TY  - CONF
AU  - Obradović, Marija
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1945
AB  - The concave polyhedral surface of CC II can be used as a structural template for architectural design of domes, roofs or other covering or stand-alone structures. Subdivision of CC II faces in geometrically defined way can be observed as a part of the design process, if done with the intention to contribute to the aesthetic quality of the building itself. In this paper we discuss certain interventions on the tiled triangular faces of the CC II by regular triangles and hexagons, in order to get patterns applicable in architecture. By using different colors and / or materials of the tiles, we can get solutions that add the decorative layer to the structural one. Examining various solutions, this research focused on the D subdivision of the lateral polyhedral triangle (LPT) and in the resulting uniform tilings, searching for the ways to overcome monotony of highly symmetrical patterns. As opposed to exploring the ways of assembling the tiled LPTs with assigned layouts of tiles into shape of the CC II in order to get desired patterns on its surface, this paper explores the creation of various patterns within the existing, formerly obtained uniform tilings (2-uniform, trihexagonal tiling). A couple of conceptual solutions are given, as an illustration of the idea.
PB  - Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS
C3  - Journal of Industrial Design and Engineering Graphics (JIDEG)
T1  - Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture
EP  - 84
IS  - 1
SP  - 79
VL  - 14
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1945
ER  - 

@conference{
author = "Obradović, Marija",
year = "2019",
abstract = "The concave polyhedral surface of CC II can be used as a structural template for architectural design of domes, roofs or other covering or stand-alone structures. Subdivision of CC II faces in geometrically defined way can be observed as a part of the design process, if done with the intention to contribute to the aesthetic quality of the building itself. In this paper we discuss certain interventions on the tiled triangular faces of the CC II by regular triangles and hexagons, in order to get patterns applicable in architecture. By using different colors and / or materials of the tiles, we can get solutions that add the decorative layer to the structural one. Examining various solutions, this research focused on the D subdivision of the lateral polyhedral triangle (LPT) and in the resulting uniform tilings, searching for the ways to overcome monotony of highly symmetrical patterns. As opposed to exploring the ways of assembling the tiled LPTs with assigned layouts of tiles into shape of the CC II in order to get desired patterns on its surface, this paper explores the creation of various patterns within the existing, formerly obtained uniform tilings (2-uniform, trihexagonal tiling). A couple of conceptual solutions are given, as an illustration of the idea.",
publisher = "Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS",
journal = "Journal of Industrial Design and Engineering Graphics (JIDEG)",
title = "Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture",
pages = "84-79",
number = "1",
volume = "14",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1945"
}

Obradović, M.. (2019). Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture. in Journal of Industrial Design and Engineering Graphics (JIDEG)
Bucharest, Romania: SORGING–ROMANIAN SOCIETYFORENGINEERINGGRAPHICS., 14(1), 79-84.
https://hdl.handle.net/21.15107/rcub_grafar_1945

Obradović M. Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture. in Journal of Industrial Design and Engineering Graphics (JIDEG). 2019;14(1):79-84.
https://hdl.handle.net/21.15107/rcub_grafar_1945 .

Obradović, Marija, "Geometric Redesign of the Subdivided Surface of CC II: Application In Architecture" in Journal of Industrial Design and Engineering Graphics (JIDEG), 14, no. 1 (2019):79-84,
https://hdl.handle.net/21.15107/rcub_grafar_1945 .

TY  - CONF
AU  - Obradović, Marija
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1944
AB  - The aim of this research is to examine and outline modularity of the selected representatives of concave pol yhedra of the second sort (C II), from the point of view of their high combinatorial potential for creating diverse polyhedral structures, some of which can be applied
in architectural design. The modularity is primarily attributed to the regular pol ygonal bases around which the solids are created. There are three basic groups of concave pol yhedra of the second sort: concave cupolae (CC II), concave pyramids (CP II) and concave antiprisms (CA.II). Since each of these groups contains the representatives with octagonal bases, they are chosen for this research, not only because of their compatibility, but also because of their accordance with the orthogonal matrix underlying the conventional modular grid, ubiquitous in architectural design. In this study, we examine the possibilities of modular conjoining of these
pol yhedra into new, composite structures, creating forms that can contribute to enrichment of architectural design expression, allowing easy execution at the same time.
PB  - Cham: Springer
C3  - Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics
T1  - Modularity of concave polyhedra of the second sort with octagonal bases
EP  - 954
SP  - 942
VL  - 809
DO  - 10.1007/978-3-319-95588-9_81
ER  - 

@conference{
author = "Obradović, Marija",
year = "2019",
abstract = "The aim of this research is to examine and outline modularity of the selected representatives of concave pol yhedra of the second sort (C II), from the point of view of their high combinatorial potential for creating diverse polyhedral structures, some of which can be applied
in architectural design. The modularity is primarily attributed to the regular pol ygonal bases around which the solids are created. There are three basic groups of concave pol yhedra of the second sort: concave cupolae (CC II), concave pyramids (CP II) and concave antiprisms (CA.II). Since each of these groups contains the representatives with octagonal bases, they are chosen for this research, not only because of their compatibility, but also because of their accordance with the orthogonal matrix underlying the conventional modular grid, ubiquitous in architectural design. In this study, we examine the possibilities of modular conjoining of these
pol yhedra into new, composite structures, creating forms that can contribute to enrichment of architectural design expression, allowing easy execution at the same time.",
publisher = "Cham: Springer",
journal = "Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics",
title = "Modularity of concave polyhedra of the second sort with octagonal bases",
pages = "954-942",
volume = "809",
doi = "10.1007/978-3-319-95588-9_81"
}

Obradović, M.. (2019). Modularity of concave polyhedra of the second sort with octagonal bases. in Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics
Cham: Springer., 809, 942-954.
https://doi.org/10.1007/978-3-319-95588-9_81

Obradović M. Modularity of concave polyhedra of the second sort with octagonal bases. in Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics. 2019;809:942-954.
doi:10.1007/978-3-319-95588-9_81 .

Obradović, Marija, "Modularity of concave polyhedra of the second sort with octagonal bases" in Advances in Intelligent Systems and Computing, ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics, 809 (2019):942-954,
https://doi.org/10.1007/978-3-319-95588-9_81 . .

TY  - JOUR
AU  - Marković, Srđan
AU  - Obradović, Marija
AU  - Demetriades, Alexandros
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1004
AB  - We are facing a number of applications for altering portrait photographs using the help of artificial intelligence. Apart from the entertainment purposes, modern computer technologies can also help us get dynamic effects from static images, an example of which is the subject of this study. Dealing with the change of lighting in portraits photographs through real-time rendering, this paper provides a method of obtaining an image with variable light source that affects the facial features generated on the basis of the face tracking data acquired from the existing static photograph. Thus, we get a portrait with altered light, as if such a source was present at the actual moment of photographing. This method aims to improve or even change the visual experience when viewing the image, so that its further application corresponds to the given context.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Interactive change of lighting in the portrait images
EP  - 330
IS  - 2
SP  - 326
VL  - 47
DO  - 10.5937/fmet1902326M
ER  - 

@article{
author = "Marković, Srđan and Obradović, Marija and Demetriades, Alexandros",
year = "2019",
abstract = "We are facing a number of applications for altering portrait photographs using the help of artificial intelligence. Apart from the entertainment purposes, modern computer technologies can also help us get dynamic effects from static images, an example of which is the subject of this study. Dealing with the change of lighting in portraits photographs through real-time rendering, this paper provides a method of obtaining an image with variable light source that affects the facial features generated on the basis of the face tracking data acquired from the existing static photograph. Thus, we get a portrait with altered light, as if such a source was present at the actual moment of photographing. This method aims to improve or even change the visual experience when viewing the image, so that its further application corresponds to the given context.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Interactive change of lighting in the portrait images",
pages = "330-326",
number = "2",
volume = "47",
doi = "10.5937/fmet1902326M"
}

Marković, S., Obradović, M.,& Demetriades, A.. (2019). Interactive change of lighting in the portrait images. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 47(2), 326-330.
https://doi.org/10.5937/fmet1902326M

Marković S, Obradović M, Demetriades A. Interactive change of lighting in the portrait images. in FME Transactions. 2019;47(2):326-330.
doi:10.5937/fmet1902326M .

