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Robust Geometric Computation
, 1997
"... Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section... ..."
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Cited by 65 (10 self)
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Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising from numerical errors. Section...
Classroom examples of robustness problems in geometric computations
- In Proc. 12th European Symposium on Algorithms, volume 3221 of Lecture Notes Comput. Sci
, 2004
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A robust and efficient implementation for the segment Voronoi diagram
- Proc. 1 st Int. Symp. on Voronoi Diagrams in Science and Engineering
, 2004
"... In this paper we present an efficient algorithm for the computation of the segment Voronoi diagram in two dimensions. Our algorithm can handle not only disjoint segments or segments that share endpoints, but also segments that may intersect at their interior. It is incremental and the expected cost ..."
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Cited by 10 (0 self)
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In this paper we present an efficient algorithm for the computation of the segment Voronoi diagram in two dimensions. Our algorithm can handle not only disjoint segments or segments that share endpoints, but also segments that may intersect at their interior. It is incremental and the expected cost of inserting n (possibly intersecting) sites (points or segments) is O((n + m) log 2 n), where m is the number of points of intersection of the (open) segments in the input site set. Finally, we describe the implementation of our algorithm, that uses techniques such as geometric filtering, and present experiments that show the robustness, efficiency and scalability of our implementation.
Computing Voronoi Diagrams of Line Segments Reliably and Efficiently
, 2000
"... We study an engineering approach to computing Voronoi diagrams of points and line segments in the two-dimensional Euclidean space. Our Voronoi code, named vroni, uses standard oating-point arithmetic. It is based on Sugihara and Iri's topology-oriented approach, a very careful implementation of the ..."
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Cited by 1 (1 self)
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We study an engineering approach to computing Voronoi diagrams of points and line segments in the two-dimensional Euclidean space. Our Voronoi code, named vroni, uses standard oating-point arithmetic. It is based on Sugihara and Iri's topology-oriented approach, a very careful implementation of the numerical computations required, an automatic relaxation of epsilon thresholds, and on a multi-level recovery process combined with \desperate mode". Vroni was tested extensively on real-world data and turned out to be reliable. CPU-time statistics document that it is always faster than other popular Voronoi codes. 1 Introduction In a recent editorial, Fortune [2] wrote that \it is notoriously dicult to obtain a practical implementation of an abstractly described geometric algorithm". According to the author's personal experience this remark is particularly true for the implementation of Voronoi diagrams of line segments. This paper discusses the design and implementation of a reliable an...
