# rcurve

Ellipsoidal radii of curvature

## Syntax

```r = rcurve(ellipsoid,lat) r = rcurve('parallel',ellipsoid,lat) r = rcurve('meridian',ellipsoid,lat) r = rcurve('transverse',ellipsoid,lat) r = rcurve(..., angleunits) ```

## Description

`r = rcurve(ellipsoid,lat)` and ```r = rcurve('parallel',ellipsoid,lat)``` return the parallel radius of curvature at the latitude `lat` for a reference ellipsoid defined by `ellipsoid`, which can be a `referenceSphere`, `referenceEllipsoid`, or `oblateSpheroid` object, or a vector of the form ```[semimajor_axis eccentricity]```. `r` is in units of length consistent with those used for the semimajor axis. `lat` is in `'degrees'`.

`r = rcurve('meridian',ellipsoid,lat)` returns the meridional radius of curvature, which is the radius of curvature in the plane of a meridian at the latitude `lat`.

`r = rcurve('transverse',ellipsoid,lat)` returns the transverse radius of curvature, which is the radius of a curvature in a plane normal to the surface of the ellipsoid and normal to a meridian, at the latitude `lat`.

`r = rcurve(..., angleunits)` specifies the units of the input `lat`. `angleunits` can be `'degrees'` or `'radians'`.

## Examples

The radii of curvature of the default ellipsoid at 45º, in kilometers:

```r = rcurve('transverse',referenceEllipsoid('earth','km'),... 45,'degrees') r = 6.3888e+03 r = rcurve('meridian',referenceEllipsoid('earth','km'),... 45,'degrees') r = 6.3674e+03 r = rcurve('parallel',referenceEllipsoid('earth','km'),... 45,'degrees') r = 4.5024e+03```

## Version History

Introduced before R2006a