TY  - 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 . .

TY  - JOUR
AU  - Vukmirovic, Srdjan
AU  - Devetakovic, Mirjana
AU  - Petrusevski, Ljiljana
PY  - 2012
UR  - https://raf.arh.bg.ac.rs/handle/123456789/129
AB  - This paper resulted from collaboration between two faculties of Belgrade University-Faculty of Mathematics, Department of Geometry, and the Faculty of Architecture, the Chair of Mathematics, Architectural Geometry and CAAD. In this case, the efforts of the two institutions have been focused on introducing topology as a quite complex and rarely covered topic, to a specific audience-the first year students of architecture. The paper gives an overview of a two-hours lecture and a workshop that has been carefully prepared and discussed by a multidisciplinary teaching team, illustrated with appropriate modelled and animated examples, photo-documented (in the workshop part), and video-recorded (a streaming video of this event is available). The Lecture and workshop followed by a series of two small "research by design" tasks for the students-the first to examine architectonics of discretized Möbius strip, and the second to model a spatial form varying the genus of a selected surface. In the conclusion part we give the selected examples of students' design work.
T2  - Pollack Periodica
T1  - Topology-Possibilities of application in architectural geometry
VL  - 7
IS  - SUPPL. 1
SP  - 29
EP  - 42
DO  - 10.1556/Pollack.7.2012.S.3
ER  - 

@article{
author = "Vukmirovic, Srdjan and Devetakovic, Mirjana and Petrusevski, Ljiljana",
year = "2012",
abstract = "This paper resulted from collaboration between two faculties of Belgrade University-Faculty of Mathematics, Department of Geometry, and the Faculty of Architecture, the Chair of Mathematics, Architectural Geometry and CAAD. In this case, the efforts of the two institutions have been focused on introducing topology as a quite complex and rarely covered topic, to a specific audience-the first year students of architecture. The paper gives an overview of a two-hours lecture and a workshop that has been carefully prepared and discussed by a multidisciplinary teaching team, illustrated with appropriate modelled and animated examples, photo-documented (in the workshop part), and video-recorded (a streaming video of this event is available). The Lecture and workshop followed by a series of two small "research by design" tasks for the students-the first to examine architectonics of discretized Möbius strip, and the second to model a spatial form varying the genus of a selected surface. In the conclusion part we give the selected examples of students' design work.",
journal = "Pollack Periodica",
title = "Topology-Possibilities of application in architectural geometry",
volume = "7",
number = "SUPPL. 1",
pages = "29-42",
doi = "10.1556/Pollack.7.2012.S.3"
}

Vukmirovic, S., Devetakovic, M.,& Petrusevski, L.. (2012). Topology-Possibilities of application in architectural geometry. in Pollack Periodica, 7(SUPPL. 1), 29-42.
https://doi.org/10.1556/Pollack.7.2012.S.3

Vukmirovic S, Devetakovic M, Petrusevski L. Topology-Possibilities of application in architectural geometry. in Pollack Periodica. 2012;7(SUPPL. 1):29-42.
doi:10.1556/Pollack.7.2012.S.3 .

Vukmirovic, Srdjan, Devetakovic, Mirjana, Petrusevski, Ljiljana, "Topology-Possibilities of application in architectural geometry" in Pollack Periodica, 7, no. SUPPL. 1 (2012):29-42,
https://doi.org/10.1556/Pollack.7.2012.S.3 . .

