TY  - CONF
AU  - Mitrovic, Djordje
AU  - Djordjevic, Djordje
AU  - Devetakovic, Mirjana
AU  - Djukanovic, Gordana
PY  - 2023
UR  - https://raf.arh.bg.ac.rs/handle/123456789/1628
AB  - In most cases, artefacts are differentiated in terms of style they belong to – mainly visually, not mathematically. So, the main research questions of this study are both how to numerically encode stylistic regularities (peculiarities) as geometric indicators of artefacts morphology and how to decode them, namely to identify architectural style those artefacts belong to. Columns, namely their capitals are chosen as the most distinctive elements among artefacts. To elaborate on the validity of the defined principles of the aim-related methodology, a few representatives (capital samples) from each of three fundamental classical architectural orders (Doric, Ionic, and Corinthian) are used. The subject of this Paper is to establish relevant indicators of capital qualification, capital classification, and thus, referred architectural order identification. The verification of those indicators is performed by processing two sets of capitals contours (that belong to the mutually equidistant transverse and equiangular radial section planes) of each of the selected samples (namely digital 3D models). The narrower research aim is to point out that it is possible to encode not only chosen but also any other capital – by using the mentioned indicators of fractal and non-fractal nature (as a control one). The wider research aim refers to a possibility to identify order a concrete fragment of capital belongs to in terms of recognising it computationally (as confidently as possible from the mathematical probability point of view) based on the established research methodology principles. Finally, it is possible to conclude that changes of the analysed indicators trendlines behaviour (expressed by changes of its slope, roughness, continuation, etc.) accurately/precisely describe morphology-wise variations of a form that could point out subject-related stylistic variation, as well. So, this Paper demonstrates not only the fact that architectural orders capitals are true fractal objects, but rather how fractal analysis as a tool can be used to scientifically numerically encode/decode their certain characteristics (fractal features) of single- or multi-scale nature.
PB  - Novi Sad : Faculty of Technical Sciences, University of Novi Sad
PB  - Belgrade : Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia
T1  - Encoding/Decoding Capitals of Classical Architectural Orders by Using Fractal Geometry: Establishing Methodology
SP  - 153
EP  - 167
UR  - https://hdl.handle.net/21.15107/rcub_raf_1628
ER  - 

@conference{
author = "Mitrovic, Djordje and Djordjevic, Djordje and Devetakovic, Mirjana and Djukanovic, Gordana",
year = "2023",
abstract = "In most cases, artefacts are differentiated in terms of style they belong to – mainly visually, not mathematically. So, the main research questions of this study are both how to numerically encode stylistic regularities (peculiarities) as geometric indicators of artefacts morphology and how to decode them, namely to identify architectural style those artefacts belong to. Columns, namely their capitals are chosen as the most distinctive elements among artefacts. To elaborate on the validity of the defined principles of the aim-related methodology, a few representatives (capital samples) from each of three fundamental classical architectural orders (Doric, Ionic, and Corinthian) are used. The subject of this Paper is to establish relevant indicators of capital qualification, capital classification, and thus, referred architectural order identification. The verification of those indicators is performed by processing two sets of capitals contours (that belong to the mutually equidistant transverse and equiangular radial section planes) of each of the selected samples (namely digital 3D models). The narrower research aim is to point out that it is possible to encode not only chosen but also any other capital – by using the mentioned indicators of fractal and non-fractal nature (as a control one). The wider research aim refers to a possibility to identify order a concrete fragment of capital belongs to in terms of recognising it computationally (as confidently as possible from the mathematical probability point of view) based on the established research methodology principles. Finally, it is possible to conclude that changes of the analysed indicators trendlines behaviour (expressed by changes of its slope, roughness, continuation, etc.) accurately/precisely describe morphology-wise variations of a form that could point out subject-related stylistic variation, as well. So, this Paper demonstrates not only the fact that architectural orders capitals are true fractal objects, but rather how fractal analysis as a tool can be used to scientifically numerically encode/decode their certain characteristics (fractal features) of single- or multi-scale nature.",
publisher = "Novi Sad : Faculty of Technical Sciences, University of Novi Sad, Belgrade : Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia",
title = "Encoding/Decoding Capitals of Classical Architectural Orders by Using Fractal Geometry: Establishing Methodology",
pages = "153-167",
url = "https://hdl.handle.net/21.15107/rcub_raf_1628"
}

Mitrovic, D., Djordjevic, D., Devetakovic, M.,& Djukanovic, G.. (2023). Encoding/Decoding Capitals of Classical Architectural Orders by Using Fractal Geometry: Establishing Methodology. in Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia
Novi Sad : Faculty of Technical Sciences, University of Novi Sad., 153-167.
https://hdl.handle.net/21.15107/rcub_raf_1628

Mitrovic D, Djordjevic D, Devetakovic M, Djukanovic G. Encoding/Decoding Capitals of Classical Architectural Orders by Using Fractal Geometry: Establishing Methodology. in Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia. 2023;:153-167.
https://hdl.handle.net/21.15107/rcub_raf_1628 .

Mitrovic, Djordje, Djordjevic, Djordje, Devetakovic, Mirjana, Djukanovic, Gordana, "Encoding/Decoding Capitals of Classical Architectural Orders by Using Fractal Geometry: Establishing Methodology" in Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia (2023):153-167,
https://hdl.handle.net/21.15107/rcub_raf_1628 .

