Intersection points for pairs of great circles

`[`

returns in `lat`

,`lon`

] = gcxgc(`lat1`

,`lon1`

,`az1`

,`lat2`

,`lon2`

,`az2`

)`lat`

and `lon`

the locations where
pairs of great circles intersect. The great circles are defined using
*great circle notation*, which consists of a point on the
great circle and the azimuth at that point along which the great circle proceeds.
For example, the first great circle in a pair would pass through the point
(`lat1`

,`lon1`

) with an azimuth of
`az1`

(in angular units).

For any pair of great circles, there are two possible intersection conditions: the circles are identical or they intersect exactly twice on the sphere.

returns
a single output consisting of the concatenated latitude and longitude coordinates of
the great circle intersection points.`latlon`

= gcxgc(___)

Given a great circle passing through (10ºN,13ºE) and proceeding on an azimuth of 10º, where does it intersect with a great circle passing through (0º, 20ºE), on an azimuth of -23º (that is, 337º)?

[newlat,newlon] = gcxgc(10,13,10,0,20,-23)

newlat = 14.3105 -14.3105 newlon = 13.7838 -166.2162

Note that the two intersection points are always antipodes of each other. As a simple example, consider the intersection points of two meridians, which are just great circles with azimuths of 0º or 180º:

[newlat,newlon] = gcxgc(10,13,0,0,20,180)

newlat = -90 90 newlon = 0 180

The two meridians intersect at the North and South Poles, which is exactly correct.