Anti-Aliased Lines Using Run-Masks

In recent work, a set of line digitization algorithms based on the hierarchy of runs in the digital line has unified and generalized the iterative line-drawing algorithms used in computer graphics. In this paper, the additional structural information generated by these algorithms is leveraged to describe a run-based approach to draw anti-aliased line segments in which anti-aliased run-masks are substituted for the individual run lengths as the line is being drawn. The run-masks are precomputed using a prefiltering technique such that one or more run-masks are defined for each of the one or two possible run lengths that occur in the line. The run-masks can be defined for any order or level of the hierarchy of runs in the digital line and the technique is illustrated using runs of pixels. Comparing the use of run-masks to applying the prefiltering technique for each pixel in the line, a line of similar visual quality can be produced more efficiently. We place no restrictions on the placement of the end points of the line, which may reside anywhere on the two-dimensional plane.