3d plot

Load plot3D package

library("plot3D")

## Warning: package 'plot3D' was built under R version 4.3.2

Prepare the data

We’ll use the iris data set in the following examples :

data(iris)
head(iris)

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

# x, y and z coordinates
x <- sep.l <- iris$Sepal.Length
y <- pet.l <- iris$Petal.Length
z <- sep.w <- iris$Sepal.Width

Scatter plots

Functions for scatter plots and texts in 2D and 3D

The function below will be used:

## scatter3D(x, y, z, ..., colvar = z, col = NULL, add = FALSE)
## text3D(x, y, z, labels, colvar = NULL, add = FALSE)
## points3D(x, y, z, ...)
## lines3D(x, y, z, ...)
## scatter2D(x, y, colvar = NULL, col = NULL, add = FALSE)
## text2D(x, y, labels, colvar = NULL, col = NULL, add = FALSE)

Basic scatter plot

scatter3D(x, y, z, clab = c("Sepal", "Width (cm)"))

In the R code below:

colvar = NULL: avoids coloring by z variable

col = “blue”: changes point colors to blue

pch = 19: changes point shapes

cex = 0.5: changes the size of points

scatter3D(x, y, z, colvar = NULL, col = "blue",
          pch = 19, cex = 0.5)

Change the type of the box around the plot

The argument bty is used. Allowed values are:

“f”: full box

“b”: default value. Only the back panels are visible

“b2”: back panels and grid lines are visible

“g”: grey background with white grid lines

“bl”: black background

“bl2”: black background with grey lines

“u”: means that the user will specify the arguments col.axis, col.panel, lwd.panel, col.grid, lwd.grid manually

“n”: no box will be drawn. This is the same as setting box = FALSE

# full box
scatter3D(x, y, z, bty = "f", colkey = FALSE, main ="bty= 'f'")

# back panels and grid lines are visible
scatter3D(x, y, z, bty = "b2", colkey = FALSE, main ="bty= 'b2'" )

# grey background with white grid lines
scatter3D(x, y, z, bty = "g", colkey = FALSE, main ="bty= 'g'")

# User defined
scatter3D(x, y, z, pch = 18, bty = "u", colkey = FALSE, 
   main ="bty= 'u'", col.panel ="steelblue", expand =0.4, 
   col.grid = "darkblue")

Color palettes

Several color palettes are available in plot3D package:

jet.col(n, alpha): generates the matlab-type colors. This is the default color palette used in plot3D

jet2.col(n, alpha): similar to jet.col() but lacks the deep blue colors

gg.col(n, alpha) and gg2.col(n, alpha) generates gg-plot-like colors

ramp.col(col = c(“grey”, “black”), n, alpha): creates color schemes by interpolation

alpha.col(col = “grey”, alpha): creates transparent colors

n: Number of colors to generate. Default value is 100

alpha: color transparency. Value in the range 0, 1. Default value is 1

col: Colors to interpolate

# gg.col: ggplot2 like color
scatter3D(x, y, z, bty = "g", pch = 18, col = gg.col(100))

# ramp.col: custom palettes
scatter3D(x, y, z, bty = "g", pch = 18,
          col = ramp.col(c("blue", "yellow", "red")) )

Change the color by groups

The colkey is customized (see ?colkey for more details):

scatter3D(x, y, z, bty = "g", pch = 18, 
          col.var = as.integer(iris$Species), 
          col = c("#1B9E77", "#D95F02", "#7570B3"),
          pch = 18, ticktype = "detailed",
          colkey = list(at = c(2, 3, 4), side = 1, 
          addlines = TRUE, length = 0.5, width = 0.5,
          labels = c("setosa", "versicolor", "virginica")) )

Change the position of the legend

# Bottom colkey
scatter3D(x, y, z, bty = "g",
          colkey = list(side = 1, length = 0.5))

3D viewing direction

The arguments theta and phi can be used to define the angles for the viewing direction. theta is the azimuthal direction and phi the co-latitude.

