Mapping Toolbox

track1

Compute great circle or rhumb line track defined by point, azimuth, and range

Syntax

• [lattrk,lontrk] = track1(lat,lon,az) 
  [lattrk,lontrk] = track1(track,lat,lon,az...)
  [lattrk,lontrk] = track1(track,lat,lon,az,units)
  [lattrk,lontrk] = track1(track,lat,lon,az,rng)
  [lattrk,lontrk] = track1(track,lat,lon,az,rng,units)
  [lattrk,lontrk] = track1(track,lat,lon,az,rng,geoid)
  [lattrk,lontrk] = track1(track,lat,lon,az,rng,geoid,units)
  [lattrk,lontrk] = track1(track,lat,lon,az,rng,geoid,units,npts)
  pts = track1(lat,lon,az)
  

Background

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.

Description

[lattrk,lontrk] = track1(lat,lon,az) returns, in lattrk and lontrk, points along a complete (great circle) track passing through the point specified by lat and lon with an initial azimuth at that point of az. When the inputs are column vectors, the successive tracks are stored in separate columns of lattrk and lontrk.

[lattrk,lontrk] = track1(track,lat,lon,az) allows the specification of the track logic to be employed. A string track of 'gc' is the default, resulting in a great circle track. A track of 'rh' results in a complete rhumb line track.

[lattrk,lontrk] = track1(track,lat,lon,az,units) specifies the units of the inputs and outputs, where units is any valid angle unit string. The default is 'degrees'.

[lattrk,lontrk] = track1(track,lat,lon,az,rng) specifies the range of the track. rng is a one- or two-column matrix. If rng has one column, the track will extend from the point (lat,lon) at an azimuth of az for a distance rng if rng is positive, or at an azimuth az+180º (or its angular equivalent) for a distance of abs(rng) if rng is negative. If rng has two columns, the end points are defined as above. In this case, the segment extends from the point associated with the first column of rng to the point associated with the second column. rng is in units (unless a geoid is input). When no rng is provided, or rng is empty, a complete track is returned.

[lattrk,lontrk] = track1(track,lat,lon,az,rng,geoid,units) specifies the elliptical definition of the Earth with a two-element geoid model vector geoid. The default geoid is a spherical Earth, which is sufficient for most applications. If used, the units of the semimajor axis of the geoid vector define the units for the rng input, overriding units for this purpose.

[lattrk,lontrk] = track1(track,lat,lon,az,rng,geoid,units,npts) specifies the number of points, npts, per output track. npts is 100 by default.

pts = track1(lat,lon,az,...) combines the outputs into a single, two-column matrix pts.

Examples

• axesm('mercator','MapLatLimit',[-60 60],'MapLonLimit',[-60 60])
  [lattrkgc,lontrkgc] = track1(0,0,45,[-55 55]);
  plotm(lattrkgc,lontrkgc,'g')
  [lattrkrh,lontrkrh] = track1('rh',0,0,45,[-55 55]);
  plotm(lattrkrh,lontrkrh,'r')
  
  
  

See Also

azimuth	Azimuth between two points on the globe
distance	Distance between two points on the globe
reckon	New point with an azimuth and distance
scircle1 scircle2	Small circle coordinates
track	Connect waypoints with track segments
track2	Great circle or rhumb line defined by two points
trackg	Interactive tracks

track

track2