Marković, Srđan, Obradović, Marija, Demetriades, Alexandros, "Interactive change of lighting in the portrait images" in FME Transactions, 47, no. 2 (2019):326-330,
https://doi.org/10.5937/fmet1902326M . .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1981
AB  - Concave polyhedra of the second sort (abbreviated: C-II-n) constitute a group of polyhedra formed over regular n-sided base polygons and having a deltahedral lateral surfaces. This group includes: concave cupolae, concave pyramids and concave antiprisms of the second sort (CC-II-n, CP-II-n and CA-II-n, respectively). The common feature of these solids is that their lateral surfaces consist of a double row of equilateral triangles which can be assembled in two ways, making two different solids’ heights: major (C-II-nM) and minor (C-II-nm). The geometrical regularities and a high level of symmetry that characterizes these polyhedra, makes them suitable for joining and combining, so they can be arrayed infinitely in space, in x, y and z direction forming 3D lattice structures. For some representatives of these solids, the congruity of their lateral deltahedral surfaces occurs, so 3D tessellations are formed. 
In this paper, we focus on a single "layer" of such a structure, a panel-like 3D lattice. It is generated by multiplication of the chosen unit cell – the selected C-II-n representative – along the x-y directions. In the z direction the lateral surfaces form a deltahedral structure which makes the thickness of the panel. 
The method we used is based on the continuous connection of the edges of the two adjacent units, by joining relevant vertices. When we remove the base polygons, the unit cells become hollow, so they can create a honeycombed structure, more desirable for the purpose of application. Then, observed in 2D, by applying symmetry transformations, we form patterns similarly to the formation of wallpaper groups. In this way, we get visually interesting patterns in 2D, which transform into 3D lattice depending on the viewing angle. 
The thickness of the panel can be halved in some cases, so we get a thinner structure with "face" and "back", having different tessellations of polygons appearing on them. As an artistic intervention, these panels can be modified by joining deltahedral surfaces of other C-II-n onto the compatible faces, whereby we add another layer of patterns to the resulting structure. 
3D patterns and lattices are currently experiencing real boom in the design and industry, thanks to the 3D printing capabilities. As for architecture, they can be applied not only as an element of ornamentation, but also as a functional component of the project, especially concerning climate responsive facades.   
Due to the simplicity of the geometry of C-II-n, such 3D structures are feasible and easy to perform in terms of production and assembly. They are achievable not only with 3D printing, but can also be manually assembled or folded like origami, which allows the use of a much wider range of materials.
PB  - Beograd: Fakultet primenjenih umetnosti, Univerzitet umetnosti u Beogradu, Srbija
C3  - Smart Art Knjiga apstrakata / Book of abstracts
T1  - 3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments
EP  - 88
SP  - 87
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1981
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2019",
abstract = "Concave polyhedra of the second sort (abbreviated: C-II-n) constitute a group of polyhedra formed over regular n-sided base polygons and having a deltahedral lateral surfaces. This group includes: concave cupolae, concave pyramids and concave antiprisms of the second sort (CC-II-n, CP-II-n and CA-II-n, respectively). The common feature of these solids is that their lateral surfaces consist of a double row of equilateral triangles which can be assembled in two ways, making two different solids’ heights: major (C-II-nM) and minor (C-II-nm). The geometrical regularities and a high level of symmetry that characterizes these polyhedra, makes them suitable for joining and combining, so they can be arrayed infinitely in space, in x, y and z direction forming 3D lattice structures. For some representatives of these solids, the congruity of their lateral deltahedral surfaces occurs, so 3D tessellations are formed. 
In this paper, we focus on a single "layer" of such a structure, a panel-like 3D lattice. It is generated by multiplication of the chosen unit cell – the selected C-II-n representative – along the x-y directions. In the z direction the lateral surfaces form a deltahedral structure which makes the thickness of the panel. 
The method we used is based on the continuous connection of the edges of the two adjacent units, by joining relevant vertices. When we remove the base polygons, the unit cells become hollow, so they can create a honeycombed structure, more desirable for the purpose of application. Then, observed in 2D, by applying symmetry transformations, we form patterns similarly to the formation of wallpaper groups. In this way, we get visually interesting patterns in 2D, which transform into 3D lattice depending on the viewing angle. 
The thickness of the panel can be halved in some cases, so we get a thinner structure with "face" and "back", having different tessellations of polygons appearing on them. As an artistic intervention, these panels can be modified by joining deltahedral surfaces of other C-II-n onto the compatible faces, whereby we add another layer of patterns to the resulting structure. 
3D patterns and lattices are currently experiencing real boom in the design and industry, thanks to the 3D printing capabilities. As for architecture, they can be applied not only as an element of ornamentation, but also as a functional component of the project, especially concerning climate responsive facades.   
Due to the simplicity of the geometry of C-II-n, such 3D structures are feasible and easy to perform in terms of production and assembly. They are achievable not only with 3D printing, but can also be manually assembled or folded like origami, which allows the use of a much wider range of materials.",
publisher = "Beograd: Fakultet primenjenih umetnosti, Univerzitet umetnosti u Beogradu, Srbija",
journal = "Smart Art Knjiga apstrakata / Book of abstracts",
title = "3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments",
pages = "88-87",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1981"
}

Obradović, M.,& Mišić, S.. (2019). 3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments. in Smart Art Knjiga apstrakata / Book of abstracts
Beograd: Fakultet primenjenih umetnosti, Univerzitet umetnosti u Beogradu, Srbija., 87-88.
https://hdl.handle.net/21.15107/rcub_grafar_1981

Obradović M, Mišić S. 3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments. in Smart Art Knjiga apstrakata / Book of abstracts. 2019;:87-88.
https://hdl.handle.net/21.15107/rcub_grafar_1981 .

Obradović, Marija, Mišić, Slobodan, "3D lattice panels based on the concave polyhedra of the second sort: ideas for architectural ornaments" in Smart Art Knjiga apstrakata / Book of abstracts (2019):87-88,
https://hdl.handle.net/21.15107/rcub_grafar_1981 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1982
AB  - We have shown that there is a link between the geometry of the CA II-nM’s  with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given  CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s  with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research.
PB  - Porto: Aproged - Associação dos Professores de Geometria e de Desenho
C3  - GEOMETRIAS’19: BOOK OF ABSTRACTS
T1  - Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort
SP  - 85
VL  - 89
DO  - 10.24840/978-989-98926-8-2
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2019",
abstract = "We have shown that there is a link between the geometry of the CA II-nM’s  with bases n∈{3, 4, 5} and that of the convex antiprisms with the same bases. An integer number (K) of CA II-nM’s fragments, can be used to form a full multilaterally symmetrical ring of concave deltahedral surfaces, either flower-like (case A) or star-like (case B). The obtained rings can also be termed “of the second sort” (denoted by CDR II-n) as they inherit from the given  CA II-nM the following: a) the linear and angular measurements needed for their graphic and mathematical elaboration, b) two rows of equilateral triangles in the lateral surface, and c) the high level of symmetry. The possible formation of CDR II-n’s  with the highest level of symmetry (i.e. excluding the cases A), and with the number of petals/star-points in which any integer K ≥ 2 can be a subject of further research.",
publisher = "Porto: Aproged - Associação dos Professores de Geometria e de Desenho",
journal = "GEOMETRIAS’19: BOOK OF ABSTRACTS",
title = "Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort",
pages = "85",
volume = "89",
doi = "10.24840/978-989-98926-8-2"
}

Obradović, M.,& Mišić, S.. (2019). Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort. in GEOMETRIAS’19: BOOK OF ABSTRACTS
Porto: Aproged - Associação dos Professores de Geometria e de Desenho., 89, 85.
https://doi.org/10.24840/978-989-98926-8-2

Obradović M, Mišić S. Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort. in GEOMETRIAS’19: BOOK OF ABSTRACTS. 2019;89:85.
doi:10.24840/978-989-98926-8-2 .

Obradović, Marija, Mišić, Slobodan, "Concave deltahedral rings based on the geometry of the concave antiprisms of the second sort" in GEOMETRIAS’19: BOOK OF ABSTRACTS, 89 (2019):85,
https://doi.org/10.24840/978-989-98926-8-2 . .

TY  - JOUR
AU  - Obradović, Marija
PY  - 2019
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/999
AB  - As architectural structures, concave cupolae of the second sort (CC II) are suitable for prefabrication, thanks to the uniformity of their elementsregular polygons. This paper discusses ways to subdivide the lateral polyhedral triangle (LPT) of CC II into new regular polygons, triangles and hexagons, which can then tile the whole deltahedral lateral surface, forming patterns applicable in architectural design. The number of different arrangements of triangles and hexagons depends on the number of unit hexagonal cells (tiles) that can be placed within the triangular grid of the equilateral triangle. Considering solutions that involve fragments of k-uniform Euclidean tilings, we explored the ones that arise when the edges of the LPT are subdivided into 3b9 (bN) segments. Without attempting to analyse all the possible cases, we focused on the ones with the D-3 symmetry, in order to propose the simplest solutions for the assembly, so it will not matter if the face of the CC II is rotated or flipped. This results in 30 different solutions, excluding the ones consisting of triangles alone. The solutions found are applicable to all the representatives of CC II. We chose several examples of these results for an architectural design proposal.
PB  - Birkhauser Verlag AG
T2  - Nexus Network Journal
T1  - Tiling the Lateral Surface of the Concave Cupolae of the Second Sort
EP  - 77
IS  - 1
SP  - 59
VL  - 21
DO  - 10.1007/s00004-018-0417-5
ER  - 

@article{
author = "Obradović, Marija",
year = "2019",
abstract = "As architectural structures, concave cupolae of the second sort (CC II) are suitable for prefabrication, thanks to the uniformity of their elementsregular polygons. This paper discusses ways to subdivide the lateral polyhedral triangle (LPT) of CC II into new regular polygons, triangles and hexagons, which can then tile the whole deltahedral lateral surface, forming patterns applicable in architectural design. The number of different arrangements of triangles and hexagons depends on the number of unit hexagonal cells (tiles) that can be placed within the triangular grid of the equilateral triangle. Considering solutions that involve fragments of k-uniform Euclidean tilings, we explored the ones that arise when the edges of the LPT are subdivided into 3b9 (bN) segments. Without attempting to analyse all the possible cases, we focused on the ones with the D-3 symmetry, in order to propose the simplest solutions for the assembly, so it will not matter if the face of the CC II is rotated or flipped. This results in 30 different solutions, excluding the ones consisting of triangles alone. The solutions found are applicable to all the representatives of CC II. We chose several examples of these results for an architectural design proposal.",
publisher = "Birkhauser Verlag AG",
journal = "Nexus Network Journal",
title = "Tiling the Lateral Surface of the Concave Cupolae of the Second Sort",
pages = "77-59",
number = "1",
volume = "21",
doi = "10.1007/s00004-018-0417-5"
}

Obradović, M.. (2019). Tiling the Lateral Surface of the Concave Cupolae of the Second Sort. in Nexus Network Journal
Birkhauser Verlag AG., 21(1), 59-77.
https://doi.org/10.1007/s00004-018-0417-5

Obradović M. Tiling the Lateral Surface of the Concave Cupolae of the Second Sort. in Nexus Network Journal. 2019;21(1):59-77.
doi:10.1007/s00004-018-0417-5 .

