R/colinear.R

In RConics: Computations on Conics

#' Test for colinearity
#' 
#' Tests if three points are colinear. The coordinates of the points have to be in homogeneous coordinates.
#' @param p1 \eqn{(3 \times 1)} vector of the homogeneous coordinates of point \eqn{1}.
#' @param p2 \eqn{(3 \times 1)} vector of the homogeneous coordinates of point \eqn{2}.
#' @param p3 \eqn{(3 \times 1)} vector of the homogeneous coordinates of point \eqn{3}.
#' @return \code{TRUE} if the three points are colinear, else \code{FALSE}.
#' @source  Richter-Gebert, Jürgen (2011). 
#' \emph{Perspectives on Projective Geometry - A Guided Tour Through Real
#' and Complex Geometry}, Springer, Berlin, ISBN: 978-3-642-17285-4
#' @examples 
#' # points: homogeneous coordinates
#' p1 <- c(3,1,1)
#' p2 <- c(0,2,1)
#' p3 <- c(1.5,-2,1)
#' p4 <- c(1,3,1)
#' 
#' # homogeneous line passing through p1 and p2
#' l1 <- join(p1,p2)
#' 
#' # homogeneous line passing through p3 and p3
#' l2 <- join(p3,p4)
#' 
#' # homogeneous points formed by the intersection of the lines
#' p5 <- meet(l1,l2)
#' 
#' # test for colinearity
#' colinear(p1, p2, p3)
#' colinear(p1, p2, p5)
#' colinear(p3, p4, p5)
#' 
#' # plot
#' plot(rbind(p1,p2,p3,p4),xlim=c(-5,5),ylim=c(-5,5),asp=1)
#' abline(h=0,v=0,col="grey",lty=3)
#' addLine(l1,col="red")
#' addLine(l2,col="blue")
#' points(t(p5),cex=1.5,pch=20,col="blue")
#' @export
#' @name colinear
#' @rdname colinear


colinear <- function(p1,p2,p3){
  if(isTRUE(all.equal(0, det(cbind(p1,p2,p3))))){
    return(TRUE)
  }else{
    return(FALSE)
  }
}