Making a ternary plot

I want to plot the projection of 3-dimensional data on their simplex using ggplot2. I thought I could manage the transformation on cartesian coordinates using coord_trans(), but do not know how to do it exactly.

This is what I tried:

simplex.y  <- function( x1, x2, x3 ) {
  return( sqrt(0.75) *  x3 / (x1+x2+x3) )
} 
simplex.x  <- function( x1, x2, x3 ) {
  return( (x2 + 0.5 * x3) / (x1+x2+x3) )
}

x  <- data.frame(
  x1 = c( 0, 0, 1, 0.1, 0.6, 0.2 ),
  x2 = c( 0, 1, 0, 0.3, 0.2, 0.8 ),
  x3 = c( 1, 0, 0, 0.6, 0.2, 0.0 )
)

require(ggplot2)
ggplot( data = x, aes( x = c(x1, x2, x3), y = c(x1, x2, x3)) ) +
  geom_point() +
  coord_trans( x="simplex.x", y="simplex.y" )

Any suggestions are appreciated. Many thanks!