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texture mapping : ウィキペディア英語版
texture mapping

Texture mapping〔http://web.cse.ohio-state.edu/~whmin/courses/cse5542-2013-spring/15-texture.pdf〕〔http://www.inf.pucrs.br/flash/tcg/aulas/texture/texmap.pdf〕〔http://www.cs.uregina.ca/Links/class-info/405/WWW/Lab5/#References〕 is a method for adding detail, surface texture (a bitmap or raster image), or color to a computer-generated graphic or 3D model. Its application to 3D graphics was pioneered by Edwin Catmull in 1974.
Originally a method that simply wrapped and mapped pixels from a texture to a 3D surface - now more technically called diffuse mapping to distinguish it from more complex mappings - in recent decades the advent of multi-pass rendering and complex mapping such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, mipmaps, occlusion mapping, and many other complex variations on the technique have made it possible to simulate near-photorealism in real time, by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene.
A texture map〔http://www.microsoft.com/msj/0199/direct3d/direct3d.aspx〕〔http://homepages.gac.edu/~hvidsten/courses/MC394/projects/project5/texture_map_guide.html〕 is applied (mapped) to the surface of a shape or polygon.〔Jon Radoff, Anatomy of an MMORPG, http://radoff.com/blog/2008/08/22/anatomy-of-an-mmorpg/〕 This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2d case is also known as a UV coordinate) either via explicit assignment or by procedural definition. Image sampling locations are then interpolated across the face of a polygon to produce a visual result that seems to have more richness than could otherwise be achieved with a limited number of polygons. Multitexturing is the use of more than one texture at a time on a polygon.〔Blythe, David. ''(Advanced Graphics Programming Techniques Using OpenGL ).'' Siggraph 1999. (see: (Multitexture ))〕 For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface, such as tree bark or rough concrete, that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in recent video games, as graphics hardware has become powerful enough to accommodate it in real-time.〔(Real-Time Bump Map Synthesis ), Jan Kautz1, Wolfgang Heidrichy2 and Hans-Peter Seidel1, (1Max-Planck-Institut für Informatik, 2University of British Columbia)〕
The way the resulting pixels on the screen are calculated from the texels (texture pixels) is governed by texture filtering. The fastest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped.
==Perspective correctness==

Texture coordinates are specified at each vertex of a given triangle, and these coordinates are interpolated using an extended Bresenham's line algorithm. If these texture coordinates are linearly interpolated across the screen, the result is affine texture mapping. This is a fast calculation, but there can be a noticeable discontinuity between adjacent triangles when these triangles are at an angle to the plane of the screen (see figure at right – textures (the checker boxes) appear bent).
Perspective correct texturing accounts for the vertices' positions in 3D space, rather than simply interpolating a 2D triangle. This achieves the correct visual effect, but it is slower to calculate. Instead of interpolating the texture coordinates directly, the coordinates are divided by their depth (relative to the viewer), and the reciprocal of the depth value is also interpolated and used to recover the perspective-correct coordinate. This correction makes it so that in parts of the polygon that are closer to the viewer the difference from pixel to pixel between texture coordinates is smaller (stretching the texture wider), and in parts that are farther away this difference is larger (compressing the texture).
:Affine texture mapping directly interpolates a texture coordinate u^_0 and u^= (1 - \alpha ) u_0 + \alpha u_1 where 0 \le \alpha \le 1
:Perspective correct mapping interpolates after dividing by depth z^_= \frac + \alpha \frac } + \alpha \frac }
All modern 3D graphics hardware implements perspective correct texturing.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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