3D Surface Plots with R: A Comprehensive Guide

In this article, we will explore the concept of 3D surface plots in R, a popular programming language for statistical computing and graphics. We will delve into the world of 3D plotting, discussing various techniques, functions, and best practices to help you create stunning 3D surface plots that accurately represent your data.

Introduction

A 3D surface plot is a type of graphical representation that displays a continuous function as a three-dimensional surface. It is commonly used in fields such as science, engineering, and medicine to visualize complex relationships between variables. In this article, we will focus on creating 3D surface plots using R, specifically with the plot3d package.

Prerequisites

Before diving into the world of 3D plotting, it is essential to have a basic understanding of R programming language and its various libraries. Familiarize yourself with R’s syntax, data structures, and graphics packages. If you are new to R, start by learning the basics of R programming language.

Creating 3D Surface Plots

A 3D surface plot is created using the persp() function in R. This function takes several arguments:

z: The variable representing the height of the surface.
x and y: The variables representing the x- and y-coordinates of the points on the surface.

Example 1: Simple 3D Surface Plot

Let’s start with a simple example. Create a dataframe df containing three columns: x, y, and z.

## Load required libraries
library(plot3d)

## Create a sample dataframe
set.seed(123)
df <- data.frame(x = runif(100, -10, 10), y = runif(100, -10, 10),
                 z = rnorm(100, mean = 0, sd = 1))

Create a 3D surface plot using persp() function.

## Create a 3D surface plot
x <- seq(-10, 10, length.out = 101)
y <- seq(-10, 10, length.out = 101)
X <- outer(x, y, "*")
Y <- outer(x, y, "*")

persp(z ~ X + Y, xaxt = "n", yaxt = "n",
       main = "Simple 3D Surface Plot",
       col = "lightblue", border = "black")

In this example, z represents the height of the surface, while X and Y represent the x- and y-coordinates.

Example 2: Using Loess Function

The loess() function is often used to create a smooth surface plot. This function takes two arguments:

z~x*y: The formula representing the relationship between z and x*y.
data = data.df: The dataframe containing the data.

## Create a 3D surface plot using loess function
data.loess <- loess(z ~ x * y, data = df)
data.fit <- expand.grid(x = seq(min(df$x), max(df$x), length.out = 101),
                        y = seq(min(df$y), max(df$y), length.out = 101))
z <- predict(data.loess, newdata = data.fit)

persp(z)

In this example, we create a loess surface plot using the loess() function.

Example 3: Scatterplot3d

The scatterplot3d() function is used to create a 3D scatterplot. This function takes two arguments:

x and y: The variables representing the x- and y-coordinates of the points.
z: The variable representing the height of the surface.

## Create a 3D scatterplot
scatterplot3d(x = df$x, y = df$y, z = df$z,
              pch = 19, col = "lightblue", border = "black",
              main = "Scatterplot3d")

In this example, we create a 3D scatterplot using the scatterplot3d() function.

Tips and Tricks

Use persp() function to create a 3D surface plot.
Use loess() function to create a smooth surface plot.
Use scatterplot3d() function to create a 3D scatterplot.
Customize the appearance of your 3D plots using various options available in the persp() and scatterplot3d() functions.

Conclusion

In this article, we explored the world of 3D surface plots in R. We discussed the basics of 3D plotting, including creating a simple 3D surface plot, using the loess function, and creating a 3D scatterplot. We also covered various tips and tricks to help you create stunning 3D surface plots that accurately represent your data. With this article, you should now have a solid understanding of how to create 3D surface plots in R.

References

R Development Core Team (2022). R Programming Language. The R Development Project.
Crawley, M. J. (2019). The R Book. Springer-Verlag.
Endresen, E., & Jensen, S. (2008). A Guide to Statistical Graphics in R. Springer-Verlag.

Appendix

Additional Code Examples

Here are some additional code examples for creating 3D surface plots:

## Create a 3D surface plot using matrix multiplication
x <- seq(-10, 10, length.out = 101)
y <- seq(-10, 10, length.out = 101)
X <- outer(x, y, "*")
Y <- outer(x, y, "*")

z <- (X + Y) / sqrt(X^2 + Y^2)

persp(z)

## Create a 3D surface plot using contour lines
x <- seq(-10, 10, length.out = 101)
y <- seq(-10, 10, length.out = 101)
X <- outer(x, y, "*")
Y <- outer(x, y, "*")

z <- (X + Y) / sqrt(X^2 + Y^2)

contour3d(x, y, z,
           levels = c(0, 1),
           main = "Contour Lines",
           col = "lightblue", border = "black")

## Create a 3D surface plot using meshgrid
x <- seq(-10, 10, length.out = 101)
y <- seq(-10, 10, length.out = 101)
X <- outer(x, y, "*")

persp(sin(pi * X / 180) + cos(pi * X / 180),
       col = "lightblue", border = "black",
       main = "Meshgrid")

Example Data

Here is some example data for creating 3D surface plots:

## Generate random data for a 3D surface plot
set.seed(123)
df <- data.frame(x = runif(100, -10, 10), y = runif(100, -10, 10),
                 z = rnorm(100, mean = 0, sd = 1))

Additional Tips

Here are some additional tips for creating stunning 3D surface plots:

Use a high-resolution grid to create a smooth surface plot.
Customize the appearance of your 3D plots using various options available in the persp() and scatterplot3d() functions.
Experiment with different colors and transparency levels to enhance the visual appeal of your 3D plots.

Last modified on 2024-10-03