Voronoi Diagram for Intersecting Convex Polygons in the Plane

被引：0

作者：

Lu J. ^{[1
]}

Xiong P. ^{[1
]}

Min W. ^{[2
]}

Liao Y. ^{[1
]}

机构：

[1] School of Information Engineering, Nanchang University, Nanchang

[2] School of Software, Nanchang University, Nanchang

来源：

Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics | 2019年 / 31卷 / 09期

关键词：

Intersecting polygons; Regionalization of Voronoi edges; Vector-based algorithm; Voronoi diagram;

D O I：

10.3724/SP.J.1089.2019.17622

中图分类号：

学科分类号：

摘要：

The traditional polygonal Voronoi diagram does not allow intersections among polygons and henceforth is hard to be applied to the fields of computer vision and ecology where polygons may intersect each other. In order to solve the problem of the nearest neighbor partitions under situations with polygon intersection, a novel Voronoi diagram for intersecting convex polygons is proposed. Firstly, the Voronoi diagram for intersecting convex polygons is defined. Then the unique regionalization feature of Voronoi edges is described, followed by the proof of the necessary and sufficient condition for its occurrence. Moreover, the relation between intersecting polygons and disjoint polygons is demonstrated. Finally, the generation algorithm of the polygonal Voronoi diagram is proposed and implemented. Experimental results show that the algorithm breaks through the constraint of having no intersecting polygons and effectively solves the problem of intersection in the polygonal Voronoi diagram, which provides the theoretic foundation for practical applications in the fields of computer vision and ecology. © 2019, Beijing China Science Journal Publishing Co. Ltd. All right reserved.

引用

页码：1609 / 1616

页数：7

共 18 条

[1]

Aurenhammer F., Voronoi diagrams-a survey of a fundamental geometric data structure, ACM Computing Surveys, 23, 3, pp. 345-405, (1991)

[2]

Liu J., Liu S., A survey on applications of Voronoi diagrams, Journal of Engineering Graphics, 25, 2, pp. 125-132, (2004)

[3]

Sung T.W., Yang C.S., Voronoi-based coverage improvement approach for wireless directional sensor networks, Journal of Network and Computer Applications, 39, pp. 202-213, (2014)

[4]

Hug D., Kiderlen M., Svane A.M., Voronoi-based estimation of Minkowski tensors from finite point samples, Discrete & Computational Geometry, 57, 3, pp. 545-570, (2017)

[5]

Liu Q.S., Jiang Y.L., Wu Z.J., Et al., Investigation of the rock fragmentation process by a single TBM cutter using a Voronoi element-based numerical manifold method, Rock Mechanics and Rock Engineering, 51, 4, pp. 1137-1152, (2018)

[6]

Min W., Tang Z., Maximum average aspect ratio property of the 2D Delaunay triangulation, Chinese Journal of Computers, 17, pp. 20-25, (1994)

[7]

Min W., Tang Z., The delaunay triangulation of a point set within an arbitrary 2D domain, Chinese Journal of Computers, 18, 5, pp. 357-364, (1995)

[8]

Min W., Tang Z., Algorithms for generating the Delaunay triangulation of a point set within an arbitrary 2D domain, Chinese Journal of Computers, 18, 5, pp. 365-371, (1995)

[9]

Mcallister M., Kirkpatrick D., Snoeyink J., A compact piecewise-linear Voronoi diagram for convex sites in the plane, Discrete & Computational Geometry, 15, 1, pp. 73-105, (1996)

[10]

Emiris I.Z., Tsigaridas E.P., Tzoumas G.M., The predicates for the exact Voronoi diagram of ellipses under the Euclidiean metric, International Journal of Computational Geometry & Applications, 18, 6, pp. 567-597, (2008)

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