I recently came accross an R package for producing ternary diagrams called ggtern. With it you can produce neat heatmaps to represent 3 dimensions.

Below is the full code used to produce this plot:

require(ggplot2)
require(ggtern)
require(MASS)
require(scales)
require(plyr)
palette <- c( "#FF9933", "#002C54", "#3375B2", "#CCDDEC", "#BFBFBF", "#000000")
# Example data
# sig <- matrix(c(3,0,0,2),2,2)
# data <- data.frame(mvrnorm(n=10000, rep(2, 2), sig))
# data$X1 <- data$X1/max(data$X1)
# data$X2 <- data$X2/max(data$X2)
# data$X1[which(data$X1<0)] <- runif(length(data$X1[which(data$X1<0)]))
# data$X2[which(data$X2<0)] <- runif(length(data$X2[which(data$X2<0)]))
# Print 2d heatmap
heatmap2d <- function(data) {
p <- ggplot(data, aes(x=X1, y=X2)) +
stat_bin2d(bins=50) +
scale_fill_gradient2(low=palette[4], mid=palette[3], high=palette[2]) +
xlab("Percentage x") +
ylab("Percentage y") +
scale_y_continuous(labels = percent) +
scale_x_continuous(labels = percent) +
theme_bw() + theme(text = element_text(size = 15))
print(p)
}
# Example data
# data$X3 <- with(data, 1-X1-X2)
# data <- data[data$X3 >= 0,]
# Auxiliary function for heatmap3d
count_bin <- function(data, minT, maxT, minR, maxR, minL, maxL) {
ret <- data
ret <- with(ret, ret[minT <= X1 & X1 < maxT,])
ret <- with(ret, ret[minL <= X2 & X2 < maxL,])
ret <- with(ret, ret[minR <= X3 & X3 < maxR,])
if(is.na(nrow(ret))) {
ret <- 0
} else {
ret <- nrow(ret)
}
ret
}
# Plot 3dimensional histogram in a triangle
# See dataframe data for example of the input dataformat
heatmap3d <- function(data, inc, logscale=FALSE, text=FALSE, plot_corner=TRUE) {
# When plot_corner is FALSE, corner_cutoff determines where to stop plotting
corner_cutoff = 1
# When plot_corner is FALSE, corner_number toggles display of obervations in the corners
# This only has an effect when text==FALSE
corner_numbers = TRUE
count <- 1
points <- data.frame()
for (z in seq(0,1,inc)) {
x <- 1- z
y <- 0
while (x>0) {
points <- rbind(points, c(count, x, y, z))
x <- round(x - inc, digits=2)
y <- round(y + inc, digits=2)
count <- count + 1
}
points <- rbind(points, c(count, x, y, z))
count <- count + 1
}
colnames(points) = c("IDPoint","T","L","R")
# base <- ggtern(data=points,aes(L,T,R)) +
# theme_bw() + theme_hidetitles() + theme_hidearrows() +
# geom_point(shape=21,size=10,color="blue",fill="white") +
# geom_text(aes(label=IDPoint),color="blue")
# print(base)
polygons <- data.frame()
c <- 1
# Normal triangles
for (p in points$IDPoint) {
if (is.element(p, points$IDPoint[points$T==0])) {
next
} else {
pL <- points$L[points$IDPoint==p]
pT <- points$T[points$IDPoint==p]
pR <- points$R[points$IDPoint==p]
polygons <- rbind(polygons,
c(c,p),
c(c,points$IDPoint[abs(points$L-pL) < inc/2 & abs(points$R-pR-inc) < inc/2]),
c(c,points$IDPoint[abs(points$L-pL-inc) < inc/2 & abs(points$R-pR) < inc/2]))
c <- c + 1
}
}
# Upside down triangles
for (p in points$IDPoint) {
if (!is.element(p, points$IDPoint[points$T==0])) {
if (!is.element(p, points$IDPoint[points$L==0])) {
pL <- points$L[points$IDPoint==p]
pT <- points$T[points$IDPoint==p]
pR <- points$R[points$IDPoint==p]
polygons <- rbind(polygons,
c(c,p),
c(c,points$IDPoint[abs(points$T-pT) < inc/2 & abs(points$R-pR-inc) < inc/2]),
c(c,points$IDPoint[abs(points$L-pL) < inc/2 & abs(points$R-pR-inc) < inc/2]))
c <- c + 1
}
}
}
# IMPORTANT FOR CORRECT ORDERING.
polygons$PointOrder <- 1:nrow(polygons)
colnames(polygons) = c("IDLabel","IDPoint","PointOrder")
df.tr <- merge(polygons,points)
Labs = ddply(df.tr,"IDLabel",function(x){c(c(mean(x$T),mean(x$L),mean(x$R)))})
colnames(Labs) = c("Label","T","L","R")
# triangles <- ggtern(data=df.tr,aes(L,T,R)) +
# geom_polygon(aes(group=IDLabel),color="black",alpha=0.25) +
# geom_text(data=Labs,aes(label=Label),size=4,color="black") +
# theme_bw()
# print(triangles)
bins <- ddply(df.tr, .(IDLabel), summarize,
maxT=max(T),
maxL=max(L),
maxR=max(R),
minT=min(T),
minL=min(L),
minR=min(R))
count <- ddply(bins, .(IDLabel), summarize, N=count_bin(data, minT, maxT, minR, maxR, minL, maxL))
df <- join(df.tr, count, by="IDLabel")
Labs = ddply(df,.(IDLabel,N),function(x){c(c(mean(x$T),mean(x$L),mean(x$R)))})
colnames(Labs) = c("Label","N","T","L","R")
if (plot_corner==FALSE){
corner <- ddply(df, .(IDPoint, IDLabel), summarize, maxperc=max(T,L,R))
corner <- corner$IDLabel[corner$maxperc>=corner_cutoff]
df$N[is.element(df$IDLabel, corner)] <- 0
if (text==FALSE & corner_numbers==TRUE) {
Labs$N[!is.element(Labs$Label, corner)] <- ""
text=TRUE
}
}
heat <- ggtern(data=df,aes(L,T,R)) +
geom_polygon(aes(fill=N,group=IDLabel),color="black",alpha=1)
if (logscale == TRUE) {
heat <- heat + scale_fill_gradient(name="Observations", trans = "log",
low=palette[2], high=palette[4])
} else {
heat <- heat + scale_fill_gradient(name="Observations",
low=palette[2], high=palette[4])
}
heat <- heat +
Tlab("x") +
Rlab("y") +
Llab("z") +
theme_bw() +
theme(axis.tern.arrowsep=unit(0.02,"npc"), #0.01npc away from ticks ticklength
axis.tern.arrowstart=0.25,axis.tern.arrowfinish=0.75,
axis.tern.text=element_text(size=12),
axis.tern.arrow.text.T=element_text(vjust=-1),
axis.tern.arrow.text.R=element_text(vjust=2),
axis.tern.arrow.text.L=element_text(vjust=-1),
axis.tern.arrow.text=element_text(size=12),
axis.tern.title=element_text(size=15))
if (text==FALSE) {
print(heat)
} else {
print(heat + geom_text(data=Labs,aes(label=N),size=3,color="white"))
}
}
# Usage examples
# heatmap3d(data, 0.2, text=TRUE)
# heatmap3d(data, 0.05)
# heatmap3d(data, 0.1, text=FALSE, logscale=TRUE)
# heatmap3d(data, 0.1, text=TRUE, logscale=FALSE, plot_corner=FALSE)
# heatmap3d(data, 0.1, text=FALSE, logscale=FALSE, plot_corner=FALSE)