The topic of my diploma thesis is the solution to exercises of volume and surface of 3D solids. The aim of the thesis is to make own didactic test and to analyse the methods of solution to math exercises in the 9th grade students of ZŠ Amálská. Also to compare the results of the tests in math and science orientated class to "normal1 " class and to find out the success rate of solutions in both classes. I focused only on pyramid and cone, because they are part of curriculum in 9th grade of basic schools after students are admitted to high schools, and after examination of educational programme of chosen school I realised that both classes had the same outputs of given schoolwork. I divided my thesis into two parts - theoretical and practical part. Theoretical part contains five chapters. In the first chapter I focus on didactic tests and their making. In the next chapter I deal with evaluation in general and school evaluation. In the third part there is the term of word exercise defined. In the fourth chapter there are solutions to the word exercises. And in the last chapter I define the term geometrical solid. In the practical part there are the aims and methods of survey, characteristic of research sample, making of didactic test, content of didactic test and analysis of students' solutions...

Ένας από τους παράγοντες που ενοχοποιούνται για την ανάπτυξη ινομυϊκής υπερπλασίας στη φλεβική αναστόμωση των συνθετικών αρτηριοφλεβικών μοσχευμάτων, είναι η διαταραχή των αιμοδυναμικών συνθηκών στην περιοχή της αναστόμωσης. Για τον υπολογισμό της ροής, δηλαδή των πεδίων ταχύτητας, διατμητικής τάσης και στροβιλισμού, στην περιοχή αυτή, χρησιμοποιούνται μέθοδοι της υπολογιστικής δυναμικής των ρευστών, οι οποίες προϋποθέτουν γνώση της τριδιάστατης γεωμετρίας των αγγείων και του μοσχεύματος. Στην παρούσα διπλωματική εργασία αναπτύσσεται μια μεθοδολογία και ο αντίστοιχος αλγόριθμος για τον προσδιορισμό της τριδιάστατης γεωμετρίας της κεντρικής γραμμής των αγγείων από διεπίπεδη αγγειογραφία, όπου η σχέση των δύο συστημάτων αναφοράς θεωρείται άγνωστη, καθώς και για τη σχεδίαση κυκλικών διατομών σε επιλεγμένες θέσεις για την προσέγγιση του αγγειακού αυλού. Η μέθοδος βασίζεται στην θεωρία των Metz – Fencil (1989) και απαιτεί την εκ των προτέρων γνώση δύο ζευγών αντίστοιχων σημείων στις προβολές για τον προσδιορισμό της σχέσης που συνδέει τα δύο συστήματα αναφοράς. Για την αναγνώριση αντίστοιχων σημείων στις προβολές χρησιμοποιείται η τεχνική της επιπολικής γραμμής, ενώ η ανακατασκευή της κεντρικής γραμμής πραγματοποιείται με χρήση παραμετρικής φυσικής spline. Πραγματοποιήθηκε έλεγχος της μεθόδου με χρήση πρότυπης γεωμετρίας και διαπιστώθηκε ότι η ακρίβεια της ανακατασκευής εξαρτάται από το πλήθος και την ποιότητα των σημείων ελέγχου της spline. Τελικά, η μέθοδος εφαρμόστηκε σε πρότυπο αντικείμενο, γνωστής γεωμετρίας, ανάλογης αυτής που λαμβάνεται σε πραγματικές αγγειογραφικές προβολές αρτηριοφλεβικής αναστόμωσης στην περιοχή της καρωτίδας και διαπιστώθηκε ότι ανακατασκευάζει με καλή ακρίβεια την κεντρική γραμμή του αντικειμένου. / One of the factors that have been incriminated for the growth of fibromuscular hyperplasia at the anastomosis of the synthetic arteriovenous implant, is the disturbance of the hemodynamic conditions at the region of the anastomosis. For the computation of the flow at this region, that is the fields of velocity, shear stress and rotation, methods of computational flow dynamics are used, which require that the 3D geometry of the vessels and the implant are known in advance. In this thesis, we developed a methodology and the respective algorithm for the determination of the 3D geometry of the central line of the vessels from biplane angiography, for which the relation of the two systems of coordinates are unknown, as well as for the drawing of circular cross section at selected positions for approximation of arterial lumen. The method is based on the theory of C.E.Metz and L.E.Fencil (1989) and requires the knowledge of two pairs of respective points on the views in advanced in order to calculate the rotation matrix and the translation vector that relate the two systems of coordinates. For recognition of respective points on the two views the epipolar line technique is being used, while the central line is reconstructed using a parametric natural spline. The method was tested using a model and it showed that the accuracy of the reconstruction depends on the number and the quality of the control points of the spline. Finally, the method was implemented on a model object with geometry, analogous to that we get from real angiographic views of arteriovenous anastomosis at the region of the carotid artery, and its central line was reconstructed with very good accuracy.

Abstract The current practice for information sharing with building information modelling (BIM) is distributed data sharing based on conversions. Conversions are problematic due to data loss, redundancy, and conflicting information. The hypotheses of this research were that i) a conversion-free data exchange is a feasible approach for BIM, ii) benefits can be achieved with a conversion-free information sharing, and iii) no impediment in principle exists for wider industrial use. The use of a single data schema by all applications is a requisite for a conversion-free data collaboration. For enabling the free evolution of the data content, a version free data schema is necessary. A model arrangement implementing partial models is needed for the growing size of models. A single shared model approach eliminates data conflicts and duplicates. For the best availability, the location for the shared model should be on a cloud service. Accessing the cloud model only through a web service, which encapsulates all model handling functionality, will ensure data integration and validity. The validity of IT solutions can only be confirmed with real software. For testing the conversion-free BIM method, a software development kit (SDK) with required functionality was programmed. Three applications and a cloud service for handling the shared model were developed with the help of SDK. In the experiments, Leonardo application was used for modelling walls, 3DTrussme for trusses, and Viewer for viewing the model. All applications were using the same shared model on the cloud. In the experimental test, the information exchange occurred without conversions, and all the data were saved only once on the cloud database. Without conversions, less conflicts and redundancies occurred, which lead to better data integrity and integration. Using SDK, there was no technical barrier for applications to join the single shared model ecosystem, but a drawback was that existing BIM programs are not compatible without remarkable changes. The performance was acceptable in the test run, but in real use, the size of the model and the number of applications and users will be much larger. However, a conversion-free single shared model approach can be a possible trend to the next generation BIM as well as a potential alternative for current data sharing methods using distributed files, conversions, and linked data. / Tiivistelmä Rakentamisen tietomallinnuksen (BIM) nykyisenä tiedonjakamisen käytäntönä on hajautettu tietojärjestelmä, joka perustuu konversioihin. Konversiot ovat ongelmallisia tiedon häviämisen, ristiriitojen ja päällekkäisyyksien vuoksi. Tämän tutkimuksen hypoteesit olivat: i) konversiovapaa tiedonjakaminen on mahdollista, ii) etuja on saavutettavissa ilman konversioita tapahtuvassa tiedonsiirrossa ja iii) laajemmalle teolliselle käytölle ei ole periaatteellisia esteitä. Konversiovapaa tiedon jakaminen edellyttää yhden dataformaatin käyttöä. Alati kasvavien tietomallien koko vaatii tiedon järjestämismenetelmän, joko mahdollistaa osamallit. Datan ristiriidat ja päällekkäisyydet voidaan estää yhden jaetun mallin menetelmällä. Informaatio on parhaiten kaikkien osapuolien saatavilla, kun jaettu malli sijoitetaan pilvipalveluun. Kun tietomallia käsitellään vain web-palvelun rajapintafunktioilla, tiedon eheys ja kelpoisuus säilyvät. Tietoteknisten ratkaisujen kelpoisuus voidaan viime kädessä osoittaa vain toimivilla ohjelmistoilla. Konversiovapaan menetelmän testausta varten kehitettiin vaadittavat ominaisuudet sisältävä ohjelmistokehityspaketti (SDK), joka on edellytys sovellusten yhteensopivuudelle. Kolme sovellusta eli 3DTrussme, Leonardo ja Viewer ohjelmoitiin SDK:n avulla. Ohjelmointirajapinta sisälsi tarvittavat toiminnallisuudet tiedonjakamiseen, ja se toteutettiin pilvipalveluna. Testiajossa Leonardo-sovelluksella mallinnettiin seinät, 3DTrussmellä suunniteltiin naulalevyristikot ja Viewer-sovelluksella tarkasteltiin mallia. Kaikki kolme sovellusta käyttivät samaa jaettua mallia pilvipalvelussa. Suoritetussa testissä kaikki informaatio jaettiin ilman konversioita ja tallennettiin vain kerran. Ilman konversioita ja päällekkäisyyksiä saavutettiin parempi datan eheys ja integraatio. SDK:n avulla uudet sovellukset pystyivät liittymään yhden jaetun mallin ekosysteemiin ilman teknisiä esteitä. Toisaalta, ilman merkittäviä muutoksia nykyiset BIM sovellukset eivät ole yhteensopivia. Testiajossa suorituskyky oli hyväksyttävä, mutta todellisuudessa mallien koko sekä sovellusten ja käyttäjien lukumäärä ovat paljon suurempia. Tutkimus osoitti, että konversiovapaa yhden jaetun mallin menetelmä voi olla seuraava BIM-kehityssuunta ja vaihtoehto nykyisille tiedonsiirtoratkaisuille, jotka käyttävät erillisiä tiedostoja, konversioita ja linkkejä.

