Centering the Origin in a Matplotlib Cosine Curve Plot

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💡 Problem Formulation: When plotting a cosine curve using Python’s Matplotlib library, the default behavior is to place the origin (0,0) at the bottom left of the figure. In many cases, particularly when dealing with trigonometric functions, having the origin in the center of the plot provides a clearer view of the function’s behavior. This article will guide you through various methods of repositioning the origin to the center of a cosine curve plot.

Method 1: Adjusting Axis Limits and Spines

This method involves manually setting the axis limits and moving the spines (the lines noting the boundaries of the plot area) to the zero position of the opposite axis. This technique is highly customizable and does not require additional libraries beyond Matplotlib.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np

# Generate data points.
x = np.linspace(-np.pi, np.pi, 100)
y = np.cos(x)

# Create the plot.
fig, ax = plt.subplots()

# Set equal scaling and limits for the x and y axis.
ax.axis('equal')
ax.set_xlim(-np.pi, np.pi)
ax.set_ylim(-1, 1)

# Move left and bottom spines to the center.
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')

# Hide right and top spines.
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')

# Plot the cosine curve.
ax.plot(x, y)

# Show the plot.
plt.show()

Output: A cosine curve with the origin centered in the figure.

The provided snippet creates a basic cosine plot and modifies the plot’s spines to reposition the origin. The 'equal' axis scaling ensures the curve is not distorted. By setting the positions of ‘left’ and ‘bottom’ spines to ‘center’, we effectively move the axes to the middle of the graph.

Method 2: Using the set_aspect() method

set_aspect('equal', adjustable='datalim') can also be used to ensure that the scales on the x and y axes remain equal, keeping the shape of the cosine curve true to form. This method is similar to the first, but it provides a different approach to axis scaling.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np

# Generate data points.
x = np.linspace(-np.pi, np.pi, 100)
y = np.cos(x)

# Create the plot.
fig, ax = plt.subplots()

# Set the aspect of the plot to be equal.
ax.set_aspect('equal', adjustable='datalim')

# Move left and bottom spines to the center and hide the top and right spines.
for spine in ['left', 'bottom']:
    ax.spines[spine].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')

# Plot the cosine curve.
ax.plot(x, y)

# Show the plot.
plt.show()

Output: A cosine curve with a centered origin and equal axis aspect.

This code creates a plot with a cosine curve, using the set_aspect() method to ensure that the unit length on both axes remains the same. It then adjusts the spine positions to centralize the origin.

Method 3: Using Matplotlib’s Axes Zero

To create plots with an origin centered in the figure, Matplotlib’s axes_zero functionality can be used. This allows for direct creation of plots with centered axes without the need to manually adjust spines or axis limits.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.axisartist import SubplotZero

# Generate data points.
x = np.linspace(-np.pi, np.pi, 100)
y = np.cos(x)

# Create a new figure and use the SubplotZero from mpl_toolkits.axisartist.
fig = plt.figure()
ax = SubplotZero(fig, 111)
fig.add_subplot(ax)

# Make the zero lines thicker and darker.
for direction in ["xzero", "yzero"]:
    ax.axis[direction].set_axisline_style("-|>")
    ax.axis[direction].set_visible(True)

# Plot the cosine curve.
ax.plot(x, y)

# Show the plot.
plt.show()

Output: A centered cosine curve with prominent zero axes.

The snippet utilizes SubplotZero from mpl_toolkits.axisartist to create axes that automatically include a visible x and y axis line through the origin. The zero-lined axes are then customized and made more prominent before the cosine curve is plotted.

Method 4: Custom Transform for Axes

Another advanced method is to create a custom transformation that moves the origin of the plot to the center. It requires a deeper understanding of Matplotlib’s transform system but provides a powerful way to manipulate the plot appearance directly.

Here’s an example:

import matplotlib.pyplot as plt
import matplotlib.transforms as transforms
import numpy as np

# Generate data points.
x = np.linspace(-np.pi, np.pi, 100)
y = np.cos(x)

# Create the plot.
fig, ax = plt.subplots()

# Create a custom transformation for the data.
trans = transforms.Affine2D().rotate_deg(45).scale(np.pi, 1) + ax.transData

# Move left and bottom spines to the center and hide the other two.
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')

# Plot the cosine curve with the custom transformation.
ax.plot(x, y, transform=trans)

# Show the plot.
plt.show()

Output: A rotated and scaled cosine curve with a centralized origin.

In this code snippet, a custom affine transformation is applied to the cosine curve data. The rotation and scaling are handled through Matplotlib’s transformation system, and then the modified data is plotted normally with the origin centered.

Bonus One-Liner Method 5: Centering with ax.set_anchor()

Matplotlib allows quick adjustments of the plot position within the figure canvas using the ax.set_anchor() method. This one-liner can help centralize the plot by adjusting the anchor of the axes.

Here’s an example:

import matplotlib.pyplot as plt
import numpy as np

# Generate data points.
x = np.linspace(-np.pi, np.pi, 100)
y = np.cos(x)

# Create the plot.
fig, ax = plt.subplots()

# Center the plot within the figure.
ax.set_anchor('C')

# Plot the cosine curve.
ax.plot(x, y)

# Show the plot.
plt.show()

Output: A cosine curve with the axes centered within the figure canvas.

This example uses ax.set_anchor('C') to simply center the plot with respect to the figure.

Summary/Discussion

  • Method 1: Adjusting Axis Limits and Spines. Provides detailed control over axis appearance. Requires adjusting multiple properties.
  • Method 2: Using the set_aspect() method. Simplifies maintaining an equal aspect ratio. Still needs spine adjustments.
  • Method 3: Using Matplotlib’s Axes Zero. Automatically centralizes axes. Less control over spine and tick appearance.
  • Method 4: Custom Transform for Axes. Offers sophisticated manipulation of data display. Can be complex to understand and implement correctly.
  • Bonus Method 5: Centering with ax.set_anchor(). Quick and straightforward. Does not adjust spines but centralizes the plot area in the canvas.