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U ovom radu kreiran je novi poluautomatski normativni sistem za generisanje prostora na osnovu perspektivnih slika. Sistem obuhvata niz postupaka čijim korišćenjem se na osnovu dvodimenzionalnih medijuma, najčešće fotografija, generiše trodimenzionalna struktura. Pristup je prilagođen rešavanju složenih problema iz oblasti vizuelizacije graditeljskog nasleđa, što je u radu potkrepljeno praktičnom primenom sistema., In this research a new semi-automated normative image-based modelling system is created. The system includes number of procedures that are used to transform two-dimensional medium, such as photographs, to threedimensional structure. The used approach is adjusted to the properties of complex projects in the domain of visualization of cultural heritage. An application of the system is given demonstrating its practical value.

Predmet istraživanja u okviru doktorske disertacije može se podeliti na nekoliko osnovnih tema. Kako se kao osnovni problem istraživanja postavlja analiza oblika kompleksne geometrije kreirane fotogrametrijskom 3D digitalizacijom, fokus istraživanja predstavlja primenu metode analize oblika, zasnovane na numeričkoj deskripciji, u cilju određivanja jasnih relacija između karakteristika oblika i stilskog pravca. Istraživanje u okviru doktorske disertacije bazira se na materijalnom kulturnom nasleđu, koje obuhvata ikonostase, kao jedinstvene elemente kulturnog nasleđa sa izrazito kompleksnom geometrijom. Osnovni cilj istraživanja predstavlja numeričku analizu i stilsku klasifikaciju karakteristika oblika kompleksne geometrije ikonostasa, kreirane fotogrametrijskom 3D digitalizacijom. U svrhu realizacije datog cilja, primenjen je multidisciplinarni pristup koji obuhvata širi kontekst tehnologija i znanja iz oblasti računarske grafike i matematike, koje se koriste za 3D digitalizaciju i analizu oblika.U cilju određivanja jasnih relacija između karakteristika oblika i stilskog pravca ikonostasa, predložen je metod za klasifikaciju oblika glavnih elemenata ikonostasa u odnosu na karakteristike stilskog pravca, zasnovan na metodi 2D analize oblika. Tehnike analize oblika, zasnovane na metodi deskripcije korišćene su za numeričko opisivanje i klasifikaciju stilskih karakteristika razmatranih karakteristika oblika glavnih strukturnih elemenata digitalizovanih modela ikonostasa. Primenjeni su 2D globalni deskriptori i njima pridružene mere oblika, koje su zasnovane na dimenzijama i proporcijama pojedinih elemenata ikonostasa, a koje su dizajnirane tako da odražavaju karakteristične atribute stvarnih oblika.U svrhu 3D digitalizacije, korišćena je fotogrametrijska digitalizacija, kao pouzdan i pristupačan način 3D rekonstrukcije realnih prostornih struktura. Istraživanje u okviru doktorske disertacije obuhvata i analizu i primenu metoda segmentacije oblaka tačaka i detektovanja kontura, u cilju kreiranja preciznih 2D modela kompleksne geometrije ikonostasa, koji se dalje mogu koristiti za 2D analizu oblika. Metod za 2D analizu oblika kompleksne 3D geometrije kreirane fotogrametrijskom 3D digitalizacijom, predložen u okviru doktorske disertacije, ilustrovan je na reprezentativnim primerima tri ikonostasa, nastala na području nekadašnje Karlovačke mitropolije u periodu umetničkih pravaca Baroka i Klasicizma. Rezultati istraživanja ukazali su na to da predložene metode i tehnnologije mogu biti korisne za 2D analizu oblika kompleksne geometrije digitalizovanih objekata kulturnog nasleđa. Naučni doprinos doktorske disertacije ogleda se u numeričkom pristupu analizi oblikovnih karakteristika kulturnog nasleđa, za koje se, zbog prirode kompleksne geometrije ne mogu jasno odrediti pravila oblikovanja, niti pripadnost određenom stilskom pravcu. Rezultati istraživanja takođe doprinose proširenju teorijskih znanja, dopunjujući ih saznanjima o numeričkim karakteristikama oblika analiziranih stilskih pravaca., The subject of the research is divided into several main topics. The basic problem defined within the dissertation was the shape analysis of complex geometry created by photogrammetric 3D digitization. According to that, the main focus of the research was the application of shape analysis, based on the numerical description, to determine clear relations between shape characteristics and stylistic movement. The research includes iconostases, as unique elements of material cultural heritage, characterized by complex geometry. The aim of the research was the numerical shape analysis and classification of the stylistic characteristics of the complex geometry of the iconostasis, created by photogrammetric 3D digitization. To achieve this goal, a multidisciplinary approach was applied, which includes a broader context of technologies and knowledge in the field of computer graphics and mathematics, which were used for 3D digitization and shape analysis.To determine relations between the shape characteristics and the stylistic movement of the iconostases, a method based on 2D shape analysis has beenproposed for the classification of the main iconostasis elements concerning the stylistic period to which it belongs. Shape analysis method, based on the description techniques, was used for numerical description and classification of stylistic characteristics of the considered shape characteristics of the main structural elements of the digitized iconostasis. The concept was based on the application of 2D global shape descriptors and associated shape measures. The shape measures were based on the dimensions and proportions of individual elements of the iconostasis and were designed to reflect the characteristic attributes of real shapes. For 3D digitization of iconostases, photogrammetric digitization was used, as a reliable and accessible way of 3D reconstruction of real spatial structures. In addition, the research included consideration and application of an approach to obtain 2D CAD-like visualizations of complex geometry from photogrammetric models so that the detected contours of particular object elements can be used for 2D shape analysis. The proposed method for 2D shape analysis based on photogrammetric 3D models was illustrated on representative examples of three iconostases, originated from the Baroque and Classicism art movements on the territory of the former Metropolitanate of Karlovci, in the Vojvodina region. The results indicated that the proposed methods and techniques, with certain improvements, could be useful for 2D shape analysis of complex geometry of digitized objects of cultural heritage. The dissertation contribution is reflected in the numerical approach to the shape analysis of cultural heritage characteristics, whereas the rules of design or belonging to a particular artistic style are not always obvious, due to the complex geometry. The obtained results also contribute to the broadening theoretical knowledge, supplementing it with the metric characteristics of the shapes of the analyzed stylistic directions.

