# R/ellipsoidalRDis.R In RLeafAngle: Estimates, Plots and Evaluates Leaf Angle Distribution Functions, Calculates Extinction Coefficients

#### Documented in ellipsoidalRDis

```#' Compute the rotated ellipsoidal distribution of leaf zenith angle.
#' @description Compute the rotated ellipsoidal distribution of leaf zenith angle.
#' @param lambdaR The parameter of rotated-ellipsoidal function.
#' @return The rotated ellipsoidal distribution of leaf zenith angle.
#' @author Wei-Min Wang (wmwang AT gmail.com)
#' @references  Wang, W. M., Li, Z. L., & Su, H. B. (2007).
#' Comparison of leaf angle distribution functions: effects on extinction coefficient and
#' fraction of sunlit foliage. Agricultural and Forest Meteorology, 143(1), 106-122.
#' @examples
#' sDis<-ellipsoidalRDis(1)
#' plot(c(4.5, 13.5, 22.5, 31.5, 40.5, 49.5, 58.5, 67.5, 76.5, 85.5), sDis,
#' xlab=expression(Leaf~zenith~angle~~(""^"o")), ylab="Leaf area freqency")
#'
#' @export
#'

ellipsoidalRDis<-function(lambdaR)
{
angz<-c(0, 9.0, 18.0, 27.0, 36.0, 45.0, 54.0, 63.0, 72.0, 81.0, 90.0)
sDis<-0
pi180<-pi/180.0

{
if((lambdaER-1)<1*10**(-5))
{
delta<-2
}
else
{
if(lambdaER>1)
{
emiga<-(1-lambdaER**(-2))**(0.5)
delta<-lambdaER+(log((1+emiga)/(1-emiga))/(2*emiga*lambdaER))
}
else
{
emiga<-(1-lambdaER**(2))**(0.5)
delta<-lambdaER+asin(emiga)/emiga
}
}
up<-2*(lambdaER**3.0)*cos(x)
#delta<-lamdaE+1.774*(lamdaE+1.182)**(-0.733)
down<-delta*(sin(x)**2+lambdaER**2*cos(x)**2)**2
up/down
}

for(i in 1:(length(angz)-1))
{