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#' Compute the cross-track distance from a great circle arc
#'
#' Compute the cross-track distance of a body, `b` (for example a ground level projection
#' position of an aircraft), from a great circle arc determined by two geographical coordinates,
#' `a1` and `a2` (for example an airport's runway thresholds).
#'
#' @param b the geographical coordinates (WGS84) of a body:
#' a vector of longitude, latitude (in decimal degrees) and
#' eventually altitude (in meters)
#' @param a1 the geographical coordinates (WGS84) of one end of a great circle arc:
#' a vector of longitude, latitude (in decimal degrees) and
#' eventually altitude (in meters)
#' @param a2 the geographical coordinates (WGS84) of the other end of a great circle arc:
#' a vector of longitude, latitude (in decimal degrees) and
#' eventually altitude (in meters)
#'
#' @return the surface cross-track distance from `b` to the arc `a1` - `a2`
#' @export
#' @family utilities
#'
#' @examples
#' \dontrun{
#' b <- c(8.086135, 49.973942, 6401)
#' # EDDF: 07R (longitude, latitude, altitude)
#' a1 <- c(8.53417, 50.0275, 328)
#' # EDDF: 25L
#' a2 <- c(8.58653, 50.0401, 362)
#' cross_track_distance(b, a1, a2)
#' }
cross_track_distance <- function(b, a1, a2) {
x <- cross_track_intersection(b, a1, a2)
geosphere::distGeo(b[1:2], x)
}
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