Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Practical segment intersection with finite precision output
Computational Geometry: Theory and Applications
The VLSI handbook
Introduction to algorithms
Computational Geometry: Theory and Applications
An intersection-sensitive algorithm for snap rounding
Computational Geometry: Theory and Applications
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Improved Output-Sensitive Snap Rounding
Discrete & Computational Geometry
Iterated snap rounding with bounded drift
Computational Geometry: Theory and Applications
Finite-resolution computational geometry
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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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 @Q(n^2). 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).