The Syntax of persp()

Before we dive into examples, let’s take a look at the basic syntax of the persp() function:

persp(x, y, z, theta = 30, phi = 30, col = "lightblue",
      border = "black", scale = TRUE, ... )

• x, y, and z are the vectors or matrices representing the x, y, and z coordinates of the data points.
• theta and phi control the orientation of the plot. theta sets the azimuthal angle (rotation around the z-axis), and phi sets the polar angle (rotation from the xy-plane). These angles are in degrees.
• col and border control the color of the surface and its border, respectively.
• scale is a logical value that determines whether the axes should be scaled to match the data range.
• Additional parameters can be passed as ... to customize the plot further.

Now, let’s jump into some examples to see how persp() works in action!

Example 1: Creating a Simple Surface Plot

# Create data for a simple surface plot
x <- seq(-5, 5, length.out = 50)
y <- seq(-5, 5, length.out = 50)
z <- outer(x, y, function(x, y) cos(sqrt(x^2 + y^2)))

# Create a 3D surface plot
persp(x, y, z, col = "lightblue", border = "black")

In this example, we generate a grid of x and y values and calculate the corresponding z values based on a mathematical function. The persp() function then creates a 3D surface plot, using the provided x, y, and z data.

Example 2: Customizing the Perspective

# Create data for a surface plot
x <- seq(-10, 10, length.out = 100)
y <- seq(-10, 10, length.out = 100)
z <- outer(x, y, function(x, y) 2 * sin(sqrt(x^2 + y^2)) / sqrt(x^2 + y^2))

# Create a customized 3D surface plot
persp(x, y, z, col = "lightblue", border = "black", theta = 60, phi = 20)

In this example, we create a similar surface plot but customize the perspective by changing the theta and phi angles. This gives the plot a different orientation, providing a unique view of the data.

Example 3: Scaling the Axes

# Create data for a surface plot
x <- seq(-2, 2, length.out = 50)
y <- seq(-2, 2, length.out = 50)
z <- outer(x, y, function(x, y) exp(-x^2 - y^2))

# Create a 3D surface plot with scaled axes
persp(x, y, z, col = "lightblue", border = "black", scale = TRUE)

Here, we enable axis scaling with the scale parameter, which ensures that the x, y, and z axes are scaled to match the data range.

Example 4: Multiple Plots

# Create data
x <- seq(-10, 10, length.out = 50)
y <- seq(-10, 10, length.out = 50)
z1 <- outer(x, y, function(x, y) dnorm(sqrt(x^2 + y^2)))
z2 <- outer(x, y, function(x, y) dnorm(sqrt((x-2)^2 + (y-2)^2)))
z3 <- outer(x, y, function(x, y) dnorm(sqrt((x+2)^2 + (y+2)^2)))

# Plot data
par(mfrow = c(1, 3))

persp(x, y, z1, theta = 30, phi = 30, col = "lightblue", border = NA, shade = 0.5, ticktype = "detailed", nticks = 5, xlab = "X", ylab = "Y", zlab = "Z1")
persp(x, y, z2, theta = 30, phi = 30, col = "lightblue", border = NA, shade = 0.5, ticktype = "detailed", nticks = 5, xlab = "X", ylab = "Y", zlab = "Z2")
persp(x, y, z3, theta = 30, phi = 30, col = "lightblue", border = NA, shade = 0.5, ticktype = "detailed", nticks = 5, xlab = "X", ylab = "Y", zlab = "Z3")

par(mfrow = c(1, 1))

In this example, we create data for three different Gaussian distributions. We define the x- and y-axes and use the outer() function to calculate the z-values based on the normal distribution. We then use the persp() function to plot the data. We set the color to light blue, the border to NA, and the shading to 0.5. We also set the tick type to detailed and the number of ticks to 5. Finally, we label the x-, y-, and z-axes. We use the par() function to create multiple 3D plots in one figure.