Lantmäteriet is developing an application that can show a three-dimensional representation of Sweden based on the data that Lantmäteriet has. The purpose of this application is to be able to crowdsource improvements and changes to the map data that Lantmäteriet has, it will also be able to be used to improve a case's information for easier and faster turnaround at Lantmäteriet. In this Project, I examine how best to use this map data to generate nature such as vegetation in this application to improve usability, and make it easier for the user to know where they are in the application. During the process, I designed a nature generator that uses polygon triangulation to better generate nature.

The symbol map (of Goncharov) takes multiple polylogarithms to a tensor product space where calculations are easier, but where important differential and combinatorial properties of the multiple polylogarithm are retained. Finding linear combinations of multiple polylogarithms in the kernel of the symbol map is an effective way to attempt finding functional equations. We present and utilise methods for finding new linear combinations of multiple polylogarithms (and specifically harmonic polylogarithms) that lie in the kernel of the symbol map. During this process we introduce a new pictorial construction for calculating the symbol, namely the hook-arrow tree, which can be used to easier encode symbol calculations onto a computer. We also show how the hook-arrow tree can simplify symbol calculations where the depth of a multiple polylogarithm is lower than its weight and give explicit expressions for the symbol of depth 2 and 3 multiple polylogarithms of any weight. Using this we give the full symbol for I_{2,2,2}(x,y,z). Through similar methods we also give the full symbol of coloured multiple zeta values. We provide introductory material including the binary tree (of Goncharov) and the polygon dissection (of Gangl, Goncharov and Levin) methods of finding the symbol of a multiple polylogarithm, and give bijections between (adapted forms of) these methods and the hook-arrow tree.

<p> A new area-based mesh simplification algorithm is described. The proposed algorithm removes the center vertex of a polygon which consists of n ≥ 3 faces and represents that polygon with n - 2 faces. A global search method is adapted that iteratively determines which vertex is to be removed using the proposed area-based distortion measurement. Although the global search method requires more computations compared to a local search method, it guarantees better quality of approximation. Various re-triangulations are also considered to improve the perceptual quality of the final approximation.</p> <p> From multiple re-triangulations, one with minimum distortion is selected to represent the original mesh. Experimental results demonstrate the performance of the proposed algorithm for data reduction while maintaining the quality of the rendered objects. The performance of multiple description decoder when not all descriptions are available depends on the decoding strategy. By approximating lost description the distortion can be reduced. When decoder reconstructs input source without having all descriptions different methods exist to approximate the lost description. We proposed two side decoding algorithms. The proposed side decoders are based on diagonal element and the probability of input source. When low bit-rate and complicated index assignment matrix are used the side decoder based on probability of input source is recommendable. To approximate the lost description we compare the performance of standard decoding method with the performance of proposed methods. A trade-off between the performance of decoder and computational complexity exists.</p> <p> An error concealment algorithm is proposed based on flow of facial expression to improve communication of animated facial data over a limited bandwidth channel with error. Facial expression flow is tracked using dominant muscles which are those with maximum change between two successive frames. By comparing the dominant muscle data with the predetermined expression information table, facial expression flow is determined. The receiver uses linear interpolation and the information on facial expression flow to interpolate the erroneous facial animation data. For objective comparison, a distortion measurement tool, which compares two 3D objects based on point-to-point difference, is introduced. Experimental results are provided to show that the proposed error concealment method improves the quality of an animated face communications.</p> / Thesis / Master of Applied Science (MASc)

The aim of this diploma thesis is the research of building polygons for the testing of autonomous vehicles, from the point of view of road technology and also designing aspects. In the thesis are mentioned 9 most important world test polygons and their description of design parameters. There are described particular stages of automation from foreign organizations which are concerned with research and development in the automotive industry. In addition, there are described basic advanced driver assistance systems and connectivity between vehicles and infrastructure. Conclusion also contains the assessment of existing aerodrome test areas for autonomous vehicles.

This thesis deals with general polygon boolean operation algorithms. Boolean operations are e.g. intersection, union or difference. A general polygon can be e.g. a selfinterecting polygon with inner hole. Clipping of polygons against a rectangular window is probably the most familiar boolean operation on polygons. At first, basic definitions are listed. Then the principles of a selected set of boolean operation algorithms are reviewed. Finally, a complex comparison of the algorithms is undertaken. Performance as well as the ability to handle degenerate cases are tested. The output of this thesis is an overall evaluation of algorithm properties and a dynamic library that contains the implementation of all of the tested algorithms.

