| Summary: | Various issues in point location problems are examined. The study is directed towards the design of efficient, simple and practical schemes and focuses on the current trends of research in the area. Practical applications of such problems in scientific visualisation are also investigated. An efficient implementation of one of the planar point location methods, the Kirkpatrick's method is developed. This includes efficient implementations of various associated algorithms and efficient formulations of data structures suitable for the subdivision and the search structure. The practical efficiencies of the implementation conform to the expected efficiencies of the method. An improved version for the search algorithm of the method is proposed and developed. It has been shown that the new improved method outperforms the original method from the computational results. The design and consideration for the extension of the method to three dimensions are also discussed. The subsequent work revolves around three major directions or interests in point location problems namely point location for close successive query points which is introduced as a new direction or area of interest, and dynamic and persistent implementations. Such implementations are applied to some of the existing point location algorithms by proposing some simple, efficient and practical methods. To affirm the practicality, conceptual simplicity and efficiency of the various new schemes, efficient implementations are developed for the Kirkpatrick's method and computational experiments are performed. The results reflect the expected efficiencies of the underlying implementations. Finally, several practical applications of point location algorithms in scientific visualisation are discussed including the use of point location algorithms for close successive query points and the importance of dynamic and persistent implementations of the problems. It has been shown that point location problems can foster scientific visualisation by providing efficient optimal algorithms for the implementations of most of the scientific visualisation techniques.
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