Basic Measures for Imprecise Point Sets in R
نویسنده
چکیده
Most algorithms in computational geometry tend to assume that all input is exact, with no imprecision or error. Most real-world data however, has some imprecision (for example due to measurement error). Thus, there exists a need for algorithms that can produce meaningful output for imprecise input data. In this thesis, I present results on the computation of upper and lower bounds on various basic measures (such as diameter, width, closest pair, volume of smallest enclosing ball and volume of minimum axis aligned bounding box) for imprecise point sets in Rd. I model the imprecision by representing an imprecise point set as a set of regions (balls or polytopes), such that each point may lie anywhere within one of the regions. This work is an extension of previous research by Löffler and van Kreveld on imprecise point sets in R2, to higher dimensions.
منابع مشابه
Largest Bounding Box, Smallest Diameter, and Related Problems on Imprecise Points
We model imprecise points as regions in which one point must be located. We study computing the largest and smallest possible values of various basic geometric measures on sets of imprecise points, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding box. We give efficient algorithms for most of these problems, and identify the hardness of others.
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تاریخ انتشار 2008