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#' Select the axes of the coordinate frame E
#'
#' This function returns the axes of the coordinate frame E (Earth-Centered,
#' Earth-Fixed, ECEF).
#'
#' There are two choices of E-axes that are described in Table 2 in Gade (2010):
#' \itemize{
#' \item \code{e}: z-axis points to the North Pole and x-axis points to the point where
#' latitude = longitude = 0. This choice is very common in many fields.
#' \item \code{E}: x-axis points to the North Pole, y-axis points towards longitude +90deg
#' (east) and latitude = 0. This choice of axis directions ensures
#' that at zero latitude and longitude, N (North-East-Down) has the
#' same orientation as E. If roll/pitch/yaw are zero, also B (Body,
#' forward, starboard, down) has this orientation. In this manner, the
#' axes of E is chosen to correspond with the axes of N and B.
#' }
#'
#' @param axes Either 'e' or 'E'
#' \itemize{
#' \item 'e': z-axis points to the North Pole along the Earth's rotation axis,
#' x-axis points towards the point where latitude = longitude = 0.
#' This choice is very common in many fields.
#' \item 'E': x-axis points to the North Pole along the Earth's rotation axis,
#' y-axis points towards longitude +90deg (east) and latitude = 0.
#' (the yz-plane coincides with the equatorial plane).
#' This choice of axis ensures that at zero latitude and longitude,
#' frame N (North-East-Down) has the same orientation as frame E.
#' If roll/pitch/yaw are zero, also frame B (forward-starboard-down)
#' has this orientation. In this manner, the axes of frame E is
#' chosen to correspond with the axes of frame N and B.
#' The functions in this library originally used this option.
#' }
#'
#' @return rotation matrix defining the axes of the coordinate frame E as
#' described in Table 2 in Gade (2010)
#' @export
#'
#' @examples
#' R_Ee()
#'
#' @references
#' Kenneth Gade (2010) \href{https://www.navlab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf}{A Nonsingular Horizontal Position Representation}.
#' \emph{The Journal of Navigation}, Volume 63, Issue 03, pp 395-417, July 2010.
R_Ee <- function(axes = "e") {
stopifnot(axes == "e" || axes == "E")
if (axes == "e")
matrix(
c( 0, 0, 1,
0, 1, 0,
-1, 0, 0),
nrow = 3, ncol = 3, byrow = TRUE)
else
matrix(
c(1, 0, 0,
0, 1, 0,
0, 0, 1),
nrow = 3, ncol = 3, byrow = TRUE)
}
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