Spindulių trasavimas ir padalijimo paviršiai yra svarbūs įrankiai realistiškai atrodantiems vaizdams generuoti. Padalijimas – tai algoritmas, leidžiantis gauti glotnius paviršius pakartotinai dalijant gardeles. Spindulių trasavimas yra technologija, kuri remiasi apšvietimo skaičiavimu. Jos dėka galima gauti atspindžius, permatomumą, spindulių lūžimą kertant skaidrius objektus, taipogi realistiškus šešėlius. Mūsų darbo tikslas buvo suderinti šiuos du metodus, kuriant programinę priemonę, kuri leistų gauti sudėtingų objektų idealiai glotnius aukštos kokybės realistiškus vaizdus. Siekdami to, mes pritaikėme ir tokias kompiuterinės grafikos technologijas, kaip dengimas tekstūromis ir tūrių algebra. / Ray tracing and subdivision surfaces are important tools for generating realistic looking images. Subdivision is an algorithmic technique to generate smooth surfaces as a sequence of successively refined polyhedral meshes. Ray tracing is a technique that performs global calculations of lighting and shading, reflection and transmission of light, casting of shadows, and other effects. The basic idea behind ray tracing is to follow the paths of light rays around a 3-D scene. Our goal is generation of a high-quality realistic images by combining these two techniques. We also implemented other computer graphics methods designed to increase image realism (Texture Mapping) and to simplify modeling process (Boolean operations with solids).

The domination subdivision number of a graph is the minimum number of edges that must be subdivided in order to increase the domination number of the graph. Likewise, the total domination subdivision number is the minimum number of edges that must be subdivided in order to increase the total domination number. First, this thesis provides a complete survey of established bounds on the domination subdivision number and the total domination subdivision number. Then in Chapter 4, new results regarding bounds on the total domination subdivision number are given. Finally, a characterization of the total domination subdivision number of caterpillars is presented in Chapter 5.

La méthode de subdivision Catmull-Clark ainsi que la méthode de subdivision Loop sont des normes industrielle de facto. D'autre part, la méthode de subdivision 4-8 est bien adaptée à la subdivision adaptative, parce que cette méthode augmente le nombre de faces ou de sommets par seulement un facteur de 2 à chaque raffinement. Cela promet d'être plus pratique pour atteindre un niveau donné de précision. Dans ce mémoire, nous présenterons une méthode permettant de paramétrer des surfaces de subdivision de la méthode Catmull-Clark et de la méthode 4-8. Par conséquent, de nombreux algorithmes mis au point pour des surfaces paramétriques pourrant être appliqués aux surfaces de subdivision Catmull-Clark et aux surfaces de subdivision 4-8. En particulier, nous pouvons calculer des bornes garanties et réalistes sur les patches, un peu comme les bornes correspondantes données par Wu-Peters pour la méthode de subdivision Loop. / The Catmull-Clark and Loop methods are de facto industry standards. On the other hand, the 4-8 subdivision method is well suited for adaptive subdivision, because this method increases the number of faces or vertices by only a factor of 2 at each step. It is therefore more convenient when trying to achieve a given practical level of precision. In this thesis we will introduce a method to parametrize the subdivision surfaces of Catmull-Clark and 4-8 subdivision. As a consequence, many algorithms developed for parametric surfaces will be able to be applied to Catmull-Clark and 4-8 subdivision surfaces. In particular, we can produce bounds on surface patches which are both guaranteed and realistic, similar to the bounds given by Wu-Peters [24] for the Loop method

[pt] Subdivisão de superfícies triangulares é um problema importante nas atividades de modelagem e animação. Ao deformar uma superfície a qualidade da triangulação pode ser bastante prejudicada na medida em que triângulos, antes equiláteros, se tornam alongados. Uma solução para este problema consiste em refinar a região deformada. As técnicas de refinamento requerem uma estrutura de dados topológica que seja eficiente em termos de memória e tempo de consulta, além de serem facilmente armazenadas em memória secundária. Esta dissertação propõe um framework baseado na estrutura Corner Table com suporte para subdivisão de malhas triangulares. O framework proposto foi implementado numa biblioteca C mais mais de forma a dar suporte a um conjunto de testes que comprovam a eficiência pretendida. / [en] Subdivision of triangular surfaces is an important problem in modeling and animation activities. Deforming a surface can be greatly affected the quality of the triangulation when as equilateral triangles become elongated. One solution to this problem is to refine the deformed region. Refinement techniques require the support of topological data structure. These structures must be efficient in terms of memory and time. An additional requirement is that these structures must also be easily stored in secondary memory. This dissertation proposes a framework based on the Corner Table data structure with support for subdivision of triangular meshes. The proposed framework was implemented in a C plus plus library. With this library this work presents a set of test results that demonstrate the desired efficiency.

