PERF: 3d draw speedups - #30994

PR summary

A collection of speedups for 3d plotting, from playing around with the py-spy profiler today.

Waiting on #30980 as a dependency. Diff to that is here:
https://github.com/matplotlib/matplotlib/compare/4ab0014840c3e86b3ca820dba7531857cb168ed6..scottshambaugh:3d_draw_speed

I measure a 40% speedup in our non-agg-rendering code from these changes, which results in a 20% speedup in total runtime for my test script.

Summary of changes:

• Prefer filling arrays with nans directly, instead of masked arrays that later get filled
• Move _get_coord_info from axis3d to axes3d, since there's nothing axis-specific in it
• Cache axes3d calculations that are used multiple times per draw by each axis: scaled_limits, bounds, transformed_cube, and coord_info.
• Call axis._update_ticks() once per axis at start of draw, instead of multiple times in methods
• Batch the axis tick 3d projections rather than calling once per tick

Before:

After (less time spent in things that aren't draw or draw_text:

Test script:

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

print("Starting...")

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x = y = np.linspace(-1, 1, 1000)
X, Y = np.meshgrid(x, y)
Z = X ** 2 + Y ** 2

print("Timing...")

start_time = time.perf_counter()
ax.plot_wireframe(X, Y, Z, axlim_clip=False)
ax.set_xlim(0, 1)
ax.set_xscale('symlog')
ax.set_yscale('symlog')
for i in range(100):
    ax.view_init(elev=i, azim=i)
    fig.canvas.draw()
end_time = time.perf_counter()

plt.close()

print(f"Time taken: {end_time - start_time:.4f} seconds")

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