Obradović, Marija, "Tiling the Lateral Surface of the Concave Cupolae of the Second Sort" in Nexus Network Journal, 21, no. 1 (2019):59-77,
https://doi.org/10.1007/s00004-018-0417-5 . .

TY  - CONF
AU  - Obradović, Marija
AU  - Grujić, Tatjana
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1943
AB  - In this paper we examine the link between the human body and architectural design. For this purpose, we combine Cognitive Metaphor Theory (CMT) and geometry. We start from the hypothesis that the organization of space and the positions of stairs within the building floor plan is the result of the embodiment of human mind, which implies that abstract aspects of human thought are grounded in physical aspects of human body. CMT claims that BALANCE is a prototypical schema consisting of countervailing forces acting on a target. This mental structure arises from living in symmetrical bodies
which are able to balance two equal halves and maintain erect posture. Having established the metaphorical mapping between the building and the human body (and, consequently, between the stairs and human spine) we examined the position of stairs in the building. We geometrically analyzed floor plans of a set of buildings applying the theoretical framework of Projective geometry and methods of Computational geometry. Our findings reveal that stairwells tend to stretch along the line which divides the building basis in two equal halves.
PB  - Novi Sad:Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Conference Proceedings „MONGEOMETRIJA 2018"
T1  - Geometry behind the position of stairs: balance in the mind
EP  - 168
SP  - 156
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1943
ER  - 

@conference{
author = "Obradović, Marija and Grujić, Tatjana",
year = "2018",
abstract = "In this paper we examine the link between the human body and architectural design. For this purpose, we combine Cognitive Metaphor Theory (CMT) and geometry. We start from the hypothesis that the organization of space and the positions of stairs within the building floor plan is the result of the embodiment of human mind, which implies that abstract aspects of human thought are grounded in physical aspects of human body. CMT claims that BALANCE is a prototypical schema consisting of countervailing forces acting on a target. This mental structure arises from living in symmetrical bodies
which are able to balance two equal halves and maintain erect posture. Having established the metaphorical mapping between the building and the human body (and, consequently, between the stairs and human spine) we examined the position of stairs in the building. We geometrically analyzed floor plans of a set of buildings applying the theoretical framework of Projective geometry and methods of Computational geometry. Our findings reveal that stairwells tend to stretch along the line which divides the building basis in two equal halves.",
publisher = "Novi Sad:Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Conference Proceedings „MONGEOMETRIJA 2018"",
title = "Geometry behind the position of stairs: balance in the mind",
pages = "168-156",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1943"
}

Obradović, M.,& Grujić, T.. (2018). Geometry behind the position of stairs: balance in the mind. in Conference Proceedings „MONGEOMETRIJA 2018"
Novi Sad:Faculty of Technical Sciences, University of Novi Sad., 156-168.
https://hdl.handle.net/21.15107/rcub_grafar_1943

Obradović M, Grujić T. Geometry behind the position of stairs: balance in the mind. in Conference Proceedings „MONGEOMETRIJA 2018". 2018;:156-168.
https://hdl.handle.net/21.15107/rcub_grafar_1943 .

Obradović, Marija, Grujić, Tatjana, "Geometry behind the position of stairs: balance in the mind" in Conference Proceedings „MONGEOMETRIJA 2018" (2018):156-168,
https://hdl.handle.net/21.15107/rcub_grafar_1943 .

TY  - GEN
AU  - Marković, Srđan
AU  - Obradović, Marija
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1979
AB  - The idea for this design came from investigation of forms created as “time imprint” of moving 2D and 3D objects through space, while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains “frozen” in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole.
The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the object’s random transformations in 3D space. The transformations are randomly generated and controlled by noise function. 
In order to examine the possibilities of such a creating of spatial forms for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes).
PB  - Novi Sad: Digital Design Center / Department of Architecture / Faculty of Technical Sciences, University of Novi Sad
PB  - Beograd: Serbian Society for Geometry and Graphics (SUGIG)
T2  - Digital design exhibition “Designing Complexity 2018”
T1  - Spatial forms create by time extrusion of moving objects
SP  - 26
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1979
ER  - 

@misc{
author = "Marković, Srđan and Obradović, Marija",
year = "2018",
abstract = "The idea for this design came from investigation of forms created as “time imprint” of moving 2D and 3D objects through space, while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains “frozen” in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole.
The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the object’s random transformations in 3D space. The transformations are randomly generated and controlled by noise function. 
In order to examine the possibilities of such a creating of spatial forms for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes).",
publisher = "Novi Sad: Digital Design Center / Department of Architecture / Faculty of Technical Sciences, University of Novi Sad, Beograd: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Digital design exhibition “Designing Complexity 2018”",
title = "Spatial forms create by time extrusion of moving objects",
pages = "26",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1979"
}

Marković, S.,& Obradović, M.. (2018). Spatial forms create by time extrusion of moving objects. in Digital design exhibition “Designing Complexity 2018”
Novi Sad: Digital Design Center / Department of Architecture / Faculty of Technical Sciences, University of Novi Sad., 26.
https://hdl.handle.net/21.15107/rcub_grafar_1979

Marković S, Obradović M. Spatial forms create by time extrusion of moving objects. in Digital design exhibition “Designing Complexity 2018”. 2018;:26.
https://hdl.handle.net/21.15107/rcub_grafar_1979 .

Marković, Srđan, Obradović, Marija, "Spatial forms create by time extrusion of moving objects" in Digital design exhibition “Designing Complexity 2018” (2018):26,
https://hdl.handle.net/21.15107/rcub_grafar_1979 .

TY  - CONF
AU  - Obradović, Marija
AU  - Marković, Srđan
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1512
AB  - The idea behind this paper is to investigate forms created as time imprint of moving 2D and 3D objects through space while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains frozen in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole. The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the objects random transformations in 3D space. The transformations are randomly generated and controlled by noise function. In order to examine the possibilities of such a creating of 3D shapes for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes). We also explore what kind of "time imprint" in space leaves the chosen starting figure in a free movement, i.e. for a non-geometric path, but also randomly generated one. The given modelling method provides simple and quick, but very intriguing options for creating a wide range of shapes that can be used in various areas of art and design: from graphic design, to a novel way of sculptural and even architectural design. These forms may convincingly represent natural and bionic forms, e.g. hair strands, vegetation growth, etc. The possibility of 3D printing enables the physical materialization of these shapes, suitable for further processing and use for decorative purposes, such as architectural ornaments or jewellery. As an integral part of the research, we include animation which shows the method of generating shapes in the described manner
PB  - Domus Argenia Publisher,
C3  - Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings
T1  - Creating 3D shapes by time extrusion of moving objects
EP  - 238
SP  - 225
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1512
ER  - 

@conference{
author = "Obradović, Marija and Marković, Srđan",
year = "2017",
abstract = "The idea behind this paper is to investigate forms created as time imprint of moving 2D and 3D objects through space while simultaneously changing their transformations: translation, rotation, scaling, etc. The movement develops along a path that can be either assigned or random. In this manner, the movement, only possible with the time component, remains frozen in the form of a solid model. Hence, we may assume time as a modelling tool, which connects and unites successive movements of an object into a whole. The procedure in question is visualized with Blender 3D animation and modeling tools. The render examples visualise time based extrusion of the objects random transformations in 3D space. The transformations are randomly generated and controlled by noise function. In order to examine the possibilities of such a creating of 3D shapes for more interesting results, we start from a 2D figure (snow flake), via elementary 3D figure (cube), and then examine how the form is enriched by introducing more complex figures as generatrices, for example concave polyhedron (CbP II-8), or a group of objects. For the procedure itself, we adopt a path which can be the simplest one (straight line, circle), or more complex (with curves, angles or nodes). We also explore what kind of "time imprint" in space leaves the chosen starting figure in a free movement, i.e. for a non-geometric path, but also randomly generated one. The given modelling method provides simple and quick, but very intriguing options for creating a wide range of shapes that can be used in various areas of art and design: from graphic design, to a novel way of sculptural and even architectural design. These forms may convincingly represent natural and bionic forms, e.g. hair strands, vegetation growth, etc. The possibility of 3D printing enables the physical materialization of these shapes, suitable for further processing and use for decorative purposes, such as architectural ornaments or jewellery. As an integral part of the research, we include animation which shows the method of generating shapes in the described manner",
publisher = "Domus Argenia Publisher,",
journal = "Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings",
title = "Creating 3D shapes by time extrusion of moving objects",
pages = "238-225",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1512"
}

Obradović, M.,& Marković, S.. (2017). Creating 3D shapes by time extrusion of moving objects. in Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings
Domus Argenia Publisher,., 225-238.
https://hdl.handle.net/21.15107/rcub_grafar_1512

Obradović M, Marković S. Creating 3D shapes by time extrusion of moving objects. in Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings. 2017;:225-238.
https://hdl.handle.net/21.15107/rcub_grafar_1512 .

