localcartesian_fwd: Local Cartesian (ENU) coordinate system

In geographiclib: Access to 'GeographicLib'

Local Cartesian (ENU) coordinate system

Description

Convert between geographic coordinates and a local Cartesian coordinate system centered at a specified origin. The local system uses East-North-Up (ENU) axes.

Usage

localcartesian_fwd(x, lon0, lat0, h = 0, h0 = 0)

localcartesian_rev(x, y, z, lon0, lat0, h0 = 0)

Arguments

x	For forward conversion: a two-column matrix or data frame of coordinates (longitude, latitude) in decimal degrees, or a list with longitude and latitude components. Can also be a length-2 numeric vector for a single point. For reverse conversion: numeric vector of x (east) coordinates in meters.
lon0	Longitude of the origin in decimal degrees.
lat0	Latitude of the origin in decimal degrees.
h	Numeric vector of heights above the ellipsoid in meters. Default is 0.
h0	Height of the origin above the ellipsoid in meters. Default is 0.
y	Numeric vector of y (north) coordinates in meters.
z	Numeric vector of z (up) coordinates in meters.

Details

The local Cartesian coordinate system is useful for:

• Local surveys where a flat Earth approximation is valid

• Converting GPS positions to a local reference frame

• Robotics and navigation applications

The coordinate system is:

• x: positive east

• y: positive north

• z: positive up (away from Earth's center)

This is also known as an ENU (East-North-Up) coordinate system.

Value

• localcartesian_fwd(): Data frame with columns:

  • x: East coordinate in meters

  • y: North coordinate in meters

  • z: Up coordinate in meters

  • lon, lat, h: Input coordinates (echoed)

• localcartesian_rev(): Data frame with columns:

  • lon: Longitude in decimal degrees

  • lat: Latitude in decimal degrees

  • h: Height above ellipsoid in meters

  • x, y, z: Input coordinates (echoed)

See Also

geocentric_fwd() for Earth-Centered Earth-Fixed (ECEF) coordinates

Examples

# Set up local system centered on London
london <- c(-0.1, 51.5)

# Convert nearby points to local coordinates
pts <- cbind(
  lon = c(-0.1, -0.2, 0.0),
  lat = c(51.5, 51.6, 51.4)
)
localcartesian_fwd(pts, lon0 = london[1], lat0 = london[2])

# Round-trip conversion
fwd <- localcartesian_fwd(pts, lon0 = -0.1, lat0 = 51.5)
localcartesian_rev(fwd$x, fwd$y, fwd$z, lon0 = -0.1, lat0 = 51.5)

geographiclib documentation built on March 4, 2026, 9:07 a.m.