th International Conference on Geometry and Graphics ... · The 6th International Conference on Geometry and Graphics MONGEOMETRIJA 2018 BOOK OF ABSTRACTS MONGEOMETRIJA 2018 June

MONGEOMETRIJA2018

Book of Abstracts

6th International Conferenceon Geometry and Graphics

The 6th International Conference on Geometry and Graphics

MONGEOMETRIJA 2018

BOOK OF ABSTRACTS

MONGEOMETRIJA

2018

June 6th – 9th 2018 Novi Sad, Serbia

Faculty of Technical Sciences

Novi Sad 2018.


MONGEOMETRIJA 2018

Publishers

Serbian Society for Geometry and Graphics (SUGIG) Faculty of Technical Sciences, University of Novi Sad

Title of Publication

BOOK OF ABSTRACTS

Editor-in-Chief

Vesna Stojaković

Co-Editor

Bojan Tepavčević

Graphic design

Vesna Stojaković

Formatters

Vesna Stojaković, Marko Vučić, Jelena Kićanović

Printing

Faculty of Technical Sciences – Graphical Center GRID

Number of copies printed 100

ISBN 978-86-6022-054-9


MONGEOMETRIJA 2018

Conference Organizers

Serbian Society for Geometry and Graphics (SUGIG)

Faculty of Technical Sciences, University of Novi Sad

Department of Architecture and Urban Planning, Faculty of Technical Sciences, University of Novi Sad

Digital Design Center

Under the auspices of

Provincial Secretariat for Higher Education and Scientific Research

CONFERENCE CHAIR

Vesna Stojaković – Serbia

SCIENTIFIC COMMITTEE

Hellmuth Stachel - Austria

Ema Jurkin - Croatia

Milena Stavrić - Austria

Albert Wiltsche - Austria

Marija Jevrić - Montenegro

Svetlana Shambina - Russia

Naomi Ando - Japan

Carmen Marza - Romania

Bölcskei Attila - Hungary

Luigi Cocchiarella - Italy

Vera Vianna - Portugal

Viktor Mileikovskyi - Ukraine

Renata Gorska - Poland

Cornelie Leopold - Germany

Emil Molnár - Hungary

Laszlo Voros - Hungary

Marija Obradović - Serbia

Gordana Đukanović - Serbia

Sonja Krasić - Serbia

Ljubica Velimirović - Serbia

Magdalena Dragović - Serbia

Aleksandar Čučaković - Serbia

ĐorĎe ĐorĎević - Serbia

Branislav Popkonstantinović - Serbia

Ljiljana Radović - Serbia

Branko Malešević - Serbia

Ksenija Hiel - Serbia

Milan Tomić - Serbia

Zorana Jeli - Serbia

Slobodan Mišić - Serbia

Miroslav Šilić - Serbia

Zoran Rakić - Serbia

Radovan Štulić - Serbia

Ratko Obradović - Serbia

Predrag ŠiĎanin - Serbia

Bojan Tepavčević - Serbia

Dejana Nedučin - Serbia

Ivana Bajšanski - Serbia

Igor Budak - Serbia

Marko Lazić - Serbia

Ana Perišić - Serbia

Radivoje Dinulović - Serbia

Jelena Atanacković Jeličić - Serbia

Darko Reba - Serbia

Milena Krklješ – Serbia

Maja Petrović – Serbia

Alina Duta – Romania

Dušan Gajić – Serbia

ASSISTANT TEAM

Marko Vučić - Serbia

Dimitrije Nikolić - Serbia

Marko Jovanović - Serbia

Dejan Mitov - Serbia

Igor Kekeljević - Serbia

Nenad Kuzmanović - Serbia

Bojan Banjac – Serbia

Jelena Kićanović - Serbia

MONGEOMETRIJA 2018, Novi Sad ISBN 978-86-6022-054-9

TABLE OF CONTENTS

ABOUT THE GEOMETRY OF TRANSITION PIECES RELATIVE TO THE FLAT-OVAL TUBING ................................... 2 CARMEN MÂRZA, GEORGIANA CORSIUC, ANA MARIA GRAUR

GEOMETRIC METHOD OF CONSTRUCTIONS OF PYTHAGOREAN TRIANGLES IN THE CONTEXT OF TRADITIONAL HINDU MATHEMATICS AND ARCHITECTURE .................................................................................................... 2

DMITRI KOZLOV

HOW PLATONIC AND ARCHIMEDEAN SOLIDS DEFINE NATURAL EQUILIBRIA OF FORCES FOR TENSEGRITY ...... 2 MARTIN FRIEDRICH EICHENAUER, DANIEL LORDICK

NON-EUCLIDEAN DESCRIPTIVE GEOMETRY, CONTEMPORARY DESIGN & VIRTUAL REALITY ............................ 2 DANAIL BREZOV, YANA KANCHEVA, TANYA NIKOVA

ON NON-EUCLIDEAN CIRCLE (SPHERE) GEOMETRY BY REFLECTION ................................................................. 3 EMIL MOLNÁR

SPATIAL INTERPRETATION OF FERMAT-WEBER’S SET OF POINTS OVER CONIC SECTIONS ................................ 3 MAJA PETROVID, BRANKO MALEŠEVID, RADOVAN ŠTULID, MARKO VUČID, RADOMIR MIJAILOVID

THE LIFE AND CONTRIBUTION OF GASPARD MONGE ....................................................................................... 4 IVANA CVETKOVID, MIŠA STOJIDEVID, BRANISLAV POPKONSTANTINOVID

RECALLING IVORY’S THEOREM ........................................................................................................................ 4 HELLMUTH STACHEL

A NEW APPROACH TO CLASSIFICATION AND CLUSTERING OF A METROPOLITAN AREA SHOPPING CENTERS – NOVI SAD AND CONNECTED CITIES IN REGION ................................................................................................ 5

SAŠA MEDID, ZORAN JELIČID, MILAN RAPAID, VUKAN TURKULOV, JELENA ATANACKOVID JELIČID

A STUDY ON THE MORPHOLOGICAL CHARACTERISTICS OF THE CONTEMPORARY ARCHITECTURE ROOFS....... 5 AKIHIRO SHIBATA, SATOI KAMIMOTO

ALGORITHM FOR SHAPE RECOGNITION OF GOTHIC WINDOW ........................................................................ 6 ISIDORA ĐURID, RATKO OBRADOVID, VERA VIANA, LIDIJA KRSTANOVID, JELENA LETID, BOJAN BANJAC, NEBOJŠA RALEVID

AN APPROACH TO THE AUTOMATIC ADDITION OF ANIMATIONS TO AVATARS IN THE FBX FILE FORMAT ....... 6 MILICA LAZOR, DUŠAN B. GAJID, DINU DRAGAN

DESIGN OF A BOARD GAME WITH AUGMENTED REALITY ................................................................................ 7 TASHKO RIZOV, JELENA DJOKIKJ, MILAN TASEVSKI

EDGE PREDICTION ALGORITHM FOR CORRECT OCCLUSION HANDLING IN ARCHITECTURAL AUGMENTED REALITY PRESENTATION .................................................................................................................................. 7

PETAR PEJIC, VESNA STOJAKOVIC, SONJA KRASIC, DRAGANA KRSTIC

FROM CARTESIAN TO TOPOLOGICAL GEOMETRY: CHALLENGING FLATNESS IN ARCHITECTURE....................... 8 YANNIS ZAVOLEAS, MARK TAYLOR

GEOMETRY BEHIND THE POSITION OF STAIRS: BALANCE IN THE MIND ........................................................... 8 MARIJA OBRADOVID, TATJANA GRUJID

GEOMETRY OF BUILDINGS FOR PRESCHOOL INSTITUTIONS IN VOJVODINA, SERBIA ....................................... 9 MILENA KRKLJEŠ, DEJANA NEDUČIN

ISBN 978-86-6022-054-9 MONGEOMETRIJA 2018, Novi Sad

GEOMETRY OF STREET SYSTEMS IN CENTRAL AREAS OF VOJVODINA'S TOWNS GEOMETRY ........................... 9 DARKO REBA, MARINA CAREVID TOMID

GLASS FRACTURING ON IMPACT WITH KINETIC OBJECTS ............................................................................... 10 ANDRIJANA KOVAČEVID

GROEBNER BASES AND FOCI OF DESCARTES OVAL ........................................................................................ 10 BRANKO MALEŠEVID, MAJA PETROVID, BOJAN BANJAC, DARKO STOŠID, MILOŠ PERIČID

HIGHER-ORDER RULED SURFACES AND POSSIBILITIES OF THEIR USAGE IN ARCHITECTURAL DESIGN ............ 11 VLADAN NIKOLID, OLIVERA NIKOLID, JASMINA TAMBURID, SANJA SPASID ĐORĐEVID, SANJA JANKOVID

INTERACTIVE RELIGHTING OF THE PORTRAIT PHOTOGRAPHS USING FACE TRACKING AND NORMAL MAPPING ....................................................................................................................................................... 11

SRĐAN MARKOVID, MARIJA OBRADOVID

MODULAR ALL PURPOSE BUILDING STRUCTURES WITH PLANAR ASSEMBLY COMPONENTS ......................... 12 STEFAN ŽIVANČEV

NEW SPACE-FILLING MOSAICS BASED ON 3D MODELS OF HIGER-DIMENSIONAL CUBES ............................... 12 LÁSZLÓ VÖRÖS

QUALITATIVE PREDICTION OF DEVELOPMENT OF INFORMAL SETTLEMENTS BY MEANS OF MATHEMATICAL MODELLING – VETERNIK PROJECT ................................................................................................................. 13

JELENA ATANACKOVID JELIČID, MILAN RAPAID, MIRNA KAPETINA, IGOR MARAŠ, DEJAN ECET, SAŠA MEDID, JELENA DESPOTOVID

SYNTHESIS OF DWELL LINKAGE MECHANISMS WITH HIGH CLASS STRUCTURAL GROUPS .............................. 13 MAJA ČAVID, MARKO PENČID, JOVAN DORID, MILAN RACKOV, ZHENLI LU

THE APPLICATION OF AUTOMATIC PHOTOGRAMMETRY IN ARCHITECTURAL RESTORATION AND CONSERVATION ............................................................................................................................................. 14

TAMARA STRIČEVID

THE APPLICATION OF NORMAL MAPPING IN CHARACTER'S FACIAL DESIGN .................................................. 14 NIKOLA GRBID

THE INFLUENCE OF URBAN GEOMETRY ON MITIGATING LAND SURFACES INSOLATION ................................ 15 MILICA IVKOVIC, IVANA BAJSANSKI, KATARINA STEFANOVIC, MIRJANA IGNJATOVIC

THE MORPHOLOGY OF ARCHITECTURAL SHAPESHIFTERS - FORMS OF REUSED BUILDINGS ........................... 15 MILAN BRZAKOVID, ALEKSANDAR MILOJKOVID, MARKO NIKOLID

TILING THE LATERAL SURFACE OF CC II BY REGULAR HEXAGONS AND TRIANGLES AS A DESIGN PROPOSAL IN ARCHITECTURE .............................................................................................................................................. 16

MARIJA OBRADOVID

VIRTUAL REALITY AS A MEDIUM FOR ARCHITECTURAL ANALYSIS .................................................................. 16 MARKO LAZID, ANA PERIŠID, PREDRAG ŠIĐANIN

3D MODELING TECHNIQUES FOR REVERSE ENGINEERING PHOTOGRAMMETRICALLY SURVEYED FREEFORM SURFACES ...................................................................................................................................................... 17

ANDRIJA MIHELČID

ANALYSIS OF DIFERENT METAMATERIAL GEOMETRY .................................................................................... 17 BORIS KOSIC, MISA STOJICEVIC, ZORANA JELI, BRANISLAV POKONSTANTINOVIC, ALEKSANDRA DRAGICEVIC


APPLICATION OF WAFFLE SECTIONING PRINCIPLES FOR GENERATING TWO VIEWING POINTS ANAMORPHIC SCULPTURE .................................................................................................................................................... 18

ANA MARJANOVID

BASIC GEOMETRY AND DESIGN OF SOLAR CONCENTRATORS ........................................................................ 18 MISA STOJICEVIC, ZORANA JELI,BRANISLAV POPKONSTANTINOVIC,MILOS OBRADOVIC,RATKO OBRADOVIC

BESPOKE GEOMETRIC GLAZING DESIGN FOR BUILDING ENERGY PERFORMANCE ANALYSIS .......................... 19 NICHOLAS MARIO WARDHANA, AIKATERINI CHATZIVASILEIADI, WASSIM JABI, ROBERT AISH, SIMON LANNON

CAD, CAE AND RAPID PROTOTYPING METHODS APPLIED IN LONG BONES ORTHOPAEDICS .......................... 19 DRAGOS-LAURENTIU POPA, BUCIU GABRIEL, DANIEL COSMIN CALIN

CREATION OF ORTHOPHOTOPLANS OF THE BUILDING FACADE USING OF UAV AND TERRESTRIAL IMAGES .. 20 PIECH IZABELA, RUZYCZKA ADAM

DESIGN AND FABRICATION OF MODULAR, RESPONSIVE MULTIFUNCTIONAL FURNITURE ............................. 21 NINA MILUTINOVID

DESIGN AND FABRICATION OF POROUS STRUCTURES USING ROBOTIC HOT KNIFE CUTTING ........................ 21 MARKO JOVANOVID, MARKO VUČID, BOJAN TEPAVČEVID, MIRKO RAKOVID

DESIGN OF A STREET-STYLE MOTORCYCLE CONCEPT ..................................................................................... 22 TASHKO RIZOV, RISTO TASHEVSKI, HRISTIJAN NAJDESKI

QUANTIFYING THE SMOOTHNESS-RELATED QUALITY OF ARCHITECTURAL/URBAN LINEAR OBJECTS’ SURFACES REPRESENTED BY PHOTOGRAMMETRICALLY CREATED POINT-CLOUDS AS A FUNCTION OF SHOOTING-DISTANCES AND NUMBER OF CAMERA POSITIONS I.E. SHOOTING-DIRECTIONS ......................... 22

DJORDJE DJORDJEVIC, GORDANA DJUKANOVIC, MIRJANA DEVETAKOVIC RADOJEVIC, NIKOLA POPOVIC

EMPLOYING MESH SEGMENTATION ALGORITHMS AS FABRICATION STRATEGIES - SKIN PATTERN GENERATION BASED ON REACTION-DIFFUSION MECHANISM ....................................................................... 23

EFFIMIA GIANNOPOULOU, PABLO BAQUERO, ANGAD WARANG, AFFONSO ORCIUOLI, ALBERTO T. ESTÉVEZ, MIGUEL A. BRUN-USAN

EPIDERMIS - AN INTRODUCTION TO ALGORITHMIC DESIGN BASED ON BIOMIMETIC MORPHOLOGICAL REFERENCES ................................................................................................................................................... 23

IOANNA SYMEONIDOU

FORM ANALYSIS OF LEGO ARCHITECTURE ..................................................................................................... 24 HIROMITSU SHIMIZU, HIROKI DAKIYAMA, NAOMI ANDO, SHOTA ISHII

GENERATING LINEAR FALSEWORK FOR FREEFORM STRUCTURES .................................................................. 24 STEFAN STOJČID, MARKO JOVANOVID

GEOMETRICAL AND CONSTRUCTION OPTIMIZATION OF CHURCH OF ST. JOSEPH THE CRAFTSMAN IN MEXICO OF ARCHITECT FELIX CANDELA ....................................................................................................................... 25

ZLATA TOŠID, SONJA KRASID, NAOMI ANDO, MILOŠ MILID

GEOMETRICAL ELABORATION OF AUXETIC STRUCTURES ............................................................................... 25 MILENA STAVRIC, ALBERT WILTSCHE

GEOMETRICAL OPTIMIZATION OF INTERCONNECTED VOIDS IN CONCRETE CEILINGS .................................... 26 KEVIN NOACK, MARTIN FRIEDRICH EICHENAUER,DANIEL LORDICK

IMPACT OF GLAZING PERCENTAGE OF THE FACADE ON IMPROVING INDOOR THERMAL COMFORT ............. 26 ANJA MILOVANOVID, IVANA BAJŠANSKI


IMPROVING THE INTEGRATION OF CGI AND PHOTOGRAPHY BY MATCHING SHADOWS BASED ON PERSPECTIVE RESTITUTION ............................................................................................................................ 27

DRAGANA MARKOVID, ANASTASIJA MARTINENKO

INTEGRATING PARAMETRIC DESIGN AND BUILDING PERFORMANCE SIMULATIONS ..................................... 27 AJLA AKSAMIJA

