Modeling of focal-directorial surfaces for application in architecture
Modelovanje fokalno-direktrisnih površi za primenu u arhitekturi
Апстракт
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.
Кључне речи:
focal-directorial surfaces / modeling / parametric model / surface discretization / 3D convex hullИзвор:
FME Transactions, 2017, 45, 2, 294-300Издавач:
- Univerzitet u Beogradu - Mašinski fakultet, Beograd
Финансирање / пројекти:
- Улога и имплементација државног просторног плана и регионалних развојних докумената у обнови стратешког истраживања, мишљења и управљања у Србији (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-47014)
DOI: 10.5937/fmet1702294P
ISSN: 1451-2092
WoS: 000408082400016
Scopus: 2-s2.0-85016318861
Институција/група
Arhitektonski fakultetTY - JOUR AU - Petruševski, Ljiljana AU - Petrović, Maja M. AU - Devetaković, Mirjana AU - Ivanović, Jelena PY - 2017 UR - https://raf.arh.bg.ac.rs/handle/123456789/265 AB - 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. AB - 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. PB - Univerzitet u Beogradu - Mašinski fakultet, Beograd T2 - FME Transactions T1 - Modeling of focal-directorial surfaces for application in architecture T1 - Modelovanje fokalno-direktrisnih površi za primenu u arhitekturi VL - 45 IS - 2 SP - 294 EP - 300 DO - 10.5937/fmet1702294P ER -
@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" }
Petruševski, L., Petrović, M. M., Devetaković, M.,& Ivanović, J.. (2017). Modeling of focal-directorial surfaces for application in architecture. in FME Transactions Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(2), 294-300. https://doi.org/10.5937/fmet1702294P
Petruševski L, Petrović MM, Devetaković M, Ivanović J. Modeling of focal-directorial surfaces for application in architecture. in FME Transactions. 2017;45(2):294-300. doi:10.5937/fmet1702294P .
Petruševski, Ljiljana, Petrović, Maja M., Devetaković, Mirjana, Ivanović, Jelena, "Modeling of focal-directorial surfaces for application in architecture" in FME Transactions, 45, no. 2 (2017):294-300, https://doi.org/10.5937/fmet1702294P . .