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To calculate the geographic distance between two points with latitude/longitude coordinates, you can use several formula's. The package geosphere has the
distCosine, distHaversine, distVincentySphere and distVincentyEllipsoid for calculating the distance. Of these,
the distVincentyEllipsoid is considered the most accurate one, but is computationally more intensive than the other ones.
With one of these functions, you can make a distance matrix. Based on that matrix you can then assign locality names based on shortest
distance with which. min and the corresponding distance with min (see for this the last part of the answer) like this: