured as angles, clockwise from true north. The North Pole has an azimuth of 0º from every other point on the globe.

Azimuth can be calculated in two manners. For great circles, the azimuth is the angle made between true north and the great circle passing through the two points at the first point. For rhumb lines, the azimuth is the constant angle made between true north and the entire rhumb line passing through the two points. For more information on this distinction, see the Mapping Toolbox User's Guide.

Description

az = azimuth(pt1,pt2) calculates the great circle azimuths from pt1 to pt2. These two-column matrices should be of the form [latitude longitude].

az = azimuth(lat1,lon1,lat2,lon2) performs the same calculation for two pairs of latitude and longitude matrices.

az = azimuth(pt1,pt2,geoid) specifies the elliptical definition of the Earth to be used with the two-element geoid vector. The default geoid model is a unit sphere, which is sufficient for most applications.

az = azimuth(pt1,pt2,units) specifies the standard angle unit string. The default value is 'degrees'.

az = azimuth(track,pt1,...) specifies whether great circle azimuths or rhumb line azimuths are desired. Great circle azimuths, the default, are indicated with the standard track string 'gc'. Rhumb line azimuths are indicated with the standard track string 'rh'.

Examples

Consider two points on the same parallel, for example, (10ºN,10ºE) and (10ºN,40ºE). The azimuth between these two points depends upon the track string selected. Using the pt1,pt2 notation, the two cases result in:

• az = azimuth('gc',[10,10],[10,40]) 
  az =
     87.3360
  az = azimuth('rh',[10,10],[10,40])
  az =
      90
  

The great circle path begins on an azimuth north of east to take the shortest route to the second point; the rhumb line proceeds along the parallel, on a constant due east heading.

Rhumb lines and great circles coincide along meridians and the Equator. Consider two points on the same meridian, say (10ºN,10ºE) and (40ºN,10ºE); this time using the lat1,lon1,lat2,lon2 notation:

• az = azimuth(10,10,40,10) % great circle sense
  az =
       0
  az = azimuth('rh',10,10,40,10)
  az =
       0
  

The azimuths are the same because the paths coincide.

See Also

distance	Distance between points
elevation	Elevation angle to a point
reckon	New point from an azimuth and
track track1 track2	Tracing paths on the globe

axesscale

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