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		<doi>10.1109/SIBGRAPI.2016.015</doi>
		<citationkey>SkalaSmolMajd:2016:ReNuPo</citationkey>
		<title>Reducing the number of points on the convex hull calculation using the polar space subdivision in E2</title>
		<format>On-line</format>
		<year>2016</year>
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		<size>2120 KiB</size>
		<author>Skala, Vaclav,</author>
		<author>Smolik, Michal,</author>
		<author>Majdisova, Zuzana,</author>
		<affiliation>University of West Bohemia</affiliation>
		<affiliation>University of West Bohemia</affiliation>
		<affiliation>University of West Bohemia</affiliation>
		<editor>Aliaga, Daniel G.,</editor>
		<editor>Davis, Larry S.,</editor>
		<editor>Farias, Ricardo C.,</editor>
		<editor>Fernandes, Leandro A. F.,</editor>
		<editor>Gibson, Stuart J.,</editor>
		<editor>Giraldi, Gilson A.,</editor>
		<editor>Gois, João Paulo,</editor>
		<editor>Maciel, Anderson,</editor>
		<editor>Menotti, David,</editor>
		<editor>Miranda, Paulo A. V.,</editor>
		<editor>Musse, Soraia,</editor>
		<editor>Namikawa, Laercio,</editor>
		<editor>Pamplona, Mauricio,</editor>
		<editor>Papa, João Paulo,</editor>
		<editor>Santos, Jefersson dos,</editor>
		<editor>Schwartz, William Robson,</editor>
		<editor>Thomaz, Carlos E.,</editor>
		<e-mailaddress>smolik@kiv.zcu.cz</e-mailaddress>
		<conferencename>Conference on Graphics, Patterns and Images, 29 (SIBGRAPI)</conferencename>
		<conferencelocation>São José dos Campos, SP, Brazil</conferencelocation>
		<date>4-7 Oct. 2016</date>
		<publisher>IEEE Computer Society´s Conference Publishing Services</publisher>
		<publisheraddress>Los Alamitos</publisheraddress>
		<booktitle>Proceedings</booktitle>
		<tertiarytype>Full Paper</tertiarytype>
		<transferableflag>1</transferableflag>
		<versiontype>finaldraft</versiontype>
		<keywords>Convex hull, iterative approximation, space subdivision, reduction of points.</keywords>
		<abstract>A convex hull of points in E2 is used in many applications. In spite of low computational complexity O(h log&#8289;n ) it takes considerable time if large data processing is needed. We present a new algorithm to speed up any planar convex hull calculation. It is based on a polar space subdivision and speed up known convex hull algorithms of  3,7 times and more. The algorithm estimates the central point using 10% of the data; this point is taken as the origin for the polar subdivision. The space subdivision enables a fast and very efficient reduction of the given points, which cannot contribute to the final convex hull. The proposed algorithm iteratively approximates the convex hull, leaving only a small number of points for the final processing, which is performed using a standard algorithm. Non-eliminated points are then processed by a selected standard convex hull algorithm. The algorithm is simple and easy to implement. Experiments proved numerical robustness as well.</abstract>
		<language>en</language>
		<targetfile>ConvexHull [SIBGRAPI_2016].pdf</targetfile>
		<usergroup>smolik@kiv.zcu.cz</usergroup>
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		<citingitemlist>sid.inpe.br/sibgrapi/2016/07.02.23.50 5</citingitemlist>
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