Stable snap rounding

Abstract

Snap rounding is a popular method for rounding the vertices of a planar arrangement of line segments to the integer grid. It has many advantages, including minimum perturbation of the segments, preservation of the arrangement topology, and ease of implementation. However, snap rounding has one significant weakness: it is not stable (i.e., not idempotent). That is, applying snap rounding to a snap-rounded arrangement of n segments may cause additional segment perturbation, and the number of iterations of snap rounding needed to reach stability may be as large as Θ(n2). This paper introduces stable snap rounding, a variant of snap rounding that has all of snap rounding's advantages and is also idempotent. In particular, stable snap rounding does not change any arrangement whose vertices are already grid points (such as those produced by stable snap rounding or standard snap rounding).