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.

中文翻译：

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基于Voronoi图和几何性质的最大内切圆算法

这项研究的目的是制定一种算法，用于计算可放置在多边形内的最大内切圆（MIC），并使用针对GIS的免费和开放源代码软件（FOSS）来实现该算法。MIC的应用范围广泛，从制图，规划，农业，林业和地质学到医学，生物学，天文学，安全和工程应用。由于问题的复杂性，没有用于计算任意多边形的MIC的简单算法。本研究中开发的用于计算MIC的算法（MICGIS）可以应用于以矢量数据格式表示的凸多边形和凹多边形。MICGIS通过受益于针对Apollonius问题的特殊情况提出的解决方案来利用Voronoi图和几何特性。由于使用了Voronoi图和FOSS for GIS，MICGIS也成功地用于带孔的多边形。为了实现MICGIS，使用了用Java编写的FOSS库。从基于MICGIS的一组任意多边形生成的脚本的各种运行中可以明显看出，与替代算法和软件相比，它可以更快，更准确地找到MIC。