Plot Several Curve Segments on the Same Graph

R is a programming language and software environment for statistical computing and graphics. It is widely used among statisticians and data scientists for developing statistical software and data analysis.

R Programming Language is known for its powerful and flexible data visualization capabilities. The base installation of R includes several libraries for creating basic plots and charts, such as the “base” graphics library and the “lattice” library. In addition, there are many other libraries available for R that provide additional visualization capabilities, such as the “ggplot2” library, which is particularly popular for creating complex and highly customizable visualizations.

Plotting a Parabola Function

R

library(ggplot2)

# Create sample data
x <- 1:10
y <- x^2

# Plot data using ggplot2
ggplot(data = data.frame(x, y)) +
  geom_line(aes(x = x, y = y)) +
  ggtitle("Curve Plot") +
  xlab("X values") +
  ylab("Y values")

Output:

Parabola curve which is a single-curve segment

Curve Segment

A “curve segment” in R generally refers to a portion of a continuous function that is defined over a specific interval of x-values. It is a way of breaking down a curve or function into smaller, manageable parts, and can be useful for understanding how a curve behaves in different regions. 

In R, xlim and ylim are used to set the limits of the x and y axis, respectively, when creating a plot. They can be used to zoom in on a specific part of a plot or to remove outliers that might skew the plot. xlim and ylim can be passed to the plot() function or to the coord_cartesian() function in ggplot2 library. The below output shows the formation of the circle using 2 different curves of different colors.

R

# Set up the plot
plot(0,0, xlim=c(-1.5,1.5), ylim=c(-1.5,1.5),
     xlab="x", ylab="y", main="Circle")

# Define the radius of the circle
r = 1

# Define the x and y values
# for the top half of the circle
x1 = seq(-r,r,length.out=100)
y1 = sqrt(r^2-x1^2)

# Define the x and y values for
# the bottom half of the circle
x2 = seq(-r,r,length.out=100)
y2 = -sqrt(r^2-x2^2)

# Plot the top half of the circle in red
lines(x1,y1, col="red")

# Plot the bottom half of the circle in blue
lines(x2,y2, col="blue")

# Add a legend to the plot
legend("topright", c("Top Half", "Bottom Half"),
       lty=1, col=c("red", "blue"))

Output:

Formation of the circle using two different segments

Below is the output generated using the looping statement. 

R

# Set up the plot
plot(1:10, type="n")

# Set up the colors
colors <- c("red", "orange", "yellow", "green",
            "blue", "purple", "pink", "brown",
            "gray", "black")

# Loop through the colors and plot each curve
for (i in 1:10) {
  curve(sin(x+i), add=TRUE, col=colors[i])
}

Output:

Multiple Sine curves on the same graph

Now let’s plot the graph for y = x² and y = x³ for 1 to 10 and 11 to 20 respectively. In this way, we will be able to plot two curve segments in the same graph.

R

# Create data for curve segments
x1 <- 1:10
y1 <- x1^2
x2 <- 11:20
y2 <- x1^3

# Plot curve segments on the same graph
plot(x1, y1, type = "l", col = "blue",
     lwd = 2, xlim = c(0, 20), ylim = c(0, 1000))
lines(x2, y2, col = "red", lwd = 2)

# Add legend and labels
legend("topright", c("Curve 1", "Curve 2"),
       col = c("blue", "red"), lty = 1, lwd = 2)
xlab("X-axis")
ylab("Y-axis")

Output:

Two Curve Segments on the same Graphs

In R, seq() is a function that generates a sequence of numbers. It takes three arguments: the first and last numbers in the sequence, and the step size between numbers.

sin(), cos(), and tan() are trigonometric functions that are commonly used when working with curves. They are used to calculate the sine, cosine, and tangent of an angle, respectively. The angle can be specified in radians or degrees, depending on the context.

For example, you can use the seq() function to create a sequence of x-values and use the trigonometric functions to calculate the corresponding y-values to plot a curve.

R

# Define the range of x values
x <- seq(0, 10, 0.1)

# Create a vector of y values for each curve
y1 <- sin(x)
y2 <- cos(x)
y3 <- tan(x)
y4 <- exp(x)
y5 <- log(x)
y6 <- sin(x) + cos(x)
y7 <- sin(x) + tan(x)
y8 <- cos(x) + tan(x)
y9 <- exp(x) + log(x)
y10 <- sin(x) + cos(x) + tan(x)

# Define a vector of colors for each curve
colors <- c("red", "orange", "yellow", "green",
            "blue", "purple", "pink", "brown",
            "gray", "black")

# Create a plot with multiple lines
plot(x, y1, type="l", col=colors[1])
lines(x, y2, col=colors[2])
lines(x, y3, col=colors[3])
lines(x, y4, col=colors[4])
lines(x, y5, col=colors[5])
lines(x, y6, col=colors[6])
lines(x, y7, col=colors[7])
lines(x, y8, col=colors[8])
lines(x, y9, col=colors[9])
lines(x, y10, col=colors[10])

# Add a legend to the plot
legend("topleft", c("Curve 1", "Curve 2", "Curve 3",
                    "Curve 4", "Curve 5", "Curve 6",
                    "Curve 7", "Curve 8", "Curve 9",
                    "Curve 10"),
       col=colors, lty=1)

Output:

Multiple curve segments on the same graph