trilinplot<-function(data, box = F, abbrv.name=F,
  vertex=dimnames(data)[[2]], 
  item=dimnames(data)[[1]], 
  ...)
{

# ------------------------------------------------------------------
# Produces trilinear plot. 
# copyright 2002 by 
# Mu Zhu 
# University of Waterloo
# Waterloo, Ontario, N2L 3G1
# Canada
#
# references:
# Allen, T. (2002), "Using and Interpreting the Trilinear Plot",
#  Chance 15(3), 29-35.
# ------------------------------------------------------------------

  if (is.null(vertex)) vertex<-c("A", "B", "C")
  if (is.null(item)) item<-1:nrow(data)

  if (abbrv.name) item <- abbreviate(item)
  # offset to make text position appear prettier
  eta <- 0.08

  # vertex position
  anchor <- diag(3)

  # projection directions onto 2-d
  alpha1 <- c(1, -1, 0)/sqrt(2)
  alpha2 <- c(-0.5, -0.5, 1)/sqrt(1.5)  

  # plot the triangle
  vert.x <- anchor %*% alpha1
  vert.y <- anchor %*% alpha2
  plot(vert.x, vert.y, type="p", xlab="", ylab="", 
    xlim = range(vert.x)+2*c(-eta, eta), 
    ylim = range(vert.y)+2*c(-eta, eta),
    axes=F, ...)
  if (box) box()
  polygon(vert.x, vert.y)           
  offset.x <- c(eta, -eta, 0)
  offset.y <- c(-eta,-eta,eta)
  text(vert.x+offset.x, vert.y+offset.y, as.character(vertex))

  # make sure each observation contains proper percentage
  rowsum <- as.vector(as.matrix(data) %*% rep(1,3))
  data <- data/rowsum

  # item position
  pts.x <- as.matrix(data) %*% alpha1 
  pts.y <- as.matrix(data) %*% alpha2

  # plot items onto triangle
  n <- nrow(data)
  points(pts.x, pts.y)
  offset.x <- eta/2*sample(c(-1, 1), size=n, replace=T)
  offset.y <- eta/2*sample(c(-1, 1), size=n, replace=T)
  text(pts.x+offset.x, pts.y+offset.y, as.character(item), cex=0.62)
}