UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Author: search.filters.author.Alborzi, HoumanSubject: search.filters.subject.Quantization

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    Geometric Issues in Spatial Indexing
    (2006-08-22) Alborzi, Houman; Samet, Hanan; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We address a number of geometric issues in spatial indexes. One area of interest is spherical data. Two main examples are the locations of stars in the sky and geodesic data. The first part of this dissertation addresses some of the challenges in handling spherical data with a spatial database. We show that a practical approach for integrating spherical data in a conventional spatial database is to use a suitable mapping from the unit sphere to a rectangle. This allows us to easily use conventional two-dimensional spatial data structures on spherical data. We further describe algorithms for handling spherical data. In the second part of the dissertation, we introduce the areal projection, a novel projection which is computationally efficient and has low distortion. We show that the areal projection can be utilized for developing an efficient method for low distortion quantization of unit normal vectors. This is helpful for compact storage of spherical data and has applications in computer graphics. We introduce the QuickArealHex algorithm, a fast algorithm for quantization of surface normal vectors with very low distortion. The third part of the dissertation deals with a CPU time analysis of TGS, an R-tree bulkloading algorithm. And finally, the fourth part of the dissertation analyzes the BV-tree, a data structure for storing multi-dimensional data on secondary storage. Contrary to the popular belief, we show that the BV-tree is only applicable to binary space partitioning of the underlying data space.