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Intersection Of A Polyhedron With A Line
In computational geometry, the problem of computing the intersection of a polyhedron with a line has important applications in computer graphics, optimization, and even in some Monte Carlo methods. It can be viewed as a three-dimensional version of the line clipping problem.. If the polyhedron is given as the intersection of a finite number of halfspaces, then one may partition the halfspaces into three subsets: the ones that include only one infinite end of the line, the ones that include the other end, and the ones that include both ends. The halfspaces that include both ends must be parallel to the given line, and do not contribute to the solution. Each of the other two subsets (if it is non-empty) contributes a single endpoint to the intersection, which may be found by intersecting the line with each of the halfplane boundary planes and choosing the intersection point that is closest to the end of the line contained by the halfspaces in the subset. This method, a variant of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by graphics hardware, computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as Computer-generated imagery, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, Sprite (computer graphics), sprite graphics, raster graphics, Rendering (computer graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (mathematics)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Methods
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on Resampling (statistics), repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic system, deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Clipping
In computer graphics, line clipping is the process of removing ( clipping) lines or portions of lines outside an area of interest (a viewport or view volume). Typically, any part of a line which is outside of the viewing area is removed. There are two common algorithms for line clipping: Cohen–Sutherland and Liang–Barsky. A line-clipping method consists of various parts. Tests are conducted on a given line segment to find out whether it lies outside the view area or volume. Then, intersection calculations are carried out with one or more clipping boundaries. Determining which portion of the line is inside or outside of the clipping volume is done by processing the endpoints of the line with regards to the intersection. Cohen–Sutherland In computer graphics, the Cohen–Sutherland algorithm (named after Danny Cohen and Ivan Sutherland) is a line-clipping algorithm. The algorithm divides a 2D space into 9 regions, of which only the middle part (viewport) is visible. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-space (geometry)
In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional, then a half-space is called a ''half-plane'' (open or closed). A half-space in a one-dimensional space is called a ''half-line'' or ray''.'' More generally, a half-space is either of the two parts into which a hyperplane divides an n-dimensional space. That is, the points that are not incident to the hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane. A half-space can be either ''open'' or ''closed''. An open half-space is either of the two open sets produced by the subtraction of a hyperplane from the affine space. A closed half-space is the union of an open half-space and the hyperplane that defines it. The open (closed) ''upper half-space'' is the half-space of all (''x''1, ''x''2, ..., ''x''''n'') suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the Function (computer programming), functions or Operator (computer programming), operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, Relational database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up Identifier (computer languages), identifiers. Data s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