Obradović, Marija, Marković, Srđan, "Creating 3D shapes by time extrusion of moving objects" in Generative Art 2017: GA2017, XX International Conference Ravenna, 13, 14, 15 Dec. 2017 at Biblioteca Classense and MAR, Museum of Art: Proceedings (2017):225-238,
https://hdl.handle.net/21.15107/rcub_grafar_1512 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Stavrić, Milena
AU  - Wiltsche, Albert
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/890
AB  - The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of the CeP II segments (C̅P II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments C̅P II-10-A, as well as of C̅P II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner.
AB  - U radu se analizira mogućnost dobijanja složenih poliedarskih oblika kombinovanjem segmenata elongiranih konkavnih piramida druge vrste (CeP II-10, tip A i tip B). U prethodnim istraživanjima, CP II su detaljno obrađeni. Istražuje se dalji potencijal ovih poliedarskih površi, na primeru njihovog spajanja sa Arhimedovim telom, zarubljenim dodekaedrom čije se strane sastoje od dekagona i trouglova. Na dekagonalne strane ovog tela dodajemo podudarne poligone poliedarskih segmenata (C̅P II-10), čime dobijamo nove forme konkavnih kompozitnih poliedara, kao i mogućnost njihovog daljeg preklapanja u poliedarska jedinjenja.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron
T1  - Poliedarske forme nastale spajanjem omotača CP II-10 i zarubljenog dodekaedra
EP  - 261
IS  - 2
SP  - 256
VL  - 45
DO  - 10.5937/fmet1702256O
ER  - 

@article{
author = "Obradović, Marija and Stavrić, Milena and Wiltsche, Albert",
year = "2017",
abstract = "The paper analyzes the possibility of obtaining polyhedral shapes formed by combining polyhedral surfaces based on the segment surface of elongated concave pyramids of the second sort (CeP II-10, type A and type B). In previous research, CP II type A and CP II type B were elaborated in detail. In this paper we discuss further potential of these polyhedral surfaces, on the example of combining them with Archimedean solid - Truncated dodecahedron (U26). The faces of this solid consist of 12 decagons and 20 triangles. On the decagonal faces, decagonal polygons of the CeP II segments (C̅P II-10) can be added, which provides the new polyhedral composite forms that are, furthermore, concave deltahedra. There are considered possibilities of obtaining polyhedral shapes by combining sheet segments C̅P II-10-A, as well as of C̅P II-10-B with U26. Finally, a couple of new shape suggestions are given: compound polyhedra, obtained by intersection of paired composite concave polyhedra originated in the described manner., U radu se analizira mogućnost dobijanja složenih poliedarskih oblika kombinovanjem segmenata elongiranih konkavnih piramida druge vrste (CeP II-10, tip A i tip B). U prethodnim istraživanjima, CP II su detaljno obrađeni. Istražuje se dalji potencijal ovih poliedarskih površi, na primeru njihovog spajanja sa Arhimedovim telom, zarubljenim dodekaedrom čije se strane sastoje od dekagona i trouglova. Na dekagonalne strane ovog tela dodajemo podudarne poligone poliedarskih segmenata (C̅P II-10), čime dobijamo nove forme konkavnih kompozitnih poliedara, kao i mogućnost njihovog daljeg preklapanja u poliedarska jedinjenja.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron, Poliedarske forme nastale spajanjem omotača CP II-10 i zarubljenog dodekaedra",
pages = "261-256",
number = "2",
volume = "45",
doi = "10.5937/fmet1702256O"
}

Obradović, M., Stavrić, M.,& Wiltsche, A.. (2017). Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 45(2), 256-261.
https://doi.org/10.5937/fmet1702256O

Obradović M, Stavrić M, Wiltsche A. Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron. in FME Transactions. 2017;45(2):256-261.
doi:10.5937/fmet1702256O .

Obradović, Marija, Stavrić, Milena, Wiltsche, Albert, "Polyhedral forms obtained by combinig lateral sheet of CP II-10 and truncated dodecahedron" in FME Transactions, 45, no. 2 (2017):256-261,
https://doi.org/10.5937/fmet1702256O . .

TY  - JOUR
AU  - Mišić, Slobodan
AU  - Obradović, Marija
AU  - Đukanović, Gordana
PY  - 2015
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1036
AB  - In this paper, the geometry of concave cupolae has been the starting
point for the generation of composite polyhedral structures, usable as formative
patterns for architectural purposes. Obtained by linking paper folding geometry
with the geometry of polyhedra, concave cupolae are polyhedra that follow the
method of generating cupolae (Johnson’s solids: J3, J4 and J5); but we removed
the convexity criterion and omitted squares in the lateral surface. Instead of alter-
nating triangles and squares there are now two or more paired series of equilateral
triangles. The criterion of face regularity is respected, as well as the criterion of
multiple axial symmetry. The distribution of the triangles is based on strictly
determined and mathematically defined parameters, which allows the creation of
such structures in a way that qualifies them as an autonomous group of polyhedra
— concave cupolae of sorts II, IV, VI (2N). If we want to see these structures as
polyhedral surfaces (not as solids) connecting the concept of the cupola (dome) in
the architectural sense with the geometrical meaning of (concave) cupola, we re-
move the faces of the base polygons. Thus we get a deltahedral structure — a shell
made entirely from equilateral triangles, which is advantageous for the purpose
of prefabrication. Due to the congruence of the major 2n-sided bases of concave
cupolae of sort II with the minor bases of the corresponding concave cupolae of
sort IV, it is possible to combine these polyhedra in composite polyhedra. But
also their elongation with concave antiprisms of sort II or the augmentation with
concave pyramids of sort II could be performed. Based on the foregoing, we exam-
ine the possibilities of combining the considered polyhedra into unified composite
structures.
T2  - Journal for Geometry and Graphics
T1  - Composite Concave Cupolae as Geometric and Architectural Forms
EP  - 91
EP  - 
EP  - 
IS  - 1
SP  - 79
VL  - 19
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1036
ER  - 

@article{
author = "Mišić, Slobodan and Obradović, Marija and Đukanović, Gordana",
year = "2015",
abstract = "In this paper, the geometry of concave cupolae has been the starting
point for the generation of composite polyhedral structures, usable as formative
patterns for architectural purposes. Obtained by linking paper folding geometry
with the geometry of polyhedra, concave cupolae are polyhedra that follow the
method of generating cupolae (Johnson’s solids: J3, J4 and J5); but we removed
the convexity criterion and omitted squares in the lateral surface. Instead of alter-
nating triangles and squares there are now two or more paired series of equilateral
triangles. The criterion of face regularity is respected, as well as the criterion of
multiple axial symmetry. The distribution of the triangles is based on strictly
determined and mathematically defined parameters, which allows the creation of
such structures in a way that qualifies them as an autonomous group of polyhedra
— concave cupolae of sorts II, IV, VI (2N). If we want to see these structures as
polyhedral surfaces (not as solids) connecting the concept of the cupola (dome) in
the architectural sense with the geometrical meaning of (concave) cupola, we re-
move the faces of the base polygons. Thus we get a deltahedral structure — a shell
made entirely from equilateral triangles, which is advantageous for the purpose
of prefabrication. Due to the congruence of the major 2n-sided bases of concave
cupolae of sort II with the minor bases of the corresponding concave cupolae of
sort IV, it is possible to combine these polyhedra in composite polyhedra. But
also their elongation with concave antiprisms of sort II or the augmentation with
concave pyramids of sort II could be performed. Based on the foregoing, we exam-
ine the possibilities of combining the considered polyhedra into unified composite
structures.",
journal = "Journal for Geometry and Graphics",
title = "Composite Concave Cupolae as Geometric and Architectural Forms",
pages = "91---79",
number = "1",
volume = "19",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1036"
}

Mišić, S., Obradović, M.,& Đukanović, G.. (2015). Composite Concave Cupolae as Geometric and Architectural Forms. in Journal for Geometry and Graphics, 19(1), 79-91.
https://hdl.handle.net/21.15107/rcub_grafar_1036

Mišić S, Obradović M, Đukanović G. Composite Concave Cupolae as Geometric and Architectural Forms. in Journal for Geometry and Graphics. 2015;19(1):79-91.
https://hdl.handle.net/21.15107/rcub_grafar_1036 .

