[R-sig-Geo] function for bearing

[Roger Bivand]

On Thu, 9 Mar 2006, Sebastian Luque wrote:

> Hello,
> 
> I have searched the archives and other sources, but cannot find an R
> function that would calculate the bearing of a pair of points (lat, lon).
> It wouldn't be difficult to write such a function, but has this already
> been done in a package?

I've an implementation that I will add to sp or maptools. It calculates 
the azimuth using Snyder's spherical equations (p. 30), or an equivalent 
solution by Abdali:

gzAzimuth <- function(from, to, type="snyder_sphere") {
  deg2rad <- function(x) x*pi/180
  rad2deg <- function(x) x*180/pi
# note negative longitudes
  if (is.matrix(from)) {
    lon <- -deg2rad(from[,1])
    lat <- deg2rad(from[,2])
  } else {
    lon <- -deg2rad(from[1])
    lat <- deg2rad(from[2])
  }
  if (is.matrix(to)) {
    if (nrow(to) > 1) stop("to: single coordinate")
    to <- c(to)
  } else {
    lon0 <- -deg2rad(to[1])
    lat0 <- deg2rad(to[2])
  }
  dflon = lon-lon0
# results in degrees from N, negative west
  if (type == "abdali") res <- atan2(sin(dflon), ((cos(lat)*tan(lat0)) -
    (sin(lat)*cos(dflon))))
  else if (type == "snyder_sphere") res <- atan2((cos(lat0)*sin(dflon)), 
    (cos(lat)*sin(lat0)) - (sin(lat)*cos(lat0)*cos(dflon)))
  else stop("type unkown")
  is.na(res) <- lon == lon0 & lat == lat0 
  rad2deg(res)
}

There is a very interesting discussion of the centrality of 
azimuth-finding in the development of mathematics and mathematical 
geography in: http://patriot.net/users/abdali/ftp/qibla.pdf. Among others, 
al-Khwarizmi was an important contributor.

It seems to work like Tim Keitt's suggestion:

> gzAzimuth(c(10,50), c(70,20))
[1] 99.76647
> 99 + (45 + (59.287/60))/60
[1] 99.76647

$ geod +ellps=sphere << EOF -I
> 50N 10E 20N 70E
> EOF
99d45'59.287"   -42d23'10.939"  6189790.454

The first argument to the function can be a matrix of coordinates, the 
second is a single coordinate.

Roger

> 
> 
> Thanks in advance,
> 
> 

-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no