Computational geometry: an introduction
Computational geometry: an introduction
On some distance problems in fixed orientations
SIAM Journal on Computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Robust Proximity Queries: An Illustration of Degree-Driven Algorithm Design
SIAM Journal on Computing
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
How to Compute the Voronoi Diagram of Line Segments: Theoretical and Experimental Results
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Critical area computation via Voronoi diagrams
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hierarchical Steiner tree construction in uniform orientations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Algorithms and theory of computation handbook
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In this paper, we present a plane sweep algorithm for constructing the Voronoi diagram of a set of non-crossing line segments in 2D space using a distance metric induced by a regular k-gon and study the robustness of the algorithm. Following the algorithmic degree model [G. Liotta, F.P. Preparata, R. Tamassia, Robust proximity queries: an illustration of degree-driven algorithm design, SIAM J. Comput. 28 (3) (1998) 864-889], we show that the Voronoi diagram of a set of arbitrarily oriented segments can be constructed with degree 14 for certain k-gon metrics (e.g., k=6,8,12). For rectilinear segments or segments with slope +1 or -1, the degree reduces to 2. The algorithm is easy to implement and finds applications in VLSI layout.