scatter3D(x, y, z, theta = 15, phi = 20)

scatter3D(x, y, z, phi = 0, bty ="g")

Titles and axis labels

scatter3D(x, y, z, pch = 18,  theta = 20, phi = 20,
          main = "Iris data", xlab = "Sepal.Length",
          ylab ="Petal.Length", zlab = "Sepal.Width")

## Tick marks and labels ### The arguments below can be used:

ticktype: Possible values are

“simple” draws just an arrow parallel to the axis to indicate direction of increase

“detailed” draws normal ticks and labels

nticks: the number of tick marks to draw on the axes. It has no effect if ticktype =“simple”.

scatter3D(x, y, z, phi = 0, bty = "g",
        pch = 20, cex = 2, ticktype = "detailed")

## Add points and text to an existing plot ### The functions below can be used:

scatter3D(x, y, z,…, add = TRUE): Adds points

text3D(x, y, z, labels, …, add = TRUE): Adds texts

Add points to an existing plot:

# Create a scatter plot
 scatter3D(x, y, z, phi = 0, bty = "g",
        pch = 20, cex = 2, ticktype = "detailed")
# Add another point (black color)
scatter3D(x = 7, y = 3, z = 3.5, add = TRUE, colkey = FALSE, 
         pch = 18, cex = 3, col = "black")

Add texts to an existing plot:

# Create a scatter plot
 scatter3D(x, y, z, phi = 0, bty = "g", pch = 20, cex = 0.5)
# Add text
text3D(x, y, z,  labels = rownames(iris),
        add = TRUE, colkey = FALSE, cex = 0.5)

Line plots

# type ="l" for lines only
 scatter3D(x, y, z, phi = 0, bty = "g", type = "l", 
           ticktype = "detailed", lwd = 4)

# type ="b" for both points and lines
 scatter3D(x, y, z, phi = 0, bty = "g", type = "b", 
           ticktype = "detailed", pch = 20, 
           cex = c(0.5, 1, 1.5))

# type ="h" for vertical lines
scatter3D(x, y, z, phi = 0, bty = "g",  type = "h", 
           ticktype = "detailed", pch = 19, cex = 0.5)

Add confidence interval

# Confidence interval
CI <- list(z = matrix(nrow = length(x),
                    data = rep(0.1, 2*length(x))))
head(CI$z)

##      [,1] [,2]
## [1,]  0.1  0.1
## [2,]  0.1  0.1
## [3,]  0.1  0.1
## [4,]  0.1  0.1
## [5,]  0.1  0.1
## [6,]  0.1  0.1

# 3D Scatter plot with CI
scatter3D(x, y, z, phi = 0, bty = "g", col = gg.col(100), 
          pch = 18, CI = CI)

3D fancy Scatter plot with small dots on basal plane

A helper function scatter3D_fancy() is used:

# Add small dots on basal plane and on the depth plane
scatter3D_fancy <- function(x, y, z,..., colvar = z)
  {
   panelfirst <- function(pmat) {
      XY <- trans3D(x, y, z = rep(min(z), length(z)), pmat = pmat)
      scatter2D(XY$x, XY$y, colvar = colvar, pch = ".", 
              cex = 2, add = TRUE, colkey = FALSE)
   
      XY <- trans3D(x = rep(min(x), length(x)), y, z, pmat = pmat)
      scatter2D(XY$x, XY$y, colvar = colvar, pch = ".", 
              cex = 2, add = TRUE, colkey = FALSE)
  }
  scatter3D(x, y, z, ..., colvar = colvar, panel.first=panelfirst,
    colkey = list(length = 0.5, width = 0.5, cex.clab = 0.75)) 
}

Fancy scatter plot:

scatter3D_fancy(x, y, z, pch = 16,
    ticktype = "detailed", theta = 15, d = 2,
    main = "Iris data",  clab = c("Petal", "Width (cm)") )

Regression plane

###The mtcars data will be used:

data(mtcars)
head(mtcars[, 1:6])

##                    mpg cyl disp  hp drat    wt
## Mazda RX4         21.0   6  160 110 3.90 2.620
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875
## Datsun 710        22.8   4  108  93 3.85 2.320
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215
## Hornet Sportabout 18.7   8  360 175 3.15 3.440
## Valiant           18.1   6  225 105 2.76 3.460

Use the function lm() to compute a linear regression model: ax + by + cz + d = 0

Use the argument surf in scatter3D() function to add a regression surface.

