Mapping Toolbox

gcxgc

Provide intersection coordinates for pairs of great circles

Syntax

• [newlat,newlong] = gcxgc(lat1,long1,az1,lat2,long2,az2)
  [newlat,newlong] = gcxgc(lat1,long1,az1,lat2,long2,az2,units)
  

Description

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

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

[newlat,newlong] = gcxgc(lat1,long1,az1,lat2,long2,az2) returns the two intersection points of pairs of great circles input in great circle notation.When the two great circles are identical (which is not, in general, apparent by inspection), two NaNs are returned instead and a warning is displayed. For multiple pairings, the inputs must be column vectors.

[newlat,newlong] = gcxgc(lat1,long1,az1,lat2,long2,az2,units)specifies the standard angle unit string. The default value is 'degrees'.

Examples

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 (i.e. 337º)?

• [newlat,newlong] = gcxgc(10,13,10,0,20,-23)
  newlat =
     14.3105  -14.3105
  newlong =
     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,newlong] = gcxgc(10,13,0,0,20,180)
  newlat =
     -90    90
  newlong =
     -174.4504   12.5094
  

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

See Also

antipode	Find antipodal points
gc2sc	Convert great circle to small circle notation
scxsc gcxsc rhxrh crossfix polyxpoly	Other intersection functions

gcwaypts

gcxsc