Create a standalone HTML file containing CSS and JavaScript to generate a billiards game based on Canvas and a simple physics engine.
Billiards Simulation Game: Create a standalone HTML file containing CSS and JavaScript to generate a billiards game based on Canvas and a simple physics engine. The game must display the following core modules through mouse interaction and vector mathematics: Canvas Physics Rendering System: Use HTML5 Canvas to draw the table, pockets, and multiple balls, implementing smooth ball movement animation via requestAnimationFrame. Mouse Interaction & Shot Control: Listen for mousedown, mousemove, and mouseup events to enable a complete interaction flow: clicking the cue ball, dragging to determine shot direction and power, and releasing to strike. Provide an aiming guideline/ghost line. Simple Physics Engine: The core includes collision detection (ball-to-ball, ball-to-boundary), reflection angle calculations based on vector math, and friction simulation to produce basic realistic motion. Game State & Scoring: Manage the game state. When the target ball is potted, increment the score, and potentially implement logic for resetting the cue ball. The interface should use a classic green table style, with all code consolidated into a single file. JavaScript must focus on vector mathematics, collision logic, and event handling to achieve an interactive physics simulation game.
