Small circles from center, range, and azimuth

`[lat,lon] = scircle1(lat0,lon0,rad)`

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

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

[lat,lon] = scircle1(lat0,lon0,rad,* units*)

[lat,lon] = scircle1(lat0,lon0,rad,az,

`units`

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

`units`

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

`units`

[lat,lon] = scircle1(

`track`

`[lat,lon] = scircle1(lat0,lon0,rad)`

computes
small circles (on a sphere) with a center at the point `lat0,lon0`

and
radius `rad`

. The inputs can be scalar or column
vectors. The input radius is in degrees of arc length on a sphere.

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

uses
the input `az`

to define the small circle arcs computed.
The arc azimuths are measured clockwise from due north. If `az`

is
a column vector, then the arc length is computed from due north. If `az`

is
a two-column matrix, then the small circle arcs are computed starting
at the azimuth in the first column and ending at the azimuth in the
second column. If `az = []`

, then a complete small
circle is computed.

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

computes
small circles on the ellipsoid defined by the input `ellipsoid`

,
rather than by assuming a sphere. `ellipsoid`

is
a `referenceSphere`

, `referenceEllipsoid`

, or `oblateSpheroid`

object, or a vector
of the form `[semimajor_axis eccentricity]`

. If the
semimajor axis is non-zero, `rad`

is assumed to be
in distance units matching the units of the semimajor axis. However,
if `ellipsoid = []`

, or if the semimajor axis is
zero, then `rad`

is interpreted as an angle and the
small circles are computed on a sphere as in the preceding syntax.

`[lat,lon] = scircle1(lat0,lon0,rad,`

, * units*)

`[lat,lon] = scircle1(lat0,lon0,rad,az,``units`

)

,
and `[lat,lon] = scircle1(lat0,lon0,rad,az,ellipsoid,``units`

)

are all valid calling forms, which use the input

`units`

`units`

`'degrees'`

is
assumed.`[lat,lon] = scircle1(lat0,lon0,rad,az,ellipsoid,`

uses
the scalar input * units*,npts)

`npts`

to determine the number of
points per small circle computed. The default value of `npts`

is
100.`[lat,lon] = scircle1(`

uses * track*,...)

`track`

`track`

=
'gc'

, then small circles are computed. If `track`

=
'rh'

, then the circles with radii of constant rhumb line
distance are computed. If you omit `track`

`'gc'`

is
assumed.`mat = scircle1(...)`

returns a single output
argument where `mat = [lat lon]`

. This is useful
if a single small circle is computed.

Multiple circles can be defined from a single starting point
by providing scalar `lat0,lon0`

inputs and column
vectors for `rad`

and `az`

if desired.

A *small circle* is the locus of all points
an equal surface distance from a given center. For true small circles,
this distance is always calculated in a great circle sense; however,
the `scircle1`

function allows a locus to be calculated
using distances in a rhumb line sense as well. An example of a small
circle is *all points exactly 100 miles from the Washington
Monument*. Parallels on the globe are all small circles.
Great circles are a subset of small circles, specifically those with
a radius of 90º or its angular equivalent, so all meridians on
the globe are small circles as well.

*Small circle notation* consists of a center
point and a radius in units of angular arc length.

Create and plot a small circle centered at (0º,0º) with a radius of 10º.

axesm('mercator','MapLatLimit',[-30 30],'MapLonLimit',[-30 30]); [latc,longc] = scircle1(0,0,10); plotm(latc,longc,'g')

If the desired radius is known in some nonangular distance unit,
use the radius returned by the `earthRadius`

function
as the ellipsoid input to set the range units. (Use an empty azimuth
entry to indicate a full circle.)

[latc,longc] = scircle1(0,0,550,[],earthRadius('nm')); plotm(latc,longc,'r')

For just an arc of the circle, enter an azimuth range.

[latc,longc] = scircle1(0,0,5,[-30 70]); plotm(latc,longc,'m')

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