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#' Compute the fraction leaf area given leaf angle intervals (in degree) and the parameters of ellipsoidal function.
#' @description Compute the fraction leaf area given leaf angle intervals (in degree) and the parameters of ellipsoidal function.
#' @param AngleLower The lower limit of leaf angle intervals in degree.
#' @param AngleUpper The upper limit of leaf angle intervals in degree.
#' @param lambda The parameter of ellipsoidal function.
#' @return Compute the fraction leaf area of ellipsoidal function.
#' @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
#' interEllip(40,50,1.1)
#' @export
#'
interEllip<-function(AngleLower, AngleUpper, lambda)
{
ellipLAD <- function(x,lambdaE)
{
if((lambdaE-1)<1*10**(-5))
{
delta<-2
}
else
{
if(lambdaE>1)
{
emiga<-(1-lambdaE**(-2))**(0.5)
delta<-lambdaE+(log((1+emiga)/(1-emiga))/(2*emiga*lambdaE))
}
else
{
emiga<-(1-lambdaE**(2))**(0.5)
delta<-lambdaE+asin(emiga)/emiga
}
}
up<-2*(lambdaE**3.0)*sin(x)
down<-delta*(cos(x)**2+lambdaE**2*sin(x)**2)**2
up/down
}
pi180<-pi/180.0
fraction<-integrate(ellipLAD, lower=AngleLower*pi180, upper=AngleUpper*pi180, lambdaE=lambda)
fraction[[1]]
}
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