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.
Keywords:
Focal-directorial surfaces / Modeling / Parametric model / Surface discretization / 3D convex hull
Source:
Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia, 2016, 278-286
Publisher:
Belgrade : Serbian Society for Geometry and Graphics (SUGIG)
Belgrade : Faculty of Civil Engineering, University
TY - CONF
AU - Petrusevski, Ljiljana
AU - Petrovic, Maja
AU - Devetakovic, Mirjana
AU - Ivanovic, Jelena
PY - 2016
UR - https://raf.arh.bg.ac.rs/handle/123456789/1171
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.
PB - Belgrade : Serbian Society for Geometry and Graphics (SUGIG)
PB - Belgrade : Faculty of Civil Engineering, University
PB - Belgrade : Akademska misao
C3 - Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia
T1 - Modeling of Focal-Directorial Surfaces for Aplication in Architecture
SP - 278
EP - 286
UR - https://hdl.handle.net/21.15107/rcub_raf_1171
ER -
@conference{
author = "Petrusevski, Ljiljana and Petrovic, Maja and Devetakovic, Mirjana and Ivanovic, Jelena",
year = "2016",
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.",
publisher = "Belgrade : Serbian Society for Geometry and Graphics (SUGIG), Belgrade : Faculty of Civil Engineering, University, Belgrade : Akademska misao",
journal = "Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia",
title = "Modeling of Focal-Directorial Surfaces for Aplication in Architecture",
pages = "278-286",
url = "https://hdl.handle.net/21.15107/rcub_raf_1171"
}
Petrusevski, L., Petrovic, M., Devetakovic, M.,& Ivanovic, J.. (2016). Modeling of Focal-Directorial Surfaces for Aplication in Architecture. in Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia
Belgrade : Serbian Society for Geometry and Graphics (SUGIG)., 278-286.
https://hdl.handle.net/21.15107/rcub_raf_1171
Petrusevski L, Petrovic M, Devetakovic M, Ivanovic J. Modeling of Focal-Directorial Surfaces for Aplication in Architecture. in Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia. 2016;:278-286.
https://hdl.handle.net/21.15107/rcub_raf_1171 .
Petrusevski, Ljiljana, Petrovic, Maja, Devetakovic, Mirjana, Ivanovic, Jelena, "Modeling of Focal-Directorial Surfaces for Aplication in Architecture" in Proceedings / The 5th International Scientific Conference on Geometry and Graphics moNGeometrija 2016, June 23th-26th 2016, Belgrade, Serbia (2016):278-286,
https://hdl.handle.net/21.15107/rcub_raf_1171 .
