#' Convert WGS84GEO coordinates to WGS84UTM coordinates
#'
#' Convert WGS84GEO coordinates to WGS84UTM coordinates
#'
#' This function uses equation 1, 2, 3 in the explanatory notes to compute the
#' WGS84UTM coordinates.
#'
#' @param latitude Latitude in decimal degrees
#' @param longitude longitude in decimal degrees
#' @return \item{N }{The northern coordinates in meters} \item{E }{The eastern
#' coordinates in meters} \item{zone}{ zone for UTM, either 49 or 50}
#' @note The coordinates should be within the range of Hong Kong. Providing
#' coordinates outside Hong Kong will lead to wrong results.
#' @author Jinlong Zhang
#' @seealso \code{\link{WGS84UTM_TO_WGS84GEO}}
#' @references Survey & Mapping Office Lands Department, Hong Kong Government
#' (1995). Explanatory Notes on Geodetic Datums in Hong Kong, available at:
#' \url{http://www.geodetic.gov.hk/smo/gsi/data/pdf/explanatorynotes.pdf}
#' @keywords WGS84GEO WGS84UTM
#' @examples
#'
#'
#' options(digits = 15)
#' WGS84GEO_TO_WGS84UTM(22 + 26/60 + 1.26/3600, 114 + 10/60 + 29.31/3600)
#'
#' #### 22.433683333333334531
#' #### 114.17480833333333123
#'
#' #### $N
#' #### [1] 2483566.19687669
#' ####
#' #### $E
#' #### [1] 209189.467417282
#' ####
#' #### $zone
#' #### [1] 50
#'
#' ### Answer from the explanatory notes
#' ### 2483566m N
#' ### 209194m
#'
#' ### Answer from
#' ### http://www.geodetic.gov.hk/smo/tform/tform.aspx
#' ### 2483568m N
#' ### 209192m E
#'
#'
#' @export WGS84GEO_TO_WGS84UTM
WGS84GEO_TO_WGS84UTM <-
function(latitude, longitude) {
#### The latitude and longitude should both in decimal format.
phi <- latitude / (180 / pi)
lambda <- longitude / (180 / pi)
#########################
#### Constants ##########
### WGS84LL
N0 <- 0
E0 <- 500000
phi0 <- 0
if (longitude < 114) {
lambda0 <- 111 / (180 / pi) ### (zone 49Q)
zone <- 49
} else {
if (longitude >= 114) {
lambda0 <- 117 / (180 / pi)
} ### (zone 50Q)
zone <- 50
}
m0 <- 0.9996
M0 <- 0
niu_s <- 6381309.467
rou_s <- 6344897.718
psi_s <- 1.005738745
a <- 6378137
e2 <- 6.694379989e-3
A0 <- 1 - ((e2) / 4) - (3 * (e2^2) / 64)
A2 <- (3 / 8) * (e2 + (e2^2) / 4)
A4 <- (15 / 256) * (e2^2)
M <- a * (A0 * phi - A2 * sin(2 * phi) + A4 * sin(4 * phi))
M0 <- a * (A0 * phi0 - A2 * sin(2 * phi0) + A4 * sin(4 * phi0))
#### Eq. 1
N <- N0 + m0 * ((M - M0) + niu_s * (sin(phi)) * ((lambda - lambda0)^2 / 2) * (cos(phi)))
#### Eq. 2
E <- E0 + m0 * (niu_s * (lambda - lambda0) * cos(phi) + niu_s * ((lambda - lambda0)^3 / 6) * (cos(phi)^3) * (psi_s - tan(phi)^2))
res <- data.frame(N, E, zone)
names(res) <- c("N", "E", "zone")
return(res)
}
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