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Clip Space
The clip coordinate system is a homogeneous coordinate system in the graphics pipeline that is used for clipping (computer graphics), clipping. Objects' coordinates are transformed via a 3D projection, projection transformation into clip coordinates, at which point it may be efficiently determined on an object-by-object basis which portions of the objects will be visible to the user. In the context of OpenGL or Vulkan (API), Vulkan, the result of executing vertex processing shaders is considered to be in clip coordinates. All coordinates may then be divided by the w component of 3D homogeneous coordinates, in what is called the perspective division. More concretely, a point in clip coordinates is represented with four components, :\beginx_c\\y_c\\z_c\\w_c\end, and the following equality defines the relationship between the normalized device coordinates x_n, y_n and z_n and clip coordinates, :\beginx_n\\y_n\\z_n\end = \beginx_c / w_c\\y_c / w_c\\z_c / w_c\end. Clip coordinates a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Coordinate System
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 than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
