Speedup

[ekiefl]

This PR is concerned with speed.

Since the large refactor that transformed System, Cue, Table, and Ball and their delegate objects into dataclasses, pooltool has been kind of slow. After profiling the code with pprofile, I was able to make some changes all in the name of speed.

I tested tracked the speed progress on two test cases: (1) a simple shot involving 3 balls, a pocket, and a couple of cushions and (2) a 9-ball break.

Here is how the following commits speed up the simple shot:

And here is how they sped up the 9-ball break:

Another important speed is how fast the ball animations are built. This is substantial, especially when the shot is played in half speed / quarter speed (which doubles / quadruples the time taken). I wrote sandbox/continuize_and_render_timer.py so that this can be compared to the time to simulate and continuize shots.

Using that script, the current state of affairs is:

✓ Trajectories simulated in: 0:00:00.143015
✓ Trajectories continuized in: 0:00:00.040777
✓ Animation sequence rendered in: 0:00:00.027906

And the break shot:

✓ Trajectories simulated in: 0:00:00.363477
✓ Trajectories continuized in: 0:00:00.151531
✓ Animation sequence rendered in: 0:00:00.138668

If I were to increase the speed further, I would avoid storing Ball.history_cts as a BallHistory object. Instead, I would create a VectorizedBallHistory object that simply stores the arrays rvws, ss, and ts. I think this would make continuize and ball animations significantly faster by avoiding interconversion from arrays to BallHistory sequences.