Calculate the great-circle distance between geographic (LL) coordinates. Also calculate the initial bearing of the great-circle arc (at its starting point).
calcGCdist(lon1, lat1, lon2, lat2, R=6371.2)Longitude coordinate (degrees) of the start point.
Latitude coordinate(degrees) of the start point.
Longitude coordinate(degrees) of the end point.
Latitude coordinate(degrees) of the end point.
Mean radius (km) of the Earth.
A list obect containing:
a -- Haversine \(a\) = square of half the chord length between the points,
c -- Haversine \(c\) = angular distance in radians,
d -- Haversine \(d\) = great-circle distance (km) between two points,
d2 -- Law of Cosines \(d\) = great-circle distance (km) between two points,
theta -- Initial bearing \(\theta\) (degrees) for the start point.
The great-circle distance is calculated between two points along a spherical surface using the shortest distance and disregarding topography.
Method 1: Haversine Formula $$a = \sin^2((\phi_2 - \phi_1)/2) + \cos(\phi_1) \cos(\phi_2) \sin^2((\lambda_2 - \lambda_1)/2)$$ $$c = 2~\mathrm{atan2}(\sqrt{a}, \sqrt{1-a})$$ $$d = R c$$
where \(\phi\) = latitude (in radians), \(\lambda\) = longitude (in radians), \(R\) = radius (km) of the Earth, \(a\) = square of half the chord length between the points, \(c\) = angular distance in radians, \(d\) = great-circle distance (km) between two points.
Method 2: Spherical Law of Cosines $$d = \mathrm{acos}(\sin(\phi_1)\sin(\phi_2) + \cos(\phi_1)\cos(\phi_2)\cos(\lambda_2 - \lambda_1)) R$$
The initial bearing (aka forward azimuth) for the start point can be calculated using:
$$\theta = \mathrm{atan2}(\sin(\lambda_2-\lambda_1)\cos(\phi_2), \cos(\phi_1)\sin(\phi_2) - \sin(\phi_1)\cos(\phi_2)\cos(\lambda_2-\lambda_1))$$
# NOT RUN {
local(envir=.PBSmapEnv,expr={
#-- Distance between southern BC waters and north geomagnetic pole
print(calcGCdist(-126.5,48.6,-72.7,80.4))
})
# }
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