Thesis (Ph. D.)--Catholic University of America, 1931.

Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 70-74). Also available on the World Wide Web.

Thesis (M.Sc.)--York University, 2005. Graduate Programme in Applied Mathematics. / Typescript. Includes bibliographical references (leaves 103-107). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url%5Fver=Z39.88-2004&res%5Fdat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11845

The objects studied in geoscience are often not man-made objects, but rather the spatial distribution of three-dimensional continuous geographical phenomena such as the salinity of a body of water, the humidity of the air or the percentage of gold in the rock (phenomena that tend to change over time). These are referred to as fields, and their modelling with geographical information systems is problematic because the structures of these systems are usually two dimensional and static. Raster structures (voxels or octrees) are the most popular solutions, but, as I argue in this thesis, they have several shortcomings for geoscientific fields. As an alternative to using rasters for representing and modelling three-dimensional fields, I propose using a new spatial model based the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT). I argue that constructing the VD/DT of the samples that were collected to study the field can be beneficial for extracting meaningful information from it. Firstly, the tessellation of space obtained with the VD gives a clear and consistent definition of neighbourhood for unconnected points in three dimensions, which is useful since geoscientific datasets often have highly anisotropic distributions. Secondly, the efficient and robust reconstruction of the field can be obtained with natural neighbour interpolation, which is entirely based on the properties of the VD. Thirdly, the tessellations of the VD and the DT make possible, and even optimise, several spatial analysis and visualisation operations. A further important consideration is that the VD/DT is locally modifiable (insertion, deletion and movement of points), which permits us to model the temporal dimension, and also to interactively explore a dataset, thus gaining insight by observing on the fly the consequences of manipulations and spatial analysis operations. In this thesis, the development of this new spatial model is from an algorithmic point of view, i.e. I describe in details algorithms to construct, manipulate, analyse and visualise fields represented with the VD/DT. A strong emphasis is put on the implementation of the spatial model, and, for this reason, the many degeneracies that arise in three-dimensional geometric computing are described and handled. A new data structure, the augmented quad-edge, is also presented. It permits us to store simultaneously both the VD and the DT, and helps in the analysis of fields. Finally, the usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications in geoscience.

This thesis describes and compares several methods for producing bilevel patterns to simulate grey level values for use in polygon regions as generated for computer graphics. Random distribution, ordered dither, and error diffusion methods are shown to be visually inferior for many grey levels to the proposed maxmin algorithm for producing patterns for polygon area filling procedures. Through even spatial arrangement of the pixels and taking into consideration the edges of the pattern, the number of artifacts is decreased and the accuracy in small subregions of the pattern is improved, especially at low grey levels where most pattern generators degrade. At these lower levels, the maxmin algorithm can produce pleasing patterns if given sufficient flexibility through enlarged grid sizes. At higher grey levels, the proximity of pixels does not leave sufficient room to eliminate all artifacts, but by varying the criteria of the algorithm, the patterns still appear more pleasing than other methods. / Science, Faculty of / Computer Science, Department of / Graduate

This thesis describes Polygon Filling System, an interactive graphics system, which fills user defined areas on a raster scan graphics display device. The areas may be concave or convex and may be nested within each other. Issues related to the underlying grid model, hexagonal or square tesselation, are discussed. A formal approach to polygon filling is compared to a heuristic domain dependent approach. Connectivity problems arise in processing boundaries. Two user rules are defined. Adherence to these rules ensures correct processing of data. These rules are appropriate for cartographic and remote sensing applications. The implementation of the system and its key data structures are described. / Science, Faculty of / Computer Science, Department of / Graduate

No description available.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-66). Also available in print.

Reconstruction results attempt to rebuild polygons from visibility information. Reconstruction of a general polygon from its visibility graph is still open and only known to be in PSPACE; thus additional information, such as the ordering of the edges around nodes that corresponds to the order of the visibilities around vertices is frequently added. The first section of this thesis extracts, in o(E) time, the Hamiltonian cycle that corresponds to the boundary of the polygon from the polygon's ordered visibility graph. Also, it converts an unordered visibility graph and Hamiltonian cycle to the ordered visibility graph for that polygon in O(E) time. The secod, and major result is an algorithm to reconstruct an arthogonal polygon that is consistent with the Hamiltonian cylce and visibility stabs of the sides of an unknown polygon. The algorithm uses O(nlogn) time, assuming there are no collinear sides, and )(n2) time otherwise. / vii, 78 leaves ; 28 cm.

In this thesis it is demonstrated that the structure of rectilinear polygons can be exploited to solve a variety of geometric problems efficiently. These problems include: (1) recognizing polygonal properties, such as star-shapedness, monotonicity, and edge-visibility, (2) removing hidden lines, (3) constructing the rectilinear convex hull, (4) decomposing rectilinear polygons into simpler components, and (5) placing guards in rectilinear polygons. / A new tool for computational geometry is introduced which extracts information about the winding properties of rectilinear polygons. Employing this tool as a preprocessing step, efficient and conceptually clear algorithms for the above problems have been designed.