gcxgc

Intersection points for pairs of great circles

Syntax

[lat,lon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2)

[lat,lon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2,units)

latlon = gcxgc(___)

Description

[lat,lon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2) returns in 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.

[lat,lon] = gcxgc(lat1,lon1,az1,lat2,lon2,az2,units) specifies the angular units used for all inputs, where units is any valid angular unit.

latlon = gcxgc(___) returns a single output consisting of the concatenated latitude and longitude coordinates of the great circle intersection points.

Examples

Find Intersection Points of Two Great Circles

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.

Input Arguments

lat1, lon1 — Coordinate of point on first great circle

numeric scalar | n-element numeric vector

Latitude or longitude coordinate of a point on the first great circle in each pair, specified as one of these values.

• A numeric scalar to find the intersection of a single pair of great circles.

• A n-element numeric vector to find the intersection of n pairs of great circles.

lat1 and lon1 must have the same length.

Example: 10

Example: [-10 20 90 -45]

az1 — Azimuth of first great circle

positive numeric scalar | n-element vector of positive numbers

Azimuth of the first great circle of each pair, in angular units, specified as one of these values.

• A positive numeric scalar to find the intersection of a single pair of great circles.

• A n-element vector of positive numbers to find the intersection of n pairs of great circles. The length of az1 matches the length of lat1 and lon1.

Example: 20

Example: [20 10 45 45]

lat2, lon2 — Coordinate of point on second great circle

numeric scalar | numeric vector

Latitude or longitude coordinate of a point on the second great circle in each pair, specified as one of these values.

• A numeric scalar to find the intersection of a single pair of great circles.

• A n-element numeric vector to find the intersection of n pairs of great circles.

lat2 and lon2 must have the same length as lat1 and lon1.

Example: 3

Example: [3 30 85 -45]

az2 — Azimuth of second great circle

positive numeric scalar | n-element vector of positive numbers

Azimuth of the second great circle of each pair, in angular units, specified as one of these values.

• A positive numeric scalar to find the intersection of a single pair of great circles.

• A n-element vector of positive numbers to find the intersection of n pairs of great circles. The length of az2 matches the length of lat2 and lon2.

Example: 15

Example: [15 15 45 50]

units — Angular units

'degrees' (default) | 'radians'

Angular units, specified as 'degrees' or 'radians'.

Output Arguments

lat, lon — Coordinates of great circle intersections

2-element vector | n-by-2 matrix

Coordinates of great circle intersections, returned as one of the following.

• 2-element vector when you find the intersection of a single pair of great circles.

• n-by-2 matrix when you find the intersection of n pairs of great circles.

If a pair of great circles are identical, then gcxgc displays a warning and returns NaNs for the latitude and longitude coordinates of the intersection points.

latlon — Concatenated coordinates of great circle intersections

4-element vector | n-by-4 matrix

Concatenated coordinates of great circle intersections, returned as one of the following. This output is identical to [lat lon].

• 4-element vector when you find the intersection of a single pair of great circles.

• n-by-4 matrix when you find the intersection of n pairs of great circles.

If a pair of great circles are identical, then gcxgc displays a warning and returns NaNs for the latitude and longitude coordinates of the intersection points.

Version History

Introduced before R2006a