Advanced Graphics and 3D Plots

The later graphics chapters of The Book of R move beyond first plots into devices, margins, annotations, colors, palettes, higher-dimensional displays, contours, surfaces, and interactive 3D graphics. These topics are not separate from statistics: visualization choices determine whether patterns, residual structure, clusters, and model surfaces can be understood.

Advanced plotting in R has two sides. One side is control over a two-dimensional figure: devices, margins, axes, clipping, legends, mathematical labels, and color. The other side is representing more than two variables: color scales, facets, contours, perspective surfaces, and interactive rotation. The goal is not decoration. It is to make structure visible without misleading the reader.

Definitions

A graphics device is an output target such as an on-screen window, PDF, or PNG. Managing devices matters when a script writes multiple figures.

Margins are controlled in base graphics with par(mar = ...) and related settings. They reserve space for titles, axes, and labels.

A palette is a set of colors used to encode groups or numeric values. Qualitative palettes distinguish categories; sequential palettes encode ordered magnitudes; diverging palettes emphasize deviations around a midpoint.

A contour plot represents a surface $z = f(x, y)$ by drawing lines of equal $z$ value. In base R, contour and filled.contour are common tools.

A perspective plot draws a 3D-looking surface in 2D using persp.

An interactive 3D plot allows rotation, zooming, or other user-driven changes. The book discusses packages for interactive 3D work; exact package choices may vary by R installation and era.

Key results

Higher-dimensional plotting requires explicit mapping:

Data dimension	Visual strategy	Base R examples
One numeric variable	Histogram, density, boxplot	hist, density, boxplot
Two numeric variables	Scatterplot, line plot	plot, lines
Two numeric plus category	Color, shape, facets	col, pch, separate panels
Two numeric plus numeric response	Contour, image, surface	contour, image, persp
Three numeric coordinates	3D scatter or projections	package-based 3D, pairs

Color should match data type. Categories need distinct hues. Ordered numeric values need ordered palettes. Diverging values need a meaningful midpoint, such as zero residual or average difference.

For surfaces, the usual base R setup is:

1. Create sequences of x and y coordinates.
2. Evaluate a function at every x-y grid pair.
3. Store z-values in a matrix.
4. Plot with contour, image, filled.contour, or persp.

The z-matrix orientation matters. Rows and columns must align with the x and y vectors expected by the plotting function. Small test grids help catch transposition errors.

Visual

Surface grid:

          y1     y2     y3
x1      z11    z12    z13
x2      z21    z22    z23
x3      z31    z32    z33
x4      z41    z42    z43

Contour lines connect equal z values across the grid.

Worked example 1: Contour plot of a bivariate function

Problem: plot contours of $z = \sin(x)\cos(y)$ over $-\pi \le x \le \pi$ and $-\pi \le y \le \pi$.

Method:

1. Create x and y coordinate sequences.
2. Use outer to evaluate the function over the grid.
3. Draw contour lines.
4. Add a title and axis labels.
5. Check a known value manually.

x <- seq(-pi, pi, length.out = 80)
y <- seq(-pi, pi, length.out = 80)
z <- outer(x, y, function(a, b) sin(a) * cos(b))

contour(
  x,
  y,
  z,
  nlevels = 12,
  xlab = "x",
  ylab = "y",
  main = "Contours of sin(x) cos(y)"
)

Checked answer: at x = 0, sin(0) = 0, so z = 0 for every y. The contour plot should include a zero contour through the vertical line at x = 0. At x = pi / 2 and y = 0, z = 1 * 1 = 1, so the surface reaches a high value near that coordinate.

The outer call is concise because it evaluates all x-y combinations without a hand-written nested loop.

Worked example 2: Color-coded residual surface

Problem: fit mpg ~ wt + hp in mtcars, compute predicted mpg over a grid of weight and horsepower values, and display the fitted surface as a filled contour.