# x, y, z variables
x <- mtcars$wt
y <- mtcars$disp
z <- mtcars$mpg
# Compute the linear regression (z = ax + by + d)
fit <- lm(z ~ x + y)
# predict values on regular xy grid
grid.lines = 26
x.pred <- seq(min(x), max(x), length.out = grid.lines)
y.pred <- seq(min(y), max(y), length.out = grid.lines)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy), 
                 nrow = grid.lines, ncol = grid.lines)
# fitted points for droplines to surface
fitpoints <- predict(fit)
# scatter plot with regression plane
scatter3D(x, y, z, pch = 18, cex = 2, 
    theta = 20, phi = 20, ticktype = "detailed",
    xlab = "wt", ylab = "disp", zlab = "mpg",  
    surf = list(x = x.pred, y = y.pred, z = z.pred,  
    facets = NA, fit = fitpoints), main = "mtcars")

text3D: plot 3-dimensionnal texts

The function text3D() is used as follow:

#text3D(x, y, z, labels, ...)

The USArrests data sets will be used in the example below:

data(USArrests)
with(USArrests, text3D(Murder, Assault, Rape, 
  labels = rownames(USArrests), colvar = UrbanPop, 
  col = gg.col(100), theta = 60, phi = 20,
  xlab = "Murder", ylab = "Assault", zlab = "Rape", 
  main = "USA arrests", cex = 0.6, 
  bty = "g", ticktype = "detailed", d = 2,
  clab = c("Urban","Pop"), adj = 0.5, font = 2))

text3D and scatter3D

# Plot texts
with(USArrests, text3D(Murder, Assault, Rape, 
  labels = rownames(USArrests), colvar = UrbanPop, 
  col = gg.col(100), theta = 60, phi = 20,
  xlab = "Murder", ylab = "Assault", zlab = "Rape", 
  main = "USA arrests", cex = 0.6, 
  bty = "g", ticktype = "detailed", d = 2,
  clab = c("Urban","Pop"), adj = 0.5, font = 2))
# Add points
 with(USArrests, scatter3D(Murder, Assault, Rape - 1, 
    colvar = UrbanPop, col = gg.col(100), 
    type = "h", pch = ".", add = TRUE))

# Zoom near origin: choose suitable ranges
 plotdev(xlim = c(0, 10), ylim = c(40, 150), 
         zlim = c(7, 25))

3D Histogram

The function hist3D() is used:

#hist3D (x, y, z, ..., colvar = z, 
#      col = NULL,  add = FALSE)

data(VADeaths)
#  hist3D and ribbon3D with greyish background, rotated, rescaled,...
hist3D(z = VADeaths, scale = FALSE, expand = 0.01, bty = "g", phi = 20,
        col = "#0072B2", border = "black", shade = 0.2, ltheta = 90,
        space = 0.3, ticktype = "detailed", d = 2)

hist3D (x = 1:5, y = 1:4, z = VADeaths,
        bty = "g", phi = 20,  theta = -60,
        xlab = "", ylab = "", zlab = "", main = "VADeaths",
        col = "#0072B2", border = "black", shade = 0.8,
        ticktype = "detailed", space = 0.15, d = 2, cex.axis = 1e-9)
# Use text3D to label x axis
 text3D(x = 1:5, y = rep(0.5, 5), z = rep(3, 5),
       labels = rownames(VADeaths),
       add = TRUE, adj = 0)
# Use text3D to label y axis
 text3D(x = rep(1, 4),   y = 1:4, z = rep(0, 4),
       labels  = colnames(VADeaths),
       add = TRUE, adj = 1)

fancy 3D histograms

hist3D_fancy<- function(x, y, break.func = c("Sturges", "scott", "FD"), breaks = NULL,
                        colvar = NULL, col="white", clab=NULL, phi = 5, theta = 25, ...){
  
