Great-circle distance

The distance along the sphere between pairs of points given in longitude and latitude. The central angle is computed as the atan2 of the cross and dot products of the two unit vectors, written so that nothing cancels: accurate to a few units in the last place from coincident points to antipodes (the spherical case of Vincenty 1975). The Earth is taken as a sphere of mean radius r; distances on the ellipsoid differ by up to about 0.5 per cent.

Usage

hvdist(from, to, r = 6371008.8)

Arguments

from, to

The two ends of each pair, in degrees: a matrix or data frame with columns lon and lat (an unnamed two-column matrix is read as longitude then latitude), or one point as c(lon, lat). Both have the same number of points, or one of them has one point, which is paired with every point of the other. Longitudes from -180 to 180, latitudes from -90 to 90; no missing values.

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 numeric vector of distances, one per pair, in the order of the input.

References

Vincenty, T. (1975). Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations. Survey Review, 23(176), 88-93. doi:10.1179/sre.1975.23.176.88

See also

eqproj() to project longitude and latitude to metres.

Examples

# Toronto to Montreal, metres
hvdist(c(-79.38, 43.65), c(-73.57, 45.50))
#> [1] 503922
pts <- data.frame(lon = c(0, 90, 180), lat = c(0, 0, 0))
hvdist(pts, c(0, 0))
#> [1]        0 10007557 20015114