💡 Problem Formulation: When visualizing data, highlighting the area under a curve can significantly help to emphasize the difference between the curve and a baseline, such as the x-axis. In Python’s Matplotlib library, there are several methods to accomplish this. For example, given a set of data points that form a curve, the desired output is a graph where the area under this curve and above the x-axis is filled with a color or pattern.
Method 1: The fill_between Function
Matplotlib’s fill_between function is a versatile and straightforward way to fill the area between a curve and the x-axis. This method allows for considerable customization of the filled area’s appearance, such as setting a specific color, pattern, or transparency.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
# Define data
x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)
# Plot the curve
plt.plot(x, y, label='Sine Wave')
# Fill the area between the curve and the x-axis
plt.fill_between(x, y, color='skyblue', alpha=0.4)
# Customize and display plot
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.title('Area under Sine Wave')
plt.legend()
plt.show()
Output of this code snippet: A plot displaying the sine wave with the area underneath filled in a semi-transparent sky blue color.
This code snippet uses NumPy to generate an array of x values and applies the sine function to get the y values. It then plots the sine wave and uses fill_between to fill the area between the plotted sine curve and the x-axis. The alpha parameter controls the transparency of the fill.
Method 2: Using the where Parameter
The where parameter within the fill_between function allows more complex region filling by specifying a condition. This is useful when you only want to fill the area under the curve where certain criteria are met.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
# Define data
x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)
# Plot the curve
plt.plot(x, y, label='Sine Wave')
# Condition for filling: fill only where the curve is positive
plt.fill_between(x, y, where=(y > 0), color='green', alpha=0.3)
# Customize and display plot
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.title('Positive Area under Sine Wave')
plt.legend()
plt.show()
Output of this code snippet: A plot of the sine wave with only the area above the x-axis (where y is positive) filled in green.
The where parameter is used to define the condition under which the filling should take place. In the example, it is set to fill the region only where the y-values of the sine curve are greater than zero, effectively filling only the positive regions of the wave.
Method 3: Combining Multiple Regions
For complex figures, multiple calls to fill_between can be made to fill different regions with different styles or colors. This approach is ideal for distinguishing between various areas under a curve relative to other curves or thresholds.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
# Define data
x = np.linspace(0, 2*np.pi, 100)
y1 = np.sin(x)
y2 = 0.8*np.cos(x)
# Plot the curves
plt.plot(x, y1, label='Sine Wave')
plt.plot(x, y2, label='Cosine Wave', linestyle='--')
# Fill the areas between curves and x-axis with different conditions and colors
plt.fill_between(x, y1, color='red', alpha=0.2, where=(y1 > y2))
plt.fill_between(x, y1, color='blue', alpha=0.2, where=(y1 <= y2))
# Customize and display plot
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.title('Area between Sine and Cosine Waves')
plt.legend()
plt.show()
Output of this code snippet: A plot of both the sine and cosine waves, with the areas where the sine wave is above the cosine wave filled in red, and the other areas in blue.
The example shows how to plot two curves and use multiple fill_between calls to fill the areas differently, depending on a condition. This allows for easy comparison of the regions where one curve is above the other.
Method 4: Filling Between Two Horizontal Curves
It’s also possible to fill the area between two curves using fill_between. This fills the region bounded by both curves, rather than the region between a curve and the x-axis. This method is useful for showing the difference or gap between two datasets.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
# Define data
x = np.linspace(0, 2*np.pi, 100)
y1 = np.sin(x)
y2 = 0.3
# Plot the curves
plt.plot(x, y1, label='Sine Wave')
# Fill the area between two curves
plt.fill_between(x, y1, y2, color='purple', alpha=0.5, where=(y1 > y2))
# Customize and display plot
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.title('Area between Sine Wave and Horizontal Line')
plt.legend()
plt.show()
Output of this code snippet: A plot showing the area between the sine wave and a horizontal line at y = 0.3 filled in purple.
This example fills the region between a dynamic curve (sine wave) and a static one (horizontal line at y=0.3). The where parameter is used to control the filling only where the sine wave is above the horizontal line.
Bonus One-Liner Method 5: Using stackplot
The stackplot function can serve as a quick, one-line solution for filling the area under a curve. This method is less flexible than fill_between but can be handy for quick plots with minimal customization.
Here’s an example:
import matplotlib.pyplot as plt
import numpy as np
# Define data
x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)
# One-liner to fill the area under the curve
plt.stackplot(x, y, colors=['lightblue'])
# Customize and display plot
plt.xlabel('x-axis')
plt.ylabel('y-axis')
plt.title('Stackplot Area under Sine Wave')
plt.show()
Output of this code snippet: A simple plot where the area under the sine wave is filled with a light blue color.
The stackplot function generates a stacked area plot. In this usage example, since there is only one dataset provided, it fills the area beneath the sine wave as if it were a stack.
Summary/Discussion
- Method 1:
fill_betweenFunction. Highly customizable. Ideal for single regions. Complexity increases with conditional fills. - Method 2:
fill_betweenwithwhereParameter. Offers conditional fills. Great for emphasizing specific data ranges. Slightly more complex syntax. - Method 3: Combining Multiple Regions. Best for comparing areas under multiple curves. Can become complicated if overused or with overlapping areas.
- Method 4: Filling Between Two Curves. Shows the gap between datasets. Less intuitive for filling under a curve relative to the x-axis.
- Bonus Method 5: Using
stackplot. Good for quick, simple fills. Limited customization and less control compared tofill_between.