Ovo istraživanje ima za cilj kreiranje pristupa za zaštitu virtuelnih 3D modela od zloupotrebe dostupnih širokom auditorijumu na internetu. Pristup predložen u istraživanju je primenjen na skulpturi, izabranom objektu od istorijskog značaja. Zasniva se na 3D digitalizaciji skulpture koja je izmenjena dodavanjem lokalnih detalja od gline, a koje je predložio vajar i na deljenju na internetu 3D virtuelnog modela dobijenog digitalizacijom skulpture sa ugrađenim zaštitnim elementom. Detalji od gline ugrađeni u skulpturu su asimetrični i diskretni da budu neprimetni prosečnom posmatraču. Originalna skulptura je takođe 3D digitalizovana i generisan je njen 3D model. Dobijeni 3D modeli su upoređeni i izmereno je odstupanje geometrije kako bi se utvrdilo u kojoj meri je ugrađeni zaštitni element neprimetan za prosečnog posmatrača, ali i da se taj element može detektovati i po potrebi ukloniti sa 3D modela sa ugrađenom zaštitom., This research aims to suggest an approach for protecting virtual 3D models from abuse while making them available on the Internet. The proposed approach was applied to a sculpture, an object of cultural heritage. It is based on the digitization of the sculpture altered by adding local clay details proposed by the sculptor and on sharing on the Internet a 3D model obtained by digitizing the sculpture with a built-in error. The clay details embedded in the sculpture are asymmetrical and discreet to be unnoticeable to an average observer. The original sculpture was also digitized and its 3D model created. The obtained 3D models were compared and the geometry deviation was measured to determine that the embedded error was invisible to an average observer and that the built-in error can be extracted.

