The Billiard Simulator is an interactive web-based pool game that simulates billiard physics, shot prediction, and cue control. Here’s a summary of how it works and its main features:

Simulator Overview Physics Simulation: The game simulates realistic billiard ball movement, including friction, spin (side and vertical), collisions (ball-ball and ball-wall), and pocket detection. Each ball is an object with position, velocity, spin, and color.

Cue Ball Control: You can aim the cue ball with your mouse. Click or drag to strike or reposition the cue ball (when in "ball in hand" mode).

Predictive Trajectories: The simulator can show predicted ball paths for your shot, including advanced multi-ball and decision-tree predictions. You can toggle and cycle through prediction modes using keyboard shortcuts.

Customizable Controls: The UI allows you to adjust shot power, spin, cue stick color and length, and toggle a 3D ball rendering effect. All controls can be accessed via sliders, color pickers, and keyboard shortcuts.

Settings & Key Bindings: There’s a settings modal where you can view and customize all keyboard shortcuts for actions like power, spin, prediction modes, and more.

Game Modes: By default, it sets up a standard 8-ball rack (16 balls), but you can cycle through different ball counts.

Controls Mouse:

Aim: Move the mouse to aim the cue. Strike: Click the canvas to shoot when the cue ball is stationary. Drag: Drag the cue ball to reposition it when in "ball in hand" mode. UI Controls:

Shot Power: Adjust with the slider. Spin: Adjust side and vertical spin with sliders. 3D View: Toggle for realistic ball shading. Cue Stick Color/Length: Change with color picker and slider. Reset, Ball In Hand, Release Cue Ball: Use buttons for quick actions. Keyboard Shortcuts (default):

Arrow Up/Down: Increase/decrease shot power. Arrow Left/Right: Adjust side spin. W/S: Adjust vertical spin. Z: Reset spin angles. X: Reset shot power. E: Reset game. H: Ball in hand mode. G: Release cue ball. R/F: Reset or cycle ball count. D/A/Q: Adjust or cycle cue stick length. C: Cycle cue stick color. B: Toggle 3D view. O/K/I/L/J/M/P: Change prediction modes and toggle sticky prediction. You can view and customize all key bindings in the Settings modal.