KERF BENDING STRATEGY FOR THE FABRICATION OF COMPLEX GEOMETRY WITH THICK PLANAR SHEET MATERIALS .................................................................................................................................................... 28

DEJAN MITOV, BOJAN TEPAVČEVID, VESNA STOJAKOVID, IVANA BAJŠANSKI

KINETIC FACADES – MODULATORS OF SUNLIGHT AND SHADOWS................................................................. 28 SANDRA VREKID

MASS CUSTOMIZATION APPROACH FOR THE CONFIGURABLE DESIGN OF ADAPTIVE FACADES ..................... 29 BOŽANA PETROVID

MULTI-CAMERA SYSTEM CALIBRATION FOR 3D SCENE RECONSTRUCTION, MODELING AND VISUALIZATIO . 29 JOVAN MIJATOV, VLADIMIR ZLOKOLICA, RATKO OBRADOVID, RELJA LJUBOBRATOVID, RADOVAN OBRADOVID, VLADIMIR

MASTILOVID, KREŠIMIR VDOVJAK, IRENA GALID

OVERVIEW OF GEOMETRIC ASPECTS OF PHOTOVOLTAIC SYSTEMS, RELEVANT FOR BUILDING INFORMATION MODELLING ................................................................................................................................................... 30

MIRJANA DEVETAKOVID, ĐORĐE ĐORĐEVID, GORDANA ĐUKANOVID, ALEKSANDRA KRSTID-FURUNDŽID, BUDIMIR SUDIMAC

PARAMETRIC DESIGN OF MASONRY VAULTS BASED ON STRUCTURAL AFFINITY ........................................... 30 DIMITRIJE NIKOLID, VESNA STOJAKOVID, RADOVAN ŠTULID

PARAMETRIC DESIGN OF SINGLE FAMILY ROW HOUSES ................................................................................ 31 JOVAN JEFTID

PARAMETRIC MODELING AS GEOMETRIC TOOL FOR DESIGNING URBAN MODEL OF BIOMORPHIC FORM INSPIRED BY FLOWER OF BELL FLOWER (CAMPANULA PERSICIFOLIA L.) ........................................................ 31

ALEKSANDAR A. ČUČAKOVID, DRAGICA D. OBRATOV- PETKOVID, BILJANA S. JOVID, ANĐELA D. MITID

PARAMETRIC OBJECT GENERATION DETERMINED BY ANAMORPHIC LIGHT SHADOW CONTOURS ................ 32 MILICA KNEZEVIC

PERCEPTION OF THREE-DIMENSIONAL GEOMETRIC SHAPES AS VIRTUAL 3D ROAD MARKINGS .................... 32 SVETLANA ČIČEVID, ALEKSANDAR TRIFUNOVID, DRAGAN LAZAREVID, MAGDALENA DRAGOVID, NATAŠA VIDOVID, MARIJANA

MOŠID

REVERSE ENGINEERING MODELING AS A TOOL OF DIGITAL SCULPTING ........................................................ 33 ŽELJKO SANTOŠI, IGOR BUDAK, MARIO ŠOKAC

ROBOTIC MATERIAL FORMATIONS - EXPLORING THE GEOMETRIC SPECTRUM UNLEASHED BY ROBOTIC

THERMOFORMING ........................................................................................................................................ 33 RENATE WEISSENBÖCK

SIMULATION AND MOTION STUDY OF MECHANICAL INTEGRATOR 3D MODEL ............................................. 34 BRANISLAV POPKONSTANTINOVIC, RATKO OBRADOVIC, MISA STOJICEVIC, ZORANA JELI, MILOS OBRADOVIC

THE INFLUENCE OF PLANAR DIFFUSER PANELS ON IMPROVING ACOUSTICAL PROPERTIES OF INTERIOR SPACES........................................................................................................................................................... 34

MARINA MUDRI


USE OF BIOMIMICRY IN THE DESIGN OF MODERN ARCHITECTURAL STRUCTURES ......................................... 35 SANJA JANKOVID, VLADAN NIKOLID, SANJA SPASID ĐORĐEVID, MILOŠ NEDELJKOVID

AND WHAT ABOUT THE HISTORY OF DESCRIPTIVE GEOMETRY IN SERBIA? ................................................... 35 KATARINA JEVTID-NOVAKOVID, SNEZANA LAWRENCE, MARIJA DIVAC

APPROACHING DESCRIPTIVE GEOMETRY WITHIN THE EVER EXPANDING CONTEXT OF COMPUTER-ASSISTED DESIGN IN ROMANIAN ACADEMIC EDUCATION ............................................................................................. 36

ALINA DUTA, LUDMILA SASS, GABRIEL – CATALIN MARINESCU

FORMS AND SPACES OF ANCIENT ASIAN ARCHITECTURE: IMAGES OF ANCIENT JAPANESE AND CHINESE ARCHITECTURE DEPICTED IN MOVIES ........................................................................................................... 36

NAOMI ANDO

IMPORTANCE OF STUDYING GEOMETRIC SURFACES IN ARCHITECTURE FOR STUDENTS IN THE FACULTY OF ENGINEERING AND DESIGN, OF HOSEI UNIVERSITY IN TOKYO, JAPAN ........................................................... 37

SONJA KRASID, NAOMI ANDO, PETAR PEJID, ZLATA TOŠID

NOVEL APPROACH FOR 3D MODELLING TEACHING METHODOLOGY ............................................................. 37 ALEKSANDRA JOKSIMOVID, EMIL VEG, MLADEN REGODID, GORAN ŠINIKOVID

SEARCH THROUGH THE PAST, SERBIAN TEXTBOOKS OF 19TH CENTURY: DIMITRIJE STOJANOVIC – METHODOLOGY OF DESCRIPTIVE GEOMETRY ................................................................................................ 38

KATARINA JEVTID-NOVAKOVID, OLGA TIMČENKO, MARIJA DIVAC

SPHERICAL PERSPECTIVE IN DESIGN EDUCATION ........................................................................................... 38 MATTHIAS KULCKE

THE HELICAL SURFACES AND THEIR APPLICATION IN STUDENTS' WORKS ...................................................... 39 ANA-MARIA GRAUR, CARMEN MÂRZA, GEORGIANA CORSIUC

VILNIUS CITY IN VIRTUAL REALITY - A WIDE AND SAFE PLAYGROUND FOR CREATIVITY DEVELOPMENT ........ 39 RYTE ZIURIENE, FRANZ FISCHNALLER,ZILVINAS LILAS

WEB TEXTBOOK FOR DESCRIPTIVE GEOMETRY .............................................................................................. 40 SONJA GORJANC, EMA JURKIN

ANALYSIS OF THE APPLICATION GEOMETRIC SURFACES IN PRACTICE - MONUMENTS IN THE SFR YUGOSLAVIA .................................................................................................................................................. 40

SANJA SPASID ĐORĐEVID, VLADAN NIKOLID, SANJA JANKOVID, HRISTINA KRSTID

ON APPROXIMATION OF OVALS IN ARCHITECTURAL DESIGN: BEST FITTING CURVE FOR THE DOME OF SAN CARLO ALLE QUATTRO FONTANE BY FRANCESCO BORROMINI ...................................................................... 41

MAJA PETROVID, BRANKO MALEŠEVID, RADOVAN ŠTULID, MARKO VUČID, ĐORĐE PETROVID, RADOMIR MIJAILOVID

PRINCIPLES OF ARCHITECTURAL COMPOSITION IN ARCHITECT JOŽE PLEČNIK’S CHURCH OF ST. MICHAEL ON BARJE ............................................................................................................................................................. 41

DOMEN KUŠAR, MATEJA VOLGEMUT

THE LANGUAGE OF PROPORTIONS IN THE PARAMETRIC FRAME: EXQUISITE SERBIAN MEDIEVAL CHURCHES OF RAŠKA STYLE GROUP ................................................................................................................................ 42

MAGDALENA DRAGOVID, ALEKSANDAR ČUČAKOVID, MARKO PEJID, MILESA SREDKOVID


ABOUT THE GEOMETRY OF TRANSITION PIECES RELATIVE TO THE FLAT-OVAL TUBING

Carmen Mârza1, Georgiana Corsiuc2, Ana Maria Graur3 1Technical University of Cluj-Napoca (ROMANIA), [email protected]

2Technical University of Cluj-Napoca (ROMANIA), [email protected] 3Technical University of Cluj-Napoca (ROMANIA), [email protected]

Abstract

Air quality - a fundamental component of well-being - is assured through ventilation and/or air conditioning installations. The air transport is made by relatively large ducts equipped with auxiliary pieces to ensure the distribution of air in the rooms and the suction of contaminated air respectively. The less generalized tubing type with a flat-oval section cumulates the benefits of both circular and rectangular ducts. In this paper, the authors present the geometry of the reducing and enlarging pieces of the flat-oval ducts section, and of the transition pieces between the flat-oval sections and circular or rectangular sections, respectively. Using the descriptive geometry methods, one obtains the patterns required to construct these pieces.

Keywords: ventilation, flat-oval tubes, transition piece, developments of surfaces, patterns.

GEOMETRIC METHOD OF CONSTRUCTIONS OF PYTHAGOREAN TRIANGLES IN THE CONTEXT OF TRADITIONAL HINDU

MATHEMATICS AND ARCHITECTURE

Dmitri Kozlov

Research Institute of Theory and History of Architecture and Urban Planning (RUSSIA), [email protected]

Abstract

The architecture and mathematics of ancient India based on the same principles of traditional geometry. The most important geometric constructions, which underlain the traditional Hindu architectural theory, were regular square grids, known as Vastu-Purusa Mandalas, and different Pythagorean triangles applied to proportioning of altars. In the paper it is demonstrated that these two as it may seem quite distant fields of geometry constitute mutually complementary processes. The regular square grids generate all possible Pythagorean triangles and the triangles in turn generate the more and more sophisticated square grids.

Keywords: architecture, geometry, history, ancient mathematics, Pythagorean triangles, square grids.

mailto:[email protected]



2

HOW PLATONIC AND ARCHIMEDEAN SOLIDS DEFINE NATURAL EQUILIBRIA OF FORCES FOR TENSEGRITY

Martin Friedrich Eichenauer1*, Daniel Lordick2 1TU Dresden (GERMANY), [email protected]

2TU Dresden (GERMANY), [email protected]

Abstract

The Platonic and Archimedean solids are a well-known vehicle to describe certain phenomena of our surrounding world. It can be stated that they define natural equilibria of forces, which can be clarified particularly through the packing of spheres. To give an example, the tetrahedron and octahedron have a rather dense packing of spheres defined by a hexagonal stacking, the cube consists of a less efficient cubic pattern, which is still known from metallurgy and crystallography. To solve the problem of the densest packing, both a geometrical and a mechanical approach can be exploited. The mechanical approach works on the principle of minimal potential energy whereas the geometrical approach searches for the minimal distances of centers of mass. If random numbers of spheres are held together by an external pressure and still have the possibility to organize regularly, one of the described configurations is formed. The vertices of the solids are given by the centers of the spheres. If we expand this idea by a contrary force, which pushes outwards, we obtain the principle of tensegrity. Tensegrity is a system, where pressure and tensile forces are in a state of equilibrium while the elements of pressure are not touching each other. We can show, that we can build up regular and half-regular polyhedra by the interaction of physical forces. This supports the idea of developing more complex and bigger structures, which are useful for several applications. Every platonic and Archimedean solid can be converted into a tensegrity structure. Following this, a vast variety of shapes defined by multiple solids can also be obtained.

Keywords: Platonic Solids, Archimedean Solids, Tensegrity, Force Density Method, Packing of Spheres, Modularization.

NON-EUCLIDEAN DESCRIPTIVE GEOMETRY, CONTEMPORARY DESIGN & VIRTUAL REALITY

Danail Brezov1*, Yana Kancheva2, Tanya Nikova3

1 University of Architecture, Civil Engineering and Geodesy (BULGARIA), [email protected] 2University of Architecture, Civil Engineering and Geodesy (BULGARIA), [email protected]

3University of Architecture, Civil Engineering and Geodesy (BULGARIA), [email protected]

Abstract

In this paper we consider the non-Euclidean descriptive geometry of three-dimensional homogeneous spaces and its possible applications to virtual reality, architecture and design. As a preparation for this mathematical adventure, we first study curved screens in Euclidean space, which are later used in the more general case. Other authors ignore the fact that the canvas of an artist, drawing objects in hyperbolic space for instance, is flat only with respect to the corresponding metric, but not from Euclidean point of view. Similar considerations apply also to the spherical case, in which the notion of perspective is rather unusual and needs to be dealt with carefully. Two-dimensional models are used as an illustration of certain features. The geometries of the

sphere and hyperbolic space are introduced projectively in straightforward analogy with the Euclidean case,

but with some new peculiar features. Potential applications can be found in physics, e.g. optics, relativity and quantum scattering, arts and design, as well as educational and gaming virtual reality technologies.

Keywords: descriptive geometry, curvature, perspective, architecture, design, virtual reality.





3

ON NON-EUCLIDEAN CIRCLE (SPHERE) GEOMETRY BY REFLECTION

Emil Molnár

Budapest University of Technology and Economics (HUNGARY), [email protected]

Abstract

In this survey we refresh the classical circle geometry and circle inversion as basic transformation, so that they can be extended to non-Euclidean planes, mainly to the Bolyai-Lobachevsky hyperbolic plane. These involve analytic discussions and extension to higher dimensions, based on projective metrics, and lead to generalized Poincaré (conformal) models of non-Euclidean geometries. Novelties arise that we reformulate and extend (slightly renew) our German papers, and ―introduce‖ them into the English electronic literature. We mainly concentrate on plane geometries, higher dimensional cases cause ―only technical‖ (but tiresome) difficulties.

Keywords: reflection, circle, cycle, inversion, absolute projective metric plane, extension to higher dimensions.

SPATIAL INTERPRETATION OF FERMAT-WEBER’S SET OF POINTS OVER CONIC SECTIONS

Maja Petrović1*, Branko Malešević2, Radovan Štulić3, Marko Vučić4, Radomir Mijailović5

1University of Belgrade (SERBIA), [email protected]


3University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected]



Abstract

The concept of the Fermat-Torricelli‘s point in the triangle is generalized to the Fermat-Torricelli‘s set of points of conics. A spatial restitution of the conics following the Pappos-Boskovic‘s definition has been devised. We have analyzed five cases of an ellipse definition and three cases of a hyperbola, and showed that the global minimum of each surface is the Fermat-Torricelli‘s set of points. Both analytical notation and graphical representation has been presented.

Keywords: Conic sections; Weberian curves; Fermat –Weber‘s set of points.


4

THE LIFE AND CONTRIBUTION OF GASPARD MONGE

Ivana Cvetković1*, Miša Stojićević2, Branislav Popkonstantinović3


2,3University of Belgrade (SERBIA), [email protected]; [email protected]

Abstract

Gaspard Monge, known as a father of modern descriptive and differential geometry, was born in Beaune in 1746. He attended the Oratorian College in his hometown where he completed his elementary and secondary education. At the age of 17, Monge continued his education in Lyon. In 1764, he returned to Beaune where he was engaged to draw a detailed plan of his birthplace, which was seen by an officer at the École Royale du Génie de Mézières. Since he was the son of a merchant, Monge could enter the school only as a draftsman, not as a student. Eventually, he was asked to draw the plan of fortification that would prevent the enemy from seeing or attacking the target no matter what the position of the enemy is. This plan was a success and his techniques were marked as a military secret for a long period of time. In 1780, he was elected to the Academy of Science and participated in the work of commission for Weights and Measures, that was in charge of moving the system from imperial to metric. Gaspard Monge was a supporter of French Revolution and in 1792 he was appointed Minister of the Marine, but he was on that position for only 8 months. Due to the National Convention (1793), Academy of Sciences was abolished and many educational institutions were closed. In 1794, Monge helped setting up of the École Centrale des Travaux Publics (later École Polytechnique) where he was lecturing Descriptive Geometry. As the participant in Italian campaign in 1796, Monge met Napoleon and since that moment, they became very close friends. In 1798, Napoleon undertook a campaign in Egypt. Famous chemist Claude Louis Berthollet was asked to recruit prominent scientists. Among them were Fourier, Monge, Dolomieu and Malus. Institut d‘Egypte was established by Napoleon and Monge was named as its president. Being defeated in the battle of Nile, Napoleon decided to return to France secretly and Monge and Berthollet were chosen to accompany him. When they returned to France in 1799, Monge was awarded with a lot of distinguished titles such as senator for life and Count of Péluse. In 1806, he was elected president of Senate. Monge supported Napoleon even after defeat at Waterloo. He left France in 1815 and returned one year later. He was expelled from the Academy (restored in 1795). Monge passed away on July 28, 1818. His students were prohibited to attend the funeral and the speech on the funeral was delivered by his friend Claude Louise Berthollet. His name is inscribed on the base of the Eiffel Tower and it is located on the third façade opposite the Military Academy. Besides descriptive geometry, he carried on many different researches in chemistry and physics. Monge was first to explain phenomenon of mirage (it fascinated him on his march across the desert from Alexandria to Cairo). He also wrote a paper about synthesis of water by ignition of a mixture of oxygen and hydrogen. In 1786, Monge, Vandermonde and Berthollete published the work which was discussing the characteristics of iron in different metallic states. Gaspard Monge worked on capillarity, color perception, gas liquefaction and decomposition of CO2 as well.

