pooltool.evolution

Shot evolution algorithm routines and utilities

Functions

continuize(system: System, dt: float = 0.01, inplace: bool = False) → System

Create a BallHistory for each ball with many timepoints

When pooltool simulates a shot, it evolves the system using an event-based shot evolution algorithm. This means pooltool only timestamps the ball states during events--not between events. This makes simulation fast, but provides insufficient trajectory information if you wanted to visualize or plot ball trajectories over time.

Continuizing the shot means tracking the ball states with higher temporal resolution, so that the ball trajectories between events can be recapitulated. It’s a misnomer because the states are still tracked over discrete time steps dt seconds apart. i.e. not continuous.

This function calculates the “continous” timestamps for each ball and stores them in pooltool.objects.Ball.history_cts (the event-based timestamps are preserved, and are stored in pooltool.objects.Ball.history)

The continous timepoints are shared between all balls and are uniformly spaced (except for the last timepoint, which occurs at the final event, which necessarily occurs less than dt after the second last timepoint).

Parameters:

• dt : float

  This is the spacing between each timepoint. 0.01 looks visually accurate at 60fps at a playback speed of 1. Function runtime is inversely proportional to dt.

• inplace : bool

  By default, a copy of the passed system is continuized and returned. This leaves the passed system unmodified. If inplace is set to True, the passed system is modified in place, meaning no copy is made and the returned system is the passed system. For a more practical distinction, see Examples below.

Return type:

System

Examples

Standard usage:

>>> import pooltool as pt
>>> system = pt.simulate(pt.System.example())

The system has been simulated, so their history attributes are populated:

>>> len(system.balls["cue"].history)
14
>>> system.balls["cue"].history[0]
BallState(rvw=array([[0.4953  , 0.9906  , 0.028575],
       [0.      , 0.      , 0.      ],
       [0.      , 0.      , 0.      ]]), s=0, t=0.0)
>>> system.balls["cue"].history[-1]
BallState(rvw=array([[0.7464286761774921, 1.247940272192023 , 0.028575          ],
       [0.                , 0.                , 0.                ],
       [0.                , 0.                , 0.                ]]), s=0, t=5.193035203405666)

However, the system has not been continuized, so their history_cts attributes are empty:

>>> len(system.balls["cue"].history_cts)
0

After continuizing, the continuous ball histories are populated with many timestamps:

>>> continuized_system = pt.continuize(system, inplace=False)
>>> continuized_system.continuized
True
>>> len(continuized_system.balls["cue"].history_cts)
523

You can also modify the system in place:

>>> import pooltool as pt
>>> system = pt.simulate(pt.System.example())
>>> continuized_system = pt.continuize(system, inplace=True)
>>> assert system.continuized
>>> assert continuized_system.continuized
>>> assert system is continuized_system

Notice that the returned system is the continuized system. Therefore, there is no point catching the return object when inplace is True:

>>> import pooltool as pt
>>> system = pt.simulate(pt.System.example())
>>> assert not system.continuized
>>> pt.continuize(system, inplace=True)
>>> assert system.continuized

See also

• pooltool.objects.Ball.history_cts

• pooltool.evolution.simulate()

interpolate_ball_states(ball: Ball, timestamps: NDArray[float64] | Sequence[float], *, extrapolate: bool = False) → list[BallState]

Calculate exact ball states at arbitrary timestamps.

This function calculates the precise ball states at arbitrary timestamps by evolving the ball from the nearest preceding event state using the same physics model as the simulation. It provides physically accurate positions, velocities, and angular velocities according to the ball’s motion equations.

Parameters:

• ball : Ball

  The Ball object containing the history and physical parameters.

• timestamps : NDArray[float64] | Sequence[float]

  A sequence or numpy array of timestamps at which to calculate ball states. Should be in ascending order and within the history’s time range.

• extrapolate : bool

  If True, timestamps outside the history’s time range will use the nearest boundary state (initial or final). If False (default), a ValueError is raised for timestamps outside the range.

Returns:

A list of BallState objects corresponding to the given timestamps.

Raises:

ValueError -- If history is empty or if timestamps are out of range and extrapolate is False.

Return type:

list[BallState]

Examples

>>> import pooltool as pt
>>> import numpy as np
>>> system = pt.simulate(pt.System.example())
>>> ball = system.balls["cue"]
>>> # Get ball states at specific timestamps
>>> timestamps = np.array([0.5, 1.0, 1.5])
>>> states = pt.interpolate_ball_states(ball, timestamps)
>>> # Use the states
>>> states[0].rvw[0]  # Position at t=0.5
array([x, y, z])

simulate(shot: System, engine: PhysicsEngine | None = None, inplace: bool = False, continuous: bool = False, dt: float | None = None, t_final: float | None = None, include: set[EventType] = INCLUDED_EVENTS, max_events: int = 0) → System

Run a simulation on a system and return it

Parameters:

• shot : System

  The system you would like simulated. The system should already have energy, otherwise there will be nothing to simulate.

• engine : PhysicsEngine | None

  The engine holds all of the physics. You can instantiate your very own pooltool.physics.PhysicsEngine object, or you can modify ~/.config/pooltool/physics/resolver.json to change the default engine.

• inplace : bool

  By default, a copy of the passed system is simulated and returned. This leaves the passed system unmodified. If inplace is set to True, the passed system is modified in place, meaning no copy is made and the returned system is the passed system. For a more practical distinction, see Examples below.

• continuous : bool

  If True, the system will not only be simulated, but it will also be “continuized”. This means each ball will be populated with a ball history with small fixed timesteps that make it ready for visualization.

• dt : float | None

  The small fixed timestep used when continuous is True.

• t_final : float | None

  If set, the simulation will end prematurely after the calculation of an event with event.time > t_final.

• include : set[EventType]

  Which EventType are you interested in resolving? By default, all detected events are resolved.

• max_events : int

  If this is greater than 0, and the shot has more than this many events, the simulation is stopped and the balls are set to stationary.

Returns:

The simulated system.

Return type:

System

Examples

Standard usage:

>>> # Simulate a system
>>> import pooltool as pt
>>> system = pt.System.example()
>>> simulated_system = pt.simulate(system)
>>> assert not system.simulated
>>> assert simulated_system.simulated

The returned system is simulated, but the passed system remains unchanged.

You can also modify the system in place:

>>> # Simulate a system in place
>>> import pooltool as pt
>>> system = pt.System.example()
>>> simulated_system = pt.simulate(system, inplace=True)
>>> assert system.simulated
>>> assert simulated_system.simulated
>>> assert system is simulated_system

Notice that the returned system _is_ the simulated system. Therefore, there is no point catching the return object when inplace is True:

>>> # Simulate a system in place
>>> import pooltool as pt
>>> system = pt.System.example()
>>> assert not system.simulated
>>> pt.simulate(system, inplace=True)
>>> assert system.simulated

You can continuize the ball trajectories with continuous

>>> # Simulate a system in place
>>> import pooltool as pt
>>> system = pt.simulate(pt.System.example(), continuous=True)
>>> for ball in system.balls.values(): assert len(ball.history_cts) > 0

See also

• pooltool.evolution.continuize()