scircle1

Small circle from center and radius

Syntax

[lat,lon] = scircle1(lat0,lon0,r)

[lat,lon] = scircle1(lat0,lon0,r,az)

[lat,lon] = scircle1(lat0,lon0,r,az,ellipsoid)

[lat,lon] = scircle1(___,units)

[lat,lon] = scircle1(lat0,lon0,r,az,ellipsoid,units,npts)

[lat,lon] = scircle1(method,___)

mat = scircle1(___)

Description

[lat,lon] = scircle1(lat0,lon0,r) finds the latitude and longitude coordinates of a small circle. Specify the geographic coordinates of the center of the small circle using lat0 and lon0. Specify the radius of the small circle using r. This syntax assumes that the radius is a spherical distance in degrees.

[lat,lon] = scircle1(lat0,lon0,r,az) finds coordinates for the section of the small circle specified by az.

[lat,lon] = scircle1(lat0,lon0,r,az,ellipsoid) specifies the reference ellipsoid ellipsoid to use for the coordinates. This syntax assumes that the radius of the small circle is a linear measurement in the same units as the semimajor axis of ellipsoid.

[lat,lon] = scircle1(___,units) specifies the angle units units of the inputs and outputs, in addition to any combination of input arguments from the previous syntaxes.

[lat,lon] = scircle1(lat0,lon0,r,az,ellipsoid,units,npts) specifies the number of points npts to include in the small circle.

[lat,lon] = scircle1(method,___), where method is "rh", specifies that distances from the center of the small circle are rhumb line distances. The default for method is "gc", which specifies that distances from the center of the small circle are great circle distances (for a sphere) or geodesic distances (for an ellipsoid).

mat = scircle1(___) returns the latitude and longitude coordinates of the small circle in the matrix mat.

Examples

Find Coordinates of Small Circle

Find the latitude and longitude coordinates of a small circle centered on Ottawa with a radius of 4º.

lat0 = 45.4215;
lon0 = -75.6972;
r = 4;
[lat,lon] = scircle1(lat0,lon0,r);

Plot the small circle on a map using a thick line.

geoplot(lat,lon,LineWidth=2)
geobasemap streets

Find Coordinates of Partial Small Circle

Find the latitude and longitude coordinates of a full small circle centered on Tokyo with a radius of 5º.

lat0 = 35.6762;
lon0 = 139.6503;
r = 5;
[lat1,lon1] = scircle1(lat0,lon0,r);

Find the coordinates of a partial small circle, in this case the section of the circle between 90º from north and 270º from north.

az = [90 270];
[lat2,lon2] = scircle1(lat0,lon0,r,az);

Display both the full circle and the partial circle on a map. Use a thick line for the partial circle.

geoplot(lat1,lon1,Color=[0.8500 0.3250 0.0980])
hold on
geoplot(lat2,lon2,Color=[0.4940 0.1840 0.5560],LineWidth=3)
geobasemap streets

Find Coordinates of Small Circle on Reference Ellipsoid

Create a World Geodetic System of 1984 (WGS84) reference ellipsoid with a length unit of kilometers.

wgs84 = wgs84Ellipsoid("km");

Find the latitude and longitude coordinates of a small circle centered on Boston with a radius of 100 kilometers. Find the coordinates of the full small circle by specifying the fourth argument as [].

lat0 = 42.3601;
lon0 = -71.0589;
r = 100;
[lat,lon] = scircle1(lat0,lon0,r,[],wgs84);

Plot the small circle on a map using a thick, black line.

geoplot(lat,lon,"k","LineWidth",2)
geobasemap streets

Find Coordinates of Multiple Small Circles

You can use the scircle1 function to find the coordinates of multiple small circles with the same center or with different centers.

Multiple Small Circles with the Same Center

Find the coordinates of three small circles centered on Portland, Oregon. Specify the radii of the small circles as 3º, 3.5º, and 4º.

lat0 = 45.5152;
lon0 = -122.6784;
r = [3 3.5 4]';
[lat,lon] = scircle1(lat0,lon0,r);

Display the small circles on a map using thick lines. Differentiate the circles by including the radii in a legend.

geobasemap streets
hold on
for i=1:size(lat,2)
    geoplot(lat(:,i),lon(:,i),LineWidth=2,DisplayName=string(r(i))+char(176))
end
legend

Multiple Small Circles with the Different Centers

Find the coordinates of three small circles with different centers.

• Center the first small circle on Boston and specify the radius as 3º.

