Convert geographic coordinates to/from Azimuthal Equidistant projection centered on a specified point. This projection preserves distances from the center point.
azeq_fwd(x, lon0, lat0)
azeq_rev(x, y, lon0, lat0)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.
Longitude of projection center in decimal degrees. Can be a vector to specify different centers for each point.
Latitude of projection center in decimal degrees. Can be a vector to specify different centers for each point.
Numeric vector of y coordinates in meters (for reverse conversion).
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)
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.
# 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)
#> x y azi scale lon lat lon0 lat0
#> 1 14579210 6568621 86.19279 0.2336719 -74.0 40.7 151.2 -33.9
#> 2 -1346704 7680058 -10.16661 0.7676383 139.7 35.7 151.2 -33.9
#> 3 -11109728 12846458 -119.39223 0.1714770 0.0 51.5 151.2 -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
#> [1] 15990.627 7797.237 16984.038
# 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])
#> x y azi scale lon lat lon0 lat0
#> 1 14579210 6568621 86.19279 0.2336719 -74 40.7 151.2 -33.9
#> 2 4608995 9847721 153.00375 0.5826567 -74 40.7 139.7 35.7
#> 3 -5302905 1761511 -128.76352 0.8770643 -74 40.7 -0.1 51.5