Mišić, Slobodan, Obradović, Marija, Đukanović, Gordana, "Composite Concave Cupolae as Geometric and Architectural Forms" in Journal for Geometry and Graphics, 19, no. 1 (2015):79-91,
https://hdl.handle.net/21.15107/rcub_grafar_1036 .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1252
AB  - Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave polyhedral structures.
PB  - Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd
C3  - Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
T1  - Concave Pyramids of Second Sort -The Occurrence, Types, Variations
EP  - 168
SP  - 157
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1252
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav",
year = "2014",
abstract = "Correspondingly to the method of generating the Concave Cupolae of second sort, the Concave Pyramids of second sort have the similar logic of origination, and their counterpart in regular faced convex pyramids (tetrahedron, Johnson's solids J1 and J2). The difference is that instead of onefold series of equilateral triangles in the lateral surface of the solid, there appear twofold series, forming deltahedral lateral surface with a common point, while bases are also regular polygons. This time, instead of the bases from n=3 to n=5, there are the basis from n=6 to n=9. The same lateral surface’s net can be folded and creased in two different ways, which produces the two types of Concave Pyramids of second sort: with a major and with a minor solid height. Combining and joining so obtained solids by the correspondent bases, the concave (ortho) bipyramids of second sort emerge, which then may be elongated, gyroelongated, and conca-elongated, creating a distinctive family of diverse concave polyhedral structures.",
publisher = "Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd",
journal = "Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia",
title = "Concave Pyramids of Second Sort -The Occurrence, Types, Variations",
pages = "168-157",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1252"
}

Obradović, M., Mišić, S.,& Popkonstantinović, B.. (2014). Concave Pyramids of Second Sort -The Occurrence, Types, Variations. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd., 157-168.
https://hdl.handle.net/21.15107/rcub_grafar_1252

Obradović M, Mišić S, Popkonstantinović B. Concave Pyramids of Second Sort -The Occurrence, Types, Variations. in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia. 2014;:157-168.
https://hdl.handle.net/21.15107/rcub_grafar_1252 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, "Concave Pyramids of Second Sort -The Occurrence, Types, Variations" in Proceedings. Vol. 2 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia (2014):157-168,
https://hdl.handle.net/21.15107/rcub_grafar_1252 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Mišić, Slobodan
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/618
AB  - There is a widespread opinion in different sources, ranging from popular to scientific, that the project of the Petrovaradin Fortress was conceived under the influence of the most important European military engineer and innovator of the time, Sebastien de Vauban. By examining the historical context as well as by comparing Vauban's geometrical methods for determination of the fortification master line (la ligne magistrale) with Austrian plans and the actual state of the Petrovaradin fortress, especially its Wasserstadt part, we have examined how well-founded this claim is.
PB  - Birkhauser Verlag AG
T2  - Nexus Network Journal
T1  - Are Vauban's Geometrical Principles Applied in the Petrovaradin Fortress?
EP  - 776
IS  - 3
SP  - 751
VL  - 16
DO  - 10.1007/s00004-014-0205-9
ER  - 

@article{
author = "Obradović, Marija and Mišić, Slobodan",
year = "2014",
abstract = "There is a widespread opinion in different sources, ranging from popular to scientific, that the project of the Petrovaradin Fortress was conceived under the influence of the most important European military engineer and innovator of the time, Sebastien de Vauban. By examining the historical context as well as by comparing Vauban's geometrical methods for determination of the fortification master line (la ligne magistrale) with Austrian plans and the actual state of the Petrovaradin fortress, especially its Wasserstadt part, we have examined how well-founded this claim is.",
publisher = "Birkhauser Verlag AG",
journal = "Nexus Network Journal",
title = "Are Vauban's Geometrical Principles Applied in the Petrovaradin Fortress?",
pages = "776-751",
number = "3",
volume = "16",
doi = "10.1007/s00004-014-0205-9"
}

Obradović, M.,& Mišić, S.. (2014). Are Vauban's Geometrical Principles Applied in the Petrovaradin Fortress?. in Nexus Network Journal
Birkhauser Verlag AG., 16(3), 751-776.
https://doi.org/10.1007/s00004-014-0205-9

Obradović M, Mišić S. Are Vauban's Geometrical Principles Applied in the Petrovaradin Fortress?. in Nexus Network Journal. 2014;16(3):751-776.
doi:10.1007/s00004-014-0205-9 .

Obradović, Marija, Mišić, Slobodan, "Are Vauban's Geometrical Principles Applied in the Petrovaradin Fortress?" in Nexus Network Journal, 16, no. 3 (2014):751-776,
https://doi.org/10.1007/s00004-014-0205-9 . .

TY  - JOUR
AU  - Malešević, Branko J.
AU  - Petrović, Maja
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1020
AB  - We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.
T2  - Mathematical Inequalities & Applications
T1  - On the extension of the Erdös-Mordell type inequalities
EP  - 281
IS  - 1
SP  - 269
VL  - 17
DO  - 10.7153/mia-17-22
ER  - 

@article{
author = "Malešević, Branko J. and Petrović, Maja and Obradović, Marija and Popkonstantinović, Branislav",
year = "2014",
abstract = "We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.",
journal = "Mathematical Inequalities & Applications",
title = "On the extension of the Erdös-Mordell type inequalities",
pages = "281-269",
number = "1",
volume = "17",
doi = "10.7153/mia-17-22"
}

Malešević, B. J., Petrović, M., Obradović, M.,& Popkonstantinović, B.. (2014). On the extension of the Erdös-Mordell type inequalities. in Mathematical Inequalities & Applications, 17(1), 269-281.
https://doi.org/10.7153/mia-17-22

Malešević BJ, Petrović M, Obradović M, Popkonstantinović B. On the extension of the Erdös-Mordell type inequalities. in Mathematical Inequalities & Applications. 2014;17(1):269-281.
doi:10.7153/mia-17-22 .

Malešević, Branko J., Petrović, Maja, Obradović, Marija, Popkonstantinović, Branislav, "On the extension of the Erdös-Mordell type inequalities" in Mathematical Inequalities & Applications, 17, no. 1 (2014):269-281,
https://doi.org/10.7153/mia-17-22 . .

TY  - CONF
AU  - Popkonstantinović, Branislav
AU  - Miladinović, Ljubomir
AU  - Obradović, Marija
AU  - Stojićević, Miša
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1220
AB  - This paper presents the geometrical properties of one special type of escapement mechanism – the grasshopper escapement, by which the first marine chronometers were equipped. The most important and distinguish mechanical feature of this escapement is also disclosed that contact surfaces between pallets and escapement teeth do not need lubrication. In addition, paper presents the escapement 3D solid model and explains briefly its operational cycle.
PB  - Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd
C3  - Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
T1  - Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism
EP  - 181
SP  - 173
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1220
ER  - 

@conference{
author = "Popkonstantinović, Branislav and Miladinović, Ljubomir and Obradović, Marija and Stojićević, Miša",
year = "2014",
abstract = "This paper presents the geometrical properties of one special type of escapement mechanism – the grasshopper escapement, by which the first marine chronometers were equipped. The most important and distinguish mechanical feature of this escapement is also disclosed that contact surfaces between pallets and escapement teeth do not need lubrication. In addition, paper presents the escapement 3D solid model and explains briefly its operational cycle.",
publisher = "Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd",
journal = "Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia",
title = "Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism",
pages = "181-173",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1220"
}

Popkonstantinović, B., Miladinović, L., Obradović, M.,& Stojićević, M.. (2014). Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism. in Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia
Faculty of Civil Engineering and Architecture ; Serbian Society for Geometry and Graphics SUGIG, Niš ; Beograd., 173-181.
https://hdl.handle.net/21.15107/rcub_grafar_1220

Popkonstantinović B, Miladinović L, Obradović M, Stojićević M. Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism. in Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia. 2014;:173-181.
https://hdl.handle.net/21.15107/rcub_grafar_1220 .

Popkonstantinović, Branislav, Miladinović, Ljubomir, Obradović, Marija, Stojićević, Miša, "Geometrical Characteristics and Solid Modeling of the Grasshopper Escapement Mechanism" in Proceedings. Vol. 1 / 4th International Scientific Conference on Geometry and Graphics moNGeometrija 2014, June 20th - 22nd, 2014 Vlasina, Serbia (2014):173-181,
https://hdl.handle.net/21.15107/rcub_grafar_1220 .

