Direct Algorithm for the Exact Voronoi Diagram on Discrete Topographic Space

被引：0
|
作者：
Duan X. [1 ,2 ,3 ]
Ge Y. [3 ,4 ]
Zhang T. [5 ]
Li L. [6 ,7 ]
Tan Y. [1 ,3 ]
机构：
[1] School of Surveying and Geoinformation Engineering, East China University of Technology, Nanchang
[2] State Key Laboratory of Resources and Environmental Information System, Beijing
[3] Key Laboratory of Mine Environmental Monitoring and Improving Around Poyang Lake, Ministry of Natural Resources, Nanchang
[4] University of Chinese Academy of Sciences, Beijing
[5] State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan
[6] School of Resources and Environmental Sciences, Wuhan University, Wuhan
[7] Geospatial Information Technology Collaborative Innovation Center, Wuhan University, Wuhan
来源：
Wuhan Daxue Xuebao (Xinxi Kexue Ban)/Geomatics and Information Science of Wuhan University | 2023年 / 48卷 / 05期
关键词：
geodesic distance field; geodesic Voronoi diagram; hyperbolic arrangement; singular growth; topographic space;
D O I：
10.13203/j.whugis20210566
中图分类号：
学科分类号：
摘要：
Objectives: Voronoi diagram is a fundamental structure in geo-computing, but it still encounters the problem of exactness and the challenge of an exact algorithm comparable to planar Voronoi diagrams in the topographic space. Methods: The geodesic distance field of computational geometry is introduced into the triangulated irregular network in the discrete topographic surface. The hyperbolic curves representing the bisector are gradually grown from the singularity of the distance field on the edge of the grid. The precise division of the discrete surface is obtained by the arrangement of the hyperbolic curves, and the exact geodesic Voronoi diagram (GVD) is obtained by clustering the divided patches. Then, the exact Voronoi diagrams are tested quantitatively and qualitatively. Results and Conclusions: It is found that the exact GVD can bring a basic improvement for the spatial analysis of topographic surface. The direct algorithm based on singular growth and hyperbolic arrangement is intuitive and easy to implement, which avoids the excessive subdivision and preprocessing of grid patches by the existing algorithms, and provides a useful exploration for the development of Voronoi diagram analysis in digital topographic analysis. © 2023 Wuhan University. All rights reserved.
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页码：799 / 806
页数：7
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