A rational rotation method for robust geometric algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Applications of a new space-partitioning technique
Discrete & Computational Geometry
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Handbook of discrete and computational geometry
Rotational polygon containment and minimum enclosure using only robust 2D constructions
Computational Geometry: Theory and Applications - Special issue on applications and challenges
Practical segment intersection with finite precision output
Computational Geometry: Theory and Applications
Improved output-sensitive snap rounding
Proceedings of the twenty-second annual symposium on Computational geometry
Iterated snap rounding with bounded drift
Proceedings of the twenty-second annual symposium on Computational geometry
An intersection-sensitive algorithm for snap rounding
Computational Geometry: Theory and Applications
Snap rounding of Bézier curves
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Iterated snap rounding with bounded drift
Computational Geometry: Theory and Applications
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Proceedings of the twenty-seventh annual symposium on Computational geometry
Computational Geometry: Theory and Applications
On robust interpretation of topological relations in identity and tolerance models
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Technical note: Robust cascading of operations on polyhedra
Computer-Aided Design
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Snap rounding is a well known method for converting arbitrary-precision arrangements of segments into a fixed-precision representation. We point out that in a snap-rounded arrangement, the distance between a vertex and a non-incident edge can be extremely small compared with the width of a pixel in the grid used for rounding. We propose and analyze an augmented procedure, iterated snap rounding, which rounds the arrangement such that each vertex is at least half-the-width-of-a-pixel away from any non-incident edge. Iterated snap rounding preserves the topology of the original arrangement in the same sense that the original scheme does. However, the guaranteed quality of the approximation degrades. Thus each scheme may be suitable in different situations. We describe an implementation of both schemes. In our implementation we substitute an intricate data structure for segment/pixel intersection that is used to obtain good worst-case resource bounds for iterated snap rounding by a simple and effective data structure which is a cluster of kd-trees. Finally, we present rounding examples obtained with the implementation.