[Bug]: Numerical Instability Of Path.arc For 0 Degree Or 360 Degree Arc

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[Bug]: Numerical Instability of Path.arc for 0 Degree or 360 Degree Arc

Matplotlib is a powerful plotting library in Python that provides a wide range of tools for creating high-quality 2D and 3D plots. However, like any other complex software, Matplotlib is not immune to bugs and numerical instability issues. In this article, we will discuss a bug in the Path.arc function of Matplotlib that causes numerical instability when creating an arc path of 0 or 360 degrees.

The bug occurs when trying to create an arc path of 0 or 360 degrees using the Path.arc function. In some cases, the function returns an arc path of 360 or 0 degrees instead, due to floating-point precision issues. This can lead to unexpected results and incorrect plots.

The following code snippet demonstrates the bug:

from matplotlib import patches, path, pyplot

fig, ax = pyplot.subplots(ncols=3)
ax[0].add_patch(patches.PathPatch(path.Path.arc(theta1=-90 - 1e-14, theta2=270)))
ax[0].set_title("arc(-90-1e-14, 270), should be a circle")
ax[1].add_patch(patches.PathPatch(path.Path.arc(theta1=-90, theta2=270)))
ax[1].set_title("arc(-90, 270), is a circle")
ax[2].add_patch(patches.PathPatch(path.Path.arc(theta1=-90, theta2=-90 - 1e-14)))
ax[2].set_title("arc(-90, -90-1e-14), should not be a circle")
for a in ax:
    a.set_xlim(-1, 1)
    a.set_ylim(-1, 1)
    a.set_aspect("equal")
pyplot.show()

This code creates three plots using the Path.arc function with different input values. The first plot should be a circle, but due to the bug, it becomes a line instead. The second plot is a circle as expected. The third plot should not be a circle, but it becomes one due to the bug.

The actual outcome of running the code is shown in the following image:

Image

The expected outcome is that the first plot should be a circle, identical to the second plot. The third plot should be empty.

The location of the bug is in the path.py file of Matplotlib, specifically in the Path.arc function. The bug occurs due to the use of floating-point arithmetic, which can lead to precision issues.

The intention of the Path.arc function is not clear, and it is not specified what should happen when the input values are not in the expected range. The docstring does not provide any clarification on this issue.

To understand the intention of the Path.arc function, we need to analyze the code and the expected behavior. The function takes two input values, theta1 and theta2, which represent the start end angles of the arc, respectively.

The function uses the np.floor function to calculate the angle range of the arc. However, this can lead to unexpected results when the input values are not in the expected range.

To fix the bug, we can propose the following solutions:

  1. Clarify the docstring to specify what should happen when the input values are not in the expected range.
  2. Raise a ValueError when the input values are not in the expected range.

In conclusion, the Path.arc function of Matplotlib has a bug that causes numerical instability when creating an arc path of 0 or 360 degrees. The bug occurs due to floating-point precision issues and the lack of clarity in the docstring.

To fix the bug, we can propose clarifying the docstring and raising a ValueError when the input values are not in the expected range. This will ensure that the function behaves as expected and provides accurate results.

Based on the analysis, we recommend the following:

  1. Update the docstring to clarify what should happen when the input values are not in the expected range.
  2. Raise a ValueError when the input values are not in the expected range.
  3. Test the function with different input values to ensure that it behaves as expected.

By following these recommendations, we can ensure that the Path.arc function behaves correctly and provides accurate results.
[Bug]: Numerical Instability of Path.arc for 0 Degree or 360 Degree Arc - Q&A

A: The bug occurs when trying to create an arc path of 0 or 360 degrees using the Path.arc function. In some cases, the function returns an arc path of 360 or 0 degrees instead, due to floating-point precision issues.

A: The expected behavior of the Path.arc function is to create an arc path with the specified start and end angles. However, the function's behavior is not clear when the input values are not in the expected range.

A: The possible causes of the bug are:

  1. Floating-point precision issues: The Path.arc function uses floating-point arithmetic, which can lead to precision issues.
  2. Lack of clarity in the docstring: The docstring does not provide any clarification on what should happen when the input values are not in the expected range.

A: The bug can be fixed by:

  1. Clarifying the docstring to specify what should happen when the input values are not in the expected range.
  2. Raising a ValueError when the input values are not in the expected range.

A: The benefits of fixing the bug are:

  1. Improved accuracy: Fixing the bug will ensure that the Path.arc function behaves correctly and provides accurate results.
  2. Reduced errors: Fixing the bug will reduce the likelihood of errors occurring due to the function's incorrect behavior.

A: The bug can be reproduced by running the following code:

from matplotlib import patches, path, pyplot

fig, ax = pyplot.subplots(ncols=3)
ax[0].add_patch(patches.PathPatch(path.Path.arc(theta1=-90 - 1e-14, theta2=270)))
ax[0].set_title("arc(-90-1e-14, 270), should be a circle")
ax[1].add_patch(patches.PathPatch(path.Path.arc(theta1=-90, theta2=270)))
ax[1].set_title("arc(-90, 270), is a circle")
ax[2].add_patch(patches.PathPatch(path.Path.arc(theta1=-90, theta2=-90 - 1e-14)))
ax[2].set_title("arc(-90, -90-1e-14), should not be a circle")
for a in ax:
    a.set_xlim(-1, 1)
    a.set_ylim(-1, 1)
    a.set_aspect("equal")
pyplot.show()

This code creates three plots using the Path.arc function with different input values. The first plot should be a circle, but due to the bug, it becomes a line instead. The second plot is a circle as expected. The third plot should not be a circle, but it becomes one due to the bug.

A: The system requirements for reproducing the bug are:

  1. Matplotlib version 3.10.0 or later
  2. Python version 3.6 or later
  3. A compatible operating system (e.g., Windows, macOS, Linux)

A: The bug can be reported by:

  1. Creating a new issue on the Matplotlib GitHub repository
  2. Providing a detailed description of the bug, including the code used to reproduce it
  3. Including any relevant system information or error messages

By following these steps, you can help ensure that the bug is properly reported and addressed.