  # Compute the number of classes for a histogram
  break.func <- break.func [1]
  if(is.null(breaks)){
    x.breaks <- switch(break.func,
                       Sturges = nclass.Sturges(x),
                       scott = nclass.scott(x),
                       FD = nclass.FD(x))
    y.breaks <- switch(break.func,
                       Sturges = nclass.Sturges(y),
                       scott = nclass.scott(y),
                       FD = nclass.FD(y))
  } else x.breaks <- y.breaks <- breaks
  
  # Cut x and y variables in bins for counting
  x.bin <- seq(min(x), max(x), length.out = x.breaks)
  y.bin <- seq(min(y), max(y), length.out = y.breaks)
  xy <- table(cut(x, x.bin), cut(y, y.bin))
  z <- xy
  
  xmid <- 0.5*(x.bin[-1] + x.bin[-length(x.bin)])
  ymid <- 0.5*(y.bin[-1] + y.bin[-length(y.bin)])
  
  oldmar <- par("mar")
  par (mar = par("mar") + c(0, 0, 0, 2))
  hist3D(x = xmid, y = ymid, z = xy, ...,
    zlim = c(-max(z)/2, max(z)), zlab = "counts", bty= "g", 
    phi = phi, theta = theta,
    shade = 0.2, col = col, border = "black",
    d = 1, ticktype = "detailed")
   
  scatter3D(x, y,
    z = rep(-max(z)/2, length.out = length(x)),
    colvar = colvar, col = gg.col(100),
    add = TRUE, pch = 18, clab = clab,
    colkey = list(length = 0.5, width = 0.5,
       dist = 0.05, cex.axis = 0.8, cex.clab = 0.8)
       )
  par(mar = oldmar)
}

hist3D_fancy(quakes$long, quakes$lat, colvar=quakes$depth,
             breaks =30)

hist3D_fancy(iris$Sepal.Length, iris$Petal.Width, 
             colvar=as.numeric(iris$Species))

scatter2D: 2D scatter plot

Create some data:

# x, y coordinates
set.seed(1234)
x  <- sort(rnorm(10)) 
y  <- runif(10)
# Variable for coloring points
col.v <- sqrt(x^2 + y^2)

Basic 2D scatter plot:

scatter2D(x, y, colvar = col.v, pch = 16, bty ="n",
          type ="b")

2D scatter plot with confidence interval:

# Confidence interval for x variable only
CI <- list()
CI$x <- matrix(nrow = length(x), data = c(rep(0.25, 2*length(x))))
scatter2D(x, y, colvar = col.v, pch = 16, bty ="n", cex = 1.5, 
          CI = CI, type = "b")

# Confidence interval for both x and y variables
CI$y <- matrix (nrow = length(y), data = c(rep(0.05, 2*length(y))))
CI$col <- "black"
scatter2D(x, y, colvar = col.v, pch = 16,  bty ="n", cex = 1.5,
          CI = CI, type ="b")

CI$y[c(2,4,8,10), ] <- NA  # Some points have no CI
CI$x[c(2,4,8,10), ] <- NA  # Some points have no CI
CI$alen <- 0.02            # increase arrow head
scatter2D(x, y, colvar = col.v, pch = 16,  bty ="n", cex = 1.5,
          CI = CI, type ="b")

## text2D

# Only text
with(USArrests, text2D(x = Murder, y = Assault + 5, colvar = Rape, 
     xlab = "Murder", ylab = "Assault", clab = "Rape", 
     main = "USA arrests", labels = rownames(USArrests), cex = 0.6, 
     adj = 0.5, font = 2))

