Ellipsoidal Distance given Latitude and Longitude
Ellipsoidal.Distance(olat, olon, tlat, tlon, a = 6378137, b = 6356752.314, tol=10^(-12))list
distance, km
azimuth, degrees
reverse azimuth, degrees
=0, if convergence failed, else=1
Origin Latitude, degrees
Origin Longitude, degrees
Target Latitude, degrees
Target Longitude, degrees
major axis, meters. If missing uses the
minor axis, meters
Tolerance for convergence, default=10^(-12)
Jonathan M. Lees<jonathan.lees@unc.edu>
Uses Vincenty's formulation to calculate the distance along a great circle on an ellipsoidal body.
If a and be are not provided, they are set by default to a=6378137.0 , b=6356752.314, the WGS-84 standard.
Only one pair of (olat, olon) and (tlat, tlon) can be given at a time. The program is not vectorized.
Quoting from the wiki page this algorithm was extracted from:
"Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of an spheroid, developed by Thaddeus Vincenty in 1975. They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods such as great-circle distance which assume a spherical Earth.
The first (direct) method computes the location of a point which is a given distance and azimuth (direction) from another point. The second (inverse) method computes the geographical distance and azimuth between two given points. They have been widely used in geodesy because they are accurate to within 0.5 mm (.020 sec) on the Earth ellipsoid"
http://en.wikipedia.org/wiki/Vincenty%27s_formulae
Vincenty, T. (April 1975). Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations. Survey Review XXIII (misprinted as XXII) (176): 88.201393. http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf. Retrieved 2009-07-11.
distaz
#### compare to spheroidal calculation distaz
####
R.MAPK = 6378.2064
N =20
OUT = list(dadist=0, ed2dist=0, ed1dist=0, dif2=0, dif1=0, pct1=0)
for( i in 1:N)
{
olat = runif(1, -90, 90)
olon = runif(1, 0, 180)
tlat = runif(1, -90, 90)
tlon = runif(1, 0, 180)
########## older spherical calculation
da = distaz(olat, olon, tlat, tlon)
##### ed1 = elliposidal earth
ed1 = Ellipsoidal.Distance(olat, olon, tlat, tlon)
##### ed2 spherical earth using
############ ellipsoidal calculations, compare with
distaz
ed2 = Ellipsoidal.Distance(olat, olon, tlat, tlon, a=R.MAPK*1000, b=R.MAPK*1000)
dif1 = da$dist-ed1$dis
dif2 = da$dist-ed2$dis
pct1 = 100*dif1/ed1$dist
############## OUT = format( c(da$dist, ed2$dist, ed1$dist, dif2, dif1, pct1) , digits=10)
OUT$dadist[i] =da$dist
OUT$ed2dist[i] =ed2$dist
OUT$ed1dist[i]=ed1$dist
OUT$dif2[i]= dif2
OUT$dif1[i]=dif1
OUT$pct1[i]=pct1
###cat(paste(collapse=" ", OUT), sep="\n")
}
print( data.frame(OUT) )
############### some extreme cases can cause problems
####### here compare Ellipsoidal.Distance with spherical program distaz
Alat = c(90, 90, 90, 90, 45, 45, 45, 45, 0, 0, 0, 0)
Alon = c(180, 180,-180, -180, 45, 45, 45, 45, 0, 0, 0, 0)
Blat = c(-90, -45, 0, 45, -45, 0, 0, -80, 45, 0, 0, 0)
Blon = c(180,-180, 180, 0, -45, 0, -180, 100, -60, -180, 180, 0)
BOUT = list(olat=0, olon=0, tlat=0, tlon=0, dadist=0, ed2dist=0, daaz=0, ed2az=0, dabaz=0, ed2baz=0)
R.MAPK = 6378.2064
for(i in 1:length(Alat))
{
olat = Alat[i]
olon = Alon[i]
tlat = Blat[i]
tlon = Blon[i]
da = distaz(olat, olon, tlat, tlon)
ed2 = Ellipsoidal.Distance(olat, olon, tlat, tlon, a=R.MAPK*1000, b=R.MAPK*1000)
cat(paste("i=", i), sep="\n")
BOUT$olon[i] =olon
BOUT$olat[i] =olat
BOUT$tlat[i] =tlat
BOUT$tlon[i] =tlon
BOUT$dadist[i] =da$dist
BOUT$ed2dist[i] =ed2$dist
BOUT$daaz[i]= da$az
BOUT$dabaz[i]= da$baz
BOUT$ed2az[i]= ed2$az
BOUT$ed2baz[i]= ed2$revaz
}
print(data.frame(BOUT))
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