Keywords: Gaspard Monge, Napoleon, Descriptive Geometry, École Polytechnique.

RECALLING IVORY’S THEOREM

Hellmuth Stachel

Vienna University of Technology (AUSTRIA), [email protected]

Abstract

Ivory's Theorem states that in each curvilinear quadrangle of a confocal net of conics the two diagonals have the same lengths. This theorem is valid not only in the Euclidean plane, but also in planar hyperbolic, spherical and pseudo-Euclidean (or Minkowski) geometry, and similar statements hold in all dimensions. Recent publications on this theorem and its generalizations on surfaces are the reason to focus again on this topic and to show a few algebraic consequences.

Keywords: Ivory's Theorem, confocal conics, incircular net, Poncelet grid.





5

A NEW APPROACH TO CLASSIFICATION AND CLUSTERING OF A METROPOLITAN AREA SHOPPING CENTERS – NOVI SAD AND

CONNECTED CITIES IN REGION

Saša Medić1*, Zoran Jeličić2, Milan Rapaić3, Vukan Turkulov4, Jelena Atanacković Jeličić5






Abstract

The emergence of shopping centers in the countries of Central and Eastern Europe represents the important topic as their expansion can particularly be noted during the past several years. Therefore, there are many authors who have dealt with the factors and impacts of their development. However, positioning of the shopping centers is the field which has not been explored at an extensive level. This paper aims at providing the basis for the shopping centers locations predictive model evolvement. The research within this paper refers to the collected data analysis from the cities comparable to Novi Sad within the same region and the results comparison to the ongoing shopping center development in the city of Novi Sad. Collected data belongs to the domain of average net wages and demographic statistics and it is set in correlation to the shopping centers proximity to the city center. Research results show the interdependence between the analysed data values. The paper presents the research results – the interdependence between the analysed data, as well as the possibilities for their future application.

Keywords: shopping centers, data analysis, clustering, predictive model.

A STUDY ON THE MORPHOLOGICAL CHARACTERISTICS OF THE CONTEMPORARY ARCHITECTURE ROOFS

Akihiro Shibata1*, Satoi Kamimoto2 1Kagoshima University (JAPAN), [email protected]

2VAGA HOUSE Ltd. (JAPAN), [email protected]

Abstract

The aim of this study is to clarify the morphological characteristics of roof form and composition of the contemporary buildings and houses that published in the architectural magazine in Japan that runs articles about architectures in the world. At the first, the roof top view forms are analyzed with their figures that are convex or concave, straight or curving, having breakpoints or not. The second, the sectional forms are analyzed with their figures in the similar way, which are concave or convex, straight or curving, having breakpoints or not, symmetry or asymmetry. Then, the sectional forms are analyzed based on grounding angle of their walls or roofs and having eaves or not. Further, the finishing materials of wall and roof are analyzed. The third, repetition of roofs are analyzed with the similarity of the sectional form of roofs and by the arrangement of roofs. Finally, 16 types of undulating roof design of the contemporary building and house are suggested by the relationship between the roof top view forms and the sectional forms and the finishing materials of wall and roof.

Keywords: Architecture, Design, Roof, Form, Space, and Symmetry.


6

ALGORITHM FOR SHAPE RECOGNITION OF GOTHIC WINDOW

Isidora Đurić1*, Ratko Obradović2, Vera Viana3, Lidija Krstanović4, Jelena Letić5, Bojan Banjac6, Nebojša Ralević7

1Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected]


3 Centre for Studies in Architecture and Urbanism of the Faculty of Architecture of Porto's University,

(PORTUGAL), [email protected] 4Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected]




Abstract

This research presents the development of an image-based algorithm for shape recognition of the Gothic window from the single image. Given an orthophoto of the Gothic window and a query image, the algorithm is supposed to estimate the closest match to the shape of the windows. In order to test the algorithm, the images of two churches of characteristics revived from the Gothic architectural style were used. The Gothic architectural style is chosen since it is widely recognizable by the distinct shape of the long opening with a pointed arch. This paper describes the proposed methodology in detail and presents the tables with the obtained results of the performed experiments.

Keywords: image-processing algorithm, shape recognition, Gothic window, orthophoto

AN APPROACH TO THE AUTOMATIC ADDITION OF ANIMATIONS TO AVATARS IN THE FBX FILE FORMAT

Milica Lazor1*, Dušan B. Gajić1 Dinu Dragan1 1University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected];

[email protected]; [email protected]

Abstract

Animated three-dimensional (3D) models are an essential component which is used frequently in present day movie and gaming industries, as well as in many other fields of human activities. However, time required for the manual development of 3D models is a limiting factor in many of their practical applications. Therefore, in order to minimize the production time of 3D models and thus lower costs, there is a need for the automation of the animation process. This paper presents an approach to the programmatic addition of animations to automatically rigged avatars which are stored using the industry-standard FBX file format. The presented custom solution is developed using the C++ programming language and the Autodesk FBX Software Development Kit (SDK). It allows significantly higher degree of automation and programmability than the approaches based on using standard 3D modelling and animation software, such as 3Ds Max or Maya.

Keywords: computer animation, computer graphics, automation, avatars, FBX, C++.


7

DESIGN OF A BOARD GAME WITH AUGMENTED REALITY

Tashko Rizov1, Jelena Djokikj1, Milan Tasevski 2 1Faculty of Mechanical Engineering, University “Ss. Cyril and Methodius” (MACEDONIA),

[email protected] 2Archona Games (MACEDONIA), [email protected]

Abstract

This paper presents the design process of a board game with augmented reality. The board games have remained attractive in this time of complete digitalization. The experience of hands on play has been the key feature of the board game. By introducing AR in the board games this key feature is kept together with digitalization of some elements of the gameplay. Augmented reality games provide players with a rich and potentially unlimited range of interaction possibilities. Implementation of AR creates added value to the game. We want to enhance the game experience by combining the best features from classical board games and video games. The benefits of playing board games are numerous in contrary to the video games. By implementing AR we will interest the video players too. This paper presents an example of the design of what is known as AR Board Game, a class of table-top games that combines handheld devices (such as smart phones) with physical game pieces to create a merged physical/virtual game on the table-top. Along with that, the paper describes the process of designing a board game that incorporates AR, along with technical implementation. The design process is performed using the well-known principles. The goal of the research is to identify the benefits for the players of introducing digital technology in the analogue world of the board games. Comparison of the user experience in the case of using just the board game and the board game with AR is conducted. For the sample under consideration were accounted board game players but also video games players. Results of the conducted comparison are presented and discussed. At the end the whole experience of designing such a product is presented along with ideas for further work.

Keywords: augmented reality; board game; design process; gameplay.

EDGE PREDICTION ALGORITHM FOR CORRECT OCCLUSION HANDLING IN ARCHITECTURAL AUGMENTED REALITY

PRESENTATION

Petar Pejic1*, Vesna Stojakovic2, Sonja Krasic3, Dragana Krstic4



3Faculty of Civil Engineering and Architecture, University of Nis (SERBIA), [email protected] 4Faculty of Civil Engineering and Architecture, University of Nis (SERBIA), [email protected]

Abstract

Augmented Reality (AR) is a computer technology where the perception of the user is enhanced by the seamless blending between real environment and computer-generated virtual objects coexisting in the same space. AR is used in architectural presentations as a novel approach in visualization of architect‘s idea, presenting a virtual 3D model inside existing surroundings. In this paper we elaborate novel solution for correct occlusion handling using the AR system with Time Of Flight (TOF) camera and a uniquely developed algorithm, based on Edge Prediction Method (EPM). Our method is compared with two other (TSDF and RANSAC) using Google Tango devices equipped with TOF camera. Testing is done on real examples of interior design and results are elaborated.

Keywords: Augmented Reality, occlusion, architecture, TOF, EMP, RANSAC, TSDF.









8

FROM CARTESIAN TO TOPOLOGICAL GEOMETRY: CHALLENGING FLATNESS IN ARCHITECTURE

Yannis Zavoleas1*, Mark Taylor2 1The University of Newcastle (AUSTRALIA), [email protected]

2Swinburne University of Technology (AUSTRALIA), [email protected]

Abstract

By focusing on the notion of surface in architecture, this paper traces a thread of transitioning from geometric regularity to topological expression since late modernism. Modernism‘s preference to Cartesian geometry goes along with concurrent innovations of the building industry promoting constancy, repetition and standardisation as aims to achieve higher quality at lower cost and within shorter time. During post-war era, there were cases where alternative studies on topological surface that challenged Cartesian geometry as a means to offer solutions both in architecture and structural engineering, however, not causing a radical shift in what is still considered as being the norm in construction. Even more, the same Cartesian logic has been transferred to the digital environment and so architectural elements are normally designed as simple geometric prisms and their direct derivatives. This paper contests the above assumption, by showing that extended computation entails bypassing geometric regularity as a starting prerequisite to define shape. Instead, it proposes to rethink architectural elements beyond Cartesian logic, and to treat surface as a soft compound perceived and resolved through its direct interactions with data inputs to produce design schemes.

Keywords: form-finding, topology, oblique, nesting, folding, soft architecture.

GEOMETRY BEHIND THE POSITION OF STAIRS: BALANCE IN THE MIND

Marija Obradović1, Tatjana Grujić2 1University of Belgrade, Faculty of civil Engineering (SERBIA), [email protected]

2University of Kragujevac, Faculty of Philology and Arts (SERBIA), [email protected]

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 strech along the line which divides the building basis in two eqal halves.

Keywords: conceptual metaphor, balance, centre of gravity, area bisector, symmetry, stairs.




9

GEOMETRY OF BUILDINGS FOR PRESCHOOL INSTITUTIONS IN VOJVODINA, SERBIA

Milena Krklješ1*, Dejana Nedučin2 1University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected]


Abstract

Preschool buildings are among the most prevalent contemporary architectural programs from the group of public buildings. They are featured in all urban and rural areas of our society and represent the basic spatial frameworks where the most important segments of children‘s development takes place. Therefore, they need to provide a physical environment for adequate care and upbringing of children. The typological classification of preschool buildings proposed by this research will refer to functional and spatial organization with the focus on their layouts. A starting point for determining the types of preschool buildings on the territory of Vojvodina, Serbia relates to their spatial organization and geometry, as well as to various interrelations of functional units that define them in a spatial sense. As the classroom represents the basic functional unit in which children spend their time, the typological classification refers to spatial disposition of classrooms in relation to the system of horizontal and vertical communications. The aim of this paper is to analyse geometry of layouts of preschool buildings in Vojvodina, determine whether their design fits the requirements of pedagogical programs, as well as functional requirements, and raise the question whether the geometry of preschool buildings has a positive or negative influence on the quality of program performance with children. The results of such a research maybe incorporated in the strategy for designing preschool buildings.

Keywords: Preschool buildings, typology, geometry, design.

GEOMETRY OF STREET SYSTEMS IN CENTRAL AREAS OF VOJVODINA'S TOWNS GEOMETRY

Darko Reba1, Marina Carević Tomić2 1Faculty of Technical Science, University of Novi Sad (SERBIA), [email protected]

2Faculty of Technical Science, University of Novi Sad (SERBIA), [email protected]

Abstract

Street system is one of the most significant features of urban morphology, and all other urban elements are influenced by its geometry - important ones such as squares, streets and urban blocks, and all the others as green spaces, river banks, sports and industrial facilities and spaces for many other uses as well. Street system geometry is a direct and exact expression of relations between built and open urban spaces. Geometry of street system is developed by many influential factors, first of all, geometry of terrain on which it is developed, urban water, vegetation and other natural elements, but at the same time by number of artificial features, such as means of traffic of the time when system was established, position in city, economic value of land, and many others which form and make the shape of open urban spaces. In theory of architecture and urbanism, there are numerous studies of urban elements as well as whole cities, which examine processes and relationships in cities, from different points of view and aspects. Study of relations between street system and its geometry is oriented to the analyses of open spaces of the cities, with the goal of understanding, reading and finding the rules and logics of complex terms of numerous elements which form street system, as well as whole "multidimensional container" - words which Lewis Mumford used to define the city. Knowing that the structure, shape and geometry of the open city space and its street system is a physical expression of multilayered and at the same time complex life and urban processes, one of the primary goals of the work is a study of the important and numerous layers which form the city. The essential idea of the work is the fact that contemporary architecture and urban design don‘t put sufficient attention to the process of connections and relations of the elements of urban morphology, for example, street system and street, with components such as architectural typology, urban equipment and parterre, or concept of urban vegetation and water… which often leads to inadequate identity, social issues, and other important aspects of urban environments and especially their open spaces. In the first part of the paper, there would be presented theoretical part of the topic which is related with studies of important questions of the structuring of street systems which influence their geometry and morphology, such as typology, analysis of



10

influential factors, as well as numerous important topics related to their social and traffic requirements. In the second, practical, part of the paper, we will establish the criteria for analysis of central part of Vojvodina‘s towns. Six central areas would be included in the study - cities like Novi Sad and Sombor, towns like Zrenjanin and Kikinda, throughout the smallest settlements as Kula and Titel. The practical part of the paper will be explained through graphical analyses, in which are presented the geometry and morphology of the central areas in dimensions of one square kilometrebecause that measure can express most important and interesting features about purpose and transformations of its geometry. Harmonization and coordination of architecture and urban design, in sense of adequate and interesting relations of built structures and open spaces, is the topic to which most part of work is dedicated to. One of the significant goals is achieving of coordination and continuity of urban space elements, which can be described as protection, addition, changing and adaptation with sensibility, with knowledge and sense of art, in direction of achieving exuberant urban picture, which will adequately express urban and cultural level of citizens and their unique way of life.

Keywords: street system, geometry, urban design, pattern, social places.

GLASS FRACTURING ON IMPACT WITH KINETIC OBJECTS

Andrijana Kovačević

Faculty of Technical Sciences (SERBIA), [email protected]

Abstract

Due to the incresing growth and development of computer graphics and their use in gaming industry, graphic design, architectural visualisation and design, a more detailed research is conducted regarding the realistic depiction of things. Specificaly, glass is a very interesting topic for it's common use in our surroundings as well as it's mechanical and physical characteristics. Because the contemporary architecture practise is growing more and more dependant on the computer generated imagery the glass attributes are interpretated and translated into the virtual models.

Keywords: glass, fracture, model, geometry, fragmentation, model.

GROEBNER BASES AND FOCI OF DESCARTES OVAL

Branko Malešević1*, Maja Petrović 2, Bojan Banjac3, Darko Stošić4, Miloš Peričić5 1University of Belgrade, School of Electrical Engineering (SERBIA), [email protected]

2University of Belgrade, Faculty of Transport and Traffic Engineering (SERBIA), [email protected]


4University of Belgrade, School of Electrical Engineering (SERBIA), [email protected]

5University of Belgrade, School of Electrical Engineering (SERBIA), [email protected]

Abstract

In this paper, by application of algebraic techniques of Groebner basis of polynomial ideal, we show that it is possible to determine the third focus of Descartes ovals as point that is generative for this oval (in the sense that any of other two foci of Descartes oval can be substituted by third focus). Also, we present one Java application for visual representation of Descartes oval with their foci and parameters.

Keywords: Groebner bases, Descartes oval, Focal points, Computer visualization.


