An analysis technique and an algorithm for line clipping

A mathematical model for the expected-time analysis of line-clipping algorithms is proposed. Assuming that all clipping windows are equally likely, we demonstrate that the probability of a line segment being totally outside the window approaches the value of 8/9, provided that the line segments tend to be short and evenly distributed within a rectangle. Acceptance-rejection matrices are introduced for a machine-independent comparison of algorithms. A new line-clipping method, called QuickClip, is also proposed. QuickClip is not only simpler and more concise than the Cohen-Sutherland algorithm, the most widely used method in computer graphics, but also faster both in terms of machine-independent analysis and timing results on random line segments. Timing results also indicate that QuickClip is significantly faster than the Nicholl-Lee-Nicholl (1987) algorithm. The theoretical results generalise to 3D, with the important consequence that the average clipping volume is 1/27 of the volume of the model.