azeq_fwd: Azimuthal Equidistant projection

In geographiclib: Access to 'GeographicLib'

Azimuthal Equidistant projection

Description

Convert geographic coordinates to/from Azimuthal Equidistant projection centered on a specified point. This projection preserves distances from the center point.

Usage

azeq_fwd(x, lon0, lat0)

azeq_rev(x, y, lon0, lat0)

Arguments

x	For forward conversion: a two-column matrix or data frame of coordinates (longitude, latitude) in decimal degrees. For reverse conversion: numeric vector of x coordinates in meters.
lon0	Longitude of projection center in decimal degrees. Can be a vector to specify different centers for each point.
lat0	Latitude of projection center in decimal degrees. Can be a vector to specify different centers for each point.
y	Numeric vector of y coordinates in meters (for reverse conversion).

Details

The Azimuthal Equidistant projection shows all points at their true distance and direction from the center point. It is commonly used for:

• Radio/telecommunications range maps

• Seismic wave propagation studies

• Air route distance calculations

• UN emblem (centered on North Pole)

The projection is neither conformal nor equal-area, but distances from the center are preserved exactly.

All parameters (x, lon0, lat0) are vectorized and recycled to a common length, allowing different projection centers for each point.

Value

Data frame with columns:

• For forward conversion:

  • x: Easting in meters from center

  • y: Northing in meters from center

  • azi: Azimuth from center to point (degrees)

  • scale: Scale factor at the point

  • lon, lat: Input coordinates (echoed)

  • lon0, lat0: Center coordinates (echoed)

• For reverse conversion:

  • lon: Longitude in decimal degrees

  • lat: Latitude in decimal degrees

  • azi: Azimuth from center to point (degrees)

  • scale: Scale factor at the point

  • x, y: Input coordinates (echoed)

  • lon0, lat0: Center coordinates (echoed)

Examples

# Project cities relative to Sydney
cities <- cbind(
  lon = c(-74, 139.7, 0),
  lat = c(40.7, 35.7, 51.5)
)
azeq_fwd(cities, lon0 = 151.2, lat0 = -33.9)

# Distance from Sydney = sqrt(x^2 + y^2)
result <- azeq_fwd(cities, lon0 = 151.2, lat0 = -33.9)
sqrt(result$x^2 + result$y^2) / 1000  # km

# Different center for each point (e.g., distance from home city)
homes <- cbind(lon = c(151.2, 139.7, -0.1), lat = c(-33.9, 35.7, 51.5))
destinations <- cbind(lon = c(-74, -74, -74), lat = c(40.7, 40.7, 40.7))
azeq_fwd(destinations, lon0 = homes[,1], lat0 = homes[,2])

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