11

HIGHER-ORDER RULED SURFACES AND POSSIBILITIES OF THEIR USAGE IN ARCHITECTURAL DESIGN

Vladan Nikolić1*, Olivera Nikolić2, Jasmina Tamburić2, Sanja Spasić ĐorĎević3, Sanja Janković3

1Faculty of Civil Engineering and Architecture in Niš (SERBIA), [email protected]

2Faculty of Civil Engineering and Architecture in Niš (SERBIA)

3Faculty of Civil Engineering and Architecture in Niš (SERBIA)

Abstract

In this paper, higher-order ruled surfaces are analyzed and processed, from the aspect of their application in architecture and design. The possibilities of applying their characteristic segments and cuttings in the design of architectural objects, as well as the possibilities of their multiplication and combining into more complex spatial structures are considered. Suggested design solutions should, in a practically applicable way, enable the implementation of higher-order surfaces into geometric shapes of future architectural structures, as well as their use in different areas of design. We have defined the criteria for the selection of higher-order ruled surfaces and their successful research, analysis and practical application are distinguished.

Keywords: architecture, design, higher-order ruled surfaces, application.

INTERACTIVE RELIGHTING OF THE PORTRAIT PHOTOGRAPHS USING FACE TRACKING AND NORMAL MAPPING

SrĎan Marković1*, Marija Obradović2 1UIUX Designer (SERBIA), [email protected]

2Faculty of Civil Engineering, University of Belgrade (SERBIA), [email protected]

Abstract

In recent years, 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 bases 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. In such a manner, we can change the expressiveness of the photograph itself, add dramatic effects, characteristics of the Baroque style or other desired results.

Keywords: depth map, normal map, lighting, face recognition, rendering.



12

MODULAR ALL PURPOSE BUILDING STRUCTURES WITH PLANAR ASSEMBLY COMPONENTS

Stefan Ţivančev

University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected]

MODULARITY is the degree to which a system's components may be separated and recombined to form various shapes and structures. ―Modular construction is a process in which a building is constructed off-site, under controlled plant conditions, using the same materials and designing to the same codes and standards as conventionally built facilities – but in about half the time. Buildings are produced in ―modules‖ that when put together on site, reflect the identical design intent and specifications of the most sophisticated site-built facility – without compromise‖. The word modularity can have many meanings in different research areas, it is used in chemistry, biology, cognitive science, construction, architecture, art, media, etc. We are surrounded by modularity, and it is the main building block of our world. The main goal of this research is to find a place for modularity in architecture.

Keywords: modularity, architecture, nature, flexibility.

NEW SPACE-FILLING MOSAICS BASED ON 3D MODELS OF HIGHER-DIMENSIONAL CUBES

László Vörös

University of Pécs (HUNGARY), [email protected]

Abstract

A special 3-dimensional zonotope model of more-dimensional cubes is described in the paper. The parts of this are 3D models of the lower-dimensional parts of the cube. These have rhombic faces that are congruent with the faces of the model of the whole cube. The suitable combination of all these elements touching each other by the congruent faces create periodical space-filling tessellations. The planar intersections of these spatial mosaics provide even series of plane-tiling patterns. The topic can have relations to industry, arts and design. The paper introduce an inventory of the already constructed mosaics and the applied stones. Some new constructions are described and showed by figures in the paper and animations of the gained patterns are viewable on a referred home page.

Keywords: constructive geometry, hyper cube, zonotope, planar and spatial tessellation, art, design.



13

QUALITATIVE PREDICTION OF DEVELOPMENT OF INFORMAL SETTLEMENTS BY MEANS OF MATHEMATICAL MODELLING –

VETERNIK PROJECT

Jelena Atanacković Jeličić1*, Milan Rapaić2, Mirna Kapetina3, Igor Maraš4, Dejan Ecet5, Saša Medić6, Jelena Despotović7

1Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected] 2Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected]






Abstract

The topic which is the center of interest of this research is the appearance and development of informal settlements in the City of Novi Sad in Republic of Serbia, as the outcome of suburbanization process, caused by clearly specified factors related to the regional geographical, socio-economic and cultural context. Informal settlements developed gradually through choices that settlers made of occupying available lots, based on closeness of space "attractors― which determined the probability of a lot being occupied. Recognition of pattern of informal settlements' sprawl contributes to the knowledge of how these structures can be treated in future planning processes in order to gain greater level of cohesion with urban structures that they are adjacent to, but without significant changes in common practices of building. Subject of the research is affiliated to informal buildings with solid structure since such condition allows settlements to develop towards greater level of comfort and sustainability with minimal destruction of existing buildings.

Keywords: informal settlements, suburbanization, mathematical model, field/based automata principles, space attractors.

SYNTHESIS OF DWELL LINKAGE MECHANISMS WITH HIGH CLASS STRUCTURAL GROUPS

Maja Čavić1*, Marko Penčić1, Jovan Dorić1, Milan Rackov1, Zhenli Lu2,3 1Faculty of Technical Sciences, University of Novi Sad (SERBIA), {scomaja, mpencic, jovan_d,

racmil}@uns.ac.rs 2School of Electrical Engineering and Automation, Changshu Institute of Technology

(CHINA),[email protected] 3State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences

(CHINA), [email protected]

Abstract

Mechanisms of machines completing a repeating operation have many applications in the processing industry. During the cycle, the output link has one or more periods of dwell, while the input link moves continuously. The traditional solutions based on cam and Geneva mechanisms can be replaced with linkage mechanisms, that can take higher velocities and loads, and have smaller losses. In this paper, the synthesis of complex mechanisms containing high class structural groups is shown. The procedure is based on the synthesis at the extreme positions of the mechanism, simplifying the problem to a problem with a finite number of precise positions. At the core of this procedure are simple, easily visible and understandable geometric constructions that are then used to form equations suitable for further analysis and optimization. Motion of the mechanism resulting from this synthesis procedure has some inaccuracy – the output link does continues moving during the dwell phase, completing an angle of ±0.5°, which is considered accurate enough for a wide range of practical applications.

Keywords: dwel linkage mechanism, high class kinematic group, kinematic synthesis.




14

THE APPLICATION OF AUTOMATIC PHOTOGRAMMETRY IN ARCHITECTURAL RESTORATION AND CONSERVATION

Tamara Stričević


Abstract

This paper explores the different uses automatic photogrammetry may have in the field of architectural restoration and conservation. Introduction is given as to explain the concept of photogrammetry and its most common uses, with the goal of narrowing it down to its role in architectural restoration and conservation. The aim of this research is to use the models created by automatic photogrammetry software to repair or sustain damaged structures from further degradation. In order to achieve this, a brief overview will be given concerning the process of photogrammetric scanning, what it is and what is necessary for it to be successful, followed by a practical example of how it should be done - a case study of a damaged area of a wall in Laze Telečkog street, in Novi Sad, Serbia. The same case study will then be used to demonstrate how the automatic photogrammetry software works and what are the advantages and disadvantages of this type of 3d mesh model-making in Agisoft Photoscan, Autodesk’s Remake and in Autodesk’s Recap Photo software. Finally, this paper will refer to the

practical use of a photogrammetric 3d mesh model in the previously mentioned damaged wall, by investigating its adaptivity in other software like Rhinoceros and its precision by creating a 3d model of the damaged wall and the produced cap.

Keywords: architecture, conservation, restoration, photogrammetry, 3d mesh models.

THE APPLICATION OF NORMAL MAPPING IN CHARACTER'S FACIAL DESIGN

Nikola Grbić


Abstract

This research is focused on analyzing the use of normal mapping in 3D modeling, particularly in character's facial design. The goal is to produce a quality model with less hardware strain to be used in interactive scenes, as found in video games. This was done by creating the detailed model and a normal map based on it, that is later applied to a simplified model. The result was a human face model with less overall complexity that at the same time possesses a satisfying amount of detail.

Keywords: character, design, normal, mapping, 3D modeling,graphics.


15

THE INFLUENCE OF URBAN GEOMETRY ON MITIGATING LAND SURFACES INSOLATION

Milica Ivkovic1*, Ivana Bajsanski2, Katarina Stefanovic3, Mirjana Ignjatovic4 1Faculty of Technical Sciences (SERBIA), [email protected]

2Faculty of Technical Sciences (SERBIA), [email protected]

3CINEARCHITECTURE (SWEDEN), [email protected]

4Faculty of Technical Sciences (SERBIA),[email protected]

Abstract

Land surface areas can contribute to effect of overheating due to its exposure to solar radiation during summer period with extreme temperatures. One of the most effective ways for mitigating solar insolation of land surfaces is overshadowing by using building geometry. Rapid development of software applications for 3D modeling, procedural modeling and solar simulation allow users to solve issues caused by overheating of built places. Accordingly, the aim of this paper is to propose method which combines geometrical parameters of built urban environment in order to decrease insolation level of land surfaces, taking into account the constant parameter of Soil Occupation Factor (SOF) of buildings bases in urban block. The research was conducted in the urban fabric of Novi Sad. The results indicate that investigated geometrical characteristics of buildings, its position and orientation affect insolation level and can be used for mitigating overheating of land surfaces in urban areas. By using method created in this paper, architects and urban planners have opportunity to generate more comfortable urban areas in summer period when the overheating of land surfaces is expected.

Keywords: building geometry, urban design, solar simulations, insolation level, extreme temperatures.

THE MORPHOLOGY OF ARCHITECTURAL SHAPESHIFTERS - FORMS OF REUSED BUILDINGS

Milan Brzaković1*, Aleksandar Milojković2, Marko Nikolić3 1Faculty of Civil Engineering and Architecture, University of Niš (SERBIA), [email protected]

2Faculty of Civil Engineering and Architecture, University of Niš (SERBIA),

[email protected] 3Faculty of Civil Engineering and Architecture, University of Niš (SERBIA),

[email protected]

Abstract

Buildings have many lives, because their functional erosion is often faster that their physical ruin, and the persistence of their shells, where the materials, energy and knowledge used in their construction are deposited encourages giving them successive uses. Working with existing buildings has long ceased to be only a question of preserving the city image and historic monuments, and it has become an economic and ecological imperative. Adaptive reuse, as an architectural intervention, offers the possibility of recycling existing buildings, both in architectural and in a functional sense. This process is commonly referred to as conversion, revitalization, adaptation or even remodelling, and it signifies any construction work and intervention that change building‘s capacity, function or performance to adjust or upgrade a building to fit new conditions or requirements. Morphology of the new architectural complexes is dictated by the new needs and the range of possibilities offered by the remaining structure. This paper proposes an analysis of the physical form of buildings undergoing various types of architectural revitalization. Key aspects of the analysis are the forms of the old buildings and their newly designed additions, with special emphasis on the relationship between these inexorably linked elements. New classification of reused objects was formulated and its subtypes were further presented in detail. The classification is based on the shape of new additions, the way in which they are put into space and both physical and geometric relationship between old and new parts of the building. The purpose of this paper is in defining the types of form of additions and recommendations for their proper use. The establishment of such a classification and definition of the characteristics of different shape types should offer possible solutions to the problems of planning and design in cases where the use of existing physical structures is required.

Keywords: architectural revitalization, geometric form, architectural form, adaptive reuse, building additions.



16

TILING THE LATERAL SURFACE OF CC II BY REGULAR HEXAGONS AND TRIANGLES AS A DESIGN PROPOSAL IN

ARCHITECTURE

Marija Obradović

University of Belgrade, Faculty of civil Engineering (SERBIA), [email protected]

Abstract

This paper discusses ways to divide the triangular faces of concave cupolae of the second sort (CC II) into unified elements, regular polygons, which can then tile the whole deltahedral lateral surface, forming patterns applicable in architectural design. Due to their deltahedral lateral surface, which implies unification of the elements, CC II are suitable for prefabrication. The question raised concerns the division of the triangle with new vertices along the edges, forming a triangular lattice within which the surface of the triangle will be divided into into the regular hexagons and triangles. Apart from solutions involving fragments of k-uniform Euclidean tilings, we explored the ones that can be obtained by dividing the triangle‘s edges into 3≤ b ≤ 9 segments. The number of ways we can divide the triangle into hexagons and triangles depends on the number of unit hexagonal cells (tiles) that can be placed in the lattice inside the triangle. Without getting into a multitude of arbitrary cases, we narrowed this research to the ones with the most symmetries, in order to propose the optimal solutions, i.e. those most suitable for performance. Thus, it will not matter if the face of the CC II is rotated or flipped during the assembly. This results in 30 different solutions, excluding the cases with just triangles. It should be emphasized that these solutions are applicable to all the representatives of CC II, and even to the other representatives of concave polyhedra of the second sort. We chose several examples of these results for the design proposal.

Keywords: equilateral triangle, hexagon, tiling, deltahedron, dome, symmetry, architecture.

VIRTUAL REALITY AS A MEDIUM FOR ARCHITECTURAL ANALYSIS

Marko Lazić1, Ana Perišić2, Predrag ŠiĎanin3 1Faculty of technical sciences, University of Novi Sad (SERBIA), [email protected]

2Faculty of technical sciences, University of Novi Sad (SERBIA), [email protected] 3Faculty of technical sciences, University of Novi Sad (SERBIA), [email protected]

Abstract

The paper discuss with the topic of displaying different types of 3D architectural analysis and its characteristics through the technology of virtual reality (VR). The aim of this study is to present aspects and information on 3D objects that are contextually changing in relation to different types of architectural analyzes through VR technology. In virtual reality, three types of architectural analysis are applied, tested and presented. The architectural analyses applied are the economic analysis/cost estimation, the energy efficiency analysis and the insulation analysis of the facade of the building. All three types of analysis required a different approach to perception in virtual reality and a creation of sub model visualization with particular influences on the structure of the main model. The presented results are an illustration of the possibility of using VR technology in the form of visualization of architectural analyzes. Applying these principles in practice and education sets the basis for more efficient decision-making at an early stage of design. This provides insight into the different levels of the architectural project, which can prevent typical errors in the design of various structures.

Keywords: virtual reality, architectural analysis, visualization techniques, BIM technology.


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3D MODELING TECHNIQUES FOR REVERSE ENGINEERING PHOTOGRAMMETRICALLY SURVEYED FREEFORM SURFACES

Andrija Mihelčić

Faculty of Technical Sciences, Novi Sad (SERBIA), [email protected]

Abstract

In the recent years a number of software solutions have been developed in order to aid both functionality and productivity in reverse engineering and rapid prototyping processes. Much of these solutions aim towards simplification, semi-automatization or full automatization of reverse engineering process. These solutions depend heavily on precise, dense and uniformly distributed point cloud data. When fed with scarce, incomplete or complex geometry point clouds these algorithms easily fail and more manual approach for surface reconstruction is needed. This paper explores two different surface reverse engineering approaches and compares precision and curvature continuity on both models. The results show the tradeoff between precision and curvature continuity of modeled surfaces.

Keywords: 3d modeling, reverse engineering, freeform surfaces.

ANALYSIS OF DIFFERENT METAMATERIAL GEOMETRY

Boris Kosic1, Misa Stojicevic2, Zorana Jeli3, Branislav Pokonstantinovic4, Aleksandra Dragicevic5

1Faculty of Mechanical Engineering, University of Belgrade (SERBIA), [email protected]


3Faculty of Mechanical Engineering, University of Belgrade(SERBIA), [email protected]

4Faculty of Mechanical Engineering, University of Belgrade (SERBIA), [email protected] 5Faculty of Mechanical Engineering, University of Belgrade (SERBIA), [email protected]

Abstract

This paper investigate influence of different geometrical structures on new concepts for formation of technical systems. Ability that some geometric structures are able to withstand a certain level of deformation, was used to replace joints in certain assemblies of technical systems. Now all movements are accomplished with deformation of geometrical structures. Obtained results from simulations, define level of deformation which structures can withstand. Designing of 3D models and simulations were conducted in SOLIDWORKS 2016. Several different structure of metamaterials will be examined. 64 simulations were conducted by changing internal structure, thickness and orientation of metamaterials. For each simulation results were presented as stresses and displacements. Additionally three model of pliers have been simulated, and its results were compared with results from previous simulations.

Key words: 3D model, metamaterial, geometric structure, 3D printing, Solidworks, simulation.







18

APPLICATION OF WAFFLE SECTIONING PRINCIPLES FOR GENERATING TWO VIEWING POINTS ANAMORPHIC SCULPTURE

Ana Marjanović


Abstract

Anamorphosis is a distorted projection of an object that can be seen in its true shape only from a certain point of view, by using foreshortening. The problem this research wants to solve is how to create a specific workflow for generating a two point anamorphic sculpture, using flat sheets of material while using as little material as possible. This paper studies how a two point anamorphosis is constructed and projected with two intersecting sets of planes. The goal is forming images that can be viewed from two points of view only. The results show that only one of the two images formed this way can have an indented contour while the other one has to have a much softer border line. However, even with this limitation there are countless possibilities and variations.

