R: 4D plot, x, y, z, colours

Could you give me an example on how to use rgl to plot 3 variables at the axes x, y and z and a fourth one with different colours?

thanks

Solution 1:

You use a combination of persp and colour according to a separate function. Here's some example code:

## Create a simple surface  f(x,y) = -x^2 - y^2
## Colour the surface according to x^2 only
nx = 31; ny = 31
x = seq(-1, 1, length = nx)
y = seq(-1, 1, length = ny)
z = outer(x, y, function(x,y) -x^2  -y^2)
## Fourth dim
z_col = outer(x, y, function(x,y) x^2)

## Average the values at the corner of each facet
## and scale to a value in [0, 1].  We will use this
## to select a gray for colouring the facet. 
hgt = 0.25 * (z_col[-nx,-ny] + z_col[-1,-ny] + z_col[-nx,-1] + z_col[-1,-1])
hgt = (hgt - min(hgt))/ (max(hgt) - min(hgt))

##  Plot the surface with the specified facet colours.
persp(x, y, z, col = gray(1 - hgt))
persp(x, y, z, col=cm.colors(32)[floor(31*hgt+1)], theta=-35, phi=10)

This gives:

RGL

It's fairly straightforward to use the above technique with the rgl library:

library(rgl)
## Generate the data using the above commands
## New window
open3d()

## clear scene:
clear3d("all")

## setup env:
bg3d(color="#887777")
light3d()

surface3d(x, y, z, color=cm.colors(32)[floor(31*hgt+1)], alpha=0.5)

Solution 2:

There is an example in ?plot3d if you are talking about plotting points in a 3d space and colouring them:

x <- sort(rnorm(1000))
y <- rnorm(1000)
z <- rnorm(1000) + atan2(x,y)
plot3d(x, y, z, col=rainbow(1000))

But if you mean to colour the points by a 4th variable, say a grouping variable, then we can modify the example above to do this by creating a grouping variable

grp <- gl(5, 200) ## 5 groups 200 members each
## now select the colours we want
cols <- 1:5

## Now plot
plot3d(x, y, z, col=cols[grp])

OK, is this more what you want?

X <- 1:10
Y <- 1:10
## Z is now a 100 row object of X,Y combinations
Z <- expand.grid(X = X, Y = Y)
## Add in Z1, which is the 3rd variable
## X,Y,Z1 define the surface, which we colour according to
## 4th variable Z2
Z <- within(Z, {
    Z1 <- 1.2 + (1.4 * X) + (-1.9 * Y)
    Z2 <- 1.2 + (1.4 * X) - (1.2 * X^2) + (1.9 * Y) + (-1.3 * Y^2)
    Z3 <- 1.2 + (1.4 * X) + (-1.9 * Y) + (-X^2) + (-Y^2)})
## show the data
head(Z)
## Set-up the rgl device
with(Z, plot3d(X, Y, Z1, type = "n"))
## Need a scale for Z2 to display as colours
## Here I choose 10 equally spaced colours from a palette
cols <- heat.colors(10)
## Break Z2 into 10 equal regions
cuts <- with(Z, cut(Z2, breaks = 10))
## Add in the surface, colouring by Z2
with(Z, surface3d(1:10,1:10, matrix(Z1, ncol = 10),
                   color = cols[cuts], back = "fill"))
with(Z, points3d(X, Y, Z1, size = 5)) ## show grid X,Y,Z1

Here's a modification where the plane surface Z1 is curved (Z3).

## Set-up the rgl device plotting Z3, a curved surface
with(Z, plot3d(X, Y, Z3, type = "n"))
with(Z, surface3d(1:10,1:10, matrix(Z3, ncol = 10),
                   color = cols[cuts], back = "fill"))

The detail of what I did to get Z2 probably doesn't matter, but I tried to get something like the graph you linked to.

If I've still not got what you want, can you edit your Q with some example data and give us a better idea of what you want?

HTH