TY  - JOUR
AU  - Devetaković, Mirjana S.
AU  - Đorđević, Đorđe D.
AU  - Đukanović, Gordana
AU  - Krstić-Furundžić, Aleksandra D.
AU  - Sudimac, Budimir S.
AU  - Scognamiglio, Alessandra
PY  - 2019
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/1009
AB  - U radu su sistematizovani najvažniji geometrijski aspekti koji su relevantni za celovito razumevanje projektovanja fotonaponskih sistema. Ova sistematizacija se bazira na pregledu literature namenjene različitim inženjerima, uključujući arhitekte koji su uključeni u multidisciplinarne procese konceptualizacije, projektovanja i realizacije fotonaponskih sistema. Razumevanje prikazanih geometrijskih aspekata, u literaturi objedinjenih pod nazivom solarna geometrija, značajno je ne samo zbog pronalaženja optimalne orijentacije i najefektnijeg nagiba fotonaponskih modula, nego i zbog adekvatnog oblikovanja geometrijski kompleksnih fasadnih elemenata, koji bi trebalo da budu optimalno osunčani tokom cele godine. Nakon detaljnog objašnjenja osnovnih elemenata solarne geometrije korišćenjem sferne trigonometrije, u radu je prodiskutovana integracija prikazanih geometrijskih koncepata u BIM okruženja, ilustrovana primerom modula za analize osunčanja u okviru softvera Revit, firme Autodesk. Analizirana je funkcionalnost svih interaktivnih komponenata 3D prikaza sunčeve putanje. Naglašena je potreba za eksplicitnijim određivanjem upadnog ugla sunčevih zraka na nagnutu površ fotonaponskog modula. U zaključnom delu izdvojeno je ono znanje o solarnoj geometriji koje bi bilo neophodno usvojiti u procesu arhitektonskog obrazovanja, kako bi projektanti koji rade u BIM okruženju bili pripremljeni za efikasnu konceptualizaciju integrisanih fotonaponskih sistema.
AB  - The paper systematizes geometric aspects relevant for understanding design of solar systems. The systematization is based on a review of literature dedicated to various kinds of engineers, including architects, involved in a multidisciplinary process of conceptualizing, designing and realization of PV systems. The understanding of the presented geometric aspects, known as solar geometry, is important not only in terms of finding optimal orientation and most effective tilt of solar modules, but also in terms of adequate geometric modelling of façade elements of a complex shape (as specific photovoltaic modules) in order to be optimally exposed to the sun all over the year. After providing detailed explanations of the main elements of solar geometry using the tools of spherical trigonometry, the paper discusses the integration of the presented geometric concepts in the BIM environments, and refers the example of Autodesk Revit software through its sun study tool. Analysed are functionalities of all interactive components of the 3D solar path representation. A need for more explicit determination of an incidence angle of the sun rays on a tilted surface is stressed. In the conclusion highlighted is the essential knowledge on solar geometry that needs to be acquired during architectural education, so that architects participating in the BIM working environments could be prepared for efficient conceptualization of integrated solar systems.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Projektovanje solarnih sistema za arhitektonske objekte i BIM alati - pregled relevantnih geometrijskih aspekata
T1  - Design of solar systems for buildings and use of BIM tools: Overview of relevant geometric aspects
EP  - 397
IS  - 2
SP  - 387
VL  - 47
DO  - 10.5937/fmet1902387D
UR  - conv_725
ER  - 

