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Backface Culling
In computer graphics, back-face culling determines whether a polygon that is part of a solid needs to be drawn. Polygons that face away from the viewer do not need to be drawn, as they will be obscured by other polygons facing the viewer. This process makes rendering objects quicker and more efficient by reducing the number of polygons to be drawn. For example, in a city street scene, there is generally no need to draw the polygons on the sides of the buildings facing away from the camera; they are completely occluded by the sides facing the camera. If multiple surfaces face towards the camera, then additional use of methods such as Z-buffering or the Painter's algorithm may be necessary to ensure the correct surface is rendered. Back-face culling is typically quite a cheap test, only requiring a dot product to be calculated, and so it is often used as a step in the graphical pipeline that reduces the number of surfaces that need to be considered. In general, back-face culling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Back Face Culling Skull Example
The human back, also called the dorsum (: dorsa), is the large posterior area of the human body, rising from the top of the buttocks to the back of the neck. It is the surface of the body opposite from the chest and the abdomen. The vertebral column runs the length of the back and creates a central area of recession. The breadth of the back is created by the shoulders at the top and the pelvis at the bottom. Back pain is a common medical condition, generally benign in origin. Structure The central feature of the human back is the vertebral column, specifically the length from the top of the thoracic vertebrae to the bottom of the lumbar vertebrae, which houses the spinal cord in its spinal canal, and which generally has some curvature that gives shape to the back. The ribcage extends from the spine at the top of the back (with the top of the ribcage corresponding to the T1 vertebra), more than halfway down the length of the back, leaving an area with less protection between the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clipping (computer Graphics)
Clipping, in the context of computer graphics, is a method to selectively enable or disable rendering (computer graphics), rendering operations within a defined region of interest. Mathematically, clipping can be described using the terminology of constructive geometry. A rendering algorithm only draws pixels in the intersection between the clip region and the scene model. Lines and surfaces outside the view volume (aka. frustum) are removed. Clip regions are commonly specified to improve render performance. A well-chosen clip allows the renderer to save time and energy by skipping calculations related to pixels that the user cannot see. Pixels that will be drawn are said to be within the clip region. Pixels that will not be drawn are outside the clip region. More informally, pixels that will not be drawn are said to be "clipped." In 2D graphics In two-dimensional graphics, a clip region may be defined so that pixels are only drawn within the boundaries of a window (computing), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Involution (mathematics)
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution is a bijection. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (), reciprocation (), and complex conjugation () in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the Beaufort polyalphabetic cipher. The composition of two involutions and is an involution if and only if they commute: . Involutions on finite sets The number of involutions, including the identity involution, on a set with elements is given by a recurrence relation found by Heinrich August Rothe in 1800: : a_0 = a_1 = 1 and a_n = a_ + (n - 1)a_ for n > 1. The first few terms of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix. They are also used in fundamental elliptic curve cryptography algorithms. If homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinant
In mathematics, the determinant is a Scalar (mathematics), scalar-valued function (mathematics), function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the matrix and the linear map represented, on a given basis (linear algebra), basis, by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible matrix, invertible and the corresponding linear map is an linear isomorphism, isomorphism. However, if the determinant is zero, the matrix is referred to as singular, meaning it does not have an inverse. The determinant is completely determined by the two following properties: the determinant of a product of matrices is the product of their determinants, and the determinant of a triangular matrix is the product of its diagonal entries. The determinant of a matrix is :\begin a & b\\c & d \end=ad-bc, and the determinant of a matrix is : \begin a & b & c \\ d & e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anticommutative Property
