Editing Graphics pipeline (section)

==== Window-Viewport transformation ====
[[File:Screen Mapping.svg|thumb|Window-Viewport-Transformation]]
To output the image to any target area (viewport) of the screen, another transformation, the ''Window-Viewport transformation'', must be applied. This is a shift, followed by scaling. The resulting coordinates are the device coordinates of the output device. The viewport contains 6 values: the height and width of the window in pixels, the upper left corner of the window in window coordinates (usually 0, 0), and the minimum and maximum values for Z (usually 0 and 1).

: Formally: <math>\begin{pmatrix}
x\\
y\\
z
\end{pmatrix}=\begin{pmatrix}
{vp}.X+(1.0+v.X)*{vp}.{width}/2.0\\
{vp}.Y+(1.0-v.Y)*{vp}.{height}/2.0\\
{vp}.{minz}+v.Z*({vp}.{maxz} - {vp}.{minz})
\end{pmatrix}</math>
: With vp=Viewport; v=Point after projection

On modern hardware, most of the geometry computation steps are performed in the [[vertex shader]]. This is, in principle, freely programmable, but generally performs at least the transformation of the points and the illumination calculation. For the DirectX programming interface, the use of a custom vertex shader is necessary from version 10, while older versions still have a standard shader.