A Sweepline Algorithm for Higher Order Voronoi Diagrams

机译：高阶Voronoi图的Sweepline算法

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摘要

We present an algorithm to construct order-k Voronoi diagrams with a sweepline technique. The sites can be points or line segments. The algorithm has O(nk^2 log n) time complexity and O(nk) space complexity.

机译：我们提出了一种使用扫掠线技术构造k阶Voronoi图的算法。站点可以是点或线段。该算法具有O（nk ^ 2 log n）时间复杂度和O（nk）空间复杂度。

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来源
《Tenth International Symposium on Voronoi Diagrams in Science and Engineering》|2013年|16-22|共7页
会议地点 Saint Petersburg(RU)
作者
Zavershynskyi Maksym; Papadopoulou Evanthia;
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原文格式 PDF
正文语种 eng
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关键词
Voronoi diagrams; computational geometry; line segments; sweep;

机译：Voronoi图;计算几何;线段;扫描;;

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1. A sweepline algorithm for Euclidean Voronoi diagram of circles [J] . Li Jin, Donguk Kim, Lisen Mu, Computer-Aided Design . 2006,第3期

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2. THEORY OF CONTINUOUS OPTIMAL SET PARTITIONING PROBLEMS AS A UNIVERSAL MATHEMATICAL FORMALISM FOR CONSTRUCTING VORONOI DIAGRAMS AND THEIR GENERALIZATIONS. Ⅱ. ALGORITHMS FOR CONSTRUCTING VORONOI DIAGRAMS BASED ON THE THEORY OF OPTIMAL SET PARTITIONING [J] . E. M. Kiseleva, L. S. Koriashkina Cybernetics and Systems Analysis . 2015,第4期

机译：连续最优集划分理论作为构造Vorono图及其通用化的通用数学形式。 Ⅱ。基于最优集合划分理论的Voroni图构造算法
3. Stable-Matching Voronoi Diagrams: Combinatorial Complexity and Algorithms [J] . Gill Barequet, David Eppstein, Michael T. Goodrich, LIPIcs : Leibniz International Proceedings in Informatics . 2018,第30期

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4. A Sweepline Algorithm for Higher Order Voronoi Diagrams [C] . Zavershynskyi Maksym, Papadopoulou Evanthia International Symposium on Voronoi Diagrams in Science and Engineering . 2013

机译：高阶voronoi图的Sweepline算法
5. On Quadtrees, Voronoi Diagrams, and Lattices: Results in Geometric Algorithms [D] . Bennett, Huxley David. 2017

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6. New Algorithms Based on the Voronoi Diagram Applied in a Pilot Study on Normal Mucosa and Carcinomas [O] . J. Sudbø, R. Marcelpoil, A. Reith 2000

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7. Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications [O] . Haim Kaplan, Wolfgang Mulzer, Liam Roditty, 2020

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8. Expected O(N) and O(N sup 4/3) Algorithms for Constructing Voronoi Diagrams in Two and Three Dimensions [R] . Bernal, J. 1987

机译：预期O（N）和O（N sup 4/3）算法构造二维和三维Voronoi图

A Sweepline Algorithm for Higher Order Voronoi Diagrams

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