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Collision Detection
Collision detection is the computational problem of detecting the intersection (Euclidean geometry), intersection of two or more objects. Collision detection is a classic issue of computational geometry and has applications in various computing fields, primarily in computer graphics, computer games, computer simulations, robotics and computational physics. Collision detection algorithms can be divided into operating on 2D and 3D objects. Overview In physical simulation, experiments such as playing billiards, are 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 their cue stick), we want to calculate the trajectories, precise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Problem
In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring :"Given a positive integer ''n'', find a nontrivial prime factor of ''n''." is a computational problem. A computational problem can be viewed as a set of ''instances'' or ''cases'' together with a, possibly empty, set of ''solutions'' for every instance/case. For example, in the factoring problem, the instances are the integers ''n'', and solutions are prime numbers ''p'' that are the nontrivial prime factors of ''n''. Computational problems are one of the main objects of study in theoretical computer science. The field of computational complexity theory attempts to determine the amount of resources ( computational complexity) solving a given problem will require and explain why some problems are intractable or undecidable. Computational problems belong to complexity classes that define broadly the resources (e.g. time, space/memory, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points. Linear interpolation between two known points If the two known points are given by the coordinates (x_0,y_0) and (x_1,y_1), the linear interpolant is the straight line between these points. For a value in the interval (x_0, x_1), the value along the straight line is given from the equation of slopes \frac = \frac, which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation with . Solving this equation for , which is the unknown value at , gives \begin y &= y_0 + (x-x_0)\frac \\ &= \frac + \frac\\ &= \frac \\ &= \frac, \end which is the formula for linear interpolation in the interval (x_0,x_1). Outside this interval, the formula is identical to linear extrapolation. This formula can also be understood as a weighted average. The weights are inv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ming C
The Ming dynasty (), officially the Great Ming, was an imperial dynasty of China, ruling from 1368 to 1644 following the collapse of the Mongol-led Yuan dynasty. The Ming dynasty was the last orthodox dynasty of China ruled by the Han people, the majority ethnic group in China. Although the primary capital of Beijing fell in 1644 to a rebellion led by Li Zicheng (who established the short-lived Shun dynasty), numerous rump regimes ruled by remnants of the Ming imperial family—collectively called the Southern Ming—survived until 1662. The Ming dynasty's founder, the Hongwu Emperor (r. 1368–1398), attempted to create a society of self-sufficient rural communities ordered in a rigid, immobile system that would guarantee and support a permanent class of soldiers for his dynasty: the empire's standing army exceeded one million troops and the navy's dockyards in Nanjing were the largest in the world. He also took great care breaking the power of the court eunuchs and unr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in the triangular arrangement with dots on each side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers, starting with the 0th triangular number, is (This sequence is included in the On-Line Encyclopedia of Integer Sequences .) Formula The triangular numbers are given by the following explicit formulas: T_n= \sum_^n k = 1+2+3+ \dotsb +n = \frac = , where \textstyle is a binomial coefficient. It represents the number of distinct pairs that can be selected from objects, and it is read aloud as " plus one choose two". The first equation can be illustrated using a visual proof. For every triangular number T_n, imagine a "half-square" arrangement of objects corresponding to the triangular numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stiction
Stiction is the static friction that needs to be overcome to enable relative motion of stationary objects in contact. The term is a portmanteau of the words ''static'' and ''friction'', and is perhaps also influenced by the verb '' to stick''. Any solid objects pressing against each other (but not sliding) will require some threshold of force parallel to the surface of contact in order to overcome static adhesion. Stiction is a ''threshold'', not a continuous force. However, stiction might also be an illusion made by the rotation of kinetic friction. In situations where two surfaces with areas below the micrometer scale come into close proximity (as in an accelerometer), they may adhere together. At this scale, electrostatic and/or Van der Waals and hydrogen bonding forces become significant. The phenomenon of two such surfaces being adhered together in this manner is also called stiction. Stiction may be related to hydrogen bonding or residual contamination. Automobiles Sticti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root-finding Algorithm
In mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function , from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number such that . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros, expressed either as floating-point numbers or as small isolating intervals, or disks for complex roots (an interval or disk output being equivalent to an approximate output together with an error bound). Solving an equation is the same as finding the roots of the function . Thus root-finding algorithms allow solving any equation defined by continuous functions. However, most root-finding algorithms do not guarantee that they will find all the roots; in particular, if such an algorithm does not find any root, that does not mean that no root exists. Most nume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Priori And A Posteriori
("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current experience (e.g., as part of a new study). Examples include mathematics,Some associationist philosophers have contended that mathematics comes from experience and is not a form of any a priori knowledge () tautologies, and deduction from pure reason.Galen Strawson has stated that an argument is one in which "you can see that it is true just lying on your couch. You don't have to get up off your couch and go outside and examine the way things are in the physical world. You don't have to do any science." () knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in ''Organon'', a collection of works by Aristotle. Prior analytic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empirical Evidence
Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and plays a role in various other fields, like epistemology and law. There is no general agreement on how the terms ''evidence'' and ''empirical'' are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which '' confirms'' or ''disconfirms'' scientific hypotheses and arbitrates between competing theories. For this role, it is important that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scene Graph
Scene (from Greek σκηνή ''skēnḗ'') may refer to: Arts, entertainment, and media Music *Scene (subculture), a youth subculture from the early 2000s characterized by a distinct music and style. Groups and performers * The Scene who recorded the song "Scenes (from Another World)" * Scene, the stage name used by Japanese Punk guitarist Minoru Kojima * Selena Gomez & the Scene, an American band * The Scene (Canadian band), a late 1960s psychedelic Canadian band * The Scene (Dutch band), a Dutch band formed by Thé Lau Albums * ''Scene'', a 2005 noise album by Merzbow * ''Scenes'' (album), a 1992 music album by Marty Friedman * ''The Scene'' (Eskimo Callboy album), an Eskimo Callboy album * ''The Scene'', the debut album of The Scene Other uses in music * S.C.E.N.E. Music Festival, an annual festival held in downtown St. Catharines, Ontario, Canada * "The Scene" (song), a song by Canadian band Big Sugar from their 1998 album ''Heated'' Periodicals * ''Scene'' (see '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Dynamics Engine
The Open Dynamics Engine (ODE) is a physics engine written in C/C++. Its two main components are a rigid body dynamics simulation engine and a collision detection engine. It is free software licensed both under the BSD license and the LGPL. ODE was started in 2001 and has already been used in many applications and games, such as ''Assetto Corsa'', ''BloodRayne 2'', ''Call of Juarez'', ''S.T.A.L.K.E.R.'', ''Titan Quest'', ''World of Goo'', '' X-Moto'' and ''OpenSimulator''. Overview The Open Dynamics Engine is used for simulating the dynamic interactions between bodies in space. It is not tied to any particular graphics package although it includes a basic one called ''drawstuff''. It supports several geometries: box, sphere, capsule (cylinder capped with hemispheres), triangle mesh, cylinder and heightmap. Simulation Higher level environments that allow non-programmers access to ODE include Player Project, Webots, Opensimulator, anyKode Marilou anV-REP ODE is a popular choi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Air Traffic Control
Air traffic control (ATC) is a service provided by ground-based air traffic controllers who direct aircraft on the ground and through a given section of controlled airspace, and can provide advisory services to aircraft in non-controlled airspace. The primary purpose of ATC worldwide is to prevent collisions, organize and expedite the flow of air traffic, and provide information and other support for pilots. Air traffic controllers monitor the location of aircraft in their assigned airspace by radar and communicate with the pilots by radio. To prevent collisions, ATC enforces traffic separation rules, which ensure each aircraft maintains a minimum amount of empty space around it at all times. In many countries, ATC provides services to all private, military, and commercial aircraft operating within its airspace. Depending on the type of flight and the class of airspace, ATC may issue ''instructions'' that pilots are required to obey, or ''advisories'' (known as ''flight infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
