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Back-face Culling
In computer graphics, back-face culling determines whether a polygon of a graphical object is drawn. It is a step in the graphical pipeline that tests whether the points in the polygon appear in clockwise or counter-clockwise order when projected onto the screen. If the user has specified that front-facing polygons have a clockwise winding, but the polygon projected on the screen has a counter-clockwise winding then it has been rotated to face away from the camera and will not be drawn. The process makes rendering objects quicker and more efficient by reducing the number of polygons for the program to draw. 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. In general, back-face culling can be assumed to produce no visible artifact in a rendered scene if it contains only closed and opaque geometry. In scenes containing transpa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Back Face Culling Skull Example
The human back, also called the dorsum, is the large Posterior (anatomy), posterior area of the human body, rising from the top of the buttocks to the back of the neck. It is the surface anatomy, surface of the body opposite from the chest and the abdomen. The human vertebral column, 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 human vertebral column, 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 do ... [...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 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." Clipping 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 or frame. Clip regio ... [...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 (x \mapsto -x), reciprocation (x \mapsto 1/x), and complex conjugation (z \mapsto \bar z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...; and reciprocal ciphers such as the ROT13 transformation and the Beaufort cipher, Beaufort polyalphabetic cipher. The Function composition, composition of two invol ... [...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. 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 infinity, the number of coordinates required to allow this extension is one more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinant
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix is denoted , , or . 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 & f \\ g & h & i \end= aei + bfg + cdh - ceg - bdi - afh. The determinant of a matrix can be defined in several equivalent ways. Leibniz formula expresses the determinant as a sum of signed products of matrix entries such that each summand is the product of different entries, and the number of these summands is n!, the factorial of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Normal
In geometry, a normal is an object such as 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) line perpendicular to the tangent line to the curve at the point. A normal vector may have length one (a unit vector) or its length may represent the curvature of the object (a '' curvature vector''); its algebraic sign may indicate sides (interior or exterior). In three dimensions, a surface normal, or simply normal, to a surface at point P is a vector perpendicular to the tangent plane of the surface at P. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality (right angles). The concept has been generalized to differentiable manifolds of arbitrary dimension embedded in a Euclidean space. The normal vector space or normal space of a manifold at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or rarely projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. I ... [...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 3-D computer graphics appear to be flat by using less shading color instead of a 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, an oil painting or an ink painting. The name comes from ''cels'' (short for celluloid), clear sheets of acetate which were painted on for use in traditional 2D animation. Basic process The cel-shading process starts with a typical 3D model. Where cel-shading differs from conventional rendering is in its non-photorealistic illumination model. Conventional smooth lighting values are calculated for each pixel and then quantized to a small number of discrete shades to create the characteristic "flat look", where the shadows and highlights appear as blocks of color ra ... [...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 modi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Surface Determination
In 3D computer graphics, hidden-surface determination (also known as shown-surface determination, hidden-surface removal (HSR), occlusion culling (OC) or visible-surface determination (VSD)) is the process of identifying what surfaces and parts of surfaces can be seen from a particular viewing angle. A hidden-surface determination algorithm is a solution to the visibility problem, which was one of the first major problems in the field of 3D computer graphics . The process of hidden-surface determination is sometimes called hiding, and such an algorithm is sometimes called a hider. When referring to line rendering it is known as hidden-line removal. Hidden-surface determination is necessary to render a scene correctly, so that one may not view features hidden behind the model itself, allowing only the naturally viewable portion of the graphic to be visible. Background Hidden-surface determination is a process by which surfaces that should not be visible to the user (for example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve. The intersection of all the convex sets that contain a given subset of Euclidean space is called the convex hull of . It is the smallest convex set containing . A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, 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 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 (CGI). The non-artistic aspects of computer graphics are the subject of computer science research. Some topics in computer graphics include user interface design, sprite graphics, rendering, ray tracing, geometry processing, computer animation, vector graphics, 3D modeling, shaders, GPU design, implicit surfaces, visualization, scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
