Cohen–Sutherland algorithm
# Cohen–Sutherland algorithm

In computer graphics, the Cohen–Sutherland algorithm is an algorithm used for line clipping. The algorithm divides a two-dimensional space into 9 regions and then efficiently determines the lines and portions of lines that are visible in the central region of interest (the viewport).

The algorithm was developed in 1967 during flight simulator work by Danny Cohen and Ivan Sutherland.

## The algorithm

The algorithm includes, excludes or partially includes the line based on whether:

* Both endpoints are in the viewport region (bitwise OR of endpoints = 0000): trivial accept.
* Both endpoints share at least one non-visible region, which implies that the line does not cross the visible region. (bitwise AND of endpoints ≠ 0000): trivial reject.
* Both endpoints are in different regions: in case of this nontrivial situation the algorithm finds one of the two points that is outside the viewport region (there will be at least one point outside). The intersection of the outpoint and extended viewport border is then calculated (i.e. with the parametric equation for the line), and this new point replaces the outpoint. The algorithm repeats until a trivial accept or reject occurs.

The numbers in the figure below are called outcodes. An outcode is computed for each of the two points in the line. The outcode will have 4 bits for two-dimensional clipping, or 6 bits in the three-dimensional case. The first bit is set to 1 if the point is above the viewport. The bits in the 2D outcode represent: top, bottom, right, left. For example, the outcode 1010 represents a point that is top-right of the viewport.

    leftcentralright top 1001 1000 1010 central 0001 0000 0010 bottom 0101 0100 0110

Note that the outcodes for endpoints must be recalculated on each iteration after the clipping occurs.

The Cohen–Sutherland algorithm can be used only on a rectangular clip window.