@article{
author = "Devetaković, Mirjana S. and Đorđević, Đorđe D. and Đukanović, Gordana and Krstić-Furundžić, Aleksandra D. and Sudimac, Budimir S. and Scognamiglio, Alessandra",
year = "2019",
abstract = "U radu su sistematizovani najvažniji geometrijski aspekti koji su relevantni za celovito razumevanje projektovanja fotonaponskih sistema. Ova sistematizacija se bazira na pregledu literature namenjene različitim inženjerima, uključujući arhitekte koji su uključeni u multidisciplinarne procese konceptualizacije, projektovanja i realizacije fotonaponskih sistema. Razumevanje prikazanih geometrijskih aspekata, u literaturi objedinjenih pod nazivom solarna geometrija, značajno je ne samo zbog pronalaženja optimalne orijentacije i najefektnijeg nagiba fotonaponskih modula, nego i zbog adekvatnog oblikovanja geometrijski kompleksnih fasadnih elemenata, koji bi trebalo da budu optimalno osunčani tokom cele godine. Nakon detaljnog objašnjenja osnovnih elemenata solarne geometrije korišćenjem sferne trigonometrije, u radu je prodiskutovana integracija prikazanih geometrijskih koncepata u BIM okruženja, ilustrovana primerom modula za analize osunčanja u okviru softvera Revit, firme Autodesk. Analizirana je funkcionalnost svih interaktivnih komponenata 3D prikaza sunčeve putanje. Naglašena je potreba za eksplicitnijim određivanjem upadnog ugla sunčevih zraka na nagnutu površ fotonaponskog modula. U zaključnom delu izdvojeno je ono znanje o solarnoj geometriji koje bi bilo neophodno usvojiti u procesu arhitektonskog obrazovanja, kako bi projektanti koji rade u BIM okruženju bili pripremljeni za efikasnu konceptualizaciju integrisanih fotonaponskih sistema., The paper systematizes geometric aspects relevant for understanding design of solar systems. The systematization is based on a review of literature dedicated to various kinds of engineers, including architects, involved in a multidisciplinary process of conceptualizing, designing and realization of PV systems. The understanding of the presented geometric aspects, known as solar geometry, is important not only in terms of finding optimal orientation and most effective tilt of solar modules, but also in terms of adequate geometric modelling of façade elements of a complex shape (as specific photovoltaic modules) in order to be optimally exposed to the sun all over the year. After providing detailed explanations of the main elements of solar geometry using the tools of spherical trigonometry, the paper discusses the integration of the presented geometric concepts in the BIM environments, and refers the example of Autodesk Revit software through its sun study tool. Analysed are functionalities of all interactive components of the 3D solar path representation. A need for more explicit determination of an incidence angle of the sun rays on a tilted surface is stressed. In the conclusion highlighted is the essential knowledge on solar geometry that needs to be acquired during architectural education, so that architects participating in the BIM working environments could be prepared for efficient conceptualization of integrated solar systems.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Projektovanje solarnih sistema za arhitektonske objekte i BIM alati - pregled relevantnih geometrijskih aspekata, Design of solar systems for buildings and use of BIM tools: Overview of relevant geometric aspects",
pages = "397-387",
number = "2",
volume = "47",
doi = "10.5937/fmet1902387D",
url = "conv_725"
}

Devetaković, M. S., Đorđević, Đ. D., Đukanović, G., Krstić-Furundžić, A. D., Sudimac, B. S.,& Scognamiglio, A.. (2019). Projektovanje solarnih sistema za arhitektonske objekte i BIM alati - pregled relevantnih geometrijskih aspekata. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 47(2), 387-397.
https://doi.org/10.5937/fmet1902387D
conv_725

Devetaković MS, Đorđević ĐD, Đukanović G, Krstić-Furundžić AD, Sudimac BS, Scognamiglio A. Projektovanje solarnih sistema za arhitektonske objekte i BIM alati - pregled relevantnih geometrijskih aspekata. in FME Transactions. 2019;47(2):387-397.
doi:10.5937/fmet1902387D
conv_725 .

Devetaković, Mirjana S., Đorđević, Đorđe D., Đukanović, Gordana, Krstić-Furundžić, Aleksandra D., Sudimac, Budimir S., Scognamiglio, Alessandra, "Projektovanje solarnih sistema za arhitektonske objekte i BIM alati - pregled relevantnih geometrijskih aspekata" in FME Transactions, 47, no. 2 (2019):387-397,
https://doi.org/10.5937/fmet1902387D .,
conv_725 .

