The ball-cloth interaction is essential for realism, and quickly gets complicated. Trajectories due to the application of forces orthogonal to the ball’s motion. Yet, depending on the ball’s spin state, this same friction also leads to curved It is somewhat obvious that the cloth provides a frictional surface that slows the ball’s In this section I review the ball-cloth interaction, aka how pool balls interact with their playing In what follows, I am going to lay out all of the physics I’m going to include in the The physics used in this postĬomes partly from this book, and partly from random sources on the internet. Treatment of billiards, “ The Physics of Pocket Billiards” by Wayland C. Reference source was necessary, so I bought the non-exhaustive but heavily referenced modern day To build a pool simulator, I’m gonna have to get my hands dirty with these equations. Sufficient is that all qualitative effects a pro-player may be expecting to observe manifest Scenarios have analytical solutions that are accurate to “sufficient” degree. Interactions, but each of these individual The jury is still out on the finer details of these I’m pretty sure the above list covers every phenomenon Interactions, aka how the ball bounces on the table. The ball behaves when it becomes airborne due to jump shots, etc. The table (2) ball-ball interactions aka how balls collide with one another (3)īall-cushion interactions, aka how balls bounce off rails (4) ball-air interactions, aka how Work would enable the theoretical treatment of the game of billiards, and as such, the game has beenĪs a result of its long history, the theoretical treatment of billiards has been sufficiently solvedįor most scenarios: (1) ball-cloth interactions, aka how the balls slide, spin, roll, and lie on Illustrious than anyone before him, and arguably ever since him. His contributions to science would spark a revolution in the physical sciences more While these jolly chaps were smacking balls together, at the the same time in history Isaac Newton was busy inventingĬalculus, his self-titled Newtonian physics, and a universal theory of gravitation that whollyĮxplained the previously disparate phenomena of tides, why things fall, and the motions of celestialīodies. Two blokes shootin’ the shit over a game of billiards. This is one of the first historical depictions of The thing about pool is that it’s pretty old. The equations in this post form the underlying physics of pooltool. With that said, let’s get started.Ī lot has happened since I initially wrote this post, and pooltool is now a fully fledged 3D game/tool. If this sounds uninteresting to you, skip ahead Both of these willĬontain a lot of equations, and little if any code. Post, and algorithms for evolving a pool shot covered in the second post. The physics of pool is what is covered in this This post is the first of many in my journey to make a realistic pool/billiards simulator called pooltool.īefore jumping into code, I have to trudge through the theory of both (a) the physics of pool,Īnd (b) the algorithms for evolving a pool shot. (1) Elastic, instantaneous, frictionless.
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