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Overview[ edit ] Billiards balls hitting each other are a classic example applicable within the science of collision detection. In physical simulation, experiments, such as playing billiardsare conducted. The physics of bouncing billiard balls are well understood, under the umbrella of rigid body motion and elastic collisions.
An initial description of the situation would be given, with a very precise physical description of the billiard table and balls, as well as initial positions of all the balls. Given a force applied to the cue ball probably resulting from a player hitting the ball with his or her cue stickwe want to calculate the trajectories, precise motion, and eventual resting places of all the balls with a computer program.
A program to simulate this game would consist of several portions, one of which would be responsible for calculating the precise impacts between the billiard balls. This particular example also turns out to be ill conditioned: Video games have similar requirements, with some crucial differences.
While physical simulation needs to simulate real-world physics as precisely as possible, video games need to simulate real-world physics in an acceptable way, in real time and robustly.
Compromises are allowed, so long as the resulting simulation is satisfying to the game players. Collision detection in physical simulation[ edit ] Physical simulators differ in the way they react on a collision.
Some use the softness of the material to calculate a force, which will resolve the collision in the following time steps like it is in reality. Due to the low softness of some materials this is very CPU intensive.
Some simulators estimate the time of collision by linear interpolationroll back the simulation, and calculate the collision by the more abstract methods of conservation laws. Some iterate the linear interpolation Newton's method to calculate the time of collision with a much higher precision than the rest of the simulation.
Collision detection utilizes time coherence to allow even finer time steps without much increasing CPU demand, such as in air traffic control. After an inelastic collision, special states of sliding and resting can occur and, for example, the Open Dynamics Engine uses constraints to simulate them.
Constraints avoid inertia and thus instability. Implementation of rest by means of a scene graph avoids drift. In other words, physical simulators usually function one of two ways, where the collision is detected a posteriori after the collision occurs or a priori before the collision occurs.
In addition to the a posteriori and a priori distinction, almost all modern collision detection algorithms are broken into a hierarchy of algorithms. Often the terms "discrete" and "continuous" are used rather than a posteriori and a priori.
A posteriori discrete versus a priori continuous [ edit ] This article's tone or style may not reflect the encyclopedic tone used on Wikipedia.
See Wikipedia's guide to writing better articles for suggestions. July Learn how and when to remove this template message In the a posteriori case, we advance the physical simulation by a small time step, then check if any objects are intersecting, or are somehow so close to each other that we deem them to be intersecting.
At each simulation step, a list of all intersecting bodies is created, and the positions and trajectories of these objects are somehow "fixed" to account for the collision.
We say that this method is a posteriori because we typically miss the actual instant of collision, and only catch the collision after it has actually happened. In the a priori methods, we write a collision detection algorithm which will be able to predict very precisely the trajectories of the physical bodies.
The instants of collision are calculated with high precision, and the physical bodies never actually interpenetrate. We call this a priori because we calculate the instants of collision before we update the configuration of the physical bodies.
The main benefits of the a posteriori methods are as follows. In this case, the collision detection algorithm need not be aware of the myriad of physical variables; a simple list of physical bodies is fed to the algorithm, and the program returns a list of intersecting bodies.
The collision detection algorithm doesn't need to understand friction, elastic collisions, or worse, nonelastic collisions and deformable bodies. In addition, the a posteriori algorithms are in effect one dimension simpler than the a priori algorithms.
Indeed, an a priori algorithm must deal with the time variable, which is absent from the a posteriori problem. On the other hand, a posteriori algorithms cause problems in the "fixing" step, where intersections which aren't physically correct need to be corrected. Moreover, if the discrete step is too large, the collision could go undetected, resulting in an object which passes through another if it is sufficiently fast or small.
The benefits of the a priori algorithms are increased fidelity and stability.This entry describes applications of known indicators and dyes as new visualizing reagents and various visualizing systems as well as photocatalytic reactions and bioautography method for the detection of bioactive compounds including drugs and compounds isolated from herbal extracts.
Broadening index, detection index, . Collision detection is the computational problem of detecting the intersection of two or more objects. While collision detection is most often associated with its use in video games and other physical simulations, it also has applications in r-bridal.com addition to determining whether two objects have collided, collision detection systems may also calculate time of impact (TOI), and report a.
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