TY  - JOUR
AU  - Petruševski, Ljiljana
AU  - Devetaković, Mirjana
AU  - Mitrović, Bojan
AU  - Dabić, Milana
PY  - 2010
UR  - https://raf.arh.bg.ac.rs/handle/123456789/80
AB  - The concept of L-Systems was created as base for axiomatic theory of biologic growth. L-systems are applied in computer graphics for fractal generation, as well as in models of biological structures and simulations of their growth. Within generic architecture, by applying L-systems, the natural growth mechanisms are used as generators of architectural geometry. After mathematical and logical explanations of the chosen generic concept of L-systems, this study examines its generic potential, which is the base for development of specific explorative tools in the field of architectural geometry. Within a wider research activity titled 'Generic Explorations', the original software parametric tools have been developed, allowing generation of a complex architectural geometry based on the concept of L-systems. Variation of parametric values facilitates creation and further exploration of generated spatial forms. The paper presents possibilities of developed explorative tools, their particularities, as well as an overview of their initial application results.
AB  - Koncept L-sistema nastao je kao osnova za aksiomatski zasnovanu teoriju biološkog razvoja. Svoje prve neposredne primene L-sistemi nalaze u okviru kompjuterske grafike za generisanje fraktala i u okviru vizuelnih realnih modela bioloških struktura i simulacije njihovog razvoja. U okviru generičke arhitekture, primenom L-sistema, mehanizmi procesa rasta u prirodi koriste se kao generatori arhitektonske geometrije. Posle matematičkih i logičkih objašnjenja generičkog koncepta L-sistema, u radu je razmotren generički potencijal, što zajedno predstavlja osnovu za razvoj eksplorativnih alata u oblasti arhitektonske geometrije zasnovane na konceptu L-sistema. U okviru šire istraživačke aktivnosti pod nazivom 'Generička istraživanja' razvijeni su originalni softverski parametarski eksplorativni alati koji omogućavaju generisanje kompleksne arhitektonske geometrije zasnovane na konceptu L-sistema. Varijacija parametarskih vrednosti omogućava istraživanje prostornih formi koje nastaju na osnovu ovog generičkog koncepta. U radu su prikazane mogućnosti razvijenih eksplorativnih alata, njihove specifičnosti i uzajamne razlike, i dat je osvrt na rezultate njihove primene.
PB  - Institut za arhitekturu i urbanizam Srbije, Beograd
T2  - Arhitektura i urbanizam
T1  - Development and application of explorative tools in the field of architectural geometry: L-systems
T1  - Razvoj i primena eksplorativnih alata u oblasti arhitektonske geometrije - L-sistemi
IS  - 28
SP  - 38
EP  - 45
UR  - https://hdl.handle.net/21.15107/rcub_raf_80
ER  - 

@article{
author = "Petruševski, Ljiljana and Devetaković, Mirjana and Mitrović, Bojan and Dabić, Milana",
year = "2010",
abstract = "The concept of L-Systems was created as base for axiomatic theory of biologic growth. L-systems are applied in computer graphics for fractal generation, as well as in models of biological structures and simulations of their growth. Within generic architecture, by applying L-systems, the natural growth mechanisms are used as generators of architectural geometry. After mathematical and logical explanations of the chosen generic concept of L-systems, this study examines its generic potential, which is the base for development of specific explorative tools in the field of architectural geometry. Within a wider research activity titled 'Generic Explorations', the original software parametric tools have been developed, allowing generation of a complex architectural geometry based on the concept of L-systems. Variation of parametric values facilitates creation and further exploration of generated spatial forms. The paper presents possibilities of developed explorative tools, their particularities, as well as an overview of their initial application results., Koncept L-sistema nastao je kao osnova za aksiomatski zasnovanu teoriju biološkog razvoja. Svoje prve neposredne primene L-sistemi nalaze u okviru kompjuterske grafike za generisanje fraktala i u okviru vizuelnih realnih modela bioloških struktura i simulacije njihovog razvoja. U okviru generičke arhitekture, primenom L-sistema, mehanizmi procesa rasta u prirodi koriste se kao generatori arhitektonske geometrije. Posle matematičkih i logičkih objašnjenja generičkog koncepta L-sistema, u radu je razmotren generički potencijal, što zajedno predstavlja osnovu za razvoj eksplorativnih alata u oblasti arhitektonske geometrije zasnovane na konceptu L-sistema. U okviru šire istraživačke aktivnosti pod nazivom 'Generička istraživanja' razvijeni su originalni softverski parametarski eksplorativni alati koji omogućavaju generisanje kompleksne arhitektonske geometrije zasnovane na konceptu L-sistema. Varijacija parametarskih vrednosti omogućava istraživanje prostornih formi koje nastaju na osnovu ovog generičkog koncepta. U radu su prikazane mogućnosti razvijenih eksplorativnih alata, njihove specifičnosti i uzajamne razlike, i dat je osvrt na rezultate njihove primene.",
publisher = "Institut za arhitekturu i urbanizam Srbije, Beograd",
journal = "Arhitektura i urbanizam",
title = "Development and application of explorative tools in the field of architectural geometry: L-systems, Razvoj i primena eksplorativnih alata u oblasti arhitektonske geometrije - L-sistemi",
number = "28",
pages = "38-45",
url = "https://hdl.handle.net/21.15107/rcub_raf_80"
}

