Stanić, Zoran Geodesic polyhedra and nets. (English) Zbl 1119.53304 Kragujevac J. Math. 28, 41-55 (2005). Geodesics of smooth surfaces generalize the idea of straight lines. They are the straightest and locally shortest curves. Discrete geodesics cannot have both of these properties. K. Polthier and M. Schmies in “Geodesic Flow on Polyhedral Surfaces”, Data Visualization, Springer-Verlag (1999), and “Straightest geodesic on polyhedral surfaces”, Mathematical Visualization, pp. 135–150, Springer-Verlag (1998; Zbl 0940.68153)] define polyhedral geodesics as straightest geodesics. The author uses this concept to define a new class of polyhedral surfaces which he names geodesic (or \(G\)-) polyhedra. Then, he gives some closer picture of them by determining theirs properties and giving several examples. A reason for that is the possibility of giving some algorithm for the generation of \(G\)-nets. At the end, by using numerical computation and theory of minimization of differentiable functions a method for geodesation of arbitrary discrete net is presented. Reviewer: Neda Bokan (Beograd) MSC: 53A04 Curves in Euclidean and related spaces 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 65D17 Computer-aided design (modeling of curves and surfaces) Keywords:polyhedral surface; total vertex angle; discrete net; geodesic polyhedral surface Citations:Zbl 0940.68153 PDFBibTeX XMLCite \textit{Z. Stanić}, Kragujevac J. Math. 28, 41--55 (2005; Zbl 1119.53304)