Keywords: anamorphosis, waffle sectioning, perspective.

BASIC GEOMETRY AND DESIGN OF SOLAR CONCENTRATORS

Misa Stojicevic1*, Zorana Jeli2, Branislav Popkonstantinovic3, Milos Obradovic4, Ratko Obradovic5



3Faculty of Mechanical Engineering, University of Belgrade (SERBIA), [email protected] 4Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected]


Abstract

This paper gives an insight into the design of concentrating solar power (CSP) systems. The basic design of several types of CSP system is presented alongside their advantages and disadvantages. These advantages and disadvantages are based on their application and construction details and the paper shows how to select the most convenient CSP system. After presenting these types of CSP systems, an example of a new type of design is explained that presents a combination of several other solar concentrators.

Keywords: solar power, CSP system, concentrator design.








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BESPOKE GEOMETRIC GLAZING DESIGN FOR BUILDING ENERGY PERFORMANCE ANALYSIS

Nicholas Mario Wardhana1*, Aikaterini Chatzivasileiadi2, Wassim Jabi3, Robert Aish4, Simon Lannon5

1Cardiff University (UNITED KINGDOM), [email protected]



4University College London (UNITED KINGDOM), [email protected]


Abstract

Geometry has been found to be one of the main architectural design issues that architects are concerned with when they assess the energy performance of their models through the use of Building Performance Simulation tools. Accurate geometry, coupled with correct energy analysis settings, can avoid errors and provide more accurate results which are among the highest priorities for architects and engineers. Current energy analysis tools commonly use the window-to-wall ratio method to provide a fast and automatic way of modelling glazing, including on multiple surfaces instantaneously. However, this method is prone to geometrical inaccuracies in terms of the size and the location of the glazing, which can in turn contribute to the energy performance gap between modelled and monitored buildings. In addition, simultaneous glazing on multiple surfaces might not be entirely supported in existing applications for complex models. To alleviate these challenges, this paper presents a mechanism for creating a bespoke glazing design on curved surfaces based on the concept of UV-mapping. The glazing can be designed on a 2D planar vector drawing as a set of interconnected curves, either as straight lines or B-Splines. These curves are then mapped unto the UV space of the subdivided and planarised input wall as the glazing. It is hypothesised that a building model with a bespoke glazing design, while more time consuming, allows a more aesthetically representative and geometrically accurate glazing design than one with glazing based on the window-to-wall ratio method, thus minimising the energy performance gap.

Keywords: architectural design, 3D modelling, parametric surfaces, glazing design, energy analysis.

CAD, CAE AND RAPID PROTOTYPING METHODS APPLIED IN LONG BONES ORTHOPAEDICS

Dragos-Laurentiu Popa1*, Buciu Gabriel2, Daniel Cosmin Calin3 1Faculty of Mechanics, University of Craiova (ROMANIA), [email protected]

2Titu Maiorescu University, Faculty of General Health Care (ROMANIA), [email protected]

3University of Medicine and Pharmacy of Craiova, Faculty of Medicine (ROMANIA),

[email protected]

Abstract

The paper presents some methods used to analyze human bone joints. The cooperation between medical research team and the engineer research group give important tools for medical devices design. To re-create a 3D parametrical environment it was used a CAD software which permits to define complex models. First, there were defined the "hard" parts as the main bone components and "soft" parts as ligaments or menisci using CT images. The objectives of the study are mainly to achieve a virtual, as complete, virtual model of the biomechanical system of human walking, which allows the study of real, accidental, clinical, pathological or surgical situations. In a first phase, three-dimensional parameterized models of bone components that contribute to human movement are obtained. Thus, the bone components are screened and then modeled in a parameterized environment based on the obtained images. These components are imported into a parameterized environment assembly module and a biomechanical model of human walking is being obtained, which is exported to a kinematic simulation environment and finite element analysis, where first the kinematic parameters are defined, dynamics, inertial and kinetostatical (forces, angular functions in joints, masses, densities, other material parameters, etc.). With these defined parameters, the kinematic and dynamic simulation of the subsystems for


20

classical, normal motion (walking, flexion-extension, etc.) can be switched. The cinematic and dynamic analysis results are obtained, namely, simulation films, position diagrams, velocity and acceleration of mass centers, energies, etc. which will be subjected to storage, analysis and interpretation operations. Following the interpretation of the results, the initial parameters of the biomechanical subsystems may be modified. In the next phase, the components of the subsystems are discretized successively and the finite element structure is obtained for the entire biomechanical system of the joints that participate in human locomotion. In the last decade, a new concept called rapid prototyping, physical coating or without solid pre-form manufacturing, has become very popular. The process starts with a 3D CAD model involving CAM techniques and polymers. Using these techniques, our team fabricated physical polymers prototypes of bones, different implants and prosthetic elements for othopaedic applications.

Keywords: virtual prototyping, computer graphics, orthopaedics, virtual bones, rapid prototyping.

CREATION OF ORTHOPHOTOPLANS OF THE BUILDING FACADE USING OF UAV AND TERRESTRIAL IMAGES

Piech Izabela1*, Ruzyczka Adam2 1University of Agriculture in Krakow (POLAND), [email protected]

2University of Agriculture in Krakow (POLAND),[email protected]

Abstract

The study aims to show the possibility of using terrestrial laser scanning and unmanned aircraft as a tool for obtaining high resolution photogrammetric material in order to develop colourful, metric orthoplans and 3D models of an architectural object. The object of the study was the church dedicated to Saint. Bartholomew the Apostle in Mogila and the chapel of St. Malgorzata at Salwator in Krakow. Field activities of the church of St. Bartholomew the Apostle in Mogila covered the execution of the raid by means of the unmanned aerial vehicle DJI Phantom 4 Pro, acquisition of ground-based photos with a non-metric Nikon D3100 camera, and the measurement of photopoints with an electronic total station. UAV was manually moved to a height of 20m in relation to the roof of the church, just above the turret (the turret located above the intersection of the transept with the nave). Then, the radius was specified by moving 10m away from the edge of the subject. After setting the minimum orbital speed (to avoid blurring the images), the object was automatically looped. In this mode, 76 images were recorded around the whole object. In the next stage the flight took place by hand. At a height of 10 m from the ground, 32 photos of the southern and eastern walls and a part of the western wall were made from a distance of approx. 15 m from the façade. After completing the BSP raid, the SLR was started. Obtained in this way, 120 photos with a longitudinal base of approx. 3.30 m (coverage above 70%). The camera allowed to reach places inaccessible to the UAV and take photos of the lowest parts of the facade, maintaining an angle close to the straight one in relation to the vertical plane. The last of the planned field activities was the measurement of the photopoints on the geodetic network for the purpose of later giving the object georeference and the right scale, as well as optimizing the position of the camera and orientation of the photos. The last, final stage of the work was the creation of orthophotoplanes for four elevations. The summary discusses the results of the work and assessed the capabilities of unmanned ships as part of the creation of orthophotoplanes and the creation of 3D models. The measurement of the object was made of 7 sites providing a common area coverage. In addition, 8 points were distributed evenly around the measured chapel indicative in the form of matte, glass balls placed on the ground, necessary in the process of clouding points from individual positions. The number of posts and balls was dictated by the nature of the measured object and the need to obtain as few dead zones as possible. Despite the efforts, it was impossible to avoid the appearance of dead zones, which are located in the place of setting up the lighthouse on the dome of the chapel. An additional obstacle turned out to be the trees growing in the vicinity of the chapel, which partially covered with its walls the walls of the building. The effect of field work was to obtain 7 images of point clouds and 8 images of landmarks. After cleaning individual images, the cloud was created and the 3D image of the object was obtained and an average error of 3 mm was obtained. The final effect of cleaning and depositing a point cloud was the three-dimensional shape of the object, which served the last stage of the work, which was modeling. Due to the conditions in the area, the cloud received had some dead zones, including the one at the connection of the lighthouse with the dome. After completing the orientation of the point cloud, the final stage of this study was to create a 3D model of the chapel.

Keywords: ground scanning, unmanned aerial vehicles, architectural inventory.



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DESIGN AND FABRICATION OF MODULAR, RESPONSIVE MULTIFUNCTIONAL FURNITURE

Nina Milutinović

(SERBIA), [email protected]

Abstract

This paper deals with the research and application of modern technologies in the design of interior furniture, specifically interactive modular shelves. The work includes the application of parametric modeling tools - Grasshopper, Arduino platform, visualization software - 3ds Max. The aim is to create a modular piece of furniture, whose design will fit into interiors with different purposes, and at the same time implement technology that allows the model to interact with the user in the form of controlling (decorative) lighting through a cell phone or a sound control.

Keywords: parametric modeling, grasshopper, interaction, arduino, modular furniture, architecture, design, technology, fabrication, education.

DESIGN AND FABRICATION OF POROUS STRUCTURES USING ROBOTIC HOT KNIFE CUTTING

Marko Jovanović1*, Marko Vučić2, Bojan Tepavčević3, Mirko Raković4 1University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected]


3University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected] 4University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected]

Abstract

With the interest towards biomimetic approaches to architectural design, the notion of porosity became an increasingly important topic, enabling new directions for tectonic thinking and functional demands in architecture. Porous structures may improve thermal, light and air circulation conditions in the building. However, porous structures have a very complex topology which is very demanding for the process of fabrication and limited only to 3D printing and CNC milling manufacturing approaches. In this research, we propose a novel design and manufacturing approach for porous structures by using a hot knife tool for cutting EPS materials with an industrial robot. The presented approach provides a faster and efficient way to fabricate porous structures compared to additive or milling techniques, while providing production of large scale prototypes and large variety of design scenarios.

Keywords: hot knife tool, porous structure, porosity, holes, sweep surface, foamed polystyrene.


22

DESIGN OF A STREET-STYLE MOTORCYCLE CONCEPT

Tashko Rizov1, Risto Tashevski1, Hristijan Najdeski2 1Faculty of Mechanical Engineering, University “Ss. Cyril and Methodius” (MACEDONIA),

[email protected] `2

Faculty of Mechanical Engineering, University “Ss. Cyril and Methodius”(MACEDONIA)

Abstract

This paper presents the design process of a motorcycle with a street-style chassis. Motorcycle design can be described as activities that define the appearance, function and engineering of motorcycles. The design process presented is consisted of several steps like analysis of the existing motorcycles in the category, analysis of the engineering design of the structures, ergonomics and design of the riding position, creating a 3D model and rendering. The main goal of the paper is to design a new chassis of a motorcycle in the street-style in compliance with the ergonomic and engineering requests. This paper aims to discuss the specific features, benefits, and precautions when using design optimization to develop a specific project. After selecting the optimized design of the product, a 3D model has been created to visualize the final result. The 3D model presents the selected geometry and materials selection. Using photo-realistic rendering the final model has been presented to provide the decision makers with the ability to visualize the product in order to analyze if the design is satisfactory.

Keywords: motorcycle; futuristic design; ergonomics; 3D model.

QUANTIFYING THE SMOOTHNESS-RELATED QUALITY OF ARCHITECTURAL/URBAN LINEAR OBJECTS’ SURFACES

REPRESENTED BY PHOTOGRAMMETRICALLY CREATED POINT-CLOUDS AS A FUNCTION OF SHOOTING-DISTANCES AND

NUMBER OF CAMERA POSITIONS I.E. SHOOTING-DIRECTIONS

Djordje Djordjevic1*, Gordana Djukanovic2, Mirjana Devetakovic Radojevic3,

Nikola Popovic4 1Faculty of Architecture, University of Belgrade (SERBIA), [email protected]

2Faculty of Forestry, University of Belgrade (SERBIA), [email protected]

3Faculty of Architecture, University of Belgrade (SERBIA), [email protected] 4Faculty of Architecture, University of Belgrade (SERBIA), [email protected]

Abstract

This paper investigates the impact of various object-to-camera distances and number of station-points i.e. horizontal shooting directions on the level of achieved smoothness-related quality of vertical architectural/urban linear objects‘ surfaces (represented by point-clouds as its photogrammetric representations), as well as to scientifically draw conclusions based on comparative analysis of obtained cross-referenced results. It is concluded that for a fixed focal length, shooting directions perpendicular to the axis of targeted linear object, station-points uniformly radially distributed around the object (at the circle of 360 deg.) and process-quality descriptors` values which belong to the satisfying/recommended ranges, regardless of level of OPC (Object‘s Photo-Coverage), all digitalized surfaces are consisted of majorities of both precise and accurate points. So, generation of those surfaces can be declared as highly precise and satisfyingly accurate in smoothness-related sense. Separately, in case of OPC-2.1%, digitalized surfaces possess satisfying smoothness-related quality (regarding levels of achieved both precision and accuracy) which is not dependent on camera-movement angle (i.e. station-points number). On the other side, according to separation angles from 15deg. to 30deg. (obtained for 24 to 12 station-points) digitalized surfaces related to the case of OPC-1.3%, have the highest quality in smoothness-related sense, less quality is in the case of OPC-0.7%, and case of OPC-2.1%, is characterized by minimal but still very acceptable quality. Contrarily, when shooting separation angles range from 30deg. to 45deg. (obtained for 12 to 6 station-points), a digitalized surface has the highest smoothness-related quality in the case of OPC-0.7%, a smaller quality in the case of OPC-1.3%, and a minimal but still very satisfying quality in the case of OPC-2.1%.

Keywords: architectural photogrammetry, dense-surface-modelling, point-cloud, smoothness, quality.



23

EMPLOYING MESH SEGMENTATION ALGORITHMS AS FABRICATION STRATEGIES - SKIN PATTERN GENERATION

BASED ON REACTION-DIFFUSION MECHANISM

Effimia Giannopoulou1, Pablo Baquero2, Angad Warang3, Affonso Orciuoli4, Alberto T. Estévez5, Miguel A. Brun-Usan6

12345UIC (SPAIN), [email protected]

6Electronics and Computer Sciences, University of Southampton (UK), [email protected]

Abstract

This paper examines how the evolution of generative architectural design processes aim to apply similar physical and geometrical principles which underlie biological processes taking place during development, to design and building of architectonic free-form shell structures. The design workflow is extended to engage collaborative fabrication processes based on intuition and knowledge of the fabrication tools, material properties, manufacturing simulations and assemble logic to steer the design and to translate biological skin patterns to fabrication processes. Mesh relaxation processes and weighted mesh graphs representations are employed as design potentials to explore the limitations of constructing branching topologies and connectivity of self-supported, free-form tubular minimal shell structures, with stripe logic in analogy to a reaction-diffusion (RD) mechanism. The paper argues that biological skin patterns and segmentation in fabrication open a new field for interdisciplinary investigation and architectural applications. The outcomes of this research have been used to fabricate a model, using three different material and three fabrication methods, during the Biodigital Master in Architecture.

Keywords: Fabrication methods, Stripes, Skin pattern, Morphogenesis, Shell structure.

EPIDERMIS - AN INTRODUCTION TO ALGORITHMIC DESIGN BASED ON BIOMIMETIC MORPHOLOGICAL REFERENCES

Ioanna Symeonidou1* 1Department of Architecture, University of Thessaly (GREECE), [email protected]

Abstract

The paper discusses the possibilities and challenges that arise when teaching algorithmic design to students with no previous experience in computational processes. Based on research on learning theories and particularly to those that involve the student‘s active involvement in the creation of new knowledge, this paper will discuss a series of guidelines and examples of good practice and will present the results of a parametric design workshop that took place at the Aristotle University of Thessaloniki, in Greece.

Keywords: parametric geometry; algorithmic design; biomimetic inspiration; computational design processes; design education.


24

FORM ANALYSIS OF LEGO ARCHITECTURE

Hiromitsu Shimizu1, Hiroki Dakiyama2, Naomi Ando3, Shota Ishii4 1Hosei university (JAPAN), [email protected]

2Tokyo Metropolitan Government (JAPAN), [email protected]

3Hosei university (JAPAN), [email protected]

4Hosei university (JAPAN), [email protected]

Abstract

The LEGO System, which features the interlocking plastic bricks through which one can build various forms, has an advantage of expressing the characteristics of architectural forms with simplicity. In this study, LEGO models of architecture were created to analyze their architectural forms.

Keywords: LEGO, architecture, form analysis.

