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An algorithm for maximum inscribed circle based on Voronoi diagrams and geometrical properties

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Abstract

The aim of this study is to formulate an algorithm for the calculation of maximum inscribed circle (MIC) that can be placed within a polygon and to implement it by using free and open source software (FOSS) for GIS. MIC is used in a wide range of fields, ranging from cartography, planning, agriculture, forestry and geology to medicine, biology, astronomy, security, and engineering applications. Due to the complexity of the problem, there is no single and simple algorithm for the computation of MIC for arbitrary polygons. The algorithm developed in this study (MICGIS) for the computation of MIC can be applied to both convex and concave polygons represented in vector data format. MICGIS makes use of the Voronoi diagrams and geometrical properties by benefiting from the solutions proposed for the special cases of Apollonius’ Problem. Thanks to the employment of Voronoi diagrams and FOSS for GIS, MICGIS also works successfully for polygons with holes. For the implementation of MICGIS, FOSS libraries written in Java are used. What is evident from the various runs of the script produced on the base of MICGIS for a set of arbitrary polygons is that it is both faster and more accurate in finding MIC compared with the alternative algorithms and software.

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Acknowledgements

Birsen F. Biçgel is thanked for her assistance in preparation of technical drawings of the first benchmark dataset (named Regular_Geopolys.shp) composed of 28 regular geometric shapes. Whereas, the second benchmark dataset (named Complex_Geopolys.shp) is composed of 491 complex polygon features representing a real-world dataset adapted from Güler et al. (2012) [https://doi.org/10.1016/j.jhydrol.2011.11.021]. The authors would like to thank them for sharing this dataset with us. The authors are also grateful to anonymous referees for their useful comments, suggestions and constructive critiques. This manuscript in draft was presented at the 7th International Conference on Cartography & GIS (7 ICC&GIS 2018) held by Bulgarian Cartographic Association in Sozopol, Bulgaria (June 18–23, 2018). The authors would like to acknowledge the participants who made insightful comments and suggestions at the presentation. This work received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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  1. Department of City and Regional Planning, Muğla Sıtkı Koçman University, Muğla, Turkey

    Burak Beyhan

  2. Department of Geological Engineering, Mersin University, Mersin, Turkey

    Cüneyt Güler & Hidayet Tağa

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  1. Burak Beyhan
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MICGIS algorithm developed in the study

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Beyhan, B., Güler, C. & Tağa, H. An algorithm for maximum inscribed circle based on Voronoi diagrams and geometrical properties. J Geogr Syst 22, 391–418 (2020). https://doi.org/10.1007/s10109-020-00325-3

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