# scircle2

Small circle from center and point on perimeter

## Description

example

[lat,lon] = scircle2(lat0,lon0,latP,lonP) 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 a point on the perimeter of the small circle using latP and lonP. This syntax assumes that the coordinates are referenced to a sphere.

example

[lat,lon] = scircle2(lat0,lon0,latP,lonP,ellipsoid) specifies the reference ellipsoid ellipsoid for the coordinates.

[lat,lon] = scircle2(___,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] = scircle2(lat0,lon0,latP,lonP,ellipsoid,units,npts) specifies the number of points npts to include in the small circle.

[lat,lon] = scircle2(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 = scircle2(___) returns the latitude and longitude coordinates of the small circle in the matrix mat.

## Examples

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Find the latitude and longitude coordinates of a small circle centered on Ottawa with Toronto on the perimeter.

lat0 = 45.4215;
lon0 = -75.6972;
latP = 43.6532;
lonP = -79.3832;
[lat,lon] = scircle2(lat0,lon0,latP,lonP);

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

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

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 Albany at the perimeter.

lat0 = 42.3601;
lon0 = -71.0589;
latP = 42.6526;
lonP = -73.7562;
[lat,lon] = scircle2(lat0,lon0,latP,lonP,wgs84);

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

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

You can use the scircle2 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 points on the perimeters of the circles using the coordinates of Seattle, Vancouver, and Calgary.

lat0 = 45.5152;
lon0 = -122.6784;
latP = [47.6062 49.2827 37.7749]';
lonP = [-122.3321 -123.1207 -122.4194]';
cities = ["Seattle" "Vancouver" "San Francisco"];
[lat,lon] = scircle2(lat0,lon0,latP,lonP);

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

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

Multiple Small Circles with the Different Centers

Find the coordinates of three small circles with different centers.

• The first small circle is centered on Boston and has New York City on its perimeter.

• The second small circle is centered on Washington, DC and has Philadelphia on its perimeter.

• The third small circle is centered on Chicago and has St. Louis on its perimeter.

lat0 = [42.3601 38.9072 41.8781]';
lon0 = [-71.0589 -77.0369 -87.6298]';
latP = [40.7128 39.9526 38.627]';
lonP = [-74.0060 -75.1652 -90.1994]';
[lat,lon] = scircle2(lat0,lon0,latP,lonP);
cities = ["Boston and New York City" "Washington, DC and Philadelphia" "Chicago and St. Louis"];

Display the small circles on a map using thick lines. Differentiate the circles by including the city name pairs 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

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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 latP and lonP as column vectors. The number of elements in the column vectors is the number of small circles.

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

The sizes of lat0 and lon0 must match.

Data Types: double

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 latP and lonP as column vectors. The number of elements in the column vectors is the number of small circles.

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

The sizes of lat0 and lon0 must match.

Data Types: double

Latitude of a point on the perimeter of the small circle, specified as a scalar or a column vector.

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

The sizes of latP and lonP must match.

Data Types: double

Longitude of a point on the perimeter of the small circle, specified as a scalar or a column vector.

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

The sizes of latP and lonP must match.

Data Types: double

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.

Angle unit, specified as one of these options:

• "degrees" — Degrees

Data Types: char | string

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.

Data Types: double

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

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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.

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.

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

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### 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 and parallels on the globe.

## Version History

Introduced before R2006a