# Slice bivariate densities, or the Joy Division “waterfall plot”

This has been on my to-do list for a long old time. Lining up slices through a bivariate density seems a much more intuitive way of depicting it than contour plots or some ghastly rotating 3-D thing (urgh). Of course, there is the danger of features being hidden, but you know I’m a semi-transparency nut, so it’s no surprise I think that’s the answer to this too.

Here’s an R function for you:

```# x, y: data
# slices: number of horizontal slices through the data
# lboost: coefficient to increase the height of the lines
# gboost: coefficient to increase the height of the graph (ylim)
# xinc: horizontal offset for each succesive slice
# (typically something like 1/80)
# yinc: vertical offset for each succesive slice
# bcol: background color
# fcol: fill color for each slice (polygon)
# lcol: line color for each slice
# lwidth: line width
# extend: Boolean to extend lines to edge of plot area
# densopt: list of strings containing density() arguments that
# are passed verbatim.
# NB if you want to cycle slice colors through vectors, you
# need to change the function code; it sounds like a
# pretty bad idea to me, but each to their own.
slicedens<-function(x,y,slices=50,lboost=1,gboost=1,xinc=0,yinc=0.01,
bcol="black",fcol="black",lcol="white",lwidth=1,extend=FALSE,
densopt=NULL) {
ycut<-min(y)+((0:(slices))*(max(y)-min(y))/slices)
height<-gboost*((slices*yinc)+max(density(x)\$y))
plot( c(min(x),max(x)+((max(x)-min(x))/4)),
c(0,height),
xaxt="n",yaxt="n",ylab="",xlab="")
rect(par("usr")[1],par("usr")[3],par("usr")[2],par("usr")[4],col=bcol)
for(i in slices:1) {
miny<-ycut[i]
maxy<-ycut[i+1]
gx<-(i-1)*(max(x)-min(x))*xinc
gy<-(i-1)*(height)*yinc
dd<-do.call(density,append(list(x=x[y>=miny & y<maxy]),
densopt))
polygon(dd\$x+gx,lboost*dd\$y+gy,col=fcol)
lines(dd\$x+gx,lboost*dd\$y+gy,col=lcol,lwd=lwidth)
if(extend) {
lines(c(par("usr")[1],dd\$x[1]+gx),
rep(lboost*dd\$y[1]+gy,2),col=lcol)
lines(c(dd\$x[length(dd\$x)]+gx,par("usr")[2]),
rep(lboost*dd\$y[length(dd\$y)]+gy,2),col=lcol)
}
}
}
# Example 1:
y<-runif(5000,min=-1,max=1)
x<-runif(5000,min=-1,max=1)+rnorm(5000,mean=1/(y+1.1),sd=0.8-(y*0.5))
slicedens(x,y,lboost=0.2,fcol=rgb(0,0,0,200,maxColorValue=255))
# Example 2:
library(iris)
slicedens(x=iris\$Sepal.Width,y=iris\$Sepal.Length,slices=12,
lboost=0.02,fcol=rgb(0,0,0,200,maxColorValue=255),
```

Some places call this a waterfall plot. Anyway, the white-on-black color scheme is clearly inspired by the Joy Division album cover. Enjoy.

Edit 9 October 2014: added the “extend” and “densopt” arguments.