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
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Practical segment intersection with finite precision output
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Dynamic Half-Space Range Reporting and Its Application
Dynamic Half-Space Range Reporting and Its Application
Improved output-sensitive snap rounding
Proceedings of the twenty-second annual symposium on Computational geometry
Improved output-sensitive snap rounding
Proceedings of the twenty-second annual symposium on Computational geometry
Snap rounding of Bézier curves
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Snap Rounding and its variant, Iterated Snap Rounding, are methods for converting arbitrary-precision arrangements of segments into a fixed-precision representation (we call them SR and ISR for short). Both methods approximate each original segment by a polygonal chain, and both may lead, for certain inputs, to rounded arrangements with undesirable properties: in SR the distance between a vertex and a non-incident edge of the rounded arrangement can be extremely small, inducing potential degeneracies. In ISR, a vertex and a non-incident edge are well separated, but the approximating chain may drift far away from the original segment it approximates. We propose a new variant, Iterated Snap Rounding with Bounded Drift, which overcomes these two shortcomings of the earlier methods. The new solution augments ISR with simple and efficient procedures that guarantee the quality of the geometric approximation of the original segments, while still maintaining the property that a vertex and a non-incident edge in the rounded arrangement are well separated. We investigate the properties of the new method and compare it with the earlier variants. We have implemented the new scheme on top of CGAL, the Computational Geometry Algorithms Library, and report on experimental results.