gc2sc (Mapping Toolbox)

Convert great circles to small circle notation

Syntax

[centerlat,centerlong,radius] = gc2sc(lat,long,az)
[centerlat,centerlong,radius] = gc2sc(lat,long,az,units)

Description

Great circles are a sub-category of small circles, having a radius of 90º.
Because of the computational circumstances under which these objects often arise, however, two different notations are convenient.

Great circle notation consists of a point on the great circle and the azimuth at that point along which the great circle proceeds.

Small circle notation consists of a center point and a radius in units of angular arc length.

[centerlat,centerlong,radius] = gc2sc(lat,long,az) returns the small circle notation for great circles entered in great circle notation.

[centerlat,centerlong,radius] = gc2sc(lat,long,az,units) specifies the standard angle unit string. The default value is 'degrees'.

Examples

Given a great circle passing through (25ºS,70ºW) on an azimuth of 45º, how can it be represented in small circle notation?

[newlat,newlong,range] = gc2sc(-25,-70,45)
newlat =
  -39.8557
newlong =
   42.9098
range =
    90

A great circle always bisects the sphere. As a demonstration of this statement, consider the Equator, which passes through any point with a latitude of 0º and proceeds on an azimuth of 90º or 270º. In small circle notation, this is:

[newlat,newlong,range] = gc2sc(0,-70,270)
newlat =
    90
newlong =
 -145.9638
range =
    90

Not surprisingly, the small circle is centered on the North Pole. As always, at the poles, the longitude is arbitrary, due to the convergence of the meridians.

Remarks

Note that the center coordinates returned by this command always lead to one of two possibilities. Since the great circle bisects the sphere, the antipode of the returned point is also a center with a radius of 90º. In the above example, the South Pole would also be a suitable center for the Equator in small circle notation.

`antipode`	Find antipodal points
`distdim`	Distance unit conversions
`gcxgc` `gcxsc` `rhxrh` `crossfix`	`I`ntersection functions