Intersection points for pairs of small circles


[newlat,newlon] = scxsc(lat1,lon1,range1,lat2,lon2,range2)


[newlat,newlon] = scxsc(lat1,lon1,range1,lat2,lon2,range2) returns in newlat and newlon the locations of the points of intersection of two small circles in small circle notation. For example, the first small circle in a pair would be centered on the point (lat1,lon1) with a radius of range1 (in angle units). The inputs must be column vectors. If the circles do not intersect, or are identical, two NaNs are returned and a warning is displayed. If the two circles are tangent, the single intersection point is returned twice.

[newlat,newlon]=scxsc(lat1,lon1,range1,lat2,lon2,range2,units) specifies the angle units used for all inputs, where units is any valid angle units string. The default units are 'degrees'.

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.

Small circle notation consists of a center point and a radius in units of angular arc length.


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,newlong] = scxsc(-10,-170,20,3,179,15)

newlat =
   -8.8368    9.8526
newlong =
   169.7578 -167.5637

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

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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).

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