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Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems, although the term "closest point problem" is also used synonymously to the nearest neighbor search. A common trait for many of these problems is the possibility to establish the Θ(''n'' log ''n'') lower bound on their computational complexity by reduction from the element uniqueness problem basing on an observation that if there is an efficient algorithm to compute some kind of minimal distance for a set of objects, it is trivial to check whether this distance equals to 0. ==Atomic problems== While these problems pose no computational complexity challenge, some of them are notable because of their ubiquity in computer applications of geometry. *Distance between a pair of line segments. It cannot be expressed by a single formula, unlike, e.g., the distance from a point to a line. Its calculation requires careful enumeration of possible configurations, especially in 3D and higher dimensions. *Bounding box, the minimal axis-aligned hyperrectangle that contains all geometric data 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Proximity problems」の詳細全文を読む スポンサード リンク
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