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Clip coordinates

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(Redirected from Clip space) Coordinate system used in computer graphics

The clip coordinate system is a homogeneous coordinate system in the graphics pipeline that is used for clipping.

Objects' coordinates are transformed via a 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, the result of executing vertex processing shaders is considered to be in clip coordinates. All coordinates may then be divided by the w {\displaystyle 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,

( x c y c z c w c ) , {\displaystyle {\begin{pmatrix}x_{c}\\y_{c}\\z_{c}\\w_{c}\end{pmatrix}},}

and the following equality defines the relationship between the normalized device coordinates x n {\displaystyle x_{n}} , y n {\displaystyle y_{n}} and z n {\displaystyle z_{n}} and clip coordinates,

( x n y n z n ) = ( x c / w c y c / w c z c / w c ) . {\displaystyle {\begin{pmatrix}x_{n}\\y_{n}\\z_{n}\end{pmatrix}}={\begin{pmatrix}x_{c}/w_{c}\\y_{c}/w_{c}\\z_{c}/w_{c}\end{pmatrix}}.}

Clip coordinates are convenient for clipping algorithms as points can be checked if their coordinates are outside of the viewing volume. For example, a coordinate x c {\displaystyle x_{c}} for a point is within the viewing volume if it satisfies the inequality − w c ≤ x c ≤ w c {\displaystyle -w_{c}\leq x_{c}\leq w_{c}} . Polygons with vertices outside of the viewing volume may be clipped to fit within the volume.

Clipping algorithms

External links

References

  1. Dave Shreiner; OpenGL Architecture Review Board (2006). OpenGL programming guide: the official guide to learning OpenGL, version 2. Addison-Wesley. ISBN 978-0-321-33573-9. Retrieved 29 December 2011.
  2. Segal, Mark; Akeley, Kurt (May 14, 2018). "OpenGL 4.6 Core Profile" (PDF). The Khronos Group.
  3. The Khronos® Vulkan Working Group (January 13, 2019). "Vulkan® 1.0.98 - A Specification". The Khronos Group. Retrieved January 23, 2019.
  4. "Vertex Post-Processing". The Khronos Group. Retrieved January 23, 2019.


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