La méthode de subdivision Catmull-Clark ainsi que la méthode de subdivision Loop sont des normes industrielle de facto. D'autre part, la méthode de subdivision 4-8 est bien adaptée à la subdivision adaptative, parce que cette méthode augmente le nombre de faces ou de sommets par seulement un facteur de 2 à chaque raffinement. Cela promet d'être plus pratique pour atteindre un niveau donné de précision. Dans ce mémoire, nous présenterons une méthode permettant de paramétrer des surfaces de subdivision de la méthode Catmull-Clark et de la méthode 4-8. Par conséquent, de nombreux algorithmes mis au point pour des surfaces paramétriques pourrant être appliqués aux surfaces de subdivision Catmull-Clark et aux surfaces de subdivision 4-8. En particulier, nous pouvons calculer des bornes garanties et réalistes sur les patches, un peu comme les bornes correspondantes données par Wu-Peters pour la méthode de subdivision Loop. / The Catmull-Clark and Loop methods are de facto industry standards. On the other hand, the 4-8 subdivision method is well suited for adaptive subdivision, because this method increases the number of faces or vertices by only a factor of 2 at each step. It is therefore more convenient when trying to achieve a given practical level of precision. In this thesis we will introduce a method to parametrize the subdivision surfaces of Catmull-Clark and 4-8 subdivision. As a consequence, many algorithms developed for parametric surfaces will be able to be applied to Catmull-Clark and 4-8 subdivision surfaces. In particular, we can produce bounds on surface patches which are both guaranteed and realistic, similar to the bounds given by Wu-Peters [24] for the Loop method

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject's topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications.

The following paper discusses the application of two subdivision algorithms for the purpose of finding an optimal way of rendering smooth spherical surfaces. Subdivision algorithms are used on three dimensional models. These algorithms typically manipulate the original object to produce one that is more visually pleasing and more realistic to the object we are attempting to recreate. We applied two popular subdivision algorithms to some simple meshes to compare their outcomes. In this project we implemented some of these algorithms in order to gain some insight into how these algorithms differ in the way that they are transforming the input mesh. Our desired goal was to see if there is any basis for which we can say that one algorithm outperforms the other. Our comparison runs through several iterations of subdivision and compares their theses meshes visually. In comparing these meshes our desired visual outcome is a mesh that is more smooth or more spherical. Another metric we looked at was the number of faces being produced for each mesh. In addition, we compared the algorithms in terms of the time they took to perform subdivision. These metrics form the basis for our comparison of performance and we discuss the details of these further in this paper.In our results we found that the two algorithms we are comparing perform quite similarly on certain meshes with respect to the visual output and the time they take to perform subdivision. On meshes of different types however the algorithms might output visually distinguishable meshes upon repeated subdivisions. Finding what factors influence whether the algorithms perform similarly provides an avenue for future work.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Includes bibliographical references. / This thesis, dealing with the land subdivision in urban areas, evaluates inefficiency of the case studies resulting from inadequate and improper existing by-laws in Kaohsiung and provides guidelines for urban development. The study consists of two parts: --Case studies and related by-laws: illustrating the existing situation, inefficient land use, misuse of required open spaces, followed by recommended changes. --Land subdivision models: studying different types of land subdivision models to provide efficient and better urban land subdivision, followed by comparative evaluations. The material in this study is based upon field surveys carried out by the author during the summer of 1980. The analysis is based on a methodology developed in the Urban Settlement Design Program, under the direction of professor Horacio Carninos. / by Hsueh-jane Chen. / M.S.

Thesis (MS)--University of Montana, 2009. / Contents viewed on February 11, 2010. Title from author supplied metadata. Includes bibliographical references.

The need to compactly represent 3D data is motivated by the ever-increasing size of these data. Furthermore, for large data sets it is useful to randomly access and process a small part of the data. In this thesis we propose two methods of compactly representing 3D data while allowing random access. The first is the multiresolution sphere-packing tree (MSP-tree). The MSP-tree is a multiresolution 3D hierarchy on regular grids based on sphere-packing arrangements. The grids of the MSP-tree compactly represent underlying point-sampled data by using more efficient grids than existing methods while maintaining high granularity and a hierarchical structure that allows random access. The second is distance-ranked random-accessible mesh compression (DR-RAMC). DR-RAMC is a lossless simplicial mesh compressor that allows random access and decompression of the mesh data based on a spatial region-of-interest. DR-RAMC encodes connectivity based on relative proximity of vertices to each other and organizes both this proximity data and vertex coordinates using a k-d tree. DR-RAMC is insensitive to a variety of topological mesh problems (e.g. holes, handles, non-orientability) and can compress simplicial meshes of any dimension embedded in spaces of any dimension. Testing of DR-RAMC shows competitive compression rates for triangle meshes and first-ever random accessible compression rates for tetrahedral meshes. / Thesis (Ph.D, Computing) -- Queen's University, 2012-07-17 15:28:39.406