Thesis (M. Soc. Sc.)--University of Hong Kong, 1991.

Thesis (M.Soc.Sc.)--University of Hong Kong, 1991. / Also available in print.

Computational geometry is the study of algorithms for manipulating sets of points, lines, polygons, planes and other geometric objects. For many problems in this realm, the sets considered are static and the data structures representing them do not permit efficient insertion and deletion of objects (e.g. points). Dynamic problems, in which the set and the geometric data structure change over time, are also of interest. The topic of this thesis is the presentation of fast algorithms for fully dynamic maintenance of some common geometric structures. The following configurations are examined: planar nearest-point and farthest-point Voronoi diagrams, convex hulls (in two and three dimensions), common intersection of halfspaces (2-D and 3-D), and contour of maximal vectors (2-D and 3-D). The principal techniques exploited are fast merging of substructures, and the use of extra storage. Dynamic geometric search structures based upon the configurations are also presented. / Science, Faculty of / Computer Science, Department of / Graduate

published_or_final_version / Economics / Master / Master of Social Sciences

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1990. / Vita. Abstract. Includes bibliographical references (leaves 88-92). Also available via the Internet.

We first handle some generalizations from the theory of functions of a single complex variable, including results regarding analytic continuation. Several "theorems of continuity" are considered, along with the associated definitions of pseudoconvexity, and these are shown to be equivalent up to a special kind of transformation. By successively applying a form of analytic continuation to a function f , a set of pseudoconvex domains is constructed, and the union of these domains is shown to be the envelope of holomorphy of f . / Science, Faculty of / Mathematics, Department of / Graduate

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Daniel M. Oberlin, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (June 18, 2004). Includes bibliographical references.

Development of a methodology of applying symbolic and computational models of conjugate geometry to several problems in design and manufacturing areas forms the basis of this study. The philosophy of this work is the development of generalized symbolic models for two-dimensional and three-dimensional conjugate geometry applications. The generalized models have been implemented using what seems to be the best tool for these kind of applications - a symbolic manipulation system. The unique feature of this research is reflected in the fruitful combination of the elegance of conjugate geometry theory and the inherent versatility of a symbolic manipulation system. The generalized conjugate geometry algorithms were programmed and run using MACSYMA. Typical cases in design of mechanisms have been studied using these symbolic programs. The manufacture of helically swept surfaces is of special interest to this work. Helically swept surfaces have been designed and three schemes of manufacturing these surfaces are presented here. Examples of these three schemes of manufacturing helically swept surfaces have been carried out using the symbolic program in MACSYMA. The results of all the examples have been presented both analytically and graphically. / Master of Science