#' Function to calculate distances between two points in metres or kilometres.
#' 
#' \code{distance_by_haversine} is used when distances between latitude and 
#' longitude-pairs need to be represented in metre or kilometre units. The 
#' distances between two points is based on the Haversine Formula which is 
#' approximate and is most appropriate when used for short-distance calculations.
#' 
#' The Haversine Formula does not compensate for Earth's non-spherical shape, 
#' will overestimate distances in the polar regions but will underestimate 
#' distances near the equator. For more information see 
#' \url{https://en.wikipedia.org/wiki/Haversine_formula}
#' 
#' \code{distance_by_haversine} is not a spatial function and does not have any
#' geographic library dependencies. If a spatial funcion is desired or distances
#' to/betwwen lines or polygons need to be calculated see 
#' \code{\link{sp_distance}}.
#' 
#' @param longitude A vector of longitude values in decimal degrees.
#' 
#' @param latitude A vector of latitude values in decimal degrees.
#' 
#' @param longitude_lag A vector of longitude values in decimal degrees.
#' 
#' @param latitude_lag A vector of latitude values in decimal degrees.
#' 
#' @param unit The unit of the returned distance values. Can be metres or 
#' kilometres. Metres is the default. 
#' 
#' @param radius The radius of the Earth in kilometres. The default value is
#' 6371, but I have seen versions of similar functions which use slightly
#' different values (plus or minus two or three kilometres) so this value can
#' be altered. 
#' 
#' @author Stuart K. Grange
#' 
#' @seealso See \code{\link{gDistance}}
#' 
#' @examples
#' \dontrun{
#' # What is the distance between Oxford's Radcliffe Camera and Cliveden House 
#' in Buckinghamshire? 
#' # In metres
#' distance_by_haversine(51.753447, -1.254024, 51.558170, -0.688250)
#' 44662.57
#' 
#' # In kilometres
#' distance_by_haversine(51.753447, -1.254024, 51.558170, -0.688250, "km")
#' 44.66257
#' 
#' # or because we are in a locale with a different distance unit, in miles
#' distance_by_haversine(51.753447, -1.254024, 51.558170, -0.688250, "km") * 0.62
#' 27.69079
#' 
#' 
#' # Data frame usage
#' # Distances of many air quality monitoring sites from the City of London
#' data_air$distance <- distance_by_haversine(
#'   data_air$latitude, data_air$longitude, 51.513468, -0.089133, "km")
#'   
#' # Arrange by distance, closest at the top
#' data_air <- plyr::arrange(data_air, distance)
#' 
#' }
#' 
#' @export
distance_by_haversine <- function(latitude, longitude, latitude_lag = NA, 
                                  longitude_lag = NA, unit = "metres", 
                                  radius = 6371) {
  # Switch units, a check
  unit <- switch(unit, 
    "m" =, "meter" =, "metre" =, "metres" =, "meters" = "meters",
    "km" =, "kilometer" =, "kilometre" =, "kilometers" =, "kilometres" = "kilometres")
  
  # Create lagged variables if not declared
  if (is.na(latitude_lag) & is.na(longitude_lag)) {
    
    latitude_lag <- dplyr::lag(latitude, 1)
    longitude_lag <- dplyr::lag(longitude, 1)
    
  }
  
  # Get degree deltas for coordinate pairs
  delta_longitude <- (longitude_lag - longitude) * pi / 180
  delta_latitude <- (latitude_lag - latitude) * pi / 180
  
  # Use the haversine function
  haversin <- sin(delta_latitude / 2) * sin(delta_latitude / 2) + 
    cos(latitude * pi / 180) * cos(latitude_lag * pi / 180) * 
    sin(delta_longitude / 2) * sin(delta_longitude / 2)
  
  # Calculate distance
  distance <- 2 * atan2(sqrt(haversin), sqrt(1 - haversin))
  
  # Calculate distance as metres
  distance <- radius * distance
  
  if (unit == "meters") distance <- distance * 1000
  
  # Return
  distance
  
}