GENERATING LINEAR FALSEWORK FOR FREEFORM STRUCTURES

Stefan Stojčić1*, Marko Jovanović2 1University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected]


Abstract

The development of digital tools in recent years, in the area of architecture and civil engineering, has brought new possibilities in designing and building freeform structures. Accordingly, the construction process of such structures had to become more complex and follow the same development. An important part of this process is the falsework which enables the construction of the final structure. Freeform structures need support during the period of construction. There are two reasons for that. The first reason is to minimize the deviation from the desired shape of the structure. The second, and more important reason, is that freeform structures are not stable and self-supporting during the building process, and therefore need temporary support which will receive the weight of the material. For these reasons, it is clear that falsework for this type of structures is very important. As they may affect the feasibility of the project to a great extent, it is important to design them in a way that satisfies the criteria in terms of cost, schedule, sustainability and ease of implementation. In this paper, a parametric approach is proposed which is based on using Grasshopper plug-in for Rhinoceros3D software. As a result, a demountable modular system is created, which provides reusability, cost and time-saving. For a given freeform structure several composing segments are generated, including the scaffolding, the trusses and the panels that are laid on top. The advantage over the existing systems is observed in the possibility of using the same elements for various freeform structures with only a small waste of material.

Keywords: falsework, support structure, temporary support, free-form structures, parametric design.


25

GEOMETRICAL AND CONSTRUCTION OPTIMIZATION OF CHURCH OF ST. JOSEPH THE CRAFTSMAN IN MEXICO OF ARCHITECT

FELIX CANDELA

Zlata Tošić1*, Sonja Krasić2, Naomi Ando3, Miloš Milić4 1Faculty of Civil Engineering and Architecture, University of Niš (SERBIA), [email protected]

2Faculty of Civil Engineering and Architecture, University of Niš (SERBIA), [email protected]

3Hosei University, Tokyo (JAPAN), [email protected]

4Faculty of Civil Engineering and Architecture, University of Niš (SERBIA), [email protected]

Abstract

The aim of this paper is to show how contemporary technology can help in process of optimization and digital fabrication in objects with non-standard geometry on the case study of Church of St. Joseph the Craftsman in Mexico of architect Felix Candela. Geometry and construction properties are optimized and the level of daylight illumination is also increased. Measured parameters are: mass and deformation, which were compared for remodeled object and existing object. It is also important to notice that these methods are not helpful only in this case study, but also in objects or future designs with similar properties.

Keywords: construction optimization, non-standard geometry, digital fabrication, Felix Candela‘s architecture.

GEOMETRICAL ELABORATION OF AUXETIC STRUCTURES

Milena Stavric1*, Albert Wiltsche2 1Graz University of Technology (AUSTRIA), [email protected]

2Graz University of Technology (AUSTRIA), [email protected]

Abstract

In this paper, we will analyze basic geometric and kinematic characteristics of auxetic structures on a macroscale and the geometric principles will be transferred to a family of new possible forms. We will cut flat material and, depending on the cuts and the material used, we will enable the kinematical movement of the structures. We will analyze monostable and bistable auxetic structure. Based on geometric considerations, we combine rigid material and composites and appropriate joint connections will allow the application of this system in an architectural scale. We investigate and elaborate auxetic behavior in a purely geometric way which is based on the kinematic movement of different frameworks. We demonstrate its usefulness by analyzing the involved geometry without computer simulations or numerical approximations

Keywords: auxetic, architecture, design, fabrication.



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GEOMETRICAL OPTIMIZATION OF INTERCONNECTED VOIDS IN CONCRETE CEILINGS

Kevin Noack1, Martin Friedrich Eichenauer2,Daniel Lordick3 1TU Dresden, Institute for Geometry (GERMANY), [email protected]

2TU Dresden, Institute for Geometry (GERMANY), [email protected]

dresden.de 3TU Dresden, Institute for Geometry (GERMANY), [email protected]

Abstract

The task to reduce the material consumption in the building industry is urgent. Conserving concrete saves nature and money. To reduce the consumption of concrete in buildings we design hollow bodies in ceiling structures. In a free geometrical optimization process we restrict to those forms which can be fabricated in half shells. Our goal is the best concrete saving ratio with respect to the restrictions of the building process. We show some possible forms and focus later on the better possibilities, the crossing channels. A smoothing step to avoid edges that causes stress peaks will raise the concrete saving even higher. We evaluate the use in technical applications under some questions like the concrete ventilation or the problem-free traversing in the fabrication process.

Keywords: voided biaxial slab, hollow ceiling, form optimization, concrete structures, smooth structures, half shell fabrication, finite elements analysis, Cross Channel technology, concreting.

IMPACT OF GLAZING PERCENTAGE OF THE FACADE ON IMPROVING INDOOR THERMAL COMFORT

Anja Milovanović1*, Ivana Bajšanski2 1Faculty of Technical Sciences (SERBIA), [email protected]

2Faculty of Technical Sciences (SERBIA), [email protected]

Abstract

Indoor thermal comfort of buildings has been defined as one of main tasks in architectural practice and design procedure during the last decades. In order to achieve the improvement of indoor thermal comfort different software applications for building simulation have been created and parametric design has been recognized as a main approach in moving towards better-performing buildings. In many researches a glazing percentage of the facade has been recognized as a parameter that has the greatest impact on indoor thermal comfort. The aim of this paper is to create a parametric model for improving indoor thermal comfort by taking into account glazing percentage of the facade, an indoor activity and the position of the analysed module inside the building. The paper results indicate that a facade glazing geometry has severe impact on indoor thermal comfort and plays an important role in its improving. Furthermore, by combining glazing percentage of the facade with the building purpose and performed activities inside the analysed module, indoor thermal comfort conditions can be improved.

Keywords: glazing percentage, facade, parametric modelling, indoor thermal comfort, summer period.






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IMPROVING THE INTEGRATION OF CGI AND PHOTOGRAPHY BY MATCHING SHADOWS BASED ON PERSPECTIVE RESTITUTION

Dragana Marković1*, Anastasija Martinenko2 1Faculty of Civil Engineering, Department for Geodesy and Geoinformatics (SERBIA),

[email protected] 2Faculty of Civil Engineering, Department for Geodesy and Geoinformatics (SERBIA),

[email protected]

Abstract

This paper examines the possibilities of improving fidelity of the rendered 3D model images integration into the given photograph. This problem is most commonly tackled by designers, architects, and other professionals who have a need for visualization of virtual content. During the integration of CGI and photography, designers often try to avoid the issue of matching the shadows both of the photograph and the model which is being, because of the complexity of the restitution process, which demands additional data besides the photograph itself. This is why we often encounter solutions which skilfully manage to avoid dealing with this issue, by choosing the light (diffused, cloudy, twilight) that does not give clearly visible shadows, or that is set in such a way that frontal areas are lighted, while the shadows remains sheltered. If necessary, shadow matching is mostly done approximately, so that any illogicality remains hidden from the eye of both non-skilled users and expert ones as well. Thus, the aim of this research is to improve the ways of the rendered image integration into photograph by applying the geometry knowledge, which enables matching the shadows more accurately, according to the requirements of the photograph. In the example of the photograph of the city square in Čačak (Serbia) together with a sculpture model made as a composition of geometric shapes, chosen to be placed on a given square in honour of geometry, a solution to this problem was given. This research is developed as a continuation of study within the subject of Visualization and Presentation of 3D Models in Geodesy, included in the program of the 3rd year of studies at the Faculty of Civil Engineering in Belgrade. As one of the methodological units in lectures and at the practical exercises, the problem of restitution of object‘s dimensions from the photograph is consider followed by the task of integrating the independent 3D model of an object (or objects) using its static 2D image – render.

Keywords: photograph, shadows, perspective restitution, 3D model, CGI, photo editing.

INTEGRATING PARAMETRIC DESIGN AND BUILDING PERFORMANCE SIMULATIONS

Ajla Aksamija

University of Massachusetts Amherst (USA), [email protected]

Abstract

This paper discusses methods for integrating parametric design with building performance analysis procedures, specifically presenting tools and design methodologies that are suitable for whole building design. In this research, an ideal framework for integration of parametric and performance analysis procedures was developed. Then, the framework was tested using existing software applications, including building information modeling (BIM), non-BIM, parametric design and building performance analysis applications. Current applications that can integrate some form of building performance simulation with parametric modelling include Rhino 3D (non-BIM), Revit (BIM), and SketchUp (non-BIM). Revit and Rhino each have visual programming plugins to aid in the creation of parametric forms. In this research, three different workflows were tested. Specifically, Honeybee and Ladybug (for Rhino 3D), Insight 360 (for Revit) and Sefaira (for Revit) were evaluated. A case study building was used to test and evaluate the workflows, interoperability, modeling strategies and results. Three different building performance aspects were analyzed for each workflow: 1) energy modeling, 2) solar radiation analysis, and 3) daylighting. Simulation results from energy modeling, solar radiation and daylight simulations were recorded and analyzed. However, besides simulation results, the paper compares modeling procedures, parametric capabilities of investigated applications, ease of integration and interoperability. The results show a promising course for integrating parametric design with building performance simulations.

Keywords: Parametric design, building performance analysis, high-performance buildings, BIM, energy-efficiency.


28

KERF BENDING STRATEGY FOR THE FABRICATION OF COMPLEX GEOMETRY WITH THICK PLANAR SHEET MATERIALS

Dejan Mitov1*, Bojan Tepavčević2, Vesna Stojaković3, Ivana Bajšanski4 1Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected] 2Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected] 3Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected] 4Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected]

Abstract

The manufacturing of double curved surface in architecture is time consuming and laborious process. There are many ways for fabrication of double curved surfaces. However, most of the approaches requires special molds, which is expensive for individual production. For creating complex surface from planar sheet materials, several design-to-fabrication strategies based on bending and forming processes have been developed in past few years. Such strategies are based on certain mechanical or geometrical properties of the material, such as elasticity or thickness. In this research we focus on design investigation for manufacturing double curved architectural panels based on geometry and material processing. We propose cost-efficient design-to-fabrication approach based on kerf bending strategy for the forming of planar sheet materials, often used in standard construction. Planar sheet materials such as wood based or gypsum boards which can be applied in such fabrication strategy, are widely used for interior wall finishing.

Keywords: Kerf bending, Digital fabrication, Low cost manufacturing, Developable surfaces, Design optimization.

KINETIC FACADES – MODULATORS OF SUNLIGHT AND SHADOWS

Sandra Vrekić

Faculty of Technical Sciences, University of Novi Sad (SERBIA), [email protected]

Abstract

The paper focuses on the analysis of kinetic facades, but also on its modeling using parametric design, which, depending on insolation, will change its configuration, and thus, influence the light in the interior.The parametric design method enabled the generation of a very flexible facade, whose algorithm can be adapted and modified at any time, which would result in a more consistent result. Such an approach shows that the process of designing and developing kinetic facades can be efficiently tested and evaluated in order to better understand the challenges and problems before the facade is made.

Keywords: kinetic facades, parametric design, insolation, algorithm, flexible.






29

MASS CUSTOMIZATION APPROACH FOR THE CONFIGURABLE DESIGN OF ADAPTIVE FACADES

Boţana Petrović


Abstract

By connecting architecture to digital technologies, it is possible to change the traditionally passive role of user in the role of the designer of the final product. This transformation is possible by the introduction of mass customization production as a production system. Customization of the architectural element is achieved through determination of a set of parameters available for user manipulation. A complete understanding of the geometry and performance of materials from which the system is made allows it to be defined through a set of parameters that can change values depending on mutual interactions and relationships with the environment parameters in which the system will function. This paper presents the parameterization of the adaptive facade system which, through the applied material, thermo-bimetalic foils, changes the shading of the room depending on the temperature changes in the environment. System parameters are then set as the basic elements of the application as variables, in which it is possible to observe changes in the system that occur when changing their value. In this way, the design decisions are made by the user of the application, while the newly updated parameter values are forwarded for further fabrication of the element.

Keywords: mass customization, thermal bimetal, adaptive façade.

MULTI-CAMERA SYSTEM CALIBRATION FOR 3D SCENE RECONSTRUCTION, MODELING AND VISUALIZATION

Jovan Mijatov1, Vladimir Zlokolica1, Ratko Obradović1, Relja Ljubobratović2, Radovan Obradović2, Vladimir Mastilović2, Krešimir Vdovjak3, Irena Galić3

1Faculty of Technical Sciences, University of Novi Sad (SERBIA)

23Lateral (SERBIA)

3Faculty of Electrical Engineering, Computer Science and Information Technology (CROATIA)

Abstract

Current state-of-the-art multi-camera-view 3D reconstruction algorithms provide high quality 3D point cloud, which is further used for 3D meshing, texture mapping and finally generating corresponding 3D model of the scene. One of the most important factors for both 3D surface reconstruction and texture mapping is accurate and robust camera calibration. This paper presents a novel approach for multi-camera system calibration where we extend and make mixture of known calibration techniques to calibrate multi-camera system with specially designed three-dimensional calibration object. More precisely, we extend calibration technique that uses planar pattern to three-dimensional pattern camera calibration. First, camera parameters are roughly estimated for all cameras in multiple camera system, then these parameters are refined using standard bundle adjustment algorithm. The proposed approach has been tested with synthetic and real data. Mean square error between re-projected and detected pattern points has been found to be in the range of 0.1px – 0.5px, for real camera data of 24MPx. The proposed method is shown to be more accurate or comparable to other calibration techniques.

Keywords: camera calibration, computer vision, photogrammetry, 3D modeling, multi-view stereo, structure-from-motion, architecture, design, technology, fabrication, education.


30

OVERVIEW OF GEOMETRIC ASPECTS OF PHOTOVOLTAIC SYSTEMS, RELEVANT FOR BUILDING INFORMATION MODELLING

Mirjana Devetaković1*, ĐorĎe ĐorĎević2, Gordana Đukanović3, Aleksandra Krstić-Furundţić4, Budimir Sudimac5

1University of Belgrade, Faculty of Architecture (SERBIA), [email protected]


3University of Belgrade, Faculty of Forestry (SERBIA), [email protected]



Abstract

The paper systematizes geometric aspects relevant for understanding design of photovoltaic (PV) 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 photovoltaic systems.

Keywords: solar geometry, photovoltaics, BIM, sun study, overshadowing.

PARAMETRIC DESIGN OF MASONRY VAULTS BASED ON STRUCTURAL AFFINITY

Dimitrije Nikolić1*, Vesna Stojaković2, Radovan Štulić3

University of Novi Sad, Faculty of Technical Sciences (SERBIA), [email protected];

[email protected];

[email protected]

Abstract

In this paper, the novel method for the design of complex affine vaults is proposed. It derives the system of complex groin vaults whose constituent parts are mutually affine cylindrical vaults, by merging the thrust line theory with structural affinity. The Rankine‘s concept of the transformation of structures is elaborated and applied to the analysis of masonry vaults. Therewith, a continuous and piecewise smooth thrust surface inside a vault, formed as a three-dimensional extension of thrust line, is proposed. Thus, the method enables the omission of the analysis of the actual structural action within a vault without jeopardising vault‘s stability. That provides simplicity of the overall computation as well as the fast evaluation of the complex vault‘s thrust. Starting from the properties of masonry arch and corresponding cylindrical vault, the equilibrium analysis of an affine vault is carried out on the basis of suitably chosen initial part, exposed to certain transformations. The parametric model for the equilibrium analysis of complex affine vaults, based on the geometrical properties of a vault, is derived, where the disposition of supports in a vault's plan becomes main input parameter for the computation. Accordingly, the derived method provides the design of the variety of complex affine vaults, as well as the automated calculation of the resultant loading exerted to supports with their graphical representation.

Keywords: masonry vaults, affine vaults, structural affinity, thrust surface, parametric design, equilibrium analysis.







31

PARAMETRIC DESIGN OF SINGLE FAMILY ROW HOUSES

Jovan Jeftić

(SERBIA), [email protected]

Abstract

Last few decades were marked by constant development in digital technologies, especially those that influence architectural development in its core, design. One of its most significant breakthroughs is use of parametric design and shape grammar in development and realization of architectural projects, or the parts of the project to its fullest potentials. But, as it sounds great, even use of parametric processes and tools are limited and often require constant control in different phases and never could fully generate fully functional object, like a home for living, with all elements generated with it, such as: furniture, appliances, fixtures, stairs, rooms or even with the complete facades and interior together. For research`s main goal is set question of structure, organization among functions and elements of facade and interior of row houses, also with consideration to realization of function through use of parametric tools in design. At the start, the fundamentals of creating and designing from around 100 different row type houses, mainly from Europe, and some researches based on the similar problematic are analysed and then added to accumulated scheme of possible correlation between elements, such as: position, orientation, type, scale of element and conditions for parameters of the next elements that will be generated and their correspondences towards every other element until the objects completion. Research is further realized in Python programming language and on CityEngine platform.