In this thesis, motivated by modelling polymers, the topological entanglement complexity of systems of two self-avoiding polygons (2SAPs), stretched polygons and systems of self-avoiding walks (SSAWs) in a tubular sublattice of Z3 are investigated. In particular, knotting and linking probabilities are used to measure a polygonfs selfentanglement and its entanglement with other polygons respectively. For the case of 2SAPs, it is established that the homological linking probability goes to one at least as fast as 1-O(n^(-1/2)) and that the topological linking probability goes to one exponentially rapidly as n, the size of the 2SAP, goes to infinity. For the case of stretched polygons, used to model ring polymers under the influence of an external force f, it is shown that, no matter the strength or direction of the external force, the knotting probability goes to one exponentially as n, the size of the polygon, goes to infinity. Associating a two-component link to each stretched polygon, it is also proved that the topological linking probability goes to unity exponentially fast as n&rightarrow;&infin;. Furthermore, a set of entangled chains confined to a tube is modelled by a system of self- and mutually avoiding walks (SSAW). It is shown that there exists a positive number &gamma; such that the probability that an SSAW of size n has entanglement complexity (EC), as defined in this thesis, greater than &gamma;n approaches one exponentially as n&rightarrow;&infin;. It is also established that EC of an SSAW is bounded above by a linear function of its size. Using a transfer-matrix approach, the asymptotic form of the free energy for the SSAW model is also obtained and the average edge-density for span m SSAWs is proved to approach a constant as m&rightarrow;&infin;. Hence, it is shown that EC is a ggoodh measure of entanglement complexity for dense polymer systems modelled by SSAWs, in particular, because EC increases linearly with system size, as the size of the system goes to infinity.

In this thesis, motivated by modelling polymers, the topological entanglement complexity of systems of two self-avoiding polygons (2SAPs), stretched polygons and systems of self-avoiding walks (SSAWs) in a tubular sublattice of Z3 are investigated. In particular, knotting and linking probabilities are used to measure a polygonfs selfentanglement and its entanglement with other polygons respectively. For the case of 2SAPs, it is established that the homological linking probability goes to one at least as fast as 1-O(n^(-1/2)) and that the topological linking probability goes to one exponentially rapidly as n, the size of the 2SAP, goes to infinity. For the case of stretched polygons, used to model ring polymers under the influence of an external force f, it is shown that, no matter the strength or direction of the external force, the knotting probability goes to one exponentially as n, the size of the polygon, goes to infinity. Associating a two-component link to each stretched polygon, it is also proved that the topological linking probability goes to unity exponentially fast as n&rightarrow;&infin;. Furthermore, a set of entangled chains confined to a tube is modelled by a system of self- and mutually avoiding walks (SSAW). It is shown that there exists a positive number &gamma; such that the probability that an SSAW of size n has entanglement complexity (EC), as defined in this thesis, greater than &gamma;n approaches one exponentially as n&rightarrow;&infin;. It is also established that EC of an SSAW is bounded above by a linear function of its size. Using a transfer-matrix approach, the asymptotic form of the free energy for the SSAW model is also obtained and the average edge-density for span m SSAWs is proved to approach a constant as m&rightarrow;&infin;. Hence, it is shown that EC is a ggoodh measure of entanglement complexity for dense polymer systems modelled by SSAWs, in particular, because EC increases linearly with system size, as the size of the system goes to infinity.

Η παρούσα μελέτη πραγματοποιήθηκε στα πλαίσια της διπλωματικής εργασίας «Ψηφιακός Επεξεργαστής και Γραφικά Υπολογιστών». Κατά τη διάρκεια αυτής της μελέτης είχαμε την ευκαιρία να προσεγγίσουμε και να κατανοήσουμε την διαδικασία που επιτελείται για την αναπαράσταση γραφικών στην οθόνη του υπολογιστή μας, του κινητού μας τηλεφώνου και κατ’ επέκταση να προτείνουμε νέες ιδέες και τεχνικές οι οποίες αποσκοπούν στην βελτίωση και αύξηση της αποδοτικότητας. Για το λόγο αυτό μελετώντας τους υπάρχοντες αλγόριθμους, καταλήξαμε στην πρόταση ενός νέου ο οποίος προορίζεται κυρίως για συσκευές απεικόνισης μικρού μεγέθους όπως τα κινητά τηλέφωνα και έχει ως βασικό σκοπό τη μείωση σύνθετων υπολογιστικών πράξεων και εξοικονόμηση ενέργειας. Στη παρούσα εργασία παρουσιάζεται η λειτουργία των υπαρχόντων αλγόριθμων καθώς και του προτεινόμενου. Πραγματοποιούνται συγκρίσεις μεταξύ αυτών προκειμένου να δούμε το ποσοστό βελτίωσης που υπεισέρχεται, ενώ αναπτύσσουμε και το υπόβαθρο για την υλοποίηση και εφαρμογή του προτεινόμενου αλγόριθμου στην πράξη. / -

Universiẗat, Diss., 2000--Dortmund. / Dateiformat: PDF.

This thesis describes the design and implementation of an application that converts CAD models into polygon models. When going from CAD models to 3D polygon models a conversion of the file type has to be performed. XperDI uses these polygon models in their tool, called sales configurator, to create a photo realistic environment to be able to have a look at the end product before it is manufactured. Existing tools are difficult to use and is missing features that is important for the Sales Configurator. The purpose of this thesis is to create a proof of concept application that converts CAD models into 3D polygon models. This new lightweight application is a simpler alternative to convert CAD models into polygon models and offers features needed for the intended use of these models, that the alternative products do not offer.