Geographic tracks from starting point, azimuth, and range

`[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`

[lat,lon] = track1(

`trackstr`

mat = track1(...)

`[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`

)

where `angleunits`

defines
the units of the input and output angles as `'degrees'`

or `'radians'`

.`[lat,lon] = track1(lat0,lon0,az,arclen,ellipsoid,`

uses
the scalar input * angleunits*,npts)

`npts`

to specify the number of
points per track. The default value of `npts`

is
100.`[lat,lon] = track1(`

where * trackstr*,...)

`trackstr`

is
a character vector that defines either a great circle (`'gc'`

)
or rhumb line track (`'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`

.

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.

% 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')

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