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Intersection points for pairs of small circles

`[`

returns in `lat`

,`lon`

] = scxsc(`lat1`

,`lon1`

,`range1`

,`lat2`

,`lon2`

,`range2`

)`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.

returns
a single output consisting of the concatenated latitude and longitude coordinates of
the small circle intersection points.`latlon`

= scxsc(___)

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.

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).