Plotting Infinite Horizontal Lines in Python Bokeh

Bokeh is a powerful Python library for creating interactive visualizations for web browsers. One common requirement in data visualization is plotting infinite horizontal lines, which can serve as reference lines or thresholds in a plot. This article explores how to achieve this using Bokeh, providing a comprehensive guide with examples and explanations.

Basic Glyphs in Bokeh

Before diving into infinite lines, it's essential to understand Bokeh's basic glyphs. A glyph in Bokeh is a visual shape that represents data, such as lines or circles. The line() function is used to draw lines by specifying lists of x and y coordinates. Here’s a simple example:

from bokeh.plotting import figure, show

p = figure(width=400, height=400)
p.line([1, 2, 3, 4], [4, 3, 2, 1], line_width=2)
show(p)

This code creates a basic line plot with specified x and y points.

Creating Infinite Horizontal Lines

To create an infinite horizontal line in Bokeh, you can use the Span glyph, which is specifically designed for this purpose. The Span glyph can draw horizontal or vertical lines that extend infinitely across the plot area.

The Span glyph is part of Bokeh's annotation tools and can be used to draw lines that span the entire plot. Here's how to create an infinite horizontal line using Span:

from bokeh.plotting import figure, show
from bokeh.models import Span

p = figure(width=400, height=400)
span = Span(location=0, dimension='width', line_color='red', line_width=2)
p.add_layout(span)
show(p)

In this example, the Span is set to a location of 0 on the y-axis, and it spans the entire width of the plot. The line_color and line_width parameters customize the appearance of the line.

Here's a complete guide to adding an infinite horizontal line to your Bokeh plot.

from bokeh.plotting import figure, show
from bokeh.io import output_file
from bokeh.models import Span

# Set up the output file
output_file("infinite_horizontal_line.html")
p = figure(width=600, height=400, title="Infinite Horizontal Line Example")

# Add some sample data
p.line([1, 2, 3, 4, 5], [6, 7, 2, 4, 6], line_width=2, color="blue", legend_label="Sample Line")

# Create a Span object for the infinite horizontal line
hline = Span(location=4, dimension='width', line_color='red', line_width=2, line_dash='dashed')

# Add the Span to the plot
p.add_layout(hline)
show(p)

Output:

Plotting Infinite Horizontal Lines Using the Ray Glyph

The ray() function can also be used to create lines that extend to the plot's edge. By setting the length parameter to 0, you can create an "infinite" ray:

from bokeh.plotting import figure, show, output_notebook

output_notebook()

# Create a new figure
p = figure(width=400, height=400, x_range=(-10, 10), y_range=(-10, 10))

# Add infinite horizontal lines
# By setting the x range to be wider than the plot, you simulate infinite lines
p.line(x=[-10, 10], y=[0, 0], line_width=2, line_color='blue')
p.line(x=[-10, 10], y=[5, 5], line_width=2, line_color='red')
p.line(x=[-10, 10], y=[-5, -5], line_width=2, line_color='green')

show(p)

Output:

Using Line with Extreme Coordinates

Another method involves using the line() function with extreme coordinate values to simulate infinity:

import numpy as np
from bokeh.plotting import figure, show, output_notebook

# Enable Bokeh to display plots in a Jupyter notebook
output_notebook()

# Create a new figure
p = figure(width=400, height=400, x_range=(-1e10, 1e10), y_range=(-10, 10))

# Add horizontal lines to simulate infinite lines
p.line(x=[-1e10, 1e10], y=[0, 0], line_width=2, line_color='green')
p.line(x=[-1e10, 1e10], y=[5, 5], line_width=2, line_color='red')
p.line(x=[-1e10, 1e10], y=[-5, -5], line_width=2, line_color='blue')

show(p)

Output:

This approach uses the maximum and minimum integer values to create a line that appears infinite within the plot's view.

Considerations and Best Practices

• Performance: Using Span is generally more efficient than other methods, as it is specifically optimized for infinite lines.
• Plot Range: Ensure that the plot range is appropriately set to visualize the infinite line as intended.
• Interactivity: Bokeh's interactive features, such as zooming and panning, work seamlessly with infinite lines, allowing users to explore data while maintaining reference lines.

Conclusion

Plotting infinite horizontal lines in Bokeh is a straightforward task with multiple approaches. The Span glyph provides a clean and efficient solution, while alternative methods like ray() and extreme coordinates offer flexibility. By leveraging these techniques, you can enhance your Bokeh visualizations with meaningful reference lines that aid in data interpretation.