R/borgIndices.R

In environmentalinformatics-marburg/Rsenal: Magic R Functions for Things Various

#' Calculate shape indices listed in Borg 1998 
#' 
#' @description used as internal function. see \code{?geometryVariables}
#' and Borg 1998: Vergleichende Analyse von Formindizes zur Charakterisierung 
#' von Landschaftsobjekten unter oekologischen Aspekten. 
#' Zeitschrift fuer Photogrammetrie und Fernerkundung 4: 108-119.
#' 
#' @param Ar Area of the entities
#' @param Ur Perimeter of the entities
#' @param De Diameter of the inner circle
#' @param Du Diameter of the outer circle
#' 
#' @return A RasterStack
#' 
#' @author Hanna Meyer
#' 
#' @seealso \code{\link{geometryVariables}}.


borgIndices<-function(Ar,Ur,De,Du){

  Dk <- sqrt((Ar/pi))*2 # Diameter of the circle of area Ar
  
  Uk <- Dk*pi # perimeter of the circle of area Ar
  Ue <- De*pi #perimeter of the inner circle
  Uu <- Du*pi #perimeter of the outer circle

  Au <- pi*((Du/2)^2) #area of outer circle
  Ae <- pi*((De/2)^2) #area of the inner circle

  CI1 <- Ue/Uk
  CO1 <- Uk/Uu
  CI2 <- (Uk-Ue)/Uk
  CO2 <- (Uu-Uk)/Uu
  CCI1 <- (CI1+CO1)/2
  CCI2 <- 1-sqrt(CI2*CO2)
  ### orientation at re circle of same area
  CO <- (2*sqrt(pi*Ar))/Ur
  SHD <- Ur/(2*sqrt(pi*Ar))
  C1 <- (4*Ar)/(Ur^2)
  E <- Ur/(sqrt(Ar))
  TR <- (4*pi*Ar)/(Ur^2)
  ###orientation at the smallest outer circle
  CR <- Ar/Au
  C2 <- sqrt(Ar/Au)
  FR <- Ar/Du^2
  EI <- (pi*Du*(0.5*Du))/Ar
  SF1 <- Uu/Ur
  GSI <- Ur/Du
  ###orientation at the largest inner circle
  SF2 <- Ae/Ar
  ###orientation on inner and outer circle
  C3 <- sqrt(De/Du)
  SF3 <- (Au-Ae)/Ar
  
  result <- stack(CI1,CO1,CI2,CO2,CCI1,CCI2,CO,SHD,C1,E,TR,CR,
               C2,FR,EI,SF1,GSI,SF2,C3,SF3)
  names(result) <- c("CI1","CO1","CI2","CO2","CCI1","CCI2","CO","SHD","C1","E",
                  "TR","CR","C2","FR","EI","SF1","GSI","SF2","C3","SF3")
  return(result)
}