Petruševski, L., Devetaković, M., Mitrović, B.,& Dabić, M.. (2010). Development and application of explorative tools in the field of architectural geometry: L-systems. in Arhitektura i urbanizam
Institut za arhitekturu i urbanizam Srbije, Beograd.(28), 38-45.
https://hdl.handle.net/21.15107/rcub_raf_80

Petruševski L, Devetaković M, Mitrović B, Dabić M. Development and application of explorative tools in the field of architectural geometry: L-systems. in Arhitektura i urbanizam. 2010;(28):38-45.
https://hdl.handle.net/21.15107/rcub_raf_80 .

Petruševski, Ljiljana, Devetaković, Mirjana, Mitrović, Bojan, Dabić, Milana, "Development and application of explorative tools in the field of architectural geometry: L-systems" in Arhitektura i urbanizam, no. 28 (2010):38-45,
https://hdl.handle.net/21.15107/rcub_raf_80 .

TY  - JOUR
AU  - Petruševski, Ljiljana
AU  - Dabić, Milana
AU  - Devetaković, Mirjana
PY  - 2010
UR  - https://raf.arh.bg.ac.rs/handle/123456789/75
AB  - Through their work in the field of generic explorations, authors of this paper have developed a series of demonstration projects, based on the software package MATHEMATICA, related to the parametric representation of curves and surfaces in space. The main purpose of the demonstrations is exploration of generic potential of curves and surfaces in order to apply it to the process of generating architectural form. The paper presents the developed demonstration projects and their application within the generic explorations of architectural form.
PB  - Institut za arhitekturu i urbanizam Srbije, Beograd
T2  - Spatium
T1  - Parametric curves and surfaces: Mathematica demonstrations as a tool in exploration of architectural form
IS  - 22
SP  - 67
EP  - 72
DO  - 10.2298/SPAT1022067P
ER  - 

@article{
author = "Petruševski, Ljiljana and Dabić, Milana and Devetaković, Mirjana",
year = "2010",
abstract = "Through their work in the field of generic explorations, authors of this paper have developed a series of demonstration projects, based on the software package MATHEMATICA, related to the parametric representation of curves and surfaces in space. The main purpose of the demonstrations is exploration of generic potential of curves and surfaces in order to apply it to the process of generating architectural form. The paper presents the developed demonstration projects and their application within the generic explorations of architectural form.",
publisher = "Institut za arhitekturu i urbanizam Srbije, Beograd",
journal = "Spatium",
title = "Parametric curves and surfaces: Mathematica demonstrations as a tool in exploration of architectural form",
number = "22",
pages = "67-72",
doi = "10.2298/SPAT1022067P"
}

Petruševski, L., Dabić, M.,& Devetaković, M.. (2010). Parametric curves and surfaces: Mathematica demonstrations as a tool in exploration of architectural form. in Spatium
Institut za arhitekturu i urbanizam Srbije, Beograd.(22), 67-72.
https://doi.org/10.2298/SPAT1022067P

Petruševski L, Dabić M, Devetaković M. Parametric curves and surfaces: Mathematica demonstrations as a tool in exploration of architectural form. in Spatium. 2010;(22):67-72.
doi:10.2298/SPAT1022067P .

Petruševski, Ljiljana, Dabić, Milana, Devetaković, Mirjana, "Parametric curves and surfaces: Mathematica demonstrations as a tool in exploration of architectural form" in Spatium, no. 22 (2010):67-72,
https://doi.org/10.2298/SPAT1022067P . .

