codep (version 0.9-1)

gcd: Great circle distances

Description

Functions to calculate great circle distances among sets of points with known longitude and lattitudes.

Usage

gcd.slc(ss, radius = 6371)
gcd.hf(ss, radius = 6371)
gcd.vife(ss, a = 6378137, b = 6356752.314245, f = 1/298.257223563)

Value

An object of class ‘"dist"’ (see dist for details) that contains the distances (in km) between the locations (rows of

ss).

Arguments

ss

A two-columns data.frame or matrix of the geographic coordinates (in degree.decimals; lattitude and then longitude) of the locations between which the geodesic distances are being calculated.

radius

Mean earth radius (mean length of parallels) in km. Default: 6371 km

a

Length (in m) of major axis of the ellipsoid (radius at equator). Default: 6378137 m (i.e. that for WGS-84).

b

Length (in m) of minor axis of the ellipsoid (radius at the poles). Default: 6356752.314245 m (i.e. that for WGS-84).

f

Flattening of the ellipsoid. Default: 1/298.257223563 (i.e. that for WGS-84).

Author

Guillaume Guénard, Departement des sciences biologiques, Universite de Montréal, Montréal, Quebec, Canada.

Details

The calculation of spatial eigenvector maps requires a distance matrix. The euclidean distance is appropriate when a cartesian plan can be reasonably assumed. The latter can be calculated with function dist. The great circle distance is appropriate when the sampling points are located on a spheroid (e.g. planet Earth). Function gcd.slc uses the spherical law of cosines, which is the fastest of the three approaches and performs relatively well for distances above 1 m. Function gcd.hf uses the the Haversine formula, which is more accurate for smaller distances (bellow 1 m). Finally, functions gcd.vife uses the Vincenty inverse formula for ellipsoids, which is an iterative approach that take substantially more computation time than the latter two methods has precision up to 0.5 mm with exact longitudes and lattitudes.

References

Mario Pineda-Krch, URL: http://www.r-bloggers.com/great-circle-distance-calculations-in-r/

Vincenty, T. (1975) Closed formulas for the direct and reverse geodetic problems. J. Geodesy 51(3): 241-342

See Also

eigenmap-class

Examples

#
# Calculating the distances between Canada's capital cities:
CapitalCitiesOfCanada <-
    matrix(c(45.417,-75.7,53.533333,-113.5,48.422151,-123.3657,
             49.899444,-97.139167,45.95,-66.666667,47.5675,-52.707222,
             44.647778,-63.571389,43.7,-79.4,46.24,-63.1399,
             46.816667,-71.216667,50.454722,-104.606667,62.442222,-114.3975,
             63.748611,-68.519722,60.716667,-135.05),14L,2L,byrow=TRUE,
             dimnames=list(c("Ottawa","Edmonton","Victoria","Winnipeg",
                             "Fredericton","St-John's","Halifax","Toronto",
                             "Charlottetown","Quebec City","Regina",
                             "Yellowknife","Iqaluit","Whitehorse"),c("Lon","Lat")))
#
sphericalcosdists <- gcd.slc(CapitalCitiesOfCanada)
vincentydists <- gcd.vife(CapitalCitiesOfCanada)
#
cor(as.numeric(sphericalcosdists),as.numeric(vincentydists))
percentdev <- 100*(vincentydists-sphericalcosdists)/vincentydists
mean(percentdev)
# Spherical Law of Cosines underestimated these distances by ~0.26
# percent.
#