PR summary

Split off from #31005

This speeds up Path.get_extents which calls these bezier operations by caching more of the polynomial coefficient calculations. These repeated calcs were taking up about 25% of the get_extents call time, and are largely eliminated now.

Circled areas in the profiler screenshots below show this code path.

Before:

After:

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)

PR checklist

• [n/a] "closes #0000" is in the body of the PR description to link the related issue
• new and changed code is tested
• [n/a] Plotting related features are demonstrated in an example
• [n/a] New Features and API Changes are noted with a directive and release note
• [n/a] Documentation complies with general and docstring guidelines