Designing with living materials require designers to look for new methods of fabrication since living cells exhibit their own agency, and are able to sense and respond to environmental stimuli. Therefore, there is an urgent demand to design a framework for fabricating living materials. This paper investigates the digital-fabrication of fungi as a new way of designing and crafting living materials without genetic manipulation. In this research, fungi act as a bio-material probe to generate and test new design strategies that enable a dialogue between digital and biological systems. Conceptual experiments, that use fungi to investigate the proposed bio-digital-fabrication scenarios, are central in this study. The research attempts to generate new information for the design process of an organism in the field of architecture. The project will expand on the latest thinking on the bio-material fabrication by allowing the living material to be engaged in the fabrication process.

Kreiranje 3D modela i njihova vizuelizacija postali su sastavni deo procesa razvoja novih ili redizajniranja postojećih proizvoda. U ovom istraživanju pažnja je posvećena rešavanju problema 3D digitalizacije kod blisko-predmetne fotogrametrije zasnovane na određivanju strukture iz kretanja, na površima bez karakterističnih obeležja primenom projektovanja sintetički generisanih slika u vidu svetlosnih tekstura. Akcenat je stavljen na generisanje novih sintetičkih slika koje imaju izraženu vizuelnu teksturu, njihovu evaluaciju i primenu na objektima sa monotonim vizuelnim površima sa ciljem podizanja ukupne tačnosti rekonstruisanih 3D modela. Verifikacija primene sintetičkih slika i njihovih svetlosnih tekstura sa aspekta geometrijske i dimenzione tačnosti je realizovana primenom računarom podržane inspekcije (CAD inspekcije)., The creation of 3D models and their visualization have become an integral part of the process of developing new or redesigning existing products. In this research, attention was paid to solving the problem of 3D digitization in close-range photogrammetry based on the structure from motion on surfaces without characteristic features by designing synthetically generated images in the form of light textures. An accent is placed on the generation of new synthetic images that have a pronounced visual texture, their evaluation, and application on objects with monotonous visual surfaces with the aim of raising the overall accuracy of reconstructed 3D models. The verification of the application of synthetic images and their light textures from the aspect of geometric and dimensional accuracy was realized through the use of computer-aided inspection (CAI inspection).

Metoda proširene stvarnosti omogućava prikaz stvarnog sveta dopunjenogvirtuelnim objektima i nalazi primenu u prezentaciji virtuelnih 3D modelaarhitektonskih objekata. U ovom istraživanju unapređen je konceptualniautomatski sistem za prezentaciju trodimenzionalnih modela arhitektonskihobjekata metodom proširene stvarnosti. Razvijen je novi algoritam zapravilan prikaz okluzije u sistemima prezentacije arhitektonskih objekatametodom proširene stvarnosti. Delovi ovog sistema su detaljnije razrađeni ucilju rešavanja određenih problema realističnosti prezentacije 3D modelaarhitektonskih objekata., The method of Augmented Reality enables a real world display,supplemented by virtual structures, and it finds its use in the presentation ofvirtual 3D models of architectural structures. In this research a conceptualautomatic system for the presentation of three-dimensional models ofarchitectural structures using the method of Augmented Reality is improved.Particular parts of this system are elaborated in more detail in order to solveparticular problems regarding the realistic displays of the presentation. Anew algorithm for correct occlusion handling in the presentation of 3D modelsof architectural structures by the method of Augmented Reality wasdeveloped.

