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reckon

Point at specified azimuth and range on sphere or ellipsoid

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    Syntax

    [lat2,lon2] = reckon(lat1,lon1,arclen,az)
    [lat2,lon2] = reckon(lat1,lon1,arclen,az,ellipsoid)
    [lat2,lon2] = reckon(___,units)
    [lat2,lon2] = reckon(method,___)

    Description

    [lat2,lon2] = reckon(lat1,lon1,arclen,az) finds the coordinates of the point at the spherical distance arclen and azimuth az from the point with coordinates lat1 and lon1. This syntax references the coordinates to a sphere, assumes that all input arguments are in degrees, and assumes a great circle azimuth.

    example

    [lat2,lon2] = reckon(lat1,lon1,arclen,az,ellipsoid) specifies the reference ellipsoid for the coordinates. This syntax assumes that arclen is a linear distance in the units of the semimajor axis of the reference ellipsoid.

    example

    [lat2,lon2] = reckon(___,units) specifies the angle units, in addition to any combination of input arguments from the previous syntaxes.

    [lat2,lon2] = reckon(method,___), where method is "rh", indicates that az is a rhumb line azimuth. The default for method is "gc", which indicates that az is a great circle azimuth (for a sphere) or a geodesic azimuth (for an ellipsoid).

    Examples

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    Open Live Script

    Find the coordinates of the point 600 nautical miles northwest of London. Convert 600 nautical miles to a spherical distance in degrees by using the nm2deg function. A northwest direction has an azimuth of 315 degrees.

    arclen = nm2deg(600);
az = 315;
[lat,lon] = reckon(51.5,0,arclen,az)
    lat = 
57.8999

    lon = 
-13.3507
    Open Live Script

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

    wgs84 = wgs84Ellipsoid("nm");

    Find the coordinates of the point 600 nautical miles northwest of London. Reference the coordinates to the ellipsoid. When you specify a reference ellipsoid as input to the reckon function, specify the arc length as a linear distance. A northwest direction has an azimuth of 315 degrees.

    arclen = 600;
az = 315;
[lat,lon] = reckon(51.5,0,arclen,az,wgs84)
    lat = 
57.8953

    lon = 
-13.3015

    Input Arguments

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    Latitude of the input point, specified as a scalar or array.

    You can specify lat1, lon1, arclen, and az using a combination of scalars and arrays, as long as the arrays are of the same size. The function expands the scalar inputs to match the size of the array inputs.

    Data Types: single | double

    Longitude of the input point, specified as a scalar or array.

    You can specify lat1, lon1, arclen, and az using a combination of scalars and arrays, as long as the arrays are of the same size. The function expands the scalar inputs to match the size of the array inputs.

    Data Types: single | double

    Azimuth from the input point to the output point, measured clockwise from north, specified as a scalar or array.

    You can specify lat1, lon1, arclen, and az using a combination of scalars and arrays, as long as the arrays are of the same size. The function expands the scalar inputs to match the size of the array inputs.

    Data Types: single | double

    Length of the arc connecting the input point and output point, specified as a scalar or array.

    • When you do not specify a reference ellipsoid as input, specify arclen as a spherical distance in degrees. You can specify a spherical distance in radians by using the units argument.

    • When you specify a reference ellipsoid as input, specify arclen as a linear distance in the units of the semimajor axis of the ellipsoid.

    You can specify lat1, lon1, arclen, and az using a combination of scalars and arrays, as long as the arrays are of the same size. The function expands the scalar inputs to match the size of the array inputs.

    Data Types: single | double

    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 coordinates, arc length, and azimuth. If you specify a reference ellipsoid, this argument only determines the angle units for the coordinates and the azimuth.

    Data Types: char | string

    Reference ellipsoid, specified as a referenceSphere object, a referenceEllipsoid object, an oblateSpheroid object, or a two-element 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.

    Type of curve connecting the input point and output point, specified as one of these options:

    • "gc" — az is a great circle azimuth (for spheres) or a geodesic azimuth (for ellipsoids).

    • "rh" — az is a rhumb line azimuth.

    For more information about rhumb lines and great circles, see Comparison of Rhumb Lines and Great Circles.

    Data Types: char | string

    Output Arguments

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    Latitude of the output point, returned as a scalar or an array that matches the size of the largest latitude or longitude input.

    Longitude of the output point, returned as a scalar or an array that matches the size of the largest latitude or longitude input.

    Version History

    Introduced before R2006a

    See Also

    Functions

    Topics