An intersection-sensitive algorithm for snap rounding

Authors:
Mark de Berg;Dan Halperin;Mark Overmars
Affiliations:
Department of Computer Science, TU Eindhoven, PO Box 513, 5600 MB Eindhoven, The Netherlands;School of Computer Science, Tel Aviv University, Tel Aviv 67789, Israel;Department of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, The Netherlands
Venue:
Computational Geometry: Theory and Applications
Year:
2007

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Abstract

Snap rounding is a method for converting arbitrary-precision arrangements of segments into fixed-precision representation. We present an algorithm for snap rounding with running time O((n+I)logn), where I is the number of intersections between the input segments. In the worst case, our algorithm is an order of magnitude more efficient than the best previously known algorithms. We also propose a variant of the traditional snap-rounding scheme. The new method has all the desirable properties of traditional snap rounding and, in addition, guarantees that the rounded arrangement does not have degree-2 vertices in the interior of edges. This simplified rounded arrangement can also be computed in O((n+I)logn) time.