145 research outputs found

    CMB Anisotropy in Compact Hyperbolic Universes II: COBE Maps and Limits

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    We calculate the CMB anisotropy in compact hyperbolic universe models using the regularized method of images described in paper-I, including the 'line-of-sight `integrated Sachs-Wolfe' effect, as well as the last-scattering surface terms. We calculate the Bayesian probabilities for a selection of models by confronting our theoretical pixel-pixel temperature correlation functions with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. This conclusion is qualitatively insensitive to the matter content of the universe, in particular, the presence of a cosmological constant. If the universe is of comparable size to the 'horizon', the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over those for the conventional infinite models. The full Bayesian analysis we use is the most complete statistical test that can be done on the COBE maps, taking into account all possible signals and their variances in the theoretical skies, in particular the high degree of anisotropic correlation that can exist. We show that standard visual measures for comparing theoretical predictions with the data such as the isotropized power spectrum Câ„“C_\ell are not so useful in small compact spaces because of enhanced cosmic variance associated with the breakdown of statistical isotropy.Comment: 29 pages, Latex, 15 figures, submitted to Phys. Rev. D, March 11, 1999. Full resolution figures can be obtained from ftp://ftp.cita.utoronto.ca/pogosyan/prdB

    A flow approach to upward drawings of toroidal maps

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    Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

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    Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment

    Towards a High Quality Real-Time Graphics Pipeline

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    Modern graphics hardware pipelines create photorealistic images with high geometric complexity in real time. The quality is constantly improving and advanced techniques from feature film visual effects, such as high dynamic range images and support for higher-order surface primitives, have recently been adopted. Visual effect techniques have large computational costs and significant memory bandwidth usage. In this thesis, we identify three problem areas and propose new algorithms that increase the performance of a set of computer graphics techniques. Our main focus is on efficient algorithms for the real-time graphics pipeline, but parts of our research are equally applicable to offline rendering. Our first focus is texture compression, which is a technique to reduce the memory bandwidth usage. The core idea is to store images in small compressed blocks which are sent over the memory bus and are decompressed on-the-fly when accessed. We present compression algorithms for two types of texture formats. High dynamic range images capture environment lighting with luminance differences over a wide intensity range. Normal maps store perturbation vectors for local surface normals, and give the illusion of high geometric surface detail. Our compression formats are tailored to these texture types and have compression ratios of 6:1, high visual fidelity, and low-cost decompression logic. Our second focus is tessellation culling. Culling is a commonly used technique in computer graphics for removing work that does not contribute to the final image, such as completely hidden geometry. By discarding rendering primitives from further processing, substantial arithmetic computations and memory bandwidth can be saved. Modern graphics processing units include flexible tessellation stages, where rendering primitives are subdivided for increased geometric detail. Images with highly detailed models can be synthesized, but the incurred cost is significant. We have devised a simple remapping technique that allowsfor better tessellation distribution in screen space. Furthermore, we present programmable tessellation culling, where bounding volumes for displaced geometry are computed and used to conservatively test if a primitive can be discarded before tessellation. We introduce a general tessellation culling framework, and an optimized algorithm for rendering of displaced BĂ©zier patches, which is expected to be a common use case for graphics hardware tessellation. Our third and final focus is forward-looking, and relates to efficient algorithms for stochastic rasterization, a rendering technique where camera effects such as depth of field and motion blur can be faithfully simulated. We extend a graphics pipeline with stochastic rasterization in spatio-temporal space and show that stochastic motion blur can be rendered with rather modest pipeline modifications. Furthermore, backface culling algorithms for motion blur and depth of field rendering are presented, which are directly applicable to stochastic rasterization. Hopefully, our work in this field brings us closer to high quality real-time stochastic rendering

    A theory of the city as object: or, how spatial laws mediate the social construction of urban space

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    A series of recent papers (Hillier et al 1993, Hillier 1996b, Hillier 2000) have outlined a generic process by which spatial configurations, through their effect on movement, first shape, and then are shaped by, land use patterns and densities. The aim of this paper is to make the spatial dimension of this process more precise. The paper begins by examining a large number of axial maps, and finds that although there are strong cultural variations in different regions of the world, there are also powerful invariants. The problem is to understand how both cultural variations and invariants can arise from the spatial processes that generate cities. The answer proposed is that socio-cultural factors generate the differences by imposing a certain local geometry on the local construction of settlement space, while micro-economic factors, coming more and more into play as the settlement expands, generate the invariants

    Canonical Ordering for Triangulations on the Cylinder, with Applications to Periodic Straight-line Drawings

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    International audienceWe extend the notion of canonical orderings to cylindric triangulations. This allows us to extend the incremental straight-line drawing algorithm of de Fraysseix, Pach and Pollack to this setting. Our algorithm yields in linear time a crossing-free straight-line drawing of a cylindric triangulation GG with nn vertices on a regular grid \mZ/w\mZ\times[0..h], with w≤2nw\leq 2n and h≤n(2d+1)h\leq n(2d+1), where dd is the (graph-) distance between the two boundaries. As a by-product, we can also obtain in linear time a crossing-free straight-line drawing of a toroidal triangulation with nn vertices on a periodic regular grid \mZ/w\mZ\times\mZ/h\mZ, with w≤2nw\leq 2n and h≤1+n(2c+1)h\leq 1+n(2c+1), where cc is the length of a shortest non-contractible cycle. Since c≤2nc\leq\sqrt{2n}, the grid area is O(n5/2)O(n^{5/2}). Our algorithms apply to any triangulation (whether on the cylinder or on the torus) that have no loops nor multiple edges in the periodic representation

    Visualization of Industrial Structures with Implicit GPU Primitives

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    International audienceWe present a method to interactively visualize large industrial models by replacing most triangles with implicit GPU primitives: cylinders, cone and torus slices. After a reverse-engineering process that recovers these primitives from triangle meshes, we encode their implicit parameters in a texture that is sent to the GPU. In rendering time, the implicit primitives are visualized seamlessly with other triangles in the scene. The method was tested on two massive industrial models, achieving better performance and image quality while reducing memory use

    A Toroidal Maxwell-Cremona-Delaunay Correspondence

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