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# track1

Geographic tracks from starting point, azimuth, and range

## Syntax

[lat,lon] = track1(lat0,lon0,az)
[lat,lon] = track1(lat0,lon0,az,arclen)
[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid)
[lat,lon] = track1(lat0,lon0,az,angleunits)
[lat,lon] = track1(lat0,lon0,az,arclen,angleunits)
[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid,angleunits)
[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid,angleunits,npts)
[lat,lon] = track1(trackstr,...)
mat = track1(...)

## Description

[lat,lon] = track1(lat0,lon0,az) computes complete great circle tracks on a sphere starting at the point lat0,lon0 and proceeding along the input azimuth, az. The inputs can be scalar or column vectors.

[lat,lon] = track1(lat0,lon0,az,arclen) uses the input arclen to specify the arc length of the great circle track. arclen is specified in units of degrees of arc. If arclen is a column vector, then the track is computed from the starting point, with positive distance measured easterly. If arclen is a two column matrix, then the track is computed starting at the range in the first column and ending at the range in the second column. If arclen = [], then the complete track is computed.

[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid) computes the track along a geodesic arc on the ellipsoid defined by the input ellipsoid, which can be a referenceSphere, referenceEllipsoid, or oblateSpheroid object, or a vector of the form [semimajor_axis eccentricity]. arclen must be expressed in length units that match the units of the semimajor axis — unless ellipsoid is [] or the semimajor axis length is zero. In these special cases, arclen is assumed to be in degrees of arc and the tracks are computed on a sphere, as in the preceding syntax.

[lat,lon] = track1(lat0,lon0,az,angleunits),
[lat,lon] = track1(lat0,lon0,az,arclen,angleunits), and
[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid,angleunits) use the string angleunits to specify the angle units of the inputs and outputs. angleunits can equal 'degrees' or 'radians'.

[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid,angleunits,npts) uses the scalar input npts to specify the number of points per track. The default value of npts is 100.

[lat,lon] = track1(trackstr,...) uses the string trackstr to define either a great circle or rhumb line track. trackstr can equal 'gc' or 'rh'. If trackstr is 'gc', then either great circle (given a sphere) or geodesic (given an ellipsoid) tracks are computed. If trackstr is 'rh', then the rhumb line tracks are computed.

mat = track1(...) returns a single output argument mat such that mat = [lat lon]. This is useful if only a single track is computed.

Multiple tracks can be defined from a single starting point by providing scalar lat0 and lon0 and column vectors for az and arclen.

## Definitions

A path along the surface of the Earth connecting two points is a track. Two types of track lines are of interest geographically, great circles and rhumb lines. Great circles represent the shortest possible path between two points. Rhumb lines are paths with constant angular headings. They are not, in general, the shortest path between two points.

Full great circles bisect the Earth; the ends of the track meet to form a complete circle. Rhumb lines with true east or west azimuths are parallels; the ends also meet to form a complete circle. All other rhumb lines terminate at the poles; their ends do not meet.

## Examples

```% Set up the axes.
axesm('mercator','MapLatLimit',[-60 60],'MapLonLimit',[-60 60])
gridm on; plabel on; mlabel on;

% Plot the great circle track in green.
[lattrkgc,lontrkgc] = track1(0,0,45,[-55 55]);
plotm(lattrkgc,lontrkgc,'g')

% Plot the rhumb line track in red.
[lattrkrh,lontrkrh] = track1('rh',0,0,45,[-55 55]);
plotm(lattrkrh,lontrkrh,'r')```