Keywords: architecture, parametric design, shape grammar, generating units for living, interior and exterior design, CityEngine, Python.

PARAMETRIC MODELING AS GEOMETRIC TOOL FOR DESIGNING URBAN MODEL OF BIOMORPHIC FORM INSPIRED BY FLOWER OF

BELL FLOWER (CAMPANULA PERSICIFOLIA L.)

Aleksandar A. Čučaković1, Dragica D. Obratov- Petković2, Biljana S. Jović3, AnĎela D. Mitić4

1Faculty of Civil Engineering, University of Belgrade (SERBIA),[email protected]

2Faculty of Forestry, University of Belgrade (SERBIA), [email protected]

3Faculty of Forestry, University of Belgrade (SERBIA),[email protected]

4Faculty of Forestry, University of Belgrade (SERBIA),[email protected]

Abstract

The aim of this research was to apply parametric modeling as appropriate geometric tool in landscape architecture design. Nature model used as inspiration in designing process was flower of the species bell flower (Campanula persicifolia L.), which could be found in Querco-Fagetea and Quercetalia pubescentis forest type. In profession of landscape architecture, this species can be used as a decorative because of its special form of the flower. The applied method of work included three main steps: field research and collection of plant material, generation of a geometric pattern using the geometric methods of Delaunay triangulation and the Voronoi diagram through the 3D Studio Max software and modeling its‘ biomorphic form that can be combined in different ways giving completely new solutions. Biomorphic form of the flower of selected species was obtained by using different vertexes as parameters in design modeling process. Parametric modeling today is an integral part of every 3D modeling software. This type of modeling involves defining and manipulating specific parameters that defines a created model. Result of this parametric modeling method was conceptual urban design model - bench. Some of new trends that designing urban spaces seeks is creating sustainable urban environment that strengthens the connection between people and nature in domains of aesthetics. This new and innovative urban element of public space could be the part of the new approach towards sustainable urban design.

Keywords: Bell flower (Campanula persicifolia L.), Delaunay triangulation, Voronoi pattern, 3D Studio Max, biomorphic form, urban design model.






32

PARAMETRIC OBJECT GENERATION DETERMINED BY ANAMORPHIC LIGHT SHADOW CONTOURS

Milica Knezević


Abstract

Anamorphosis presents a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point to reconstitute the image. On the other hand, requiring a special device to reconstitute the image has been reinterpreted in shadow and light art. It refers to the process of creating incredible shadow silhouettes and artwork on flat surfaces, by using a single light source along with an assortment of perfectly placed objects. Specifically, light source requires a specific position in order to create a certain shadow. The goal of this research study, based on shadow and art technique, is to generate those objects creating a certain shadow shape. This paper explains the method for the object generation. In other words, the research presents parametric object generation determined by a certain contour.

Keywords: light, shadow, art technique, object generation, contour.

PERCEPTION OF THREE-DIMENSIONAL GEOMETRIC SHAPES AS VIRTUAL 3D ROAD MARKINGS

Svetlana Čičević1, Aleksandar Trifunović2*, Dragan Lazarević3, Magdalena Dragović4, Nataša Vidović5, Marijana Mošić6

1Faculty of Transport and Traffic Engineering, University of Belgrade (SERBIA), [email protected]

2Faculty of Transport and Traffic Engineering, University of Belgrade (SERBIA),

[email protected] 3Faculty of Transport and Traffic Engineering, University of Belgrade (SERBIA),

[email protected] 4Faculty of Civil Engineering, University of Belgrade (SERBIA), [email protected] 5Faculty of Transport and Traffic Engineering, University of Belgrade (SERBIA),

[email protected] 6Faculty of Transport and Traffic Engineering, University of Belgrade (SERBIA),

[email protected]

Abstract

Excessive speed and poor driver perception are the causes of a large number of traffic accident. Analysis of the influence of geometry in driver behaviour has been widely performed by different researchers. One way to improve road safety is to provide adequate visibility in order to help drivers adopt adequate behaviours. When budget and financial situation do not allow the implementation of expensive traffic solutions, some of them can be replaced by innovative, but simple solutions. In this study, the experiment was performed to explore how driver perception and behaviour are influenced by two virtual 3D shapes projections - 3D alternative crosswalk pattern and speed bumps consisted from triangular prisms. The results show statistically significant differences between willingness to reduce vehicle speed as a response to the road marking using the square (rectangular prism) as the basis compared to one that has been used triangle (triangular prism).

Keywords: Three-dimensional geometric shapes, Perception, 3D Road bumpers, 3D zebra crossing, Design.








33

REVERSE ENGINEERING MODELING AS A TOOL OF DIGITAL SCULPTING

Ţeljko Santoši1, Igor Budak2, Mario Šokac3 1Faculty of Technical Science, University of Novi Sad (SERBIA), [email protected]



Abstract

3D technologies with their vast improvement and development enables their integration in different fields. This integration of 3D technologies paved new paths for further expansion of other fields, most recently the field of arts. 3D technology aims to create virtual or physical 3D models using computers and other devices that support data processing in digital form. In this paper the integration of reverse engineering modelling (REM) within the digital sculpting was presented. As a result of 3D digitization, a 3D model of a sculpted head was obtained. In order to obtain an ideal symmetrical 3D model of a sculpted head, the symmetry correction was performed. The symmetry analysis was carried out which provides an easy visual inspection and location of critical areas.

Keywords: 3D digitization, digital sculpting, reverse engineering.

ROBOTIC MATERIAL FORMATIONS EXPLORING THE GEOMETRIC SPECTRUM UNLEASHED BY

ROBOTIC THERMOFORMING

Renate Weissenböck

Graz University of Technology (AUSTRIA), [email protected]

Abstract

This research investigates the potential of robotic thermoforming to discover new processes in architectural design and production, thereby unlocking a new geometric spectrum. It explores design-by-making processes, where production tools are key part of the design process. The robot is one of the actors in a dynamic design network, where humans, materials, tools and machines interact. Thereby, the final geometry is not pre-defined in the digital realm - it emerges during the actual production process in an iterative cycle. The paper describes selected design experiments that are the outcome of three seminars conducted by the author at the Graz University of Technology, where students thermoformed planar sheets into 3-dimensional objects, by hand and by robot. Through the integration of fabrication and material issues into the design process, students were able to explore formal potentials and reach material results that could not have been conceived otherwise. By analyzing the produced prototypes, the paper describes the detailed production process and the interdependencies between material properties, cut pattern, forming motion, forming tool and resulting geometry.

Keywords: digital fabrication, robotic fabrication, design by making, thermoforming, material behavior, human-machine interaction.





34

SIMULATION AND MOTION STUDY OF MECHANICAL INTEGRATOR 3D MODEL

Branislav Popkonstantinovic1, Ratko Obradovic2, Misa Stojicevic3, Zorana Jeli4, Milos Obradovic5


2Faculty of Technical Sciences, University of Novi Sad (SERBIA),[email protected]




Abstract

A Mechanical Integrator is a mechanical device by which the continual integration of the input variable value can be obtained. This paper explains the operational principles and discloses the simulation and motion study results of the mechanical integrator 3D model assembly. Specifically, 3D models of the input function generator, the ball and disc integrator and the output x-y plotter are created and their operations are simulated. This work is significant mainly for education in the fields of solid modelling, mechanism synthesis and scientific visualization of the mechanism motion and operation. In particular, the motion analysis presented in this paper visualizes and discloses the mutual relationship between the integration calculus as the mathematical operation and the geometrical and kinematical characteristics of one special type of mechanical computing device.

Keywords: function, integrator, mechanism, motion, simulation, visualization.

THE INFLUENCE OF PLANAR DIFFUSER PANELS ON IMPROVING ACOUSTICAL PROPERTIES OF INTERIOR SPACES

Marina Mudri


Abstract

We mostly perceive architecture spaces as only visual entities, and we forget they have a tactile and acoustic properties that can be (or should be) treated as well. There are many ideas addressed to this issue, yet they come in most cases from research and academic realm, rarely are found in real projects. One such interesting idea comes from Delft University of Technology alumni, Jelmer Niesten, in a form of master thesis research, by the name ‗Sound reflections in an Urban Context: The influence of facades on urban noise levels‘. As the name suggest, the subject propose the solution to reduce an environmental noise levels by giving a greater notability to the façades of the buildings (Jelmer Niesten, 2016). In a form of more artistic and less functional approach, but still interesting and engaging, there are the two following works. One is by a Christopher Janney, MIT alumni, with his work ‘The Light Shadow: MLK project‘ – which represents an interactive wall that ‘sings and dances‘ (Christopher Janney, 2016). The other one is by a French artist David Letellier with his work ‘‘TESSEL‘‘ that investigates the perception of a sound in space (David Letellier, 2010). The aim of this paper is to examine how the diffusers affect the acoustics of the enclosure, through all relevant factors, bearing an aesthetic as well as good acoustic qualities. Considering my technical limits, only the diffusing role in the acoustics is encountered, for obtaining information on the overall propagation of the sound. Hence, the truly good quality acoustic characteristics can hardly be obtained, as there are not taken into account all influencing factors. Accordingly, the material is not taken into consideration for the final conclusions, i.e. all of the used models are defined as ‗timber‘, as a software requires a material, yet it should be thought of just as any reflective surface. Attention should not be given to the exact form of the diffusing panels, nor to the exact shape of the concert hall, but on the theoretical potential way of resolving some acoustical issues that large spaces meet. Results will be derived from Ecotect Analysis software while working with simple geometry models such as cube and a cylinder and the sound diffusing panels tessellated to a quad form will be introduced to them in a variant number. Examples will consist of variations in the number of tessellations in the panels, as well as the number of whole panels (made of tessellations) on the sides and the top of the room. This way, by using a digital model of architectural interiors for acoustical property simulation, may be possible to test which configuration of panels enhances the it in the best manner.

Keywords: concert halls, acoustics, sound reflections, diffuser panels.







35

USE OF BIOMIMICRY IN THE DESIGN OF MODERN ARCHITECTURAL STRUCTURES

Sanja Janković1*, Vladan Nikolić2, Sanja Spasić ĐorĎević3, Miloš Nedeljković4 1Department of Architecture, University of Nis (SERBIA), [email protected] 2Department of Architecture, University of Nis (SERBIA), [email protected]

3Department of Architecture, University of Nis (SERBIA), [email protected]

4Department of Architecture, University of Nis (SERBIA), [email protected]

Abstract

Biomimicry is a design discipline that seeks sustainable solutions using patterns and strategies from nature. Biomimetic study by system analysis in nature strives for better exploitation and lower energy consumption. It is necessary that the architects utilize a biological consultant on all projects, incorporating the biologist into the design team early on for optimal benefit. In addition to collaboration between biologists and engineers, the use of digital and parametric tools is important for modeling patterns from nature. Generic approach to modeling, performance-based design and generative-performance design have been recognized as a framework for new opportunities in researching architectural forms. For the purpose of the analysis, the paper presents examples from the field of architecture whose solutions are based on the principles of nature that contribute to sustainability and energy saving.

Keywords: biomimicry, patterns, parametric tools, generative-performative design, sustainable architecture.

AND WHAT ABOUT THE HISTORY OF DESCRIPTIVE GEOMETRY IN SERBIA?

Katarina Jevtić-Novaković1, Snezana Lawrence2, Marija Divac3 1College of Civil Engineering and Geodesy, Belgrade (SERBIA), [email protected]

2Anglia Ruskin University, Faculty of Health, Social Care, and EducationCambridge (UK),

[email protected] 3College of Civil Engineering and Geodesy, Belgrade (SERBIA), [email protected]

Abstract

This paper aims to trace the history of descriptive geometry in Serbia. Whilst Serbia was part of the federation of South-Slav countries for majority of the 20th century, the history of its mathematics, and in particular the history of descriptive geometry in the country is sufficiently independent from that of the 20th century Yugoslavia to merit a separate historical analysis. We will discuss the importance the discipline gave to the general improvement of its students‘ cognitive faculties. Secondarily, we consider the importance of the descriptive geometry in promoting national prestige at the time when the concept of nation states arose throughout Europe and the Americas. We will therefore look at how the conception of polytechnic and military schools, and formalization of education systems followed closely the introduction of the teaching of descriptive geometry, its introduction into the national languages and its use as a communication tool throughout national territories in which it spread.

Key words: descriptive geometry, history, Serbia, Monge, European countries.



36

APPROACHING DESCRIPTIVE GEOMETRY WITHIN THE EVER EXPANDING CONTEXT OF COMPUTER-ASSISTED DESIGN IN

ROMANIAN ACADEMIC EDUCATION

Alina Duta1, Ludmila Sass2, Gabriel – Catalin Marinescu3

1University of Craiova (ROMANIA), [email protected]



Abstract

Geometry remains the first science to come closest to art, joining forces for the evolution of culture. It is well-known that descriptive geometry studies and applies methods to enhance plane representation of different spatial forms, securing a bi-univocal correspondence between the three-dimensional geometric elements and their projections from the plane. The study of descriptive geometry is based on the knowledge of plane and spatial geometry, as well as projective geometry to provide quick solutions in the study of other disciplines. The essence of technical drawing, as a universal means of communication, along with speech and writing, would make use of various conventions of descriptive geometry. Hence, computer assistance within this field has led to the implementation of multiple features in graphic representations, i.e.: drawings precision and accuracy, precise quotations, constructive elements modulation, data libraries, the easier writing of the drawing texts, etc. Beyond current technological developments, we must acknowledge that descriptive geometry is and will remain a core subject in engineering academic curricula and not only. The present paper aims at emphasising the importance of descriptive geometry as an essential academic subject within the technical higher education system and beyond. Descriptive geometry assists students to increase their ability to perceive three-dimensional objects and their interaction. In what follows, we shall highlight a series of approaches to descriptive geometry as an attractive field of specialisation versus computer-assisted graphics. Undoubtedly, computer-assisted graphics are not excluded, as these two areas of expertise complement each other so as to lead to rapid and spectacular representations and graphic solutions.

Keywords: descriptive geometry, computer-assisted graphics, modelling and simulation, education.

FORMS AND SPACES OF ANCIENT ASIAN ARCHITECTURE: IMAGES OF ANCIENT JAPANESE AND CHINESE ARCHITECTURE

DEPICTED IN MOVIES

Naomi Ando

Hosei University (JAPAN), [email protected]

Abstract

Architecture is depicted in several movies as part of expression or as backgrounds. This paper discusses the method of image interpretation of cinematographic architecture, and presents the educational material to learn the characteristics of architecture through the movies. Since it was constructed by wood, most of the Asian (Japan and China) architecture was burnt or destroyed; only a few foundations and grottos of ancient structures could be excavated. Although ancient Japanese and Chinese architecture no longer exist, there are some commercial movies that depict ancient architecture. This study investigates the forms and spaces of ancient Asian architecture depicted in movies in order to clarify the characteristics of their images.

Keywords: Architecture, Ancient Asia, Form, Space, Movie, Education.


37

IMPORTANCE OF STUDYING GEOMETRIC SURFACES IN ARCHITECTURE FOR STUDENTS IN THE FACULTY OF

ENGINEERING AND DESIGN, OF HOSEI UNIVERSITY IN TOKYO, JAPAN

Sonja Krasić1, Naomi Ando2, Petar Pejić3, Zlata Tošić4 1Faculty of Civil Engineering and Architecture, Niš (SERBIA), [email protected]

2Hosei University, Tokyo (JAPAN), [email protected]

3Faculty of Technical Science, Novi Sad (SERBIA), [email protected]

4Faculty of Civil Engineering and Architecture, Niš (SERBIA), [email protected]

Abstract

In order to design and perform architectural objects with complex geometry and shape it is necessary to have knowledge of geometric surfaces. Architecture of 21st century implies knowledge of parametric modeling in which free-form objects can be designed, especially in high developed countries. This includes knowledge of software packages where such modeling is possible, and one of them is Rhinoceros. Before designing free forms, it is necessary to obtain knowledge of geometric surfaces. Their use in architectural practice, which began in the 20th century, is not lagging behind even today. Knowledge of geometric surfaces, and then their use in architectural practice, develops architectural design among students. This was also noticed by the Faculty of Design and Engineering, Hosei University in Tokyo, Japan. The teaching staff at this University had the opinion that the introduction of the subject of Geometric Surfaces in Architecture will improve the quality of studies, as students will use the knowledge gained in this subject for more creative design of architectural objects, which will be shown in this paper.

Keywords: Architectural objects, Geometric Surfaces, Modeling, Rhinoceros program.