TY  - CONF
AU  - Mišić, Slobodan
AU  - Obradović, Marija
AU  - Lazović, Goran
AU  - Popkonstantinović, Branislav
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1977
AB  - The paper discusses the generation of a specific group of polyhedra, Concave Cupolae of Fourth Sort (CC IV) with regular polygonal bases, using constructive and analytical procedures. Beside determination of the parameters of these polyhedra, the paper deals with their visualization, by the application of graphical software MATLAB. We consider one of the four possible types of forming the lateral surfaces of the Concave Cupolae of fourth sort.
PB  - Timişoara: Editura Politehnica
C3  - Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics
T1  - Generating a Type of Concave Cupolae of Fourth Sort
EP  - 82
IS  - 1
SP  - 79
VL  - 58(72)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1977
ER  - 

@conference{
author = "Mišić, Slobodan and Obradović, Marija and Lazović, Goran and Popkonstantinović, Branislav",
year = "2013",
abstract = "The paper discusses the generation of a specific group of polyhedra, Concave Cupolae of Fourth Sort (CC IV) with regular polygonal bases, using constructive and analytical procedures. Beside determination of the parameters of these polyhedra, the paper deals with their visualization, by the application of graphical software MATLAB. We consider one of the four possible types of forming the lateral surfaces of the Concave Cupolae of fourth sort.",
publisher = "Timişoara: Editura Politehnica",
journal = "Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics",
title = "Generating a Type of Concave Cupolae of Fourth Sort",
pages = "82-79",
number = "1",
volume = "58(72)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1977"
}

Mišić, S., Obradović, M., Lazović, G.,& Popkonstantinović, B.. (2013). Generating a Type of Concave Cupolae of Fourth Sort. in Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics
Timişoara: Editura Politehnica., 58(72)(1), 79-82.
https://hdl.handle.net/21.15107/rcub_grafar_1977

Mišić S, Obradović M, Lazović G, Popkonstantinović B. Generating a Type of Concave Cupolae of Fourth Sort. in Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics. 2013;58(72)(1):79-82.
https://hdl.handle.net/21.15107/rcub_grafar_1977 .

Mišić, Slobodan, Obradović, Marija, Lazović, Goran, Popkonstantinović, Branislav, "Generating a Type of Concave Cupolae of Fourth Sort" in Scientific Bulletin of the "Politehnica" University of Timişoara. Transactions on Hydrotechnics, 58(72), no. 1 (2013):79-82,
https://hdl.handle.net/21.15107/rcub_grafar_1977 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Popkonstantinović, Branislav
AU  - Petrović, Maja
AU  - Malešević, Branko
AU  - Obradović, Ratko
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1928
AB  - Concave cupolae of second sort, combined with the other regular faced polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The
paper presents research on regular-faced polyhedral structures obtained by joining the bases of square concave cupolae of second sort, with the appropriate sides of Archimedean solid - truncated 
cube, and its application in architecture, based on geometric, structural, and functional analysis.
PB  - Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)
T2  - Technics Technologies Education Management
T1  - Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture
EP  - 1214
IS  - 3
SP  - 1198
VL  - 8
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1928
ER  - 

@article{
author = "Obradović, Marija and Mišić, Slobodan and Popkonstantinović, Branislav and Petrović, Maja and Malešević, Branko and Obradović, Ratko",
year = "2013",
abstract = "Concave cupolae of second sort, combined with the other regular faced polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The
paper presents research on regular-faced polyhedral structures obtained by joining the bases of square concave cupolae of second sort, with the appropriate sides of Archimedean solid - truncated 
cube, and its application in architecture, based on geometric, structural, and functional analysis.",
publisher = "Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)",
journal = "Technics Technologies Education Management",
title = "Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture",
pages = "1214-1198",
number = "3",
volume = "8",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1928"
}

Obradović, M., Mišić, S., Popkonstantinović, B., Petrović, M., Malešević, B.,& Obradović, R.. (2013). Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture. in Technics Technologies Education Management
Sarajevo: Society for development of teaching and business processes in New net environment in B&H (DRUNPP)., 8(3), 1198-1214.
https://hdl.handle.net/21.15107/rcub_grafar_1928

Obradović M, Mišić S, Popkonstantinović B, Petrović M, Malešević B, Obradović R. Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture. in Technics Technologies Education Management. 2013;8(3):1198-1214.
https://hdl.handle.net/21.15107/rcub_grafar_1928 .

Obradović, Marija, Mišić, Slobodan, Popkonstantinović, Branislav, Petrović, Maja, Malešević, Branko, Obradović, Ratko, "Investigation of Concave Cupolae Based Polyhedral Structures and Their Potential Application in Architecture" in Technics Technologies Education Management, 8, no. 3 (2013):1198-1214,
https://hdl.handle.net/21.15107/rcub_grafar_1928 .

TY  - CONF
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Petrović, Maja
AU  - Đukanović, Gordana
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1983
AB  - The starting constructions is the well known ellipse construction using the concentric circles c1 and c2. By eccentricity of the center C2 for some value w, and for the preserved center of the transformation in the center C1, the degree of the obtained curve rises from two to three, as done by mathematician Fritz Hügelschäffer. If we also displace the center of the transformation from C1, we obtain a variety of higher order curves using the same principle in the constructive procedure.
PB  - Timişoara: Editura Politehnica
C3  - Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS
T1  - Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction
EP  - 114
IS  - 1
SP  - 110
VL  - 58(72)
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1983
ER  - 

@conference{
author = "Obradović, Marija and Malešević, Branko and Petrović, Maja and Đukanović, Gordana",
year = "2013",
abstract = "The starting constructions is the well known ellipse construction using the concentric circles c1 and c2. By eccentricity of the center C2 for some value w, and for the preserved center of the transformation in the center C1, the degree of the obtained curve rises from two to three, as done by mathematician Fritz Hügelschäffer. If we also displace the center of the transformation from C1, we obtain a variety of higher order curves using the same principle in the constructive procedure.",
publisher = "Timişoara: Editura Politehnica",
journal = "Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS",
title = "Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction",
pages = "114-110",
number = "1",
volume = "58(72)",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1983"
}

Obradović, M., Malešević, B., Petrović, M.,& Đukanović, G.. (2013). Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction. in Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS
Timişoara: Editura Politehnica., 58(72)(1), 110-114.
https://hdl.handle.net/21.15107/rcub_grafar_1983

Obradović M, Malešević B, Petrović M, Đukanović G. Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction. in Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS. 2013;58(72)(1):110-114.
https://hdl.handle.net/21.15107/rcub_grafar_1983 .

Obradović, Marija, Malešević, Branko, Petrović, Maja, Đukanović, Gordana, "Generating Curves of Higher Order Using the Generalisation of Hügelschäffer’ Egg Curve construction" in Scientific Bulletin of the "POLITEHNICA" University of Timişoara, Romania TRANSACTIONS on HYDROTECHNICS, 58(72), no. 1 (2013):110-114,
https://hdl.handle.net/21.15107/rcub_grafar_1983 .

TY  - JOUR
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
AU  - Mišić, Slobodan
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/487
AB  - The paper examines geometrical, static and dynamic properties of the polyhedral structures obtained by folding and creasing the two-rowed segment of equilateral triangular net. Bases of these concave polyhedra are regular, identical polygons in parallel planes, connected by the alternating series of triangles, as in the case of convex antiprisms. There are two ways of folding such a net, and therefore the two types of concave antiprisms of second sort. The paper discusses the methods of obtaining the accurate position of the vertices and other linear parameters of these polyhedra, with the use of mathematical algorithm. Structural analysis of a representative of these polyhedra is presented using the SolidWorks program applications.
AB  - Rad se bavi ispitivanjem geometrijskih, statičkih i dinamičkih osobina jedne poliedarske strukture nastale nabiranjem dvorednog segmenta mreže jednakostraničnih trouglova. Osnove ovih konkavnih poliedara su pravilni, identični poligoni u paralelnim ravnima, povezani nizom naizmeničnih trouglova, kao i u slučaju konveksnih antiprizmi. Postoje dve varijante savijanja ovakve mreže, pa samim tim i dva tipa konkavnih antiprizmi druge vrste (KA II) za svaku posmatranu osnovu od n=5, n=∞. U radu su razmotreni načini dobijanja tačnog položaja temena i drugih linearnih parametara ovih poliedara, uz primenu algoritma za njihovo matematičko izračunavanje. Strukturalna analiza jednog predstavnika ovih poliedara data je korišćenjem aplikacija programa SolidWorks, kako bi se ispitala mogućnost primene ovih oblika u inženjerstvu.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - On the properties of the concave antiprisms of second sort
T1  - O osobinama konkavnih antiprizmi druge vrste
EP  - 263
IS  - 3
SP  - 256
VL  - 41
UR  - https://hdl.handle.net/21.15107/rcub_grafar_487
ER  - 

