What makes it unique is that it runs on top of other apps. You only have to open the Pool Guideline Tool and once activated, you can start playing other pool apps like Billiards Nation APK or Billiards Master, although support for apps often changes.
Essentially, the Pool Guideline Tool acts like an aimbot, but for billiards and pool apps. Since most of these games feature the cue stick behind the white ball, it gives the app a sense of direction of where the shot is coming from. With that said, the app simply tells you how the balls will go and interact with the others so you can always take the best options available.
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While these jolly chaps were smacking balls together, at the the same time in history Isaac Newton was busy inventingcalculus, his self-titled Newtonian physics, and a universal theory of gravitation that whollyexplained the previously disparate phenomena of tides, why things fall, and the motions of celestialbodies. His contributions to science would spark a revolution in the physical sciences moreillustrious than anyone before him, and arguably ever since him.
As a result of its long history, the theoretical treatment of billiards has been sufficiently solvedfor most scenarios: (1) ball-cloth interactions, aka how the balls slide, spin, roll, and lie onthe table; (2) ball-ball interactions aka how balls collide with one another; (3)ball-cushion interactions, aka how balls bounce off rails; (4) ball-air interactions, aka howthe ball behaves when it becomes airborne due to jump shots, etc.; and (5) ball-slateinteractions, aka how the ball bounces on the table.
This is the null model. The friction coefficients at the point of contact (PoC) between ball andcloth are 0. This means no energy dissipates from the ball, and it rolls indefinitely. It also spinsindefinitely.
Figure 1. Force contributions acting on a ball that has o spin. Here, $ \vecv $ is thevelocity of the ball, $ m $ its mass, and $ R $ its radius. Additionally, we got good old $ \vecg $,the gravitational constant, and the normal force $ \vecN $.
In the $ y $-axis, there is agravitational force (mass $ \times $ gravitational constant $ = m\vecg $) pulling the ballinto the table. Since the table is supporting the ball, it exerts an equal and opposite force ontothe ball. This is called the normal force, $ \vecN $. Without it, the ball would fall throughthe table.
By the ball can be in an arbitrary state, what I mean is that it can have an arbitrary velocity$(\vecv)$, angular velocity $(\vec\omega)$, and displacement relative to some origin$(\vecr)$. These 3 vectors fully characterize the state of the ball.
As for the second assumption, a single point of contact is a fairly accurate assumption, buttechnically the weight of the ball bunches up the cloth as it moves. The amount of bunching up depends onhow loosely the cloth is stretched over the slate. Additionally, the cloth itself can be compressed,and cloth fibers and other non-idealities can contact the ball at multiple points. And so inactuality there does not exist a point of contact, but rather, an area of contact.
This isbecause a ball spinning in place has zero speed at the infinitesimally small PoC. Inother words, the relative velocity between the ball and cloth at the PoC is 0, and this meansthere can exist no frictional force.
Such a ball will move in a straight line until it comes to a rest. As it travels, it will be sloweddown by a frictional force proportional to its velocity, which implies that its velocity will decaylinearly with time:
Now for angular velocity. To discuss this, I should formalize the concept of rolling, which isformally defined as the state in which the relative velocity, $\vecu(t)$, between the ball andcloth at the PoC is $\vec0$.
This refers to the condition in which every time the ball does a complete rotation about the$y-$axis (according to the axes defined in Figure 4), the ball must travel exactly one circumference(aka $2 \pi R$ in the $x-$axis). Unless this exact condition is met, a moving ball is sliding, notrolling.
For how particular this condition seems, it is interesting that in the game of pool,balls are most often rolling. The reason is that any sliding ball experiences friction that reducesthe magnitude of $\vecu(t)$ until it is rolling. In that sense, rolling is somewhat of anequilibrium state.
Using Eq. $\eqrefroll_condition$, it follows that $\omega_y(t) = \vecv(t)/R$. Since$\vecv(t)$ is known via Eq. $\eqrefrolling_velocity$, this equation solves the timeevolution of $\omega_y(t)$. Note that $\omega_y(t)$ is strictly positive, which intuitivelyrefers to the fact that in order to be rolling, the ball must have top spin, not back spin.
Points 1 & 2 solve the time evolution for $\omega_x(t)$ and $\omega_y(t)$, respectively. Meanwhile, point3 has consequences that you may find highly surprising. For example, we know that in therolling state, the ball path is a straight line. Yet the model predicts this is true regardless of$\omega_z$. Is that really sensical? It may not match your initial intuition, but it does match thereality:
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