TY  - CONF
AU  - Djukanovic, Gordana
AU  - Djordjevic, Djordje
AU  - Devetakovic, Mirjana
AU  - Mitrovic, Djordje
PY  - 2023
UR  - https://raf.arh.bg.ac.rs/handle/123456789/1729
AB  - In this paper, an elliptical pencil of circles is mapped by homology (perspective collineation) into a parabolic-parabolic pencil of hyperbolas because it has two by two common points 1 = 2 and 3 = 4 in infinity, i.e., four overlapping points in the antipode. The mapping also includes the mapping of degenerated conics decomposed into corresponding pairs of straight lines. The elliptical pencil of circles (the ellipses on plane 1) is mapped into a hyperbolic pencil (on plane 2) by perspective collineation for pole S1. The vanishing line v1 intersects all the circles of the pencil so that by homology all the circles are mapped into hyperbolas. To apply supersymmetry to the obtained pencils, the angle between plane 1 and plane 2 must be 45°. The pencil of hyperbolas is mapped by supersymmetry into a pencil of higher-order curves. The obtained pencils are further mapped by inversion and then again by supersymmetry to obtain higher-order curves rich in different shapes. In the second example, the elliptical pencil of circles is placed to the vanishing line v1 so that by homology, it is mapped into a pencil of conics containing an ellipse (circle 1 does not intersect the vanishing line), a parabola (circle 2 touches the vanishing line), a hyperbola (circle 3 intersects the vanishing line). The pencil of conics is elliptical-parabolic because it has two real and separate points and two infinite, i.e., two overlapping points in the antipode. This pencil of conic is also mapped by supersymmetry into a pencil of higher-order curves that intersect at the same number and type of base points as the starting pencil. Higher order curves obtained by mapping are rational line curves.
PB  - Novi Sad : Faculty of Technical Sciences, University of Novi Sad
PB  - Belgrade : Serbian Society for Geometry and Graphics (SUGIG)
C3  - Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia
T1  - Transformation of Pencils of Circles into Pencils of Conics and These into Pencils of Higher-Order Curves
SP  - 133
EP  - 141
UR  - https://hdl.handle.net/21.15107/rcub_raf_1729
ER  - 

@conference{
author = "Djukanovic, Gordana and Djordjevic, Djordje and Devetakovic, Mirjana and Mitrovic, Djordje",
year = "2023",
abstract = "In this paper, an elliptical pencil of circles is mapped by homology (perspective collineation) into a parabolic-parabolic pencil of hyperbolas because it has two by two common points 1 = 2 and 3 = 4 in infinity, i.e., four overlapping points in the antipode. The mapping also includes the mapping of degenerated conics decomposed into corresponding pairs of straight lines. The elliptical pencil of circles (the ellipses on plane 1) is mapped into a hyperbolic pencil (on plane 2) by perspective collineation for pole S1. The vanishing line v1 intersects all the circles of the pencil so that by homology all the circles are mapped into hyperbolas. To apply supersymmetry to the obtained pencils, the angle between plane 1 and plane 2 must be 45°. The pencil of hyperbolas is mapped by supersymmetry into a pencil of higher-order curves. The obtained pencils are further mapped by inversion and then again by supersymmetry to obtain higher-order curves rich in different shapes. In the second example, the elliptical pencil of circles is placed to the vanishing line v1 so that by homology, it is mapped into a pencil of conics containing an ellipse (circle 1 does not intersect the vanishing line), a parabola (circle 2 touches the vanishing line), a hyperbola (circle 3 intersects the vanishing line). The pencil of conics is elliptical-parabolic because it has two real and separate points and two infinite, i.e., two overlapping points in the antipode. This pencil of conic is also mapped by supersymmetry into a pencil of higher-order curves that intersect at the same number and type of base points as the starting pencil. Higher order curves obtained by mapping are rational line curves.",
publisher = "Novi Sad : Faculty of Technical Sciences, University of Novi Sad, Belgrade : Serbian Society for Geometry and Graphics (SUGIG)",
journal = "Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia",
title = "Transformation of Pencils of Circles into Pencils of Conics and These into Pencils of Higher-Order Curves",
pages = "133-141",
url = "https://hdl.handle.net/21.15107/rcub_raf_1729"
}

Djukanovic, G., Djordjevic, D., Devetakovic, M.,& Mitrovic, D.. (2023). Transformation of Pencils of Circles into Pencils of Conics and These into Pencils of Higher-Order Curves. in Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia
Novi Sad : Faculty of Technical Sciences, University of Novi Sad., 133-141.
https://hdl.handle.net/21.15107/rcub_raf_1729

Djukanovic G, Djordjevic D, Devetakovic M, Mitrovic D. Transformation of Pencils of Circles into Pencils of Conics and These into Pencils of Higher-Order Curves. in Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia. 2023;:133-141.
https://hdl.handle.net/21.15107/rcub_raf_1729 .

Djukanovic, Gordana, Djordjevic, Djordje, Devetakovic, Mirjana, Mitrovic, Djordje, "Transformation of Pencils of Circles into Pencils of Conics and These into Pencils of Higher-Order Curves" in Proceedings / The 9th International Scientific Conference on Geometry, Graphics and Design in the Digital Age, MoNGeomatrija 2023, June 7-10, 2023, Novi Sad, Serbia (2023):133-141,
https://hdl.handle.net/21.15107/rcub_raf_1729 .