How to Draw a Point in Polar Coordinates with Negative using R?

In R Language plotting in polar coordinates is an advanced technique that involves transforming Cartesian coordinates (x, y) to polar coordinates (r, θ). Polar coordinates define a point by its distance from the origin (r) and the angle (θ) it makes with the positive x-axis, usually measured in radians.

Polar Coordinates

In polar coordinates, a point is represented by:

• r: The radial distance from the origin.
• θ (theta): The angle in radians from the positive x-axis.

Drawing a point in negative polar coordinates requires special handling, as the negative radius can impact the position of the point relative to the origin. In this article, we will explain how to plot points in polar coordinates, including how to manage negative radius values using R.

Plotting Points in Polar Coordinates in R

R does not have a built-in function for polar plots by default, so we rely on transformation from polar to Cartesian coordinates to plot the point. To achieve this, we can use either the base plotting system or the ggplot2 package. Below is a step-by-step guide for both methods.

Step 1: Define Polar Coordinates

We first define the polar coordinates including negative.

# Define a point in polar coordinates
r <- -5           # radial distance (negative)
theta <- pi / 4   # angle in radians (45 degrees)

Step 2: Convert Polar to Cartesian Coordinates

Next, convert the polar coordinates to Cartesian coordinates using the formulas mentioned earlier:

# Convert to Cartesian coordinates
x <- r * cos(theta)
y <- r * sin(theta)

Step 3: Plot the Point

Now that you have the Cartesian coordinates, plot the point using the plot() function in base R:

# Create an empty plot
plot(NA, xlim = c(-6, 6), ylim = c(-6, 6), xlab = "X", ylab = "Y", 
                         main = "Negative Polar Coordinate Point")
# Draw axes
abline(h = 0, v = 0)
# Plot the point
points(x, y, col = "red", pch = 19, cex = 1.5)

Output:

Draw Using ggplot2 to Plot Polar Coordinates

The ggplot2 package provides a more flexible and aesthetic way of visualizing polar plots. You can plot Cartesian coordinates and label them.

install.packages("ggplot2")
library(ggplot2)
# Data frame for polar coordinates
polar_data <- data.frame(
  x = r * cos(theta),
  y = r * sin(theta)
)
# Create the plot using ggplot2
ggplot(polar_data, aes(x = x, y = y)) +
  geom_point(color = "blue", size = 4) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  labs(title = "Negative Polar Coordinate Point", x = "X", y = "Y") +
  theme_minimal()

Output:

Drawing Multiple Polar Coordinates points

Let’s plot multiple points with both positive and negative.

# Define multiple points in polar coordinates
r_values <- c(4, -4, 5, -5)
theta_values <- c(pi/6, pi/3, pi/4, pi/2)

# Convert to Cartesian coordinates
x_values <- r_values * cos(theta_values)
y_values <- r_values * sin(theta_values)

# Data frame for the points
multi_polar_data <- data.frame(
  x = x_values,
  y = y_values
)

# Plot using ggplot2
ggplot(multi_polar_data, aes(x = x, y = y)) +
  geom_point(color = "purple", size = 3) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  geom_vline(xintercept = 0, linetype = "dashed") +
  labs(title = "Multiple Polar Coordinate Points", x = "X", y = "Y") +
  theme_minimal()

Output:

This code will plot four points, two with negative radii, and show the proper positioning by reflecting the points across the origin.

Conclusion

Drawing points in negative polar coordinates in R requires converting polar coordinates to Cartesian coordinates. Negative radii reflect the points across the origin, and both base R and ggplot2 offer ways to visualize this. Using these methods, you can handle polar coordinates efficiently and create clear, accurate visualizations of data.