@article{
author = "Petruševski, Ljiljana and Petrović, Maja M. and Devetaković, Mirjana and Ivanović, Jelena",
year = "2017",
abstract = "The theme of this paper is the modeling of focal-directorial surfaces, starting with their definition, as a locus of points, whose sum of the distances to the focus and/or directrix is constant and predefined. We presented a heuristic algorithm for modeling surfaces and their isocurves, achieved through the use of the Grasshopper visual programming editor in the RhinoCeros environment. Surfaces and their isocurves were generated in a spherical grid, because a Cartesian grid proved unsuitable for the task and the chosen approach. This paper additionally proposes a modeling algorithm of a discrete variation of focal-directorial surfaces. The proposed modeling method is a 3D convex hull implemented on a set of surface points, with the selected points close to that surface. The discrete model is realized both in a Cartesian and spherical grid. There are significant differences between the obtained results., Tema ovog rada je modelovanje fokalno-direktrisnih površi polazeći od njihove definicije, kao geometrijskog mesta tačaka čiji je zbir rastojanja do fokusa i/ili direktrisa konstantan i unapred zadat. Predložen je jedan heuristički algoritam za modelovanje površi i njihovih izolinija koji je realizovan pomoću vizuelnog grafičkog editora Grasshoper u RhinoCeros okruženju. Generisanje površi i njihovih izolinija realizovano je u sfernom gridu, pravougli grid se pokazao kao nepodesan za postavljeni zadatak i pristup. U ovom radu je, dodatno, predložen i algoritam modelovanja diskretne varijante fokalno-direktrisnih površi. Kao način modelovanja, predložen je 3D convex hull primenjen na skupu tačaka površi i izabranih tačaka bliskih toj površi. Diskretni model je realizovan u pravouglom, i u sfernom gridu. Dobijeni su rezultati koji se značajno međusobno razlikuju.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Modeling of focal-directorial surfaces for application in architecture, Modelovanje fokalno-direktrisnih površi za primenu u arhitekturi",
volume = "45",
number = "2",
pages = "294-300",
doi = "10.5937/fmet1702294P"
}