@article{
author = "Obradović, Marija and Popkonstantinović, Branislav and Mišić, Slobodan",
year = "2013",
abstract = "The paper examines geometrical, static and dynamic properties of the polyhedral structures obtained by folding and creasing the two-rowed segment of equilateral triangular net. Bases of these concave polyhedra are regular, identical polygons in parallel planes, connected by the alternating series of triangles, as in the case of convex antiprisms. There are two ways of folding such a net, and therefore the two types of concave antiprisms of second sort. The paper discusses the methods of obtaining the accurate position of the vertices and other linear parameters of these polyhedra, with the use of mathematical algorithm. Structural analysis of a representative of these polyhedra is presented using the SolidWorks program applications., Rad se bavi ispitivanjem geometrijskih, statičkih i dinamičkih osobina jedne poliedarske strukture nastale nabiranjem dvorednog segmenta mreže jednakostraničnih trouglova. Osnove ovih konkavnih poliedara su pravilni, identični poligoni u paralelnim ravnima, povezani nizom naizmeničnih trouglova, kao i u slučaju konveksnih antiprizmi. Postoje dve varijante savijanja ovakve mreže, pa samim tim i dva tipa konkavnih antiprizmi druge vrste (KA II) za svaku posmatranu osnovu od n=5, n=∞. U radu su razmotreni načini dobijanja tačnog položaja temena i drugih linearnih parametara ovih poliedara, uz primenu algoritma za njihovo matematičko izračunavanje. Strukturalna analiza jednog predstavnika ovih poliedara data je korišćenjem aplikacija programa SolidWorks, kako bi se ispitala mogućnost primene ovih oblika u inženjerstvu.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "On the properties of the concave antiprisms of second sort, O osobinama konkavnih antiprizmi druge vrste",
pages = "263-256",
number = "3",
volume = "41",
url = "https://hdl.handle.net/21.15107/rcub_grafar_487"
}

Obradović, M., Popkonstantinović, B.,& Mišić, S.. (2013). On the properties of the concave antiprisms of second sort. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 41(3), 256-263.
https://hdl.handle.net/21.15107/rcub_grafar_487

Obradović M, Popkonstantinović B, Mišić S. On the properties of the concave antiprisms of second sort. in FME Transactions. 2013;41(3):256-263.
https://hdl.handle.net/21.15107/rcub_grafar_487 .

Obradović, Marija, Popkonstantinović, Branislav, Mišić, Slobodan, "On the properties of the concave antiprisms of second sort" in FME Transactions, 41, no. 3 (2013):256-263,
https://hdl.handle.net/21.15107/rcub_grafar_487 .

TY  - CONF
AU  - Banjac, B.D.
AU  - Malesević, B.J.
AU  - Petrović, M.M.
AU  - Obradović, Marija
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/554
AB  - In this paper we consider Erdös-Mordell inequality and its extension in the plane of triangle to the Erdös-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one conjecture that relates to Erdös-Mordell curve.
C3  - 2013 21st Telecommunications Forum Telfor, TELFOR 2013 - Proceedings of Papers
T1  - A computer verification of a conjecture about the Erdös-Mordell curve
EP  - 1034
SP  - 1031
DO  - 10.1109/TELFOR.2013.6716408
ER  - 

@conference{
author = "Banjac, B.D. and Malesević, B.J. and Petrović, M.M. and Obradović, Marija",
year = "2013",
abstract = "In this paper we consider Erdös-Mordell inequality and its extension in the plane of triangle to the Erdös-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one conjecture that relates to Erdös-Mordell curve.",
journal = "2013 21st Telecommunications Forum Telfor, TELFOR 2013 - Proceedings of Papers",
title = "A computer verification of a conjecture about the Erdös-Mordell curve",
pages = "1034-1031",
doi = "10.1109/TELFOR.2013.6716408"
}

Banjac, B.D., Malesević, B.J., Petrović, M.M.,& Obradović, M.. (2013). A computer verification of a conjecture about the Erdös-Mordell curve. in 2013 21st Telecommunications Forum Telfor, TELFOR 2013 - Proceedings of Papers, 1031-1034.
https://doi.org/10.1109/TELFOR.2013.6716408

Banjac B, Malesević B, Petrović M, Obradović M. A computer verification of a conjecture about the Erdös-Mordell curve. in 2013 21st Telecommunications Forum Telfor, TELFOR 2013 - Proceedings of Papers. 2013;:1031-1034.
doi:10.1109/TELFOR.2013.6716408 .

Banjac, B.D., Malesević, B.J., Petrović, M.M., Obradović, Marija, "A computer verification of a conjecture about the Erdös-Mordell curve" in 2013 21st Telecommunications Forum Telfor, TELFOR 2013 - Proceedings of Papers (2013):1031-1034,
https://doi.org/10.1109/TELFOR.2013.6716408 . .

TY  - CONF
AU  - Obradović, Marija
AU  - Mišić, Slobodan
AU  - Petrović, Maja
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2031
AB  - Concave cupolae of II sort, combined with the other concave or convex polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The paper presents research on regular –faced polyhedral structures obtained by joining bases of some concave cupolae of II sort, with the appropriate sides of Archimedean solids: truncated cube, truncated dodecahedron and great rhombicosidodecahedron.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - Investigating Composite Polyhedral forms obtained by combining concave cupolae of  II sort with Archimedean Solids
EP  - 123
SP  - 109
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2031
ER  - 

@conference{
author = "Obradović, Marija and Mišić, Slobodan and Petrović, Maja",
year = "2012",
abstract = "Concave cupolae of II sort, combined with the other concave or convex polyhedra with at least one matching side, provide many possibilities for the formation of various composite polyhedra. The paper presents research on regular –faced polyhedral structures obtained by joining bases of some concave cupolae of II sort, with the appropriate sides of Archimedean solids: truncated cube, truncated dodecahedron and great rhombicosidodecahedron.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "Investigating Composite Polyhedral forms obtained by combining concave cupolae of  II sort with Archimedean Solids",
pages = "123-109",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2031"
}

Obradović, M., Mišić, S.,& Petrović, M.. (2012). Investigating Composite Polyhedral forms obtained by combining concave cupolae of  II sort with Archimedean Solids. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 109-123.
https://hdl.handle.net/21.15107/rcub_grafar_2031

Obradović M, Mišić S, Petrović M. Investigating Composite Polyhedral forms obtained by combining concave cupolae of  II sort with Archimedean Solids. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:109-123.
https://hdl.handle.net/21.15107/rcub_grafar_2031 .

Obradović, Marija, Mišić, Slobodan, Petrović, Maja, "Investigating Composite Polyhedral forms obtained by combining concave cupolae of  II sort with Archimedean Solids" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):109-123,
https://hdl.handle.net/21.15107/rcub_grafar_2031 .

TY  - CONF
AU  - Obradović, Marija
AU  - Popkonstantinović, Branislav
AU  - Mišić, Slobodan
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2033
AB  - The paper discusses determining the positions and spatial coordinates of the vertices of polyhedral structures - concave antiprisms of second sort. These polyhedra originate from folding the double row strip of equilateral triangles, closed by two identical regular polygons, the principle akin to the way of the concave cupolae of second sort formation. The paper considers constructive -geometrical solution, including the method of solving the problem using the mechanisms, by application of SolidWorks software package.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - Concave Antiprisms of Second Sort with Regular Polygonal Bases
EP  - 143
SP  - 133
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2033
ER  - 

@conference{
author = "Obradović, Marija and Popkonstantinović, Branislav and Mišić, Slobodan",
year = "2012",
abstract = "The paper discusses determining the positions and spatial coordinates of the vertices of polyhedral structures - concave antiprisms of second sort. These polyhedra originate from folding the double row strip of equilateral triangles, closed by two identical regular polygons, the principle akin to the way of the concave cupolae of second sort formation. The paper considers constructive -geometrical solution, including the method of solving the problem using the mechanisms, by application of SolidWorks software package.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "Concave Antiprisms of Second Sort with Regular Polygonal Bases",
pages = "143-133",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2033"
}

Obradović, M., Popkonstantinović, B.,& Mišić, S.. (2012). Concave Antiprisms of Second Sort with Regular Polygonal Bases. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 133-143.
https://hdl.handle.net/21.15107/rcub_grafar_2033

Obradović M, Popkonstantinović B, Mišić S. Concave Antiprisms of Second Sort with Regular Polygonal Bases. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:133-143.
https://hdl.handle.net/21.15107/rcub_grafar_2033 .

Obradović, Marija, Popkonstantinović, Branislav, Mišić, Slobodan, "Concave Antiprisms of Second Sort with Regular Polygonal Bases" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):133-143,
https://hdl.handle.net/21.15107/rcub_grafar_2033 .

