R/poly5_hi.R

In timbeR: Calculate Wood Volumes from Taper Functions

#' Estimate the height at which a given diameter occurs in a tree, based on a 5th degree polynomial function.
#'
#' Estimates the height at which a given diameter occurs in a tree, from the diameter at breast height, total height and coefficients of the 5th degree polynomial function that describes the tree's taper.
#'
#' @param dbh tree diameter at breast height, in centimeters.
#' @param h total tree height, in meters.
#' @param di diameter whose height of occurrence will be estimated, in centimeters.
#' @param coef numerical vector containing six coefficients of the 5th degree polynomial function that describes the tree's taper.
#'
#' @return as numeric value indicating the height at which the given diameter occurs.
#'
#' @examples
#'
#' library(dplyr)
#' library(minpack.lm)
#' library(timbeR)
#'
#' tree_scaling <- tree_scaling %>%
#' mutate(did = di/dbh,
#'        hih = hi/h)
#'
#' poli5 <- lm(did~hih+I(hih^2)+I(hih^3)+I(hih^4)+I(hih^5),tree_scaling)
#'
#' coef_poli <- coef(poli5)
#'
#' dbh <- 25
#' h <- 20
#' hi <- 15
#'
#' poly5_hi(dbh, h, hi, coef_poli)
#'
#' @export
poly5_hi <- function(dbh, h, di, coef){
  b0 <- coef[1]; b1 <- coef[2]; b2 <- coef[3]; b3 <- coef[4]; b4 <- coef[5]; b5 <- coef[6]
  fun_opt_hi <- function(hi){
    ((b0+b1*(hi/h)+b2*(hi/h)^2+b3*(hi/h)^3+b4*(hi/h)^4+b5*(hi/h)^5)-(di/dbh))^2
  }

  stats::optimise(fun_opt_hi,lower=0,upper=h,tol=0.0001)$minimum
}