TY  - JOUR
AU  - Salemović, Duško
AU  - Dedić, Aleksandar
AU  - Ćuprić, Nenad Lj.
PY  - 2015
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/668
AB  - This paper presents a mathematical model and numerical analysis of the convective drying process of small particles of potatoes slowly moving through the flow of a drying agent - hot moist air. The drying process was analyzed in the form of a one-dimensional thin layer. The mathematical model of the drying process is a system of two ordinary non-linear differential equations with constant coefficients and an equation with a transcendent character. The appropriate boundary conditions of the mathematical model were given. The presented model is suitable in the automated control. The presented system of differential equations was solved numerically. The analysis presented here and the obtained results could be useful in predicting the drying kinetics of potatoes and similar natural products in a conveyor-belt dryer.
PB  - Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd
T2  - Thermal Science
T1  - A mathematical model and simulation of the drying process of thin layers of potatoes in a conveyor-belt dryer
EP  - 1118
IS  - 3
SP  - 1107
VL  - 19
DO  - 10.2298/TSCI130920020S
UR  - conv_927
ER  - 

@article{
author = "Salemović, Duško and Dedić, Aleksandar and Ćuprić, Nenad Lj.",
year = "2015",
abstract = "This paper presents a mathematical model and numerical analysis of the convective drying process of small particles of potatoes slowly moving through the flow of a drying agent - hot moist air. The drying process was analyzed in the form of a one-dimensional thin layer. The mathematical model of the drying process is a system of two ordinary non-linear differential equations with constant coefficients and an equation with a transcendent character. The appropriate boundary conditions of the mathematical model were given. The presented model is suitable in the automated control. The presented system of differential equations was solved numerically. The analysis presented here and the obtained results could be useful in predicting the drying kinetics of potatoes and similar natural products in a conveyor-belt dryer.",
publisher = "Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd",
journal = "Thermal Science",
title = "A mathematical model and simulation of the drying process of thin layers of potatoes in a conveyor-belt dryer",
pages = "1118-1107",
number = "3",
volume = "19",
doi = "10.2298/TSCI130920020S",
url = "conv_927"
}

Salemović, D., Dedić, A.,& Ćuprić, N. Lj.. (2015). A mathematical model and simulation of the drying process of thin layers of potatoes in a conveyor-belt dryer. in Thermal Science
Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd., 19(3), 1107-1118.
https://doi.org/10.2298/TSCI130920020S
conv_927

Salemović D, Dedić A, Ćuprić NL. A mathematical model and simulation of the drying process of thin layers of potatoes in a conveyor-belt dryer. in Thermal Science. 2015;19(3):1107-1118.
doi:10.2298/TSCI130920020S
conv_927 .

Salemović, Duško, Dedić, Aleksandar, Ćuprić, Nenad Lj., "A mathematical model and simulation of the drying process of thin layers of potatoes in a conveyor-belt dryer" in Thermal Science, 19, no. 3 (2015):1107-1118,
https://doi.org/10.2298/TSCI130920020S .,
conv_927 .

TY  - THES
AU  - Đukanović, Gordana D.
PY  - 2012
UR  - http://eteze.bg.ac.rs/application/showtheses?thesesId=398
UR  - https://nardus.mpn.gov.rs/handle/123456789/1990
UR  - https://fedorabg.bg.ac.rs/fedora/get/o:6102/bdef:Content/download
UR  - http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=43936271
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/7
AB  - Harmonijskom simetrijom, kao potpuno bijektivnom i konformnom centralnom inverzijom, prikazana je transformacija svih tipova pramenova konika i njihovih specifičnosti u pramenove krivih trećeg i četvrtog reda i njihove preslikane specifičnosti, i obrnuto. Prepoznavanjem ekvivalentnosti inverzije sa klasičnom osnom simetrijom (nekomformna simetrija) ukazano je na neograničene mogućnosti za preslikavanje krivih i površi i dobijanje novih oblika koji će biti od koristi i u teoriji geometrije kao i u arhitektonskoj praksi
AB  - Harmonic symmetry, which is a completely bijective and conformal central inversion, is used to present the transformation of all types of pencils of conics and their specific features into the pencils of curves of the 3rd and 4th order and their mapped specific features and vice versa. The recognition of the equivalence of inversion with the classical axial symmetry (non-conformal symmetry) has created numerous possibilities for mapping curves and surfaces and obtaining new forms which can be of great use both in the theory of geometry and in the practice of architecture.
PB  - Univerzitet u Beogradu, Arhitektonski fakultet
T1  - Pramenovi krivih trećeg i četvrtog reda dobijeni preslikavanjem pramenova konika
T1  - The pencils of curves of the third and fourth order obtained by mapping the pencils of conics
UR  - https://hdl.handle.net/21.15107/rcub_nardus_1990
UR  - t-116
ER  - 