In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the ''inverse'' of the result with unswapped arguments. The notion '' inverse'' refers to a group structure on the operation's codomain, possibly with another operation. Subtraction is an anticommutative operation because commuting the operands of gives for example, Another prominent example of an anticommutative operation is the Lie bracket. In mathematical physics, where symmetry is of central importance, or even just in multilinear algebra these operations are mostly (multilinear with respect to some vector structures and then) called antisymmetric operations, and when they are not already of arity greater than two, extended in an associative setting to cover more than two arguments. Definition If A, B are two abelian groups, a bilinear map f\colon A^2 \to B is antico ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). The magnitude of the cross product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The units of the cross-product are the product of the units of each vector. If two vectors are parallel or are anti-parallel (that is, they are linearly dependent), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Normal
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular to a given object at a particular point. A normal vector of length one is called a unit normal vector or normal direction. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point is a vector perpendicular to the tangent plane of the surface at . The vector field of normal directions to a surface is known as '' Gauss map''. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elite (video Game)
''Elite'' is a space trading and combat simulator, space trading video game. It was written and developed by David Braben and Ian Bell (programmer), Ian Bell and was originally published by Acornsoft for the BBC Micro and Acorn Electron computers in September 1984. ''Elites Open-ended (gameplay), open-ended game model, and revolutionary 3D graphics led to it being ported to virtually every contemporary home computer system and earned it a place as a classic and a genre maker in gaming history. The game's title derives from one of the player's goals of raising their combat rating to the exalted heights of "Elite". ''Elite'' was one of the first home computer games to use Wire-frame model, wire-frame 3D graphics with hidden-line removal. It added graphics and twitch gameplay aspects to the genre established by the 1974 game ''Star Trader''. Another novelty was the inclusion of ''The Dark Wheel (novella), The Dark Wheel'', a novella by Robert Holdstock which gave players insight in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BBC Micro
The BBC Microcomputer System, or BBC Micro, is a family of microcomputers developed and manufactured by Acorn Computers in the early 1980s as part of the BBC's Computer Literacy Project. Launched in December 1981, it was showcased across several educational BBC television programmes, such as ''The Computer Programme'' (1982), ''Making the Most of the Micro'' and ''Computers in Control'' (both 1983), and ''Micro Live'' (1985). Created in response to the BBC's call for bids for a microcomputer to complement its broadcasts and printed material, Acorn secured the contract with its rapidly prototyped “Proton” system, which was subsequently renamed the BBC Micro. Although it was announced towards the end of 1981, production issues initially delayed the fulfilment of many orders, causing deliveries to spill over into 1982. Nicknamed the “Beeb”, it soon became a fixture in British schools, advancing the BBC’s goal of improving computer literacy. Renowned for its strong build q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toon Shaders
Cel shading or toon shading is a type of non-photorealistic rendering designed to make 3D computer graphics appear to be flat by using less shading color instead of a Color gradient, shade gradient or tints and shades. A cel shader is often used to mimic the style of a comic book or cartoon and/or give the render a characteristic paper-like texture. There are similar techniques that can make an image look like a Sketch (drawing), sketch, an oil painting or an ink painting. The name comes from cel, ''cels'' (short for celluloid), clear sheets of acetate which are painted on for use in Traditional animation, traditional 2D animation. Basic process The cel-shading process starts with a typical 3D computer graphics#Modeling, 3D model. Where cel-shading differs from conventional rendering is in its non-photorealistic shader, shading algorithm. Conventional smooth lighting values are calculated for each pixel and then Color quantization, quantized to a small number of discrete s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contour Drawing
Contour drawing is an art technique in which the artist sketches the style of the subject by drawing lines that result in a drawing that is essentially an outline (the French word meaning "outline"). The purpose of contour drawing is to emphasize the mass and volume of the subject rather than the detail; the focus is on the outlined shape of the subject and not the minor details. However, because contour can convey a three-dimensional perspective, length and width as well as thickness and depth are important; not all contours exist along the outlines of a subject.Sutherland, Jane. 1997. "Gesture drawings." American Artist (VNU eMedia, Inc.) 61, no. 656: 11. Academic Search Complete, EBSCOhost . Retrieved 9 February 2010. This technique is manifested in different styles and practiced in drawing development and learning. Importance Contour drawing is an essential technique in the field of art because it is a strong foundation for any drawing or painting; it can potentially mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