TY  - JOUR
AU  - Petruševski, Ljiljana
AU  - Devetaković, Mirjana
AU  - Mitrović, Bojan
PY  - 2009
UR  - https://raf.arh.bg.ac.rs/handle/123456789/53
AB  - The self-replicating systems introduced theoretically by von Neumann, are widely examined in biology, computing, geometry, engineering sciences etc. In this study the authors are focused on the concept of cellular automata (CA) and its possible application in processes of spatial form generation. The study has been realized with participation of 60 senior architecture students, creating various spatial forms by using the CA concept, within the series of elective courses titled Generic Explorations. The experimental activity is supported by the software Fun3D, i.e. its CA module, which has been created at the University of Belgrade, Faculty of Architecture, to support generative processes in the field of architecture. After introducing a general idea of the self-replicating systems, the authors explain the major principles of CA, particularly the issues of layered 2D automata, discussing possible approaches to spatial form creation. The study examines CA based on a cubic cell, evolving to a rectangular cuboid where width/height/length ratio can differ, as well as the gap between cells and some of the visual features, like color, transparency, texture etc. Creators of various spatial forms can set a pattern of initial cells, and define a rule for a self-reproduction of a single cell. Combinations of multiple CA systems have been introduced, as an entirely original approach to the problem of form generation in general. A variety of approaches to the generation of spatial form, resulted from the experimental activity, indicate a significant potential of the CA concept application in many areas of spatial design. The authors suggest a range of interpretations of a resulted generic form, such as architectural, urban, product design, exhibition systems etc.
PB  - Institut za arhitekturu i urbanizam Srbije, Beograd
T2  - Spatium
T1  - Self-replicating systems in spatial form generation: The concept of cellular automata
IS  - 19
SP  - 8
EP  - 14
DO  - 10.2298/SPAT0919008P
ER  - 

@article{
author = "Petruševski, Ljiljana and Devetaković, Mirjana and Mitrović, Bojan",
year = "2009",
abstract = "The self-replicating systems introduced theoretically by von Neumann, are widely examined in biology, computing, geometry, engineering sciences etc. In this study the authors are focused on the concept of cellular automata (CA) and its possible application in processes of spatial form generation. The study has been realized with participation of 60 senior architecture students, creating various spatial forms by using the CA concept, within the series of elective courses titled Generic Explorations. The experimental activity is supported by the software Fun3D, i.e. its CA module, which has been created at the University of Belgrade, Faculty of Architecture, to support generative processes in the field of architecture. After introducing a general idea of the self-replicating systems, the authors explain the major principles of CA, particularly the issues of layered 2D automata, discussing possible approaches to spatial form creation. The study examines CA based on a cubic cell, evolving to a rectangular cuboid where width/height/length ratio can differ, as well as the gap between cells and some of the visual features, like color, transparency, texture etc. Creators of various spatial forms can set a pattern of initial cells, and define a rule for a self-reproduction of a single cell. Combinations of multiple CA systems have been introduced, as an entirely original approach to the problem of form generation in general. A variety of approaches to the generation of spatial form, resulted from the experimental activity, indicate a significant potential of the CA concept application in many areas of spatial design. The authors suggest a range of interpretations of a resulted generic form, such as architectural, urban, product design, exhibition systems etc.",
publisher = "Institut za arhitekturu i urbanizam Srbije, Beograd",
journal = "Spatium",
title = "Self-replicating systems in spatial form generation: The concept of cellular automata",
number = "19",
pages = "8-14",
doi = "10.2298/SPAT0919008P"
}

Petruševski, L., Devetaković, M.,& Mitrović, B.. (2009). Self-replicating systems in spatial form generation: The concept of cellular automata. in Spatium
Institut za arhitekturu i urbanizam Srbije, Beograd.(19), 8-14.
https://doi.org/10.2298/SPAT0919008P

Petruševski L, Devetaković M, Mitrović B. Self-replicating systems in spatial form generation: The concept of cellular automata. in Spatium. 2009;(19):8-14.
doi:10.2298/SPAT0919008P .

Petruševski, Ljiljana, Devetaković, Mirjana, Mitrović, Bojan, "Self-replicating systems in spatial form generation: The concept of cellular automata" in Spatium, no. 19 (2009):8-14,
https://doi.org/10.2298/SPAT0919008P . .