R/V2Pdim.R

In marchtaylor/EwEvis: Ecopath with Ecosim visualization

#' Trophic level volume to pyramid dimensions
#'
#' @param V vector of volumes (i.e. throughput) from lowest to highest trophic level (TL)
#' @param TEgm geometric mean transfer efficiency (TLs 2-4)
#' 
#' @description Used internally by \link[EwEvis]{Vpyramid3d}. The angle (i.e. steepness) 
#' of the pyramid is determined by the mean transfer efficiency (\code{TEgm}). 
#' The top angle is proportional to the inverse of the TEgm value. 
#'
#' @return A list containing (from lowest to highest TL): base widths (a), heights (h), 
#' cumulative height (cum.h), a:h ratio (ah_ratio), top angle(angle), volumes (V), 
#' geometric mean transfer efficiency (TEgm), cumulative volume (cum.V).
#' 
#' 
#' @export
#'
#' @examples
#' # From Tam et al (2008) - Northern Humboldt Current Ecosystem (1995-1996)
#' TEgm <- 0.1014
#' Ts <- c(27165, 22349, 1658, 266.3, 17.45, 0.607, 0.00515, 6e-06)
#' V2Pdim(V = Ts, TEgm = TEgm)

V2Pdim <- function(V, TEgm){
  cum.ro.V = cumsum(rev(V)) # cumulative reverse-order volume
  angle <- (1/TEgm)*6
  ah_ratio <- tan(angle/2*(pi/180))*2 # a/h ratio
  # ah_ratio <- -log10(TEgm) # a/h ratio ###OLD###
  # angle <- atan(ah_ratio/2)*(180/pi)*2 ###OLD###
  a <- rev((cum.ro.V * 3 * ah_ratio)^(1/3)) # base length
  cum.ro.h <- rev(a / ah_ratio) # cumulative reverse-order heights
  h <- rev(c(cum.ro.h[1], diff(cum.ro.h))) # heights
  r <- a / 2 # half base length
  cum.ro.s <- sqrt(cum.ro.h^2 + rev(r)^2) # cumulative reverse-order slant heights
  s <- rev(c(cum.ro.s[1], diff(cum.ro.s))) # slant heights
  rs_ratio <- (rev(r)/cum.ro.s)[1] # ratio of r to s
  theta <- asin(rs_ratio) # base angle
  cum.h <- cumsum(h) # cumulative height
  return(list(
    a=a, 
    h=h, 
    cum.h=cum.h, 
    ah_ratio=ah_ratio, 
    angle=angle, 
    V=V, 
    TEgm=TEgm, 
    cum.V=cumsum(V)
  ))
}