Best way to plot an angle between two lines in Matplotlib

The best way to plot an angle between two lines in Matplotlib is to use the Arc class to create an angular arc that visually represents the angle between two intersecting lines.

Basic Approach

To plot an angle between two lines, we need to:

• Calculate the slopes of both lines
• Convert slopes to angles using math.atan()
• Create an Arc patch using the calculated angles
• Add the arc to the plot using add_patch()

Complete Example

Here's a complete implementation that creates two lines and displays the angle between them ?

from matplotlib import pyplot as plt, patches
import math

plt.rcParams["figure.figsize"] = [7.50, 3.50]
plt.rcParams["figure.autolayout"] = True

def angle_plot(line1, line2, offset=1.0, color=None, origin=(0, 0),
               len_x_axis=1, len_y_axis=1):
    xy1 = line1.get_xydata()
    xy2 = line2.get_xydata()
    
    slope1 = (xy1[1][1] - xy1[0][1]) / float(xy1[1][0] - xy1[0][0])
    angle1 = abs(math.degrees(math.atan(slope1)))
    
    slope2 = (xy2[1][1] - xy2[0][1]) / float(xy2[1][0] - xy2[0][0])
    angle2 = abs(math.degrees(math.atan(slope2)))
    
    theta1 = min(angle1, angle2)
    theta2 = max(angle1, angle2)
    angle = theta2 - theta1
    
    if color is None:
        color = line1.get_color()

    return patches.Arc(origin, len_x_axis * offset, len_y_axis * offset, 
                       0, theta1, theta2, color=color, 
                       label=str(angle) + u"°")

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)

l1 = plt.Line2D([0, 1], [0, 4], linewidth=2, linestyle="-", color="green")
l2 = plt.Line2D([0, 4.5], [0, 3], linewidth=2, linestyle="-", color="red")

ax.add_line(l1)
ax.add_line(l2)

angle_arc = angle_plot(l1, l2, 0.25)
ax.add_patch(angle_arc)

ax.set_xlim(-0.5, 5)
ax.set_ylim(-0.5, 4.5)
ax.grid(True, alpha=0.3)
ax.set_aspect('equal')

plt.show()

How It Works

The angle_plot() function performs these key steps:

• Extract coordinates: Gets the start and end points of each line
• Calculate slopes: Uses the rise-over-run formula
• Convert to angles: Uses math.atan() and converts to degrees
• Create arc: Uses patches.Arc() with calculated angles

Key Parameters

Enhanced Version with Labels

Here's an improved version that adds angle labels and better formatting ?

import matplotlib.pyplot as plt
import matplotlib.patches as patches
import math

def plot_angle_with_label(line1, line2, offset=0.3, origin=(0, 0)):
    xy1 = line1.get_xydata()
    xy2 = line2.get_xydata()
    
    slope1 = (xy1[1][1] - xy1[0][1]) / float(xy1[1][0] - xy1[0][0])
    slope2 = (xy2[1][1] - xy2[0][1]) / float(xy2[1][0] - xy2[0][0])
    
    angle1 = math.degrees(math.atan(slope1))
    angle2 = math.degrees(math.atan(slope2))
    
    theta1 = min(angle1, angle2)
    theta2 = max(angle1, angle2)
    angle_diff = theta2 - theta1
    
    arc = patches.Arc(origin, offset*2, offset*2, 0, theta1, theta2, 
                      color='blue', linewidth=2)
    
    # Calculate label position
    mid_angle = math.radians((theta1 + theta2) / 2)
    label_x = origin[0] + (offset + 0.1) * math.cos(mid_angle)
    label_y = origin[1] + (offset + 0.1) * math.sin(mid_angle)
    
    return arc, (label_x, label_y, f'{angle_diff:.1f}°')

fig, ax = plt.subplots(figsize=(8, 6))

# Create two lines
l1 = plt.Line2D([0, 2], [0, 3], linewidth=2, color="green", label="Line 1")
l2 = plt.Line2D([0, 3], [0, 1], linewidth=2, color="red", label="Line 2")

ax.add_line(l1)
ax.add_line(l2)

# Add angle arc and label
arc, label_info = plot_angle_with_label(l1, l2, offset=0.4)
ax.add_patch(arc)
ax.text(label_info[0], label_info[1], label_info[2], fontsize=12, 
        ha='center', va='center')

ax.set_xlim(-0.5, 3.5)
ax.set_ylim(-0.5, 3.5)
ax.grid(True, alpha=0.3)
ax.set_aspect('equal')
ax.legend()
ax.set_title('Angle Between Two Lines')

plt.show()

Conclusion

Use patches.Arc() with calculated slopes and angles to visualize the angle between two lines. The key is converting line slopes to degrees and using them as arc parameters for accurate angle representation.