2.5.2 Cohen-Sutherland Line-Clipping Algorithm

Cf. [FvDFH90, 3.12.3].

First we test whether both endpoints are inside (and hence draw the line segment) or whether both are left of $x=x_{\min}$, right of $x=x_{\max}$, below $y=y_{\min}$, or above $y=y_{\max}$ (then we ignore line segment). Otherwise we split the line segment into two pieces at a clipping edge (and thus reject one part). Now we proceed iteratively.

A rather simple accept-reject test is the following:

Divide the plane into 9 regions and assign a 4 bit code to each:

1000

...above top edge $y>y_{\max}$

0100

...below bottom edge $y<y_{\min}$

0010

...right of right edge $x>x_{\max}$

0001

...left of left edge $x<x_{\min}$

mathcalculate the corresponding bit-codes for both endpoints.

Figure: Codes for the 9 regions associated to clipping rectangle

If both codes are zero then the line segment is completely inside the rectangle. If the bitwise-and of these codes is not zero then the line does not hit since both endpoints lie on the wrong side of at least one boundary line (corresponding to a bit equal to 1). Otherwise take a line which is met by the segment (for this find one non-zero bit), divide the given line at the intersection point in two parts and reject the one lying in the outside halfplane.

Figure: Example of Cohen-Sutherland line-clipping algorithm