Line clipping is an important operation in almost every graphical application. The most commonly used techniques are based on line end point encodings or the parametric representation of straight line segments. In this paper both techniques are combined in a new algorithm that computes accurately rounded coordinates, without the use of any floating point operations. It is shown that the new method is suited for implementations in software as well as in hardware. A performance study of the new and several other well-known line clipping algorithms indicates the superiority over all other examined algorithms.