Method:

1. Fit the linear model.
2. Create grid sequences for wt and hp.
3. Use expand.grid to create prediction points.
4. Predict mpg for every grid point.
5. Reshape predictions into a matrix.
6. Plot with filled.contour.

fit <- lm(mpg ~ wt + hp, data = mtcars)

wt_grid <- seq(min(mtcars$wt), max(mtcars$wt), length.out = 40)
hp_grid <- seq(min(mtcars$hp), max(mtcars$hp), length.out = 40)
grid <- expand.grid(wt = wt_grid, hp = hp_grid)

grid$mpg_hat <- predict(fit, newdata = grid)
z <- matrix(grid$mpg_hat, nrow = length(wt_grid), ncol = length(hp_grid))

filled.contour(
  wt_grid,
  hp_grid,
  z,
  xlab = "Weight",
  ylab = "Horsepower",
  color.palette = terrain.colors,
  main = "Predicted mpg from linear model"
)

Checked answer: the fitted model has negative coefficients for weight and horsepower in this data set, so predicted mpg should generally decrease as either axis increases. The contour colors should reflect higher mpg in the low-weight, low-horsepower corner and lower mpg in the high-weight, high-horsepower corner.

This plot visualizes a model surface. It should be interpreted inside the observed data range; empty corners of the grid may represent combinations not well supported by actual cars.

Code

# Build a reusable surface plot for any two-predictor lm object.

plot_lm_surface <- function(fit, data, xvar, yvar, n = 50) {
  x_grid <- seq(min(data[[xvar]]), max(data[[xvar]]), length.out = n)
  y_grid <- seq(min(data[[yvar]]), max(data[[yvar]]), length.out = n)
  grid <- expand.grid(x = x_grid, y = y_grid)
  names(grid) <- c(xvar, yvar)

  grid$z <- predict(fit, newdata = grid)
  z <- matrix(grid$z, nrow = n, ncol = n)

  image(x_grid, y_grid, z, xlab = xvar, ylab = yvar, col = heat.colors(20))
  contour(x_grid, y_grid, z, add = TRUE)
  points(data[[xvar]], data[[yvar]], pch = 19, cex = 0.7)
}

fit <- lm(mpg ~ wt + hp, data = mtcars)
plot_lm_surface(fit, mtcars, "wt", "hp")

The reusable surface function assumes that the model can predict from only xvar and yvar. That is true for lm(mpg ~ wt + hp, data = mtcars), but it would not be enough for a model with additional predictors unless those predictors were fixed at reference values. This is an important modeling-graphics issue: every surface is a slice through a model, and the slice must be described.

The code uses image plus contour rather than persp because a 2D view is often easier to read. Color shows the fitted response level, contour lines show equal fitted values, and points show where observed data exist. The observed points are crucial: they reveal whether the surface is supported by data or whether large regions are extrapolation.

When plotting in higher dimensions, decide what the viewer must compare. If exact numeric values matter, a contour with labeled levels or a heat map with a legend is usually better than a tilted 3D surface. If shape and interaction are the main message, a perspective or interactive plot may help. If categories are involved, facets may be clearer than adding another color scale.

Advanced graphics should still be reproducible. Store palette choices, device sizes, and grid definitions in code. Avoid manual rotation or point-and-click annotation as the only copy of an important figure unless the coordinates or view settings are saved.

Color deserves particular care in higher-dimensional graphics. A palette should be perceptually ordered when it represents magnitude, and it should remain interpretable when printed or viewed by readers with color-vision differences. Avoid rainbow-like palettes for ordered data because equal numeric steps do not look like equal visual steps. Prefer palettes with a clear light-to-dark progression or a meaningful diverging midpoint.

Interactive 3D plots are useful for exploration, but static notes need a stable view. If an interactive view reveals an important structure, capture the camera angle, axis labels, and color mapping in code or a written caption. Otherwise, a reader cannot reproduce what the analyst saw. Often the final report should include a 2D projection, contour, or set of facets even if interactive rotation was useful during exploration.

For surfaces and contours, always state what the z-value represents. It might be a mathematical function, a fitted response, a density estimate, a residual, or an error surface. The same visual form can mean very different things depending on that definition, so captions and axis labels are part of the analysis.

Common pitfalls

• Using color palettes that imply order for unordered categories.
• Forgetting legends or scales when color encodes numeric values.
• Plotting a model surface far outside observed data and interpreting extrapolation as evidence.
• Transposing the z-matrix accidentally and labeling axes incorrectly.
• Overusing 3D perspective when a contour or faceted 2D plot would be easier to read.
• Making margins too small for labels, especially when exporting to file devices.
• Changing global graphical parameters and not restoring them.

Connections

• Base graphics
• ggplot2 graphics
• Linear and generalized models
• Matrices and arrays