TY  - JOUR
AU  - Đukanović, Gordana
AU  - Obradović, Marija
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/462
AB  - This paper shows the process of inverting the 4th ordered space curve of the first category with a self-intersecting point (with two planes of symmetry) and determining its harmonic equivalent. There are harmonic equivalents for five groups of surfaces obtained through the 4th order space curve of the 1st category. Mapping was done through a system of circular cross-sections. Both classical and relativistic geometry interpretations are presented. We also designed spatial models - a spatial model of the pencil of quadrics and a spatial model of the pencil of equivalent quadrics. Besides the boundary surfaces, one surface of the 3rd order, which is an equivalent to a triaxial ellipsoid, passes through this pencil of surface of the 4th order. The center of inversion is located on the contour of the ellipsoid. The parabolic cylinder is mapped into its equivalent, by mapping the contour parabola of the cylinder, in the frontal projection, in relation to the center and the sphere of inversion into a contour curve of the 4th order surface. The generating lines of the parabolic cylinder, which are in a projecting position and pass through the antipode, are mapped into circles (also in a projecting position) whose diameters are from the center of inversion to the contour line. The application of the 4th order surfaces in architectural practice is also presented.
AB  - U radu je inverzijom preslikana prostorna kriva 4. reda prve vrste sa samopresečnom tačkom (sa dve ravni simetrije) i određen je njen harmonijski ekvivalent. Prikazani su harmonijski ekvivalenti za pet grupa površi koje su dobijene kroz prostornu krivu 4 reda 1 vrste. Preslikavanje je rađeno preko sistema kružnih preseka. Dato je klasično i tumačenje u relativističkooj geometriji. Takođe su urađeni i prostorni modeli - prostorni model pramena kvadrika i pramena ekvivalentnih kvadrika. Kroz ovaj pramen površi 4. reda, osim graničnih površi, prolazi i jedna površ 3. reda koja je ekvivalent troosnom elipsoidu. Centar inverzije nalazi se na konturi elipsoida. Parabolički cilindar se preslikava u svoj ekvivalent, tako što se konturna parabola cilindra, za drugu projekciju, preslika u odnosu na centar i sferu inverzije u konturnu krivu površi 4. reda. Izvodnice paraboličkog cilindra, koje su u projicirajućem položaju i prolaze kroz antipod, preslikavaju se u krugove (takođe u projicirajućem položaju) čiji su prečnici od centra inverzije do konturne linije. Prikazana je i primena površi 4. reda u arhitektonskoj praksi.
PB  - Univerzitet u Nišu, Niš
T2  - Facta universitatis - series: Architecture and Civil Engineering
T1  - The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category
T1  - Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste
EP  - 207
IS  - 2
SP  - 193
VL  - 10
DO  - 10.2298/FUACE1202193D
ER  - 

@article{
author = "Đukanović, Gordana and Obradović, Marija",
year = "2012",
abstract = "This paper shows the process of inverting the 4th ordered space curve of the first category with a self-intersecting point (with two planes of symmetry) and determining its harmonic equivalent. There are harmonic equivalents for five groups of surfaces obtained through the 4th order space curve of the 1st category. Mapping was done through a system of circular cross-sections. Both classical and relativistic geometry interpretations are presented. We also designed spatial models - a spatial model of the pencil of quadrics and a spatial model of the pencil of equivalent quadrics. Besides the boundary surfaces, one surface of the 3rd order, which is an equivalent to a triaxial ellipsoid, passes through this pencil of surface of the 4th order. The center of inversion is located on the contour of the ellipsoid. The parabolic cylinder is mapped into its equivalent, by mapping the contour parabola of the cylinder, in the frontal projection, in relation to the center and the sphere of inversion into a contour curve of the 4th order surface. The generating lines of the parabolic cylinder, which are in a projecting position and pass through the antipode, are mapped into circles (also in a projecting position) whose diameters are from the center of inversion to the contour line. The application of the 4th order surfaces in architectural practice is also presented., U radu je inverzijom preslikana prostorna kriva 4. reda prve vrste sa samopresečnom tačkom (sa dve ravni simetrije) i određen je njen harmonijski ekvivalent. Prikazani su harmonijski ekvivalenti za pet grupa površi koje su dobijene kroz prostornu krivu 4 reda 1 vrste. Preslikavanje je rađeno preko sistema kružnih preseka. Dato je klasično i tumačenje u relativističkooj geometriji. Takođe su urađeni i prostorni modeli - prostorni model pramena kvadrika i pramena ekvivalentnih kvadrika. Kroz ovaj pramen površi 4. reda, osim graničnih površi, prolazi i jedna površ 3. reda koja je ekvivalent troosnom elipsoidu. Centar inverzije nalazi se na konturi elipsoida. Parabolički cilindar se preslikava u svoj ekvivalent, tako što se konturna parabola cilindra, za drugu projekciju, preslika u odnosu na centar i sferu inverzije u konturnu krivu površi 4. reda. Izvodnice paraboličkog cilindra, koje su u projicirajućem položaju i prolaze kroz antipod, preslikavaju se u krugove (takođe u projicirajućem položaju) čiji su prečnici od centra inverzije do konturne linije. Prikazana je i primena površi 4. reda u arhitektonskoj praksi.",
publisher = "Univerzitet u Nišu, Niš",
journal = "Facta universitatis - series: Architecture and Civil Engineering",
title = "The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category, Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste",
pages = "207-193",
number = "2",
volume = "10",
doi = "10.2298/FUACE1202193D"
}

Đukanović, G.,& Obradović, M.. (2012). The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category. in Facta universitatis - series: Architecture and Civil Engineering
Univerzitet u Nišu, Niš., 10(2), 193-207.
https://doi.org/10.2298/FUACE1202193D

Đukanović G, Obradović M. The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category. in Facta universitatis - series: Architecture and Civil Engineering. 2012;10(2):193-207.
doi:10.2298/FUACE1202193D .

Đukanović, Gordana, Obradović, Marija, "The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category" in Facta universitatis - series: Architecture and Civil Engineering, 10, no. 2 (2012):193-207,
https://doi.org/10.2298/FUACE1202193D . .

TY  - CONF
AU  - Obradović, Marija
AU  - Malešević, Branko
AU  - Petrović, Maja
AU  - Popkonstantinović, Branislav
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2032
AB  - We discuss the spatial interpretation of the Erdös-Mordell inequality on the area of triangle ABC, and also consider the plane extension of this inequality.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - One Application of the  Cone Surfaces on the Erdosh-Mordell inequality
EP  - 351
SP  - 335
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2032
ER  - 

@conference{
author = "Obradović, Marija and Malešević, Branko and Petrović, Maja and Popkonstantinović, Branislav",
year = "2012",
abstract = "We discuss the spatial interpretation of the Erdös-Mordell inequality on the area of triangle ABC, and also consider the plane extension of this inequality.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "One Application of the  Cone Surfaces on the Erdosh-Mordell inequality",
pages = "351-335",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2032"
}

Obradović, M., Malešević, B., Petrović, M.,& Popkonstantinović, B.. (2012). One Application of the  Cone Surfaces on the Erdosh-Mordell inequality. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 335-351.
https://hdl.handle.net/21.15107/rcub_grafar_2032

Obradović M, Malešević B, Petrović M, Popkonstantinović B. One Application of the  Cone Surfaces on the Erdosh-Mordell inequality. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:335-351.
https://hdl.handle.net/21.15107/rcub_grafar_2032 .

Obradović, Marija, Malešević, Branko, Petrović, Maja, Popkonstantinović, Branislav, "One Application of the  Cone Surfaces on the Erdosh-Mordell inequality" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):335-351,
https://hdl.handle.net/21.15107/rcub_grafar_2032 .

TY  - CONF
AU  - Šušić, Vladimir
AU  - Abolmasov, Biljana
AU  - Obradović, Marija
PY  - 2012
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/1994
AB  - Under the notion of visualization we mean any technique of creating images, diagrams, 3D models or other animations as a form of visual communication. Tree-dimensional view of buildings on Google Earth allows us insight into the real world. Belgrade has recently started to publish 3D content on Google Earth, but Faculty of Mining and Geology is not among the published items, and from there arose the idea for the theme of this paper. The aim is to create 3D model of building of the Faculty and its publishing on Google Earth. During the production of this paper it has been used an open source software for 3D modeling, Google Sketchup.
PB  - Novi Sad: Faculty of Technical Sciences, University of Novi Sad
PB  - Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
T1  - Development of 3D Object Model by Applying Google Sketchup Software Package
EP  - 132
SP  - 125
UR  - https://hdl.handle.net/21.15107/rcub_grafar_1994
ER  - 

@conference{
author = "Šušić, Vladimir and Abolmasov, Biljana and Obradović, Marija",
year = "2012",
abstract = "Under the notion of visualization we mean any technique of creating images, diagrams, 3D models or other animations as a form of visual communication. Tree-dimensional view of buildings on Google Earth allows us insight into the real world. Belgrade has recently started to publish 3D content on Google Earth, but Faculty of Mining and Geology is not among the published items, and from there arose the idea for the theme of this paper. The aim is to create 3D model of building of the Faculty and its publishing on Google Earth. During the production of this paper it has been used an open source software for 3D modeling, Google Sketchup.",
publisher = "Novi Sad: Faculty of Technical Sciences, University of Novi Sad, Novi Sad: Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012",
title = "Development of 3D Object Model by Applying Google Sketchup Software Package",
pages = "132-125",
url = "https://hdl.handle.net/21.15107/rcub_grafar_1994"
}

Šušić, V., Abolmasov, B.,& Obradović, M.. (2012). Development of 3D Object Model by Applying Google Sketchup Software Package. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012
Novi Sad: Faculty of Technical Sciences, University of Novi Sad., 125-132.
https://hdl.handle.net/21.15107/rcub_grafar_1994

Šušić V, Abolmasov B, Obradović M. Development of 3D Object Model by Applying Google Sketchup Software Package. in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012. 2012;:125-132.
https://hdl.handle.net/21.15107/rcub_grafar_1994 .

Šušić, Vladimir, Abolmasov, Biljana, Obradović, Marija, "Development of 3D Object Model by Applying Google Sketchup Software Package" in Proceedings of the 3rd International Scientific Conference MoNGeometrija 2012 (2012):125-132,
https://hdl.handle.net/21.15107/rcub_grafar_1994 .