Accelerating the pace of engineering and science

# Documentation Center

• Trial Software

# gc2sc

Center and radius of great circle

mat = gc2sc(...)

## Description

[lat,lon,radius] = gc2sc(lat0,lon0,az) converts a great circle from great circle notation (i.e., lat, lon, azimuth, where (lat, lon) is on the circle) to small circle notation (i.e., lat, lon, radius, where (lat, lon) is the center of the circle and the radius is 90 degrees, which is a definition of a great circle). A great circle has two centers and one is chosen arbitrarily. The other is its antipode. All inputs and outputs are in units of degrees.

[lat,lon,radius] = gc2sc(lat0,lon0,az,angleunits) uses the string angleunits to specify the angle units of the inputs and outputs. angleunits can equal either 'degrees' or 'radians'.

mat = gc2sc(...) returns a single output, where mat = [lat lon radius].

## Definitions

A small circle is the intersection of a plane with the surface of a sphere. A great circle is a small circle with a radius of 90º.

## Examples

Represent a great circle passing through (25ºS,70ºW) on an azimuth of 45º as a small circle:

```[lat,lon,radius] = gc2sc(-25,-70,45)

lat =
-39.8557
lon =
42.9098
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. Represent the Equator as a small circle:

```[lat, lon, radius] = gc2sc(0,-70,270)

lat =
90
lon =
-145.9638