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2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. The word may stand for the branch of computer science that comprises such techniques, or for the models themselves. 2D computer graphics are mainly used in applications that were originally developed upon traditional printing and drawing technologies, such as typography, cartography, technical drawing, advertising, etc. In those applications, the two-dimensional image is not just a representation of a real-world object, but an independent artifact with added semantic value; two-dimensional models are therefore preferred, because they give more direct control of the image than 3D computer graphics (whose approach is more akin to photography than to typography). In many domains, such as desktop publishing, engineering, and business, a description of a document based on 2D computer graphics techniques can be much smaller than the corresponding digital image—often by a factor of 1/1000 or more. This representation is also more flexible since it can be rendered at different resolutions to suit different output devices. For these reasons, documents and illustrations are often stored or transmitted as 2D graphic files. 2D computer graphics started in the 1950s, based on vector graphics devices. These were largely supplanted by raster-based devices in the following decades. The PostScript language and the X Window System protocol were landmark developments in the field. ==2D graphics techniques== 2D graphics models may combine geometric models (also called vector graphics), digital images (also called raster graphics), text to be typeset (defined by content, font style and size, color, position, and orientation), mathematical functions and equations, and more. These components can be modified and manipulated by two-dimensional geometric transformations such as translation, rotation, scaling. In object-oriented graphics, the image is described indirectly by an object endowed with a self-rendering method—a procedure which assigns colors to the image pixels by an arbitrary algorithm. Complex models can be built by combining simpler objects, in the paradigms of object-oriented programming. In Euclidean geometry, a translation moves every point a constant distance in a specified direction. A translation can be described as a rigid motion: other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. A translation operator is an operator such that If v is a fixed vector, then the translation ''T''v will work as ''T''v(p) = p + v. If ''T'' is a translation, then the image of a subset ''A'' under the function ''T'' is the translate of ''A'' by ''T''. The translate of ''A'' by ''T''v is often written ''A'' + v. In a Euclidean space, any translation is an isometry. The set of all translations forms the translation group ''T'', which is isomorphic to the space itself, and a normal subgroup of Euclidean group ''E''(''n'' ). The quotient group of ''E''(''n'' ) by ''T'' is isomorphic to the orthogonal group ''O''(''n'' ): :''E''(''n'' ) ''/ T'' ≅ ''O''(''n'' ). == Translation == Since a translation is an affine transformation but not a linear transformation, homogeneous coordinates are normally used to represent the translation operator by a matrix and thus to make it linear. Thus we write the 3-dimensional vector w = (''w''''x'', ''w''''y'', ''w''''z'') using 4 homogeneous coordinates as w = (''w''''x'', ''w''''y'', ''w''''z'', 1).〔Richard Paul, 1981, (Robot manipulators: mathematics, programming, and control : the computer control of robot manipulators ), MIT Press, Cambridge, MA〕 To translate an object by a vector v, each homogeneous vector p (written in homogeneous coordinates) would need to be multiplied by this translation matrix: : As shown below, the multiplication will give the expected result: : The inverse of a translation matrix can be obtained by reversing the direction of the vector: : Similarly, the product of translation matrices is given by adding the vectors: : Because addition of vectors is commutative, multiplication of translation matrices is therefore also commutative (unlike multiplication of arbitrary matrices). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「2D computer graphics」の詳細全文を読む スポンサード リンク
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