The recent development of virtual reality (VR) technology carries powerful potential that can be utilised to facilitate the learning of 3D geometry. Therefore, a new approach for teaching and learning of 3D geometry that utilises a virtual reality learning environment (VRLE) is proposed in this research study. This research study aimed to: (a) design and evaluate a VRLE to facilitate the learning of 3D geometry concepts and processes by upper primary school students, and (b) generate theoretical and design principles that will have application both within and beyond the immediate research study. The research methodology employed was design experiments or design-based research. Informed by this methodology, the research design consisted of iterative cycles of developing/revising a conceptual framework, designing/prototyping a VRLE, enacting/evaluating the VRLE, and reflecting/redesigning the research. An initial conceptual framework was generated through extensive literature review to inform the design and evaluation of a VRLE. Based on the conceptual framework, a prototype VRLE named VRMath was then designed and implemented. The enactment and evaluation of VRMath consisted of two iterations. Iteration 1 (six hours/sessions with two students of Year 5 and 6) was conducted using the prototype VRMath (Yeh & Nason, 2004). Based on the findings from Iteration 1, nine learning activities were developed and research protocols (e.g., observation and interview) were revised for Iteration 2. Iteration 2 involved six primary school students (Year 4-5) for eight weeks (two hours/sessions per week). Findings from Iteration 2 confirmed and identified some usability issues of VRMath system and many new ways of thinking and doing 3D geometry when students interacted with VRMath. These have implications on the design of VRMath and the teaching and learning of 3D geometry within the VRMath environment. Justifications about the conceptual framework and students' learning within VRMath were made after the two iterations of enactment and evaluation. The learning activities and VRMath were also revised and redesigned for the preparation of future iterations. After a full cycle of the design-experiments, this research study concluded with a proto-theory (semiotic framework) for the design of and learning within VRLEs, and visions for using VRLEs in mathematic and technology education.

This article is intended to contribute to greater knowledge regarding the importance offlow and the time used to perform an activity, with a focus on students’ mathematicalexperiences of 3D bodies. Thirty-one 9th-grade students took part in the study. Flow andvariation theory was used in the analysis of lesson observations, submission tasks, audiorecordings, logbooks, tests and nationwide tests. The results indicate that the selectedmathematics problem is characterised by seven components, which serve as the basis foridentifying intended critical aspects; a variation is evident in the balance between skillsand challenges that is characterised by the critical aspects that the students discern; avariation is evident in the experience of flow that is dependent upon the students’approach to their work on various activities; the students’ mathematical experiences arebased, both short- and long-term, on discerned critical aspects and on the time spent onthe activity that generates flow. Theoretical contributions as well as implications forteaching are presented at the end of the article.

This thesis is aimed at creating work sheets from the area of solid geometry. It should make easy spatial imagination to students and help teachers at basic schools by teaching solid geometry as well. These work sheets are made by using Cabri 3D geometry software.

Diplomová práce je zaměřena na problematiku detekce a sledování polohy hlavy v obraze jako jednu s možností jak zlepšit možnosti interakce mezi počítačem a člověkem. Hlavním přínosem diplomové práce je využití inovativních hardwarových a softwarových technologií jakými jsou Microsoft Kinect, Point Cloud Library a CImg Library. Na úvod je představeno shrnutí předchozích prací na podobné téma. Následuje charakteristika a popis databáze, která byla vytvořena pro účely diplomové práce. Vyvinutý systém pro detekci a sledování polohy hlavy je založený na akvizici 3D obrazových dat a registračním algoritmu Iterative Closest Point. V závěru diplomové práce je nabídnuto hodnocení vzniklého systému a jsou navrženy možnosti jeho budoucího zlepšení.