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PERF: Bezier root finding speedup#31005

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scottshambaugh wants to merge 3 commits intomatplotlib:mainfrom
scottshambaugh:bezier_speedups
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PERF: Bezier root finding speedup#31005
scottshambaugh wants to merge 3 commits intomatplotlib:mainfrom
scottshambaugh:bezier_speedups

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@scottshambaugh scottshambaugh commented Jan 20, 2026 •
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PR summary

This speeds up Path.get_extents which calls these bezier operations.

Instead of np.roots which does expensive eigenvalue decomposition, we can take advantage of the fact that we are only looking for roots on the limited [0, 1] interval and just do bisection for degree >= 3. Or we can calculate exactly for degree == 2. These both end up being much faster.

This code section is circled below in the profiler runs.

Before:
image

After:
image

Profiling test script:

import numpy as np
import matplotlib.pyplot as plt

fig, ax = plt.subplots()

n = 1000
rng = np.random.default_rng(42)
x = rng.random(n)
y = rng.random(n)
for i in range(n):
    ax.scatter(x[i], y[i])

fig.canvas.draw()
plt.close(fig)

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@scottshambaugh scottshambaugh marked this pull request as ready for review January 20, 2026 23:58
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timhoffm commented Feb 2, 2026

Can you please split the two changes? I would like to review and discuss them separately.

For the coefficient matrices, I'd like to have a built-in guarantee that the matrix and the formula yield the same result. This can be achieved in one of two ways:

  • use caching instead of hard-coding; i.e. calculate them the first time they occur.
  • or factor out the calculation into a separate private function and write a test that the hard-coded matices and calculated matrices for n<=4 match.

@scottshambaugh scottshambaugh mentioned this pull request Feb 2, 2026
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scottshambaugh commented Feb 2, 2026 •
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Sure thing @timhoffm, I split the coefficient calcs into #31059 and refactored that to cache the poly coefficient matrices rather than hardcoding them. The root-finding changes remain in this PR, and the description is updated with some screenshots of the profiling changes.

@scottshambaugh scottshambaugh changed the title PERF: Bezier speedups PERF: Bezier root finding speedup Feb 2, 2026
timhoffm
timhoffm reviewed Feb 3, 2026
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timhoffm approved these changes Feb 3, 2026
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timhoffm commented Feb 3, 2026

Please fix the stubtest

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