# text with point
 with(USArrests, text2D(x = Murder, y = Assault + 5, colvar = Rape, 
     xlab = "Murder", ylab = "Assault", clab = "Rape", 
     main = "USA arrests", labels = rownames(USArrests), cex = 0.6, 
     adj = 0.5, font = 2))
 with(USArrests, scatter2D(x = Murder, y = Assault, colvar = Rape, 
     pch = 16, add = TRUE, colkey = FALSE))

Other functions

#It’s also possible to draw arrows, segments and rectangles in a 3D or 2D plot using the functions below:

#arrows3D(x0, y0, z0, x1, y1, z1, ..., colvar = NULL,
#         col = NULL, type = "triangle", add = FALSE)
#segments3D(x0, y0, z0, x1, y1, z1, ..., colvar = NULL,
#           col = NULL, add = "FALSE")
#rect3D(x0, y0, y0, x1, y1, z1, ..., colvar = NULL,
#       col = NULL, add = FALSE)
#arrows2D(x0, y0, z0, x1, y1, z1, ..., colvar = NULL,
#         col = NULL, type = "triangle", add = FALSE)
#segments2D(x0, y0, z0, x1, y1, z1, ..., colvar = NULL,
#           col = NULL, add = "FALSE")
#rect2D(x0, y0, y0, x1, y1, z1, ..., colvar = NULL,
#       col = NULL, add = FALSE)

x0 <- c(0, 0, 0, 0)
y0 <- c(0, 0, 0, 0)
z0 <- c(0, 0, 0, 0)
x1 <- c(0.89, -0.46, 0.99, 0.96)
y1 <- c(0.36,  0.88, 0.02, 0.06)
z1 <- c(-0.28, 0.09, 0.05, 0.24)
cols <- c("#1B9E77", "#D95F02", "#7570B3", "#E7298A")

3D Arrows:

arrows3D(x0, y0, z0, x1, y1, z1, colvar = x1^2, col = cols,
         lwd = 2, d = 3, clab = c("Quality", "score"), 
         main = "Arrows 3D", bty ="g", ticktype = "detailed")
# Add starting point of arrow
points3D(x0, y0, z0, add = TRUE, col="darkred", 
          colkey = FALSE, pch = 19, cex = 1)
# Add labels to the arrows
text3D(x1, y1, z1, c("Sepal.L", "Sepal.W", "Petal.L", "Petal.W"),
       colvar = x1^2, col = cols, add=TRUE, colkey = FALSE)

2D arrows:

#arrows2D(x0, y0,  x1, y1,  colvar = x1^2, col = cols,lwd = 2, clab = c("Quality", "score"),bty ="n", xlim = c(-1, 1), ylim = c(-1, 1))
# Add vertical and horizontal lines at c(0,0)
#abline(h =0, v = 0, lty = 2)
# Add starting point of arrow
#points2D(x0, y0, add = TRUE, col="darkred", 
#          colkey = FALSE, pch = 19, cex = 1)
# Add labels to the arrows
#text2D(x1, y1, c("Sepal.L", "Sepal.W", "Petal.L", "Petal.W"),
#       colvar = x1^2, col = cols, add=TRUE, colkey = FALSE)

3D rectangle: the R code below creates a rectangle with a transparent fill color (alpha = 0.5)

rect3D(x0 = 0, y0 = 0.5, z0 = 0, x1 = 1, z1 = 5, 
       ylim = c(0, 1), bty = "g", facets = TRUE, 
       border = "red", col ="#7570B3", alpha=0.5,
       lwd = 2, phi = 20)

2D rectangle:

rect2D(x0 = runif(3), y0 = runif(3), 
       x1 = runif(3), y1 = runif(3), colvar = 1:3, 
       alpha = 0.4, lwd = 2, main = "rect2D")

## Interactive plot ## To draw an interactive 3D plot the package plot3Drgl can be used.