# Documentation

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# scxsc

Intersection points for pairs of small circles

## Syntax

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

## Description

`[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 `NaN`s 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. 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.

## Examples

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.

## 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).