Azimuth between points on sphere or ellipsoid
az = azimuth(lat1,lon1,lat2,lon2)
az = azimuth(lat1,lon1,lat2,lon2,ellipsoid)
az = azimuth(lat1,lon1,lat2,lon2,units)
az = azimuth(lat1,lon1,lat2,lon2,ellipsoid,
az = azimuth(
az = azimuth(lat1,lon1,lat2,lon2) calculates
the great circle azimuth from point 1 to point 2, for pairs of points
on the surface of a sphere. The input latitudes and longitudes can
be scalars or arrays of matching size. If you use a combination of
scalar and array inputs, the scalar inputs will be automatically expanded
to match the size of the arrays. The function measures azimuths clockwise
from north and expresses them in degrees or radians.
az = azimuth(lat1,lon1,lat2,lon2,ellipsoid) computes
the azimuth assuming that the points lie on the ellipsoid defined by the input
ellipsoid is a
oblateSpheroid object, or a vector of the form
eccentricity]. The default ellipsoid is a unit sphere.
az = azimuth(lat1,lon1,lat2,lon2,units) uses the input
units to define the angle units of
az and the
latitude-longitude coordinates. Use
'degrees' (the default value), in
the range from 0 to 360, or
'radians', in the range from 0 to
az = azimuth(lat1,lon1,lat2,lon2,ellipsoid, specifies
ellipsoid vector and the units of
az = azimuth( uses
track to specify either a great
circle or a rhumb line azimuth calculation. Enter
track (the default value), to obtain
great circle azimuths for a sphere or geodesic azimuths for an ellipsoid.
(Hint to remember name: the letters “g” and “c”
are in both great circle and geodesic.) Enter
track to obtain rhumb line azimuths
for either a sphere or an ellipsoid.
Find the azimuth between two points on the same parallel, for
example, (10ºN, 10ºE) and (10ºN, 40ºE). The azimuth
between two points depends on the
% Try the 'gc' track value. az = azimuth('gc',10,10,10,40) % Compare to the result obtained from the 'rh' track value. az = azimuth('rh',10,10,10,40)
Find the azimuth between two points on the same meridian, say (10ºN, 10ºE) and (40ºN, 10ºE):
% Try the 'gc' track . az = azimuth(10,10,40,10) % Compare to the 'rh' track . az = azimuth('rh',10,10,40,10)
Rhumb lines and great circles coincide along meridians and the Equator. The azimuths are the same because the paths coincide.
An azimuth is the angle at which a smooth curve crosses a meridian, taken clockwise from north. The North Pole has an azimuth of 0º from every other point on the globe. You can calculate azimuths for great circles or rhumb lines.
A geodesic is the shortest distance between two points on a curved surface, such as an ellipsoid.
A great circle is a type of geodesic that lies on a sphere. It is the intersection of the surface of a sphere with a plane passing through the center of the sphere. For great circles, the azimuth is calculated at the starting point of the great circle path, where it crosses the meridian. In general, the azimuth along a great circle is not constant. For more information, see Great Circles.
A rhumb line is a curve that crosses each meridian at the same angle. For rhumb lines, the azimuth is the constant angle between true north and the entire rhumb line passing through the two points. For more information, see Rhumb Lines.
Azimuth calculations for geodesics degrade slowly with increasing
distance and can break down for points that are nearly antipodal or
for points close to the Equator. In addition, for calculations on
an ellipsoid, there is a small but finite input space. This space
consists of pairs of locations in which both points are nearly antipodal and both
points fall close to (but not precisely on) the Equator. In such cases,
you will receive a warning and
az will be set to
NaN for the “problem pairs.”
Geodesic azimuths on an ellipsoid are valid only for small eccentricities typical of the Earth (for example, 0.08 or less).
If you are calculating both the distance and the azimuth, you
can call just the
distance function. The function
returns the azimuth as the second output argument. It is unnecessary