R/shape.R

In swaRm: Processing Collective Movement Data

#' @title Sphericity
#'
#' @description Given a set of locations, this function approximates the 
#'  sphericity of the set by calculating the bivariate 95% confidence ellipse of 
#'  the set. 
#' 
#' @param x A vector of x coordinates. 
#' 
#' @param y A vector of y coordinates.
#' 
#' @return A single numeric value corresponding to the ratio between the minor 
#'  and major axis of the bivariate 95% confidence ellipse of the set. A value 
#'  close to 1 indicates that the set is approximately circular; a value close 
#'  to 0 indicates that the set is strongly elongated. 
#' 
#' @author Simon Garnier, \email{garnier@@njit.edu}
#' 
#' @seealso \code{\link{stretch}}
#' 
#' @examples
#' x <- rnorm(25)
#' y <- rnorm(25, sd = 3)
#' sphericity(x, y)
#' 
#' @export
sphericity <- function(x, y) {
  if (length(x) != length(y)) 
    stop("x and y should have the same length.")
  
  if (!is.numeric(x) | !is.numeric(y))
    stop("x and y should be numeric.")
  
  tryCatch({
    ell <- .ellipse(x, y)
    ell$b / ell$a}, 
    error = function(e) as.numeric(NA))
}


#' @title Stretching Direction
#'
#' @description Given a set of locations, this function approximates the 
#'  stretching direction of the set by calculating the angle of the main axis of 
#'  the bivariate 95% confidence ellipse of the set. 
#' 
#' @param x A vector of x coordinates. 
#' 
#' @param y A vector of y coordinates.
#' 
#' @return A single numeric value corresponding to the angle (in radians) of the 
#'  main axis of the bivariate 95% confidence ellipse of the set. 
#' 
#' @author Simon Garnier, \email{garnier@@njit.edu}
#' 
#' @seealso \code{\link{sphericity}}
#' 
#' @examples
#' x <- rnorm(25)
#' y <- rnorm(25, sd = 3)
#' stretch(x, y)
#'
#' @export
stretch <- function(x, y) {
  if (length(x) != length(y)) 
    stop("x and y should have the same length.")
  
  if (!is.numeric(x) | !is.numeric(y))
    stop("x and y should be numeric.")
  
  tryCatch({
    ell <- .ellipse(x, y)
    ell$alpha}, 
    error = function(e) as.numeric(NA))
}