У овоj дисертациjи обрађен jе проблем равнотеже засвођених масивнихконструкциjа. На основу подробне разраде теориjе потпорне линиjе иконцепта конструкциjског афинитета, уведен jе модел афиних сводова.Установљена jе зависност између облика сводних поља и одговараjу-ћих деjстава свода, те jе начињен параметарски модел за проjектовањесложених афиних сводова. Њиме jе обухваћен аутоматизовани прора-чун и графички приказ резултантних деjстава на ослонце, у виду рачу-нарског алата применљивог у проjектовању и савременом обликовањузасвођених архитектонских простора. С обзиром на раванске проблеме– лукове коjи могу бити ободни лукови афиног свода, аналитички jеобрађено чак десет скупина различитих симетричних конвексних лу-кова те jе извршено и одговараjуће нумеричко моделирање., U ovoj disertaciji obrađen je problem ravnoteže zasvođenih masivnihkonstrukcija. Na osnovu podrobne razrade teorije potporne linije ikoncepta konstrukcijskog afiniteta, uveden je model afinih svodova.Ustanovljena je zavisnost između oblika svodnih polja i odgovaraju-ćih dejstava svoda, te je načinjen parametarski model za projektovanjesloženih afinih svodova. NJime je obuhvaćen automatizovani prora-čun i grafički prikaz rezultantnih dejstava na oslonce, u vidu raču-narskog alata primenljivog u projektovanju i savremenom oblikovanjuzasvođenih arhitektonskih prostora. S obzirom na ravanske probleme– lukove koji mogu biti obodni lukovi afinog svoda, analitički jeobrađeno čak deset skupina različitih simetričnih konveksnih lu-kova te je izvršeno i odgovarajuće numeričko modeliranje., In this dissertation, the problem of the equilibriumof vaulted masonry structuresis considered. On the basis of detailed analysis of the thrust line theory andthe concept of structural affinity, the model of affine vaults is introduced. Therelation between the shape of the vault’s bays and the structural action isestablished, and the parametric model for the design of complex affine vaultsis defined. It involves the automated calculation and graphic representation ofthe resultant loads; thus, the computational tool applicable in the design andcontemporary shaping of vaulted architectural spaces is created. Regarding twodimensionalproblems – arches which can be peripheral arches of affine vaults,for ten groups of different symmetrical convex arches, the analytical treatmentand a corresponding numerical modelling are carried out.

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.

Integrisanjem višerazličitih oblasti arhitekture, poznavanja svojstava materijala, fabrikacije, zajedno sa primenom digitalnih alata, postalo je moguće lakše I efikasnije fabrikovati složene arhitektonske forme. Primena penastog polistirena u arhitektonskoj fabrikaciji je pogodna zbog dobrih svojstava polistirena, prevashodno njegove lake obradivosti. Upotrebom zagrejane žice za obradu materijala I industrijskog robota kao mašine za fabrikaciju, u ovom istraživanju su pokazana tri projektantska scenarija, koja predlažu automatizovan proces fabrikovanja složenih arhitektonskih formi različitih veličina od penastog polistirena I primenom različitih strategija za fabrikaciju. Rezultati su predstavljeni u vidu fabrikovanih prototipova. Theintegrationofmultipledifferentfields-architecture,materialproperties,fabrication,combinedwiththeapplicationofdigitaltoolshasmadethefabricationofcomplexarchitecturalformseasyandefficient.Theapplicationoffoamedpolystyreneinarchitecturalfabricationissuitableduetothegoodpropertiesoffoamedpolystyrene,especiallytheeaseofmillingorcuttingthematerial.Inthisresearch,theapplicationofahot-wireasatoolandanindustrialrobotasafabricationmachinehasenabledthreedifferentdesignscenarios,whichsuggestanautomatedfabricationprocessforcomplexarchitecturalformsofdifferentsizes,madefrompolystyreneandbysuingdifferentfabricationstrategies.Theresultsarepresentsin a form of fabricated prototypes.

In this paper we examine the link between the human body and architectural design. For this purpose, we combine Cognitive Metaphor Theory (CMT) and geometry. We start from the hypothesis that the organization of space and the positions of stairs within the building floor plan is the result of the embodiment of human mind, which implies that abstract aspects of human thought are grounded in physical aspects of human body. CMT claims that BALANCE is a prototypical schema consisting of countervailing forces acting on a target. This mental structure arises from living in symmetrical bodies which are able to balance two equal halves and maintain erect posture. Having established the metaphorical mapping between the building and the human body (and, consequently, between the stairs and human spine) we examined the position of stairs in the building. We geometrically analyzed floor plans of a set of buildings applying the theoretical framework of Projective geometry and methods of Computational geometry. Our findings reveal that stairwells tend to stretch along the line which divides the building basis in two equal halves. [http://www.arhns.uns.ac.rs/mongeometrija/] 6th International Conference on Geometry and graphics, Novi Sad, Serbia, 6-8 June 2018.