Generate Small Circles

A small circle is the intersection of a plane with the surface of a sphere, such as a parallel of latitude on a spherical representation of the Earth. You can generate a small circle from the center point and a point on the perimeter by using the scircle2 function. You can generate a small circle from the center point and the arc length of the radius by using the scircle1 function.

For this example, create a small circle that surrounds Norway, Sweden, and Finland by using the scircle2 function and then create an identical small circle by using the scircle1 function.

First, specify the coordinates of a center point and a point along the perimeter. Find the coordinates of 100 points that make up the small circle by using the scircle2 function.

centerLat = 62; 
centerLon = 20;
perimeterLat = 72;
perimeterLon = 19;
[lat2,lon2] = scircle2(centerLat,centerLon, ...
    perimeterLat,perimeterLon);

Calculate the arc length in degrees between the center point and the point along the perimeter. Find the coordinates of the same small circle by using the scircle1 function.

[arclen,~] = distance(centerLat,centerLon, ...
    perimeterLat,perimeterLon);
[lat1,lon1] = scircle1(centerLat,centerLon,arclen);

Verify that the small circles are identical, within a tolerance.

dLat = abs(lat1-lat2);
dLon = abs(lon1-lon2);
all(dLat < 1e-12)

ans = logical
   1

all(dLon < 1e-12)

ans = logical
   1

Display the center point, perimeter point, and small circle on the surface of a geographic globe. Change the view by using the campos function.

uif = uifigure;
g = geoglobe(uif,'Terrain','none');
hold(g,'on')

geoplot3(g,centerLat,centerLon,0,'ro','LineWidth',2)
geoplot3(g,perimeterLat,perimeterLon,0,'ro','LineWidth',2)
geoplot3(g,lat1,lon1,0,'r','LineWidth',2)

campos(g,40,-18,10000000)