Ternary plot and filled contour

Question

Users, I'd like to have some tips for a ternaryplot ("vcd").

I have this dataframe:

a <- c(0.1, 0.5, 0.5, 0.6, 0.2, 0, 0, 0.004166667, 0.45) 
b <- c(0.75,0.5,0,0.1,0.2,0.951612903,0.918103448,0.7875,0.45)
c <- c(0.15,0,0.5,0.3,0.6,0.048387097,0.081896552,0.208333333,0.1) 
d <- c(500,2324.90,2551.44,1244.50, 551.22,-644.20,-377.17,-100, 2493.04) 
df <- data.frame(a, b, c, d)

and I'm building a ternary plot:

ternaryplot(df[,1:3], df$d)

How can I map the continuous variable d, obtaining a result similar to this one?

Answer 1

This is probably not the most elegant way to do this but it works (from scratch and without using ternaryplot though: I couldn't figure out how to do it).

a<- c (0.1, 0.5, 0.5, 0.6, 0.2, 0, 0, 0.004166667, 0.45) 
b<- c (0.75,0.5,0,0.1,0.2,0.951612903,0.918103448,0.7875,0.45)
c<- c (0.15,0,0.5,0.3,0.6,0.048387097,0.081896552,0.208333333,0.1) 
d<- c (500,2324.90,2551.44,1244.50, 551.22,-644.20,-377.17,-100, 2493.04) 
df<- data.frame (a, b, c)


# First create the limit of the ternary plot:
plot(NA,NA,xlim=c(0,1),ylim=c(0,sqrt(3)/2),asp=1,bty="n",axes=F,xlab="",ylab="")
segments(0,0,0.5,sqrt(3)/2)
segments(0.5,sqrt(3)/2,1,0)
segments(1,0,0,0)
text(0.5,(sqrt(3)/2),"c", pos=3)
text(0,0,"a", pos=1)
text(1,0,"b", pos=1)

# The biggest difficulty in the making of a ternary plot is to transform triangular coordinates into cartesian coordinates, here is a small function to do so:
tern2cart <- function(coord){
    coord[1]->x
    coord[2]->y
    coord[3]->z
    x+y+z -> tot
    x/tot -> x  # First normalize the values of x, y and z
    y/tot -> y
    z/tot -> z
    (2*y + z)/(2*(x+y+z)) -> x1 # Then transform into cartesian coordinates
    sqrt(3)*z/(2*(x+y+z)) -> y1
    return(c(x1,y1))
    }

# Apply this equation to each set of coordinates
t(apply(df,1,tern2cart)) -> tern

# Intrapolate the value to create the contour plot
resolution <- 0.001
require(akima)
interp(tern[,1],tern[,2],z=d, xo=seq(0,1,by=resolution), yo=seq(0,1,by=resolution)) -> tern.grid

# And then plot:
image(tern.grid,breaks=c(-1000,0,500,1000,1500,2000,3000),col=rev(heat.colors(6)),add=T)
contour(tern.grid,levels=c(-1000,0,500,1000,1500,2000,3000),add=T)
points(tern,pch=19)