# Find the delta position from two positions A and B

Source:`R/n_EA_E_and_n_EB_E2p_AB_E.R`

`n_EA_E_and_n_EB_E2p_AB_E.Rd`

Given the n-vectors for positions A (`n_EA_E`

) and B (`n_EB_E`

), the
output is the delta vector from A to B (`p_AB_E`

).

## Usage

```
n_EA_E_and_n_EB_E2p_AB_E(
n_EA_E,
n_EB_E,
z_EA = 0,
z_EB = 0,
a = 6378137,
f = 1/298.257223563
)
```

## Arguments

- n_EA_E
n-vector of position A, decomposed in E (3x1 vector) (no unit)

- n_EB_E
n-vector of position B, decomposed in E (3x1 vector) (no unit)

- z_EA
Depth of system A, relative to the ellipsoid (z_EA = -height) (m, default 0)

- z_EB
Depth of system B, relative to the ellipsoid (z_EB = -height) (m, default 0)

- a
Semi-major axis of the Earth ellipsoid (m, default [WGS-84] 6378137)

- f
Flattening of the Earth ellipsoid (no unit, default [WGS-84] 1/298.257223563)

## Details

The calculation is exact, taking the ellipticity of the Earth into account.
It is also nonsingular as both n-vector and p-vector are nonsingular
(except for the center of the Earth).
The default ellipsoid model used is WGS-84, but other ellipsoids (or spheres) might be specified
via the optional parameters `a`

and `f`

.

## References

Kenneth Gade A Nonsingular Horizontal Position Representation.
*The Journal of Navigation*, Volume 63, Issue 03, pp 395-417, July 2010.

## Examples

```
lat_EA <- rad(1); lon_EA <- rad(2); z_EA <- 3
lat_EB <- rad(4); lon_EB <- rad(5); z_EB <- 6
n_EA_E <- lat_lon2n_E(lat_EA, lon_EA)
n_EB_E <- lat_lon2n_E(lat_EB, lon_EB)
n_EA_E_and_n_EB_E2p_AB_E(n_EA_E, n_EB_E, z_EA, z_EB)
#> [1] -34798.44 331985.66 331375.96
```