# enu2geodetic

Transform local east-north-up coordinates to geodetic

## Description

example

[lat,lon,h] = enu2geodetic(xEast,yNorth,zUp,lat0,lon0,h0,spheroid) transforms the local east-north-up (ENU) Cartesian coordinates specified by xEast, yNorth, and zUp to the geodetic coordinates specified by lat, lon, and h. Specify the origin of the local ENU system with the geodetic coordinates lat0, lon0, and h0. Each coordinate input argument must match the others in size or be scalar. Specify spheroid as the reference spheroid for the geodetic coordinates.

[___] = enu2geodetic(___,angleUnit) specifies the units for latitude and longitude. Specify angleUnit as 'degrees' (the default) or 'radians'.

## Examples

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Find the geodetic coordinates of the Matterhorn, using the ENU coordinates of the Matterhorn with respect to the geodetic coordinates of Zermatt, Switzerland.

First, specify the reference spheroid as WGS84. For more information about WGS84, see Comparison of Reference Spheroids. The units for ellipsoidal height and ENU coordinates must match the units specified by the LengthUnit property of the reference spheroid. The default length unit for the reference spheroid created by wgs84Ellipsoid is 'meter'.

wgs84 = wgs84Ellipsoid;

Specify the geodetic coordinates of the local origin. In this example, the local origin is Zermatt. Specify h0 as ellipsoidal height in meters.

lat0 = 46.017;
lon0 = 7.750;
h0 = 1673;

Specify the ENU coordinates of the point of interest. In this example, the point of interest is the Matterhorn.

xEast = -7134.8;
yNorth = -4556.3;
zUp = 2852.4;

Then, calculate the geodetic coordinates of the Matterhorn. The result h is the ellipsoidal height of the mountain in meters. To view the results in standard notation, specify the display format as shortG.

format shortG
[lat,lon,h] = enu2geodetic(xEast,yNorth,zUp,lat0,lon0,h0,wgs84)
lat =
45.976

lon =
7.658

h =
4531

Reverse the transformation using the geodetic2enu function.

[xEast,yNorth,zUp] = geodetic2enu(lat,lon,h,lat0,lon0,h0,wgs84)
xEast =
-7134.8

yNorth =
-4556.3

zUp =
2852.4

## Input Arguments

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ENU x-coordinates of one or more points in the local ENU system, specified as a scalar, vector, matrix, or N-D array. Specify values in units that match the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

Data Types: single | double

ENU y-coordinates of one or more points in the local ENU system, specified as a scalar, vector, matrix, or N-D array. Specify values in units that match the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

Data Types: single | double

ENU z-coordinates of one or more points in the local ENU system, specified as a scalar, vector, matrix, or N-D array. Specify values in units that match the LengthUnit property of the spheroid argument. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

Data Types: single | double

Geodetic latitude of the local origin, specified as a scalar, vector, matrix, or N-D array. The local origin can refer to one point or a series of points (for example, a moving platform). Specify the values in degrees. To use values in radians, specify the angleUnit argument as 'radians'.

Data Types: single | double

Geodetic longitude of the local origin, specified as a scalar, vector, matrix, or N-D array. The local origin can refer to one point or a series of points (for example, a moving platform). Specify the values in degrees. To use values in radians, specify the angleUnit argument as 'radians'.

Data Types: single | double

Ellipsoidal height of the local origin, specified as a scalar, vector, matrix, or N-D array. The local origin can refer to one point or a series of points (for example, a moving platform). Specify values in units that match the LengthUnit property of the spheroid object. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

Data Types: single | double

Reference spheroid, specified as a referenceEllipsoid object, oblateSpheroid object, or referenceSphere object. The term reference spheroid is used synonymously with reference ellipsoid. To create a reference spheroid, use the creation function for the object. To specify the reference ellipsoid for WGS84, use the wgs84Ellipsoid function.

Example: spheroid = referenceEllipsoid('GRS 80');

Angle units, specified as 'degrees' (the default) or 'radians'.

## Output Arguments

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Geodetic latitude of one or more points, returned as a scalar, vector, matrix, or N-D array. Values are specified in degrees within the interval [-90 90]. To use values in radians, specify the angleUnit argument as 'radians'.

Geodetic longitude of one or more points, returned as a scalar, vector, matrix, or N-D array. Values are specified in degrees within the interval [-180 180]. To use values in radians, specify the angleUnit argument as 'radians'.

Ellipsoidal height of one or more points, returned as a scalar, vector, matrix, or N-D array. Values are specified in units that match the LengthUnit property of the spheroid object. For example, the default length unit for the reference ellipsoid created by wgs84Ellipsoid is 'meter'.

## Version History

Introduced in R2012b

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