scxsc

Intersection points for pairs of small circles

Syntax

[lat,lon] = scxsc(lat1,lon1,range1,lat2,lon2,range2)

[lat,lon] = scxsc(lat1,lon1,range1,lat2,lon2,range2,units)

latlon = scxsc(___)

Description

[lat,lon] = scxsc(lat1,lon1,range1,lat2,lon2,range2) returns in lat and lon the locations where pairs of small circles intersect. The small circles are defined using small circle notation, which consists of a center point and a radius in units of angular arc length. For example, the first small circle in a pair would be centered on the point (lat1,lon1) with a radius of range1 (in angular units).

For any pair of small circles, there are four possible intersection conditions: the circles are identical, they do not intersect, they are tangent to each other and hence they intersect once, or they intersect twice.

[lat,lon] = scxsc(lat1,lon1,range1,lat2,lon2,range2,units) specifies the angular units used for all inputs, where units is any valid angular unit.

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

Examples

Find Intersection Points of Two Small Circles

Given a small circle centered at (10ºS,170ºW) with a radius of 20º (~1200 nautical miles), where does it intersect with a small circle centered at (3ºN, 179ºE), with a radius of 15º (~900 nautical miles)?

[newlat,newlon] = scxsc(-10,-170,20,3,179,15)

newlat =

   -8.8368    9.8526

newlon =

   169.7578 -167.5637

Note that in this example, the two small circles cross the date line.

Input Arguments

lat1, lon1 — Center coordinate of first small circle

numeric scalar | n-element numeric vector

Latitude or longitude coordinate of the center of the first small circle in each pair, specified as one of these values.

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

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

lat1 and lon1 must have the same length.

Example: -10

Example: [-10 20 90 -45]

range1 — Radius of first small circle

positive numeric scalar | n-element vector of positive numbers

Radius of the first small 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 small circles.

• A n-element vector of positive numbers to find the intersection of n pairs of small circles. The length of range1 matches the length of lat1 and lon1.

Example: 20

Example: [20 10 45 45]

lat2, lon2 — Center coordinate of second small circle

numeric scalar | numeric vector

Latitude or longitude coordinate of the center of the second small circle in each pair, specified as one of these values.

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

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

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

Example: 3

Example: [3 30 85 -45]

range2 — Radius of second small circle

positive numeric scalar | n-element vector of positive numbers

Radius of the second small 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 small circles.

• A n-element vector of positive numbers to find the intersection of n pairs of small circles. The length of range2 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 small circle intersections

2-element vector | n-by-2 matrix

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

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

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

If a pair of small circles do not intersect, or are identical, then scxsc displays a warning and returns NaNs for the latitude and longitude coordinates of the intersection points. If a pair of small circles are tangent, then the single intersection point is returned twice.

latlon — Concatenated coordinates of small circle intersections

4-element vector | n-by-4 matrix

Concatenated coordinates of small 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 small circles.

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

If a pair of small circles do not intersect, or are identical, then scxsc displays a warning and returns NaNs for the latitude and longitude coordinates of the intersection points. If a pair of small circles are tangent, then the single intersection point is returned twice.

Tips

Great circles are a subset of small circles — a great circle is just a small circle with a radius of 90º. This provides two methods of notation for defining great circles. Great circle notation consists of a point on the circle and an azimuth at that point. Small circle notation for a great circle consists of a center point and a radius of 90º (or its equivalent in radians).

Version History

Introduced before R2006a