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# geodetic2ecef

Transform geodetic coordinates to geocentric Earth-centered Earth-fixed

## Syntax

``````[X,Y,Z] = geodetic2ecef(spheroid,lat,lon,h)``````
``````[X,Y,Z] = geodetic2ecef(___,angleUnit)``````
``[X,Y,Z] = geodetic2ecef(lat,lon,h,spheroid)``

## Description

example

``````[X,Y,Z] = geodetic2ecef(spheroid,lat,lon,h)``` transforms the geodetic coordinates specified by `lat`, `lon`, and `h` to the geocentric Earth-Centered Earth-Fixed (ECEF) Cartesian coordinates specified by `X`, `Y`, and `Z`. Specify `spheroid` as the reference spheroid for the geodetic coordinates.```
``````[X,Y,Z] = geodetic2ecef(___,angleUnit)``` specifies the units for latitude and longitude. Specify `angleUnit` as `'degrees'` (the default) or `'radians'`.```
````[X,Y,Z] = geodetic2ecef(lat,lon,h,spheroid)` is supported but not recommended. Unlike the previous syntaxes, specify `lat` and `lon` in radians. Specify `spheroid` as either a reference spheroid or an ellipsoid vector of the form `[semimajor_axis, eccentricity]`. Specify `h` in the same units as the length unit of the `spheroid` argument. Additionally, the outputs `X`, `Y`, and `Z` return in the same units as the length unit of the `spheroid` argument.```

## Examples

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Find the ECEF coordinates of Paris, France, using its geodetic coordinates.

First, specify the reference spheroid as WGS84 with length units measured in kilometers. For more information about WGS84, see Reference Spheroids. The units for the ellipsoidal height and ECEF coordinates must match the units specified by the `LengthUnit` property of the reference spheroid.

`wgs84 = wgs84Ellipsoid('kilometer');`

Specify the geodetic coordinates of Paris. Specify `h` as ellipsoidal height in kilometers.

```lat = 48.8562; lon = 2.3508; h = 0.0674;```

Then, calculate the ECEF coordinates of Paris. In this example, `x` and `y` display in scientific notation.

`[x,y,z] = geodetic2ecef(wgs84,lat,lon,h)`
```x = 4.2010e+03 ```
```y = 172.4603 ```
```z = 4.7801e+03 ```

Reverse the transformation using the `ecef2geodetic` function.

`[lat,lon,h] = ecef2geodetic(wgs84,x,y,z)`
```lat = 48.8562 ```
```lon = 2.3508 ```
```h = 0.0674 ```

## Input Arguments

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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');`

Geodetic latitude of one or more points, specified as a scalar, vector, matrix, or N-D array. Specify the values in degrees. To use values in radians, specify the `angleUnit` argument as `'radians'`.

Data Types: `single` | `double`

Geodetic longitude of one or more points, specified as a scalar, vector, matrix, or N-D array. Specify the values in degrees. To use values in radians, specify the `angleUnit` argument as `'radians'`.

Data Types: `single` | `double`

Ellipsoidal height of one or more points, specified as a scalar, vector, matrix, or N-D array. 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`

Units of angles, specified as `'degrees'` (the default) or `'radians'`.

Data Types: `char` | `string`

## Output Arguments

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ECEF x-coordinates of one or more points in the geocentric ECEF system, returned as a scalar, vector, matrix, or N-D array. Units are specified by the `LengthUnit` property of the `spheroid` argument. For example, the default length unit for the reference ellipsoid created by `wgs84Ellipsoid` is `'meter'`.

ECEF y-coordinates of one or more points in the geocentric ECEF system, returned as a scalar, vector, matrix, or N-D array. Units are specified by the `LengthUnit` property of the `spheroid` argument. For example, the default length unit for the reference ellipsoid created by `wgs84Ellipsoid` is `'meter'`.

ECEF z-coordinates of one or more points in the geocentric ECEF system, returned as a scalar, vector, matrix, or N-D array. Units are specified by the `LengthUnit` property of the `spheroid` argument. For example, the default length unit for the reference ellipsoid created by `wgs84Ellipsoid` is `'meter'`.

## Tips

• The geocentric Cartesian (ECEF) coordinate system is fixed with respect to the Earth, with its origin at the center of the spheroid and its positive x-, y-, and z-axes intersecting the surface at the following points:

LatitudeLongitude Notes
x-axis00Equator at the Prime Meridian
y-axis090Equator at 90-degrees East
z-axis900North Pole 