Equal-area projection of longitude and latitude, and its inverse

eqproj() maps longitude and latitude to planar metres by the Lambert azimuthal equal-area projection of the sphere about a centre; eqinv() maps them back. Areas are exact, so intensities, nearest-neighbour expectations and K functions computed on the result are right; lengths are scaled by cos(c / 2) along the radius from the centre and its inverse across it (c the central angle), so within 100 km of the centre every length is right to 3.1e-5 relative. Every planar function of the package takes the projected coordinates; those with a lonlat argument call this projection themselves.

Usage

eqproj(x, y = NULL, lon0 = NULL, lat0 = NULL, r = 6371008.8)

eqinv(x, y = NULL, lon0, lat0, r = 6371008.8)

Arguments

x, y: The points: x and y numeric vectors, or x a matrix or data frame with columns named lon and lat for eqproj() and x and y for eqinv() (an unnamed two-column matrix is read in that order) and y NULL. Longitudes from -180 to 180, latitudes from -90 to 90; no missing values.
lon0, lat0: The centre of the projection in degrees. For eqproj(), NULL (both) takes the circular mean of the longitudes and the mean of the latitudes.
r: The radius of the sphere, positive; the distances come back in its unit. The default is the mean Earth radius in metres.

Value

A data frame with one row per point, in input order: x and y (east and north, in the unit of r) from eqproj(), with the centre used as the attribute centre; lon and lat from eqinv().

References

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395, chapter 24. doi:10.3133/pp1395

Examples

p <- eqproj(c(-79.40, -79.38, -79.35), c(43.64, 43.66, 43.65))
p
#>            x             y
#> 1 -1877.6518 -1111.6869087
#> 2  -268.1467  1111.9561852
#> 3  2145.5306     0.3446339
a <- attr(p, "centre")
eqinv(p, lon0 = a[1], lat0 = a[2])
#>      lon   lat
#> 1 -79.40 43.64
#> 2 -79.38 43.66
#> 3 -79.35 43.65