The clip coordinate system is a

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. T ...

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

component of 3D homogeneous coordinates, in what is called the

perspective division In linear algebra, linear transformations can be represented by matrices. If T is a linear transformation mapping \mathbb^n to \mathbb^m and \mathbf x is a column vector with n entries, then T( \mathbf x ) = A \mathbf x for some m \times n mat ...

. 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 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

for a point is within the viewing volume if it satisfies the inequality

-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

* Newman–Sproull * Cyrus–Beck *

Sutherland–Hodgman algorithm The Sutherland–Hodgman algorithm is an algorithm used for clipping polygons. It works by extending each line of the convex ''clip polygon'' in turn and selecting only vertices from the ''subject polygon'' that are on the visible side. De ...

External links

Official OpenGL website

References

Clipping (computer graphics) {{Compu-graphics-stub