Acketa, Dragan M.; Matić-Kekić, Snežana; Žunić, Joviša D. A linear algorithm for construction of optimal digital convex \(2K\)-gons. (English) Zbl 0804.68149 Yugosl. J. Oper. Res. 3, No. 2, 159-170 (1993). Summary: The paper gives a linear algorithm (w.r.t. the number of vertices) for a construction of optimal digital convex \(2k\)-gons, that is, those digital convex polygons, which have the smallest possible diameter with a given even number of edges. The construction for \(k\) even is based on the efficient construction of a Farey sequence, while the construction for \(k\) odd uses, in addition, two families of auxiliary 6-gons. MSC: 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 68Q25 Analysis of algorithms and problem complexity 11B57 Farey sequences; the sequences \(1^k, 2^k, \dots\) Keywords:digital geometry; optimization; time complexity; computational geometry; convex polygons; Farey sequence PDFBibTeX XMLCite \textit{D. M. Acketa} et al., Yugosl. J. Oper. Res. 3, No. 2, 159--170 (1993; Zbl 0804.68149)