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.
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.
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).