On the space restitution of the laguerre’s points associated to the perspective elliptical involuted ranges

Ovaj rad izlaže dokaz, zasnovan na metodi prostorne restitucije, da geometrijsko mesto Lagerovih tačaka perspektivnih eliptičnih involutornih nizova predstavlja dva kruga. Osim što daje doprinos teoriji Projektivne geometrije, izložena teorema omogućava veću efikasnost konstruktivnih postupaka i kompjuterskih algoritama osne rotacije objekata u centralnoj projekciji.This paper discloses the proof, based on the method of the space restitution that geometrical loci of Laguerre's points of perspective elliptical involuted ranges represent two circles. The exposed theorem is a contribution to the theory of Projective geometry; moreover it makes the constructive methods and computational algorithms of an object axial rotations in central projection more effective

Built environment fractality as a criterion of space management

U skladu sa holografskom paradigmom univerzuma, novija istraživanja ukazuju na važnost fraktalnosti ljudskog okruženja za njegovo mentalno i fizičko dobro stanje. Primjeri starijih naselja, gdje je fraktalni koncept primjenjen, pokazuju da je u prošlosti postojala svijest o tome, a koja je u konvencionalnim metodama planiranja gradova zaboravljena. Nedostatak hijerarhičnosti i čovjekomjerne razmjere, geometrijski pravilni oblici i zaravnjene linije modernih gradova, vezuju se za negativne društvene pojave. Stoga ovaj rad ima za cilj da ukaže na važnost fraktalnosti građene sredine i da predloži mogućnosti njenog korišćenja kao kriterijuma upravljanja prostorom.In accordance with the holographic paradigm of the universe, recent studies indicate the importance of fractality of the human environment for his mental and physical well-being. There was awareness of that in the past, but the conventional methods of planning cities have forgotten that. The lack of hierarchy and human scale in modern cities, as so as its geometrically regular shapes and flattened lines, are associated with some negative social phenomena. Therefore, this paper aims to highlight the importance of fractality of built environment and to suggest the possibilities of its use as a criterion of space management

Built environment fractality as a criterion of space management

U skladu sa holografskom paradigmom univerzuma, novija istraživanja ukazuju na važnost fraktalnosti ljudskog okruženja za njegovo mentalno i fizičko dobro stanje. Primjeri starijih naselja, gdje je fraktalni koncept primjenjen, pokazuju da je u prošlosti postojala svijest o tome, a koja je u konvencionalnim metodama planiranja gradova zaboravljena. Nedostatak hijerarhičnosti i čovjekomjerne razmjere, geometrijski pravilni oblici i zaravnjene linije modernih gradova, vezuju se za negativne društvene pojave. Stoga ovaj rad ima za cilj da ukaže na važnost fraktalnosti građene sredine i da predloži mogućnosti njenog korišćenja kao kriterijuma upravljanja prostorom.In accordance with the holographic paradigm of the universe, recent studies indicate the importance of fractality of the human environment for his mental and physical well-being. There was awareness of that in the past, but the conventional methods of planning cities have forgotten that. The lack of hierarchy and human scale in modern cities, as so as its geometrically regular shapes and flattened lines, are associated with some negative social phenomena. Therefore, this paper aims to highlight the importance of fractality of built environment and to suggest the possibilities of its use as a criterion of space management

The constructive-graphical stability of the mapping methods in the general collinear fields

Ovaj rad analizira konstruktivno grafičku stabilnost postupaka preslikavanja u opštim i perspektivno kolinearnim poljima koja se zasnivaju na Lagerovim tačkama preslikanih apsolutnih involucija. Za ovaj metod preslikavanja određene su zone slabe uslovljenosti i odgovarajuće zone nestabilnosti a, sa ciljem korekcije, predloženi su i neki alternativni postupci preslikavanja. Kao rezultat ove analize, kreiran je i objašnjen stabilan i dobro uslovljen metod preslikavanja koji se može iskoristiti za izgradnju softverskih algoritama projektivnih transformacija. Izložena analiza ne predstavlja samo doprinos teoriji kompjuterske i projektivne geometrije, već omogućava da procedure preslikavanja u softverskim modelima opšte i perspektivne kolineacije postanu tačnije i delotvornije.This paper considers and analyzes the constructive-graphical stability of the mapping methods in the general collinear fields based on Laguerre's points of the absolute involution mapped. The ill-conditioned and corresponding unstable zones for this mapping method are defined and some alternative procedures for their correction are proposed. As the result of this analysis, the stabile and well-conditioned general collineation mapping methods, which can be used in the design of the projective transformations software algorithms, are created and explained. The exposed analysis is a contribution to the theory of computational and projective geometry moreover, it makes the mapping procedures in software models of general and perspective collinear fields more accurate and effective