@phdthesis{
author = "Đukanović, Gordana D.",
year = "2012",
abstract = "Harmonijskom simetrijom, kao potpuno bijektivnom i konformnom centralnom inverzijom, prikazana je transformacija svih tipova pramenova konika i njihovih specifičnosti u pramenove krivih trećeg i četvrtog reda i njihove preslikane specifičnosti, i obrnuto. Prepoznavanjem ekvivalentnosti inverzije sa klasičnom osnom simetrijom (nekomformna simetrija) ukazano je na neograničene mogućnosti za preslikavanje krivih i površi i dobijanje novih oblika koji će biti od koristi i u teoriji geometrije kao i u arhitektonskoj praksi, Harmonic symmetry, which is a completely bijective and conformal central inversion, is used to present the transformation of all types of pencils of conics and their specific features into the pencils of curves of the 3rd and 4th order and their mapped specific features and vice versa. The recognition of the equivalence of inversion with the classical axial symmetry (non-conformal symmetry) has created numerous possibilities for mapping curves and surfaces and obtaining new forms which can be of great use both in the theory of geometry and in the practice of architecture.",
publisher = "Univerzitet u Beogradu, Arhitektonski fakultet",
title = "Pramenovi krivih trećeg i četvrtog reda dobijeni preslikavanjem pramenova konika, The pencils of curves of the third and fourth order obtained by mapping the pencils of conics",
url = "https://hdl.handle.net/21.15107/rcub_nardus_1990, t-116"
}

Đukanović, G. D.. (2012). Pramenovi krivih trećeg i četvrtog reda dobijeni preslikavanjem pramenova konika. 
Univerzitet u Beogradu, Arhitektonski fakultet..
https://hdl.handle.net/21.15107/rcub_nardus_1990

Đukanović GD. Pramenovi krivih trećeg i četvrtog reda dobijeni preslikavanjem pramenova konika. 2012;.
https://hdl.handle.net/21.15107/rcub_nardus_1990 .

Đukanović, Gordana D., "Pramenovi krivih trećeg i četvrtog reda dobijeni preslikavanjem pramenova konika" (2012),
https://hdl.handle.net/21.15107/rcub_nardus_1990 .

TY  - JOUR
AU  - Đukanović, Gordana
AU  - Obradović, Marija
PY  - 2012
UR  - https://omorika.sfb.bg.ac.rs/handle/123456789/414
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.
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.
PB  - Univerzitet u Nišu, Niš
T2  - Facta universitatis - series: Architecture and Civil Engineering
T1  - Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste
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
EP  - 207
IS  - 2
SP  - 193
VL  - 10
DO  - 10.2298/FUACE1202193D
UR  - conv_585
ER  - 

@article{
author = "Đukanović, Gordana and Obradović, Marija",
year = "2012",
abstract = "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., 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.",
publisher = "Univerzitet u Nišu, Niš",
journal = "Facta universitatis - series: Architecture and Civil Engineering",
title = "Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste, 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",
pages = "207-193",
number = "2",
volume = "10",
doi = "10.2298/FUACE1202193D",
url = "conv_585"
}

Đukanović, G.,& Obradović, M.. (2012). Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste. in Facta universitatis - series: Architecture and Civil Engineering
Univerzitet u Nišu, Niš., 10(2), 193-207.
https://doi.org/10.2298/FUACE1202193D
conv_585

Đukanović G, Obradović M. Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste. in Facta universitatis - series: Architecture and Civil Engineering. 2012;10(2):193-207.
doi:10.2298/FUACE1202193D
conv_585 .

Đukanović, Gordana, Obradović, Marija, "Pramen površi 4. i 3. reda dobijen kao harmonijski ekvivalent pramena kvadrika kroz prostornu krivu 4. reda 1. vrste" in Facta universitatis - series: Architecture and Civil Engineering, 10, no. 2 (2012):193-207,
https://doi.org/10.2298/FUACE1202193D .,
conv_585 .