R/great_circle_distance.R

In caesar0301/movr: Analyzing and Visualizing Human Mobility Data

# Calculate great circle distance. See
# http://www.r-bloggers.com/great-circle-distance-calculations-in-r/

#' Great Circle Distance (GCD)
#' 
#' Calculates the geodesic distance between two points specified by radian
#' latitude/longitude using one of the Spherical Law of Cosines (slc),
#' the Haversine formula (hf), or the Vincenty inverse formula for
#' ellipsoids (vif).
#' 
#' @param p1 Location of point 1 with (lat, long) coordinates.
#' @param p2 Location of point 2 with (lat, long) coordinates.
#' @param type Specific algorithm to use, c('slc', 'hf', 'vif').
#' @return Distance in kilometers (km).
#' @references \url{
#' http://www.r-bloggers.com/great-circle-distance-calculations-in-r/}
#' @export
#' @examples
#' # Point in (lat, long) format
#' p1 <- c(30.0, 120.0)
#' p2 <- c(30.5, 120.5)
#' 
#' gcd(p1, p2)
#' gcd(p1, p2, type="hf")
#' gcd(p1, p2, type="vif")
gcd <- function(p1, p2, type="hf", na=0) {
  lat1 = deg2rad(p1[1])
  lon1 = deg2rad(p1[2])
  lat2 = deg2rad(p2[1])
  lon2 = deg2rad(p2[2])
  
  if (type == "slc") {
    ddd <- gcd.slc(lat1, lon1, lat2, lon2)
  } else if (type == "hf") {
    ddd <- gcd.hf(lat1, lon1, lat2, lon2)
  } else if (type == "vif") {
    ddd <- gcd.vif(lat1, lon1, lat2, lon2)[1]
  } else {
    stop("Unknown type argument: supporting one of 'slc', 'hf', 'vif'.")
  }

  if(is.na(ddd))
    ddd <- na
  ddd
}

# Calculates the geodesic distance between two points specified by radian
# latitude/longitude using the Spherical Law of Cosines (slc).
gcd.slc <- function(lat1, long1, lat2, long2) {
  # Earth mean radius [km]
  R <- 6371
  t <- acos(sin(lat1)*sin(lat2)
            + cos(lat1)*cos(lat2) * cos(long2-long1))
  t * R
}

# Calculates the geodesic distance between two points specified by radian
# latitude/longitude using the Haversine formula (hf).
gcd.hf <- function(lat1, long1, lat2, long2) {
  # Earth mean radius [km]
  R <- 6371
  delta.long <- (long2 - long1)
  delta.lat <- (lat2 - lat1)
  a <- sin(delta.lat/2)^2 + cos(lat1) * cos(lat2) * sin(delta.long/2)^2
  c <- 2 * asin(min(1,sqrt(a)))
  R * c
}

# Calculates the geodesic distance between two points specified by radian
# latitude/longitude using Vincenty inverse formula for ellipsoids (vif).
gcd.vif <- function(lat1, long1, lat2, long2) {
  # WGS-84 ellipsoid parameters:
  # length of major axis of the ellipsoid (radius at equator)
  a <- 6378137
  # ength of minor axis of the ellipsoid (radius at the poles)
  b <- 6356752.314245
  # flattening of the ellipsoid
  f <- 1/298.257223563
  
  # difference in longitude
  L <- long2-long1
  # reduced latitude
  U1 <- atan((1-f) * tan(lat1))
  # reduced latitude
  U2 <- atan((1-f) * tan(lat2))
  
  sinU1 <- sin(U1)
  cosU1 <- cos(U1)
  sinU2 <- sin(U2)
  cosU2 <- cos(U2)
  
  cosSqAlpha <- NULL
  sinSigma <- NULL
  cosSigma <- NULL
  cos2SigmaM <- NULL
  sigma <- NULL
  
  lambda <- L
  lambdaP <- 0
  iterLimit <- 100
  while (abs(lambda-lambdaP) > 1e-12 & iterLimit>0) {
    sinLambda <- sin(lambda)
    cosLambda <- cos(lambda)
    sinSigma <- sqrt(
      (cosU2*sinLambda) * (cosU2*sinLambda) +
        (cosU1*sinU2-sinU1*cosU2*cosLambda) * 
        (cosU1*sinU2-sinU1*cosU2*cosLambda) )
    
    if (sinSigma==0)
      return(0)  # Co-incident points
    
    cosSigma <- sinU1*sinU2 + cosU1*cosU2*cosLambda
    sigma <- atan2(sinSigma, cosSigma)
    sinAlpha <- cosU1 * cosU2 * sinLambda / sinSigma
    cosSqAlpha <- 1 - sinAlpha*sinAlpha
    cos2SigmaM <- cosSigma - 2*sinU1*sinU2/cosSqAlpha
    
    if (is.na(cos2SigmaM))
      cos2SigmaM <- 0  # Equatorial line: cosSqAlpha=0
    
    C <- f/16*cosSqAlpha*(4+f*(4-3*cosSqAlpha))
    lambdaP <- lambda
    lambda <- L + (1-C) * f * sinAlpha *
      (sigma + C*sinSigma*(cos2SigmaM+C*cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)))
    iterLimit <- iterLimit - 1
  }
  
  if (iterLimit==0)
    return(NA)  # formula failed to converge
  
  uSq <- cosSqAlpha * (a*a - b*b) / (b*b)
  A <- 1 + uSq/16384*(4096+uSq*(-768+uSq*(320-175*uSq)))
  B <- uSq/1024 * (256+uSq*(-128+uSq*(74-47*uSq)))
  deltaSigma = B*sinSigma*(
    cos2SigmaM+
      B/4*(cosSigma*(-1+2*cos2SigmaM^2)-
             B/6*cos2SigmaM*(-3+4*sinSigma^2)*(-3+4*cos2SigmaM^2)))
  s <- b*A*(sigma-deltaSigma) / 1000
  s
}