A MAXIMUM INSCRIBED CIRCLE ALGORITHM BASED ON VORONOI DIAGRAMS AND GEOMETRY EQUATIONS Burak Beyhan 1 , Cüneyt Güler 2 , Hidayet Tağa 3 1 Assoc. Prof. Dr. Burak Beyhan, Mersin University, Department of City and Regional Planning Mersin Üniversitesi, Mimarlık Fakültesi, Çiftlikköy Kampüsü, Yenişehir / Mersin Turkey phone: +90-324-3610001 (17739) fax: +90-324- 3610109 e-mail: burakbeyhan@mersin.edu.tr 2 Prof. Dr. Cüneyt Güler, Mersin University, Department of Geological Engineering Mersin Üniversitesi, Mühendislik Fakültesi, Çiftlikköy Kampüsü, Yenişehir / Mersin Turkey phone: +90-324-3610001 (17314) e-mail: cguler@mersin.edu.tr 3 Assist. Prof. Dr. Hidayet Tağa, Mersin University, Department of Geological Engineering Mersin Üniversitesi, Mühendislik Fakültesi, Çiftlikköy Kampüsü, Yenişehir / Mersin Turkey; phone: +90-324-3610001 (17326) e-mail: htaga@mersin.edu.tr Abstract The aim of this study is to develop an algorithm for the calculation of Maximum Inscribed Circle (MIC) that can be placed within a polygon feature (PF) by using Free and Open Source Software (FOSS) for GIS. Compared with other parameters developed for PFs, there is no simple algorithm for the computation of MIC for different PFs. The algorithm developed in this study for the computation of MIC is based on the Voronoi diagrams and analytical geometry equations. The algorithm developed for the approximation of MIC can be applied to both convex and concave PFs. For the implementation of the algorithm, Eclipse IDE platform and OpenJUMP libraries written in Java is used. What is evident from the various runs of the script produced on the base of the algorithm for a set of regular and irregular PFs is that it is successful in finding MIC. Keywords: Maximum Inscribed Circle, Algorithm, Vector Data, Free and Open Source Software for GIS INTRODUCTION The aim of this paper is to develop an algorithm for the calculation of MIC that can be placed within a polygon feature in vector data format by using FOSS for GIS. MIC is used in a wide range of fields, ranging from cartography (Shen et al., 2015; Sun, 2016), planning (Walz and Schumacher, 2005; Li, Goodchild, and Church, 2013; Brezina, Graser, and Leth, 2017) and geology (Powers, 1953) to biology (Tsygankov et al., 2014), military-security (Cheng, Li, and Zhu, 2012), and engineering applications (Meng et al., 2011; Liu et al. 2016, 2016; Li and Shi, 2009). Compared with other parameters developed for polygon features (PF), there is no simple algorithm for the calculation of MIC for different PFs. As it is suggested in various studies (Petrík et al., 2009; Shen et al., 2015; Sun, 2016), the Voronoi diagrams can be used for the calculation of MIC. Parallel to these suggestions in the algorithm developed in this study, Voronoi diagrams are effectively used. If it is assumed that MIC should be tangent to at least three edges of a PF (Sun, 2016) (though under certain conditions it can be tangent to only two edges), it follows that analytical geometry equations can also be effectively used for the calculation of MIC. Within this context, the algorithm developed for this study is composed of a number of sub-components; 1. Extraction of the points that are candidates for being center of MIC by using Voronoi diagrams, 2. Calculation of the first candidate point that can be used as the center of MIC, 3. Detection of the centers of the cores that may be used for the approximation of the center of MIC, 4. Processing of each core in order to approximate MIC of PF by using analytical geometry equations created on the base of the candidate points, and 5. Selection of the best circle calculated by using all possible cores and stages of analytical geometry equations in order to approximate MIC. Each of these sub-components is elaborated in the subsequent parts of the paper in separate sections. After elaboration of these components and discussion of the results of the running the script created in OpenJUMP (2018), a FOSS for GIS, to implement the algorithm in comparison with other software alternatives, we draw on some concluding remarks. Proceedings, 7th International Conference on Cartography and GIS, 18-23 June 2018, Sozopol, Bulgaria ISSN: 1314-0604, Eds: Bandrova T., Konečný M. 63