• Center the second small circle on New York City and specify the radius as 4º.

• Center the third small circle on Chicago and specify the radius as 5º.

lat0 = [42.3601 40.7128 41.8781]';
lon0 = [-71.0589 -74.0060 -87.6298]';
cities = ["Boston" "New York City" "Chicago"];
r = [3 4 5]';
[lat,lon] = scircle1(lat0,lon0,r);

Display the small circles on a map using thick lines. Differentiate the circles by including the city names in a legend.

figure
geobasemap streets
hold on
for i=1:size(lat,2)
    geoplot(lat(:,i),lon(:,i),LineWidth=2,DisplayName=cities(i))
end
legend

Input Arguments

lat0 — Latitude of center of small circle

scalar | column vector

Latitude of the center of the small circle, specified as a scalar or a column vector.

• To find the coordinates of multiple small circles with the same center, specify lat0 and lon0 as scalars and specify r as a column vector. The number of elements in the column vector is the number of small circles.

• To find the coordinates of multiple small circles with different centers, specify lat0, lon0, and r as column vectors of the same size.

The sizes of lat0 and lon0 must match.

Data Types: single | double

lon0 — Longitude of center of small circle

scalar | column vector

Longitude of the center of the small circle, specified as a scalar or a column vector.

• To find the coordinates of multiple small circles with the same center, specify lat0 and lon0 as scalars and specify r as a column vector. The number of elements in the column vector is the number of small circles.

• To find the coordinates of multiple small circles with different centers, specify lat0, lon0, and r as column vectors of the same size.

The sizes of lat0 and lon0 must match.

Data Types: single | double

r — Radius of small circle

scalar | column vector

Radius of the small circle, specified as scalar or column vector.

When lat0 and lon0 are column vectors, the number of elements in r must match the number of elements in lat0 and lon0.

Data Types: single | double

az — Azimuth indicating section of small circle to find

[] (default) | column vector | two-column matrix

Azimuth indicating the section of the small circle to find, specified as one of these options:

• A column vector — Find coordinates of the small circle from north to the specified azimuth. Each element of az corresponds to an element of r. The size of az must match the number of small circles.

• A two-column matrix — Find coordinates of the small circle between the azimuth in the first column and the azimuth in the second column. Each row of az corresponds to an element of r. The number of rows in az must match the number of small circles.

Azimuths are measured clockwise from north.

The default value of [] specifies a full small circle.

Data Types: single | double

ellipsoid — Reference ellipsoid

[1 0] (default) | referenceSphere object | referenceEllipsoid object | oblateSpheroid object | two-element numeric vector

Reference ellipsoid, specified as a referenceSphere object, a referenceEllipsoid object, an oblateSpheroid object, or a two-element numeric vector of the form [semimajor_axis eccentricity], where semimajor_axis is the length of the semimajor axis and eccentricity is the eccentricity. The values semimajor_axis and eccentricity must be of data type double.

The default value of [1 0] represents the unit sphere.

units — Angle unit

"degrees" (default) | "radians"

Angle unit, specified as one of these options:

• "degrees" — Degrees

• "radians" — Radians

If you do not specify a reference ellipsoid, this argument determines the angle units for the input and output coordinates, the radius, and the azimuth. If you specify a reference ellipsoid, this argument determines the angle units for only the input and output coordinates and the azimuth.

Data Types: char | string

npts — Number of points

100 (default) | scalar

Number of points to include in the small circle, specified as a scalar. If you specify more than one small circle, then the function finds npts points per small circle.

method — Type of distance from center of small circle

"gc" (default) | "rh"

Type of distance from the center of the small circle, specified as one of these options:

• "gc" — Use the great circle distance.

• "rh" — Use the rhumb line distance.

Data Types: char | string

Output Arguments

lat — Latitude coordinates of small circle

column vector | matrix

Latitude coordinates of the small circle, returned as a column vector with npts elements or a matrix of size npts-by-m, where m is the number of small circles.

lon — Longitude coordinates of small circle

column vector | matrix

Longitude coordinates of the small circle, returned as a column vector with npts elements or a matrix of size npts-by-m, where m is the number of small circles.

mat — Latitude and longitude coordinates of small circle

matrix

Latitude and longitude coordinates of the small circle, returned as a matrix equivalent to [lat lon].

More About

Small Circle

A small circle is the set of points with the same surface distance from a given center. Examples of small circles include the set of points exactly 100 miles from the Washington Monument, parallels on the globe, and meridians on the globe.

Version History

Introduced before R2006a