Performance improvement for most scenes

[mikemag]

tl;dr: this is a significant performance improvement for many scenes. 1.7x - 2.6x improvement in animation it/s.

This is a small change to some of the hotest paths in rendering objects. The biggest win comes from not using np.allclose() to check if two points are close enough. In general, NumPy is awesome at operating on large arrays, but overkill for very tiny questions like this. Created a small function to determine if two points are close using the same algorithm, and limited it to 2D points since that's all we need in set_cairo_context_path().

A couple of other minor tweaks to reduce or eliminate other uses of NumPy in this path.

In general, it is better to avoid wrapping lists in np.array when a real NumPy array isn't actually needed.

Added a new file for performance test scenes, with a single scene from the end of a video I've been working on.

Data:

MacBook Pro (16-inch, 2019)
macOS Catalina 10.15.4
2.4 GHz 8-Core Intel Core i9
64 GB 2667 MHz DDR4
Python 3.7.3 (default, Mar 6 2020, 22:34:30)

Profiler: yappi under Pycharm.

Using the scene Perf1 from the included perf_scenes.py, averaged over 5 runs and rendered with:
manim.py perf_scenes.py Perf1 -pl --leave_progress_bars

Before:
Animation 0: FadeInTextMobject, etc.: 8.93it/s
Animation 1: ShowCreationParametricFunction, etc.: 84.66it/s

Profiler shows 48.5% of the run spent under Camera.set_cairo_context_path()

After
Animation 0: FadeInTextMobject, etc.: 23.45it/s -- 2.63x improvement
Animation 1: ShowCreationParametricFunction, etc.: 149.62it/s -- 1.77x improvement

Profiler shows 19.9% of the run spent under Camera.set_cairo_context_path()

Less improvement with production-quality renders, and percent improvement varies with scene of course. This appears to be a good win for every scene I'm working on though. I hope it will be for others, too.

NB: there are more perf improvements to be had, of course, but this is the best one I currently have.

Thanks for contributing to manim!

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[eulertour]

Alright, looks good!