NOVEL APPROACH FOR 3D MODELLING TEACHING METHODOLOGY

Aleksandra Joksimović1, Emil Veg2, Mladen Regodić3, Goran Šiniković4 1(SERBIA), [email protected]

Abstract

3D modelling in SolidWorks is taught at the Faculty of mechanical engineering (University of Belgrade) for the past thirteen years. Although the software is intuitive and user friendly, mastering its features was not an easy task for the students. It would be the best for the learning process if the whole group of 80 students could simultaneously follow the teacher‘s instructions and immediately apply them on their computers. Instead of it, due to lack of sufficient space (classrooms) with adequate equipment (enough computers), a professor would gather the whole group (80 students) in the classroom with just one computer and video projector. He would project his computer‘s screen on the wall and explain the steps he is taking in the 3D modelling process. After this presentation, a group of students would split into four other classrooms, with twenty computers each, and exercise the tasks that teacher presented. More than three major problems were recognized in this method and it was decided to implement changes in the course. This paper presents a novel teaching methodology and achieved results in the teaching process improvement.

Keywords: Education in engineering, 3D modelling, inverted classroom.






38

SEARCH THROUGH THE PAST, SERBIAN TEXTBOOKS OF 19TH CENTURY: DIMITRIJE STOJANOVIC – METHODOLOGY OF

DESCRIPTIVE GEOMETRY

Katarina Jevtić-Novaković1, Olga Timčenko2, Marija Divac3 1College of Civil Engineering and Geodesy, Belgrade (SERBIA), [email protected]

2Department of Architecture, Design and Media Technology, Aalborg University (DENMARK),

[email protected] 3College of Civil Engineering and Geodesy, Belgrade (SERBIA), [email protected]

Abstract

In this paper we will analyze the initial history of teaching descriptive geometry in Serbia, but we will start with a brief description of the historical way of learning geometry in Serbia. The need for highly educated people, primarily in the state administration, resulted in the opening of the first Serbian high school, called Lyceum, in Kragujevac in 1838, the capital city of that time. The Lyceum, together with the capital city, was relocated to Belgrade in 1841. Biographical facts of Dimitrije Stojanovic are very scarce. He started his education in Pozarevac, continued in Belgrade, and graduated Polytechnics in Vienna. He was employed as a District Engineer in Pozarevac in 1867, and since 1874 he was a professor of descriptive geometry at the HigherSchool. He was a founder and director of the Railway Department at the Ministry of Construction from 1880. He was the Minister of Construction and the Advisor several times, and the Minister of Finance in the government of Jovan Avakumovic in 1892. He was a regular member of the Serbian Scholar Society and of the Committee for the Promotion of Science and Literature, and he was among the founders of the Technical Society. The work on the book "Methodology of Descriptive Geometry" lasted for 25 years. Dimitrije Stojanovic started writing this textbook in 1874, and completed and published it in 1899. This extensive work has 692 pages of text and 462 drawings, which were separately printed at the end of the book. "Methodology of Descriptive Geometry" is the first attempt to synthesize descriptive and projective geometry. In many sciences, it is difficult to set the boundary between theoretical and practical work, because their interpenetration contributes to the very development of science.

Key words: Dimitrije Stojanovic, Otto Wilhelm Fiedler, descriptive geometry, projective geometry, synthesis, Serbia.

SPHERICAL PERSPECTIVE IN DESIGN EDUCATION

Matthias Kulcke

Hamburg University of Technology and HafenCity University Hamburg (GERMANY), [email protected]

Abstract

The spherical perspective, as the curvilinear perspective par excellence, has not yet been widely introduced into design education. And if it is, then usually as an "outside the box" model, an effect rather than as what it should be viewed as: A meta-class model of vanishing point perspective systems, giving a lecturer the opportunity to present approximations of the straight linear perspective models (with one, two or three vanishing points) all in one system. The mathematical basis for the resulting spherical grid as a curvilinear approximation to one-eyed human vision and a didactic approach for its integration into design oriented perspective freehand drawing are discussed in this paper.

Keywords: Spherical perspective; curvilinear perspective; explanatory model; augmented reality; optical see-through display.


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THE HELICAL SURFACES AND THEIR APPLICATION IN STUDENTS' WORKS

Ana-Maria Graur1*, Carmen Mârza2, Georgiana Corsiuc3 1Faculty of Architecture and Urban Planning, Technical University of Cluj-Napoca (ROMANIA),

[email protected] 2Department of Building Services Engineering, Technical University of Cluj-Napoca

(ROMANIA),[email protected] 3Department of Building Services Engineering, Technical University of Cluj-Napoca (ROMANIA),

[email protected]

Abstract

Architecture as part of the artistic design culture is an aesthetic concept, a complex phenomenon based on scientific, technological and artistic interdisciplinarity, through which any designer manifests itself as a creative being, capable of capitalizing and enriching nature. Nature, in turn, offers the inspiration for various structural efficient forms. These organically inspired structural systems typically exhibit interesting aesthetic. Nature has the art of creating complex structures through simple forms. The spiral found in different forms in nature is interpreted and applied to architectural concepts. These architectural concepts are adapted to technical and constructive thinking through descriptive geometry, developing others structural geometric forms. Notions of shape and design of space in architecture are totally linked together. One of the most known spiral in space is the cylindrical, conical and spherical helix. It is a curve for which the tangent makes a constant angle with axis line. This work analyses the ways in which descriptive geometry, by helical surfaces allows architect students to achieve volumes and architectural spaces, and especially to understand the role it plays in the development of spatial thinking. An architect must be able to see problems from many different directions, in order to design spaces and volumes, he must know the geometry of the structural forms, firstly that of the basic geometric forms.

Keywords: education, helical surface, descriptive geometry, architectural design, architectural space.

VILNIUS CITY IN VIRTUAL REALITY-A WIDE AND SAFE PLAYGROUND FOR CREATIVITY DEVELOPMENT

Ryte Ziuriene1, Franz Fischnaller2, Zilvinas Lilas3 1Vilnius Gediminas Technical University (LITHUANIA), [email protected]

2Albertina Academy of Fine Arts, Turin (ITALY),[email protected]

3Academy of Media Arts (GERMANY), [email protected]

Abstract

In this paper we discuss the process and results of courses based on an experiential knowledge-led program with project-based learning an instructional hands-on method with focus in fostering cross-disciplinary knowledge creation. The courses focus on practical skills and theoretical background, foundation learning and transfer of know-how, while simultaneously gaining advanced knowledge, combined with strategy conducted by trans-disciplinary media artists, researchers and guest scholars. Students were from diverse universities, countries and with different specialties such as: art, design, information technologies, architecture, communication, culture and entertainment. The students were introduced to the use of advanced 3D scanning technologies in architecture and real urban space, based in Vilnius city, building up the optimal database for the 3D scanned data which were using it for the creation and implementation for works such as virtual narratives, digital storytelling, an augmented reality application, computer games and 3D animation creation. Students learned the fundamentals of the art of visualization, 3D animation, virtual and augmented reality, simulation of effective narrative solutions, inclusive with gamification strategies. The course provided the framework for a methodology and learning that guided the students to create a project and to effectively manage its implementation within cross-disciplinary working team(s), from the very start-up, to the final project, getting accomplished the job on planed basis, to be on time and on budget. This paper presents a number creations and project developments by the students during the courses.

Keywords: Vilnius city, 3D scanning, 3D modeling, virtual reality.


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WEB TEXTBOOK FOR DESCRIPTIVE GEOMETRY

Sonja Gorjanc1, Ema Jurkin2 1University of Zagreb, Faculty of Civil Engineering (CROATIA), [email protected]

2University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering (CROATIA),

[email protected]

Abstract

In this paper we present educational material which is a basis for a web textbook designed for the lectures on geometric subjects.The textbook is available online for free. It differs from previous textbooks in the application of information technologies in presenting classic contents and introducing 3D modelling in descriptive geometry teaching.

Keywords: geometry education, descriptive geometry, web textbook.

ANALYSIS OF THE APPLICATION GEOMETRIC SURFACES IN PRACTICE - MONUMENTS IN THE SFR YUGOSLAVIA

Sanja Spasić ĐorĎević1, Vladan Nikolić2, Sanja Janković3, Hristina Krstić4 1Faculty of Civil Engineering and Architecture, University of Niš (SERBIA),



[email protected] 4Faculty of Civil Engineering and Architecture, University of Niš (SERBIA), [email protected]

Abstract

On the territory of SFR Yugoslavia, between 1960. and 1980. a large number of monuments and memorials were built. These complexes testified to the pain suffered as a result of previous wars. Each of the monuments represents a combination of unique structure, size and shape. In addition to witnessing the history of a nation, these monuments represent extremely attractive architectural and artistic works. At a time when the buildings were built, they are called futuristic, and still today they attract with their unusual form. Through design of these monuments, many geometric shapes had been used, and final appearance of these monuments is achieved by their integration, matching of their masses and their proportions. The aim of the paper is to analyze the geometric surfaces from which memorial monuments that marked one epoch are made, but also to show how architects used geometric surfaces in practice.

Keywords: architecture, geometric surfaces, monuments, SFR Yugoslavia, remodeling.





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ON APPROXIMATION OF OVALS IN ARCHITECTURAL DESIGN: BEST FITTING CURVE FOR THE DOME OF SAN CARLO ALLE

QUATTRO FONTANE BY FRANCESCO BORROMINI

Maja Petrović1*, Branko Malešević2, Radovan Štulić3, Marko Vučić4, ĐorĎe Petrović5, Radomir Mijailović6

1University of Belgrade, Faculty of Transport and Traffic Engineering (SERBIA), [email protected]

2University of Belgrade , School of Electrical Engineering (SERBIA), [email protected]



5University of Belgrade, Faculty of Transport and Traffic Engineering (SERBIA),

[email protected] 6University of Belgrade, The Faculty of Transport and Traffic Engineering (SERBIA),

[email protected]

Abstract

The fact that the historical buildings are no rarely deprived of their original design project leads to the ignorance of the exact geometry applied at the time when they were built. This is particularly important when curvilinear forms appear. Such a situation produces the need for the investigation of the curvilinear structures, for the implementation of the contemporary geometric forms of the known properties which best approximates the available data of the building of the interest. In this paper we derive a mathematical procedure for the determination of the Weberian focal curve, as best fitting curve for the floor plan contour of the Dome of San Carlo alle Quatro Fontane by Francesco Borromini.

Keywords: Curve fitting; Weberian curves; Coefficient of determinations.

PRINCIPLES OF ARCHITECTURAL COMPOSITION IN ARCHITECT JOŢE PLEČNIK’S CHURCH OF ST. MICHAEL ON BARJE

Domen Kušar1, Mateja Volgemut2 1University of Ljubljana, Faculty of Architecture (SLOVENIA), [email protected]

2University of Ljubljana, Faculty of Architecture (SLOVENIA), [email protected]

Abstract

Joţe Plečnik (1872–1957) is Slovenian‘s most prominent architect. He studied in Vienna with the architect Otto Wagner, and he created works in Vienna, Prague, Belgrade, Zagreb, the Brijuni Islands, and various places in Slovenia—most of them in Ljubljana. He was a very frugal man and he dedicated his life to architecture and creating beauty. He drew on traditions from antiquity and also Italian Baroque and Renaissance architectural creations while taking into account local features. An effort is currently underway to add his architecture to the UNESCO World Heritage List. In contrast to some of his contemporaries, such as Gaudí, Loos, Le Corbusier, and others, Plečnik‘s designs were primarily based on simple geometric forms, and he sought to achieve harmony by using tried and true proportions. This article analyzes Archangel Michael‘s Church in the Ljubljana Marsh, built in 1939. The church was basically placed in the middle of nowhere, and so the architect did not need to concern himself with harmonizing it with the architecture already built in the surrounding environment. The specific terrain features—poor bearing capacity and proneness to flooding—meant that the architect could not design an ordinary building. As a result of its swampy soil and frequent floods, the Ljubljana Marsh offers poor conditions for farming and thus making a living. Because of the residents‘ disadvantageous economic situation, one could not expect them to contribute much to construction. On the other hand, various complications arose due to some residents‘ opposition to the construction. Plečnik created several versions of his plans, and he also modified them as he went along. Because of various pressures, he was also prepared to withdraw from designing the building. It was only due to the persistence of Plečnik‘s nephew Karel Matkovič—a curate in Ljubljana‘s Trnovo neighborhood, who provided the main impetus for the construction—that the architect was convinced to continue designing the church. Considering the time, energy, and also funds that he used, it can be concluded that Plečnik achieved the beauty of the structure not through the use of expensive materials, but primarily by


42

taking into account the geometric and compositional principles of creating beauty and using inexpensive material. On the other hand, this is a religious structure that was ahead of its time in some respects. The architecture of Archangel Michael‘s Church combines both the ancient and eastern religious architectural tradition with Renaissance elements. Then again, this is a religious structure that in some respects is revolutionary, modern, and at the same time traditional. According to one researcher the compositional key is based on the seal of Hermes. The same author uses gematria to try to decipher the secret messages that the architect is believed to have built into the church. The results presented are based on determining the compositional characteristics of the structure. Namely, an analysis and comparison of the scales of the plans for the current building shows that the church is a veritable treasure house of different proportions. The supporting structure is rationally based on a square raster network of 2.5 m x 2.5 m. The composition of the distribution of the other elements of the building is based on the "Hermetic Seal," the golden cut, and others. The composition appears in the layout as well as on the facades and individual elements of the church and its furnishings. At the same time, it links the layout and facades together. It is only in this way that it is possible to prove the beauty and harmony that a person feels when visiting this sacred place.

Keywords: architecture, Plečnik, Archangel Michael‘s church, composition.

THE LANGUAGE OF PROPORTIONS IN THE PARAMETRIC FRAME: EXQUISITE SERBIAN MEDIEVAL CHURCHES OF RAŠKA STYLE

GROUP

Magdalena Dragović1, Aleksandar Čučaković2, Marko Pejić3, Milesa Srećković4 1Faculty of Civil Engineering, University of Belgrade (SERBIA),[email protected]



4Faculty of Electrical Engineering, University of Belgrade (SERBIA), [email protected]

Abstract

Architectural overview of some historical building is certainly not complete without its proportional analyzes. This study is conducted by the proportion-as-ratio principles for analyzing sacred structures, hence highlighting geometry, both in the sense of geometric interplay of basic shapes (equilateral triangle and circle) and

mathematical ratio expressed by formula such as 1:1, 1:2, 1:√ , 1:1.61 (the golden mean),1: √ , 1: √ , 1: √ ,

1: √ , etc. Among thethree common types of proportional systems, applied in Serbian medieval architecture (square, triangular and golden section), triangular proportional system is specifically related to the so-called Raška style group. The guiding idea of the paper is to test three similar floor plan design patterns of the three exquisite medieval structures on unique proportioning system and 3D modeling of the interior space by parametric interpretation of each structural element of the whole (arch, vault, dome and apse). Parallel overview of the main churches of Studenica, Ţiča and Gradac contains 2D drawings (floor plans and vertical sections), along with proportional analyzes of their structural elements. Each of the three floor plan design patterns complies with I. Štambuk's proportional canon, additionally enriched with intriguing triangular scheme. 3D models are created as "empty space molds" of the church interior, by modeling each element of the structure in Autodesk Revit software.

Keywords: medieval Serbian churches, church floor and section pattern, triangular proportional system, parametric 3D model, the so-called Raška style.

Publisher

Faculty of Technical Sciences

Trg Dositeja Obradovića 6, Novi Sad, Serbia

CIP - Каталогизација у публикацији Библиотека Матице српске, Нови Сад 514.18(048) 004.92(048) INTERNATIONAL Scientific Conference moNGeometrija (6 ; 2018 ; Novi Sad) Book of Abstracts / The 6th International Scientific Conference on Geometry and Graphics moNGeometrija 2018, June 6th-9th 2018, Novi Sad, Serbia ; [editor-in- chief Vesna Stojaković]. - Belgrade : Serbian Society for Geometry and Graphics (SUGIG) ; Novi Sad : Faculty of Technical Sciences, 2018 (Novi Sad : Grid). - 56 str. ; 30 cm Tiraţ 100. ISBN 978-86-6022-054-9 a) Нацртна геометрија - Апстракти b) Рачунарска графика - Апстракти COBISS.SR-ID 323606791

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th International Conference on Geometry and Graphics ... · The 6th International Conference on Geometry and Graphics MONGEOMETRIJA 2018 BOOK OF ABSTRACTS MONGEOMETRIJA 2018 June