# forward

Convert geodetic latitude to authalic, conformal, isometric, or rectifying latitude

## Syntax

``lat = forward(converter,phi)``
``lat = forward(converter,phi,angleUnit)``

## Description

````lat = forward(converter,phi)` returns the authalic, conformal, isometric, or rectifying latitude coordinates corresponding to geodetic latitude coordinates `phi`.```

example

````lat = forward(converter,phi,angleUnit)` specifies the units of input `phi`.```

example

## Examples

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Specify geodetic latitude coordinates and create an authalic latitude converter. Then, convert the coordinates.

``` phi = [-90 -67.5 -45 -22.5 0 22.5 45 67.5 90]; conv = map.geodesy.AuthalicLatitudeConverter(wgs84Ellipsoid); beta = forward(conv,phi)```
```beta = 1×9 -90.0000 -67.4092 -44.8717 -22.4094 0 22.4094 44.8717 67.4092 90.0000 ```

Specify geodetic latitude coordinates and create an isometric latitude converter. Then, convert the coordinates.

```phi = [-90 -67.5 -45 -22.5 0 22.5 45 67.5 90]; conv = map.geodesy.IsometricLatitudeConverter(wgs84Ellipsoid); psi = forward(conv,phi)```
```psi = 1×9 -Inf -1.6087 -0.8766 -0.4006 0 0.4006 0.8766 1.6087 Inf ```

Specify geodetic latitude coordinates and convert them to radians. Create a rectifying latitude converter. Then, convert the coordinates by specifying the angle unit as `'radians'`.

```phi = [-90 -67.5 -45 -22.5 0 22.5 45 67.5 90]; phirad = deg2rad(phi); conv = map.geodesy.RectifyingLatitudeConverter(wgs84Ellipsoid); mu = forward(conv,phirad,'radians')```
```mu = 1×9 -1.5708 -1.1763 -0.7829 -0.3909 0 0.3909 0.7829 1.1763 1.5708 ```

## Input Arguments

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Geodetic latitude coordinates, specified as a numeric scalar value, vector, matrix, or N-D array. If `angleUnit` is not supplied, `phi` is in degrees. Otherwise, values of `phi` must be consistent with the units of `angleUnit`.

Data Types: `single` | `double`

Units of geodetic latitude coordinates, specified as `'degrees'` or `'radians'`.

## Output Arguments

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Converted latitude coordinates, returned as a numeric scalar, vector, matrix, or N-D array. `lat` is the same size as `phi`.

The interpretation of `lat` depends on the latitude converter. If the conversion is:

• authalic, `lat` represents the variable β (beta), and has the same units as `phi`.

• conformal, `lat` represents χ (chi), and has the same units as `phi`.

• isometric, `lat` represents ψ (psi). `lat` is a dimensionless number and does not have an angle unit.

• rectifying, `lat` represents μ (mu), and has the same units as `phi`.

## Version History

Introduced in R2013a