why do you need the azimuth in the gcxgc (Intersection points for pairs of great circles, mapping toolbox)

Two great circles that are not identical to one another would always have two intersection points, what does varying the azimuth do? What is the significance of the azimuths chosen in this example? I would like to implement a version of this function in python but I don't understand where the formulas are coming from.

In the documentation for gxgc:

Example

-------

lat1 = 10;

lon1 = 13;

az1 = 12;

lat2 = 0;

lon2 = 20;

az2 = -23;

[ilat,ilon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2)

% ilat =

% 14.0725 -14.0725

% ilon =

% 13.8919 -166.1081

https://www.mathworks.com/help/map/ref/gcxgc.html

Answer 1

[Pratyush]

Hi Una.

I understand that you want to know the significance of azimuth passed along with latitude and longitude of a point on great circle in "gcxgc" function. The parameter in the example refers to:

• The first pair of latitude and longitude coordinates represents the starting point of the first great circle. In this case, the starting point is at latitude 10 and longitude 13.
• The second pair of latitude and longitude coordinates represents the starting point of the second great circle. Here, the starting point is at latitude 10 and longitude 0.
• The azimuth angle of the first great circle is 20 degrees.
• The azimuth angle of the second great circle is -23 degrees.
• Azimuth determines the direction of the great circle from a starting point. A touple {latitude,longitude,azimuth} defines a unique great circle (there could be multiple great circles passing through a given latitude and longitude if azimuth is not specified). So "gcxc" function takes 2 unique circle and finds the intersection points of pairs of great circles.
• Refer to this link for more details on Azimuth: Azimuth Wikipedia