Modeling, Motion Study, and Computer Simulation of Thomas Earnshaw’s Chronometer Detent Escapement Mechanism

The escapement is a very important horological invention and it is commonly used in theory of clocks and chronometers. It transfers energy to the timekeeping element and allows the number of its oscillations to be counted. The chronometer detent escapement used in marine chronometers was modified and simplified by Thomas Earnshaw, English renowned watchmaker, in order to make it available to the public. This chapter deals with 3D modeling and assembling of all escapement parts in SolidWorks, as well as constructive geometry of mechanism and computer simulation. The whole process has been accomplished in program “SolidWorks 2016,” where all parts are assembled by using standard mates since this approach is suitable for motion and dynamical analysis. Generated simulation results are very close to the real ones, thereby using computationally strong kinematic solvers

Fly-through animation as a way of modern presentation in civil engineering and architecture

U ovom radu dat je pregled korišćenja Fly Through animacije, posebno u građevinarstvu i arhitekturi. Prikazana su tri istorijski značajna objekta - Gimnazija 'Jovan Jovanović Zmaj', Departman za arhitekturu i urbanizam i Gradska kuća u Novom Sadu - na čijim modelima su urađene animacije. Takođe, prikazane su animacije nekoliko mostova različitih konstrukcija. Predstavljena je i animacija karaktera koja se može koristiti za realističniji prikaz objekata u građevinarstvu i arhitekturi. Ovaj rad takođe pruža opis modelovanja i animacije 3D karaktera. Postupak izrade ovih animacija opisan je detaljno, redom - kako su objekti i animacije napravljeni.This article describes application of Fly-Through animation, especially in civil engineering and architecture. Three historically significant buildings have been modeled and animated: Grammar School Jovan Jovanovic Zmaj, Department of Architecture and Urban Planning and a City Hall in Novi Sad. Furthermore, animations of couple bridges with different constructions are shown. In addition, this paper presents a description of the modeling procedure and animation of 3D characters. Development process of these models and animations are described in details, step by step

On the properties of the concave antiprisms of second sort

Rad se bavi ispitivanjem geometrijskih, statičkih i dinamičkih osobina jedne poliedarske strukture nastale nabiranjem dvorednog segmenta mreže jednakostraničnih trouglova. Osnove ovih konkavnih poliedara su pravilni, identični poligoni u paralelnim ravnima, povezani nizom naizmeničnih trouglova, kao i u slučaju konveksnih antiprizmi. Postoje dve varijante savijanja ovakve mreže, pa samim tim i dva tipa konkavnih antiprizmi druge vrste (KA II) za svaku posmatranu osnovu od n=5, n=∞. U radu su razmotreni načini dobijanja tačnog položaja temena i drugih linearnih parametara ovih poliedara, uz primenu algoritma za njihovo matematičko izračunavanje. Strukturalna analiza jednog predstavnika ovih poliedara data je korišćenjem aplikacija programa SolidWorks, kako bi se ispitala mogućnost primene ovih oblika u inženjerstvu.The paper examines geometrical, static and dynamic properties of the polyhedral structures obtained by folding and creasing the two-rowed segment of equilateral triangular net. Bases of these concave polyhedra are regular, identical polygons in parallel planes, connected by the alternating series of triangles, as in the case of convex antiprisms. There are two ways of folding such a net, and therefore the two types of concave antiprisms of second sort. The paper discusses the methods of obtaining the accurate position of the vertices and other linear parameters of these polyhedra, with the use of mathematical algorithm. Structural analysis of a representative of these polyhedra is presented using the SolidWorks program applications