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Point location : ウィキペディア英語版 | Point location
The point location problem is a fundamental topic of computational geometry. It finds applications in areas that deal with processing geometrical data: computer graphics, geographic information systems (GIS), motion planning, and computer aided design (CAD). In its most general form, the problem is, given a partition of the space into disjoint regions, determine the region where a query point lies. As an example application, each time you click a mouse to follow a link in a web browser, this problem must be solved in order to determine which area of the computer screen is under the mouse pointer. A simple special case is the point in polygon problem. In this case, we need to determine whether the point is inside, outside, or on the boundary of a single polygon. In many applications, we need to determine the location of several different points with respect to the same partition of the space. To solve this problem efficiently, it is useful to build a data structure that, given a query point, quickly determines which region contains the query point (e.g. Voronoi Diagram). ==Planar case==
In the planar case, we are given a planar subdivision ''S'', formed by multiple polygons called faces, and need to determine which face contains a query point. A brute force search of each face using the point-in-polygon algorithm is possible, but usually not feasible for subdivisions of high complexity. Several different approaches lead to optimal data structures, with O(''n'') storage space and O(log ''n'') query time, where ''n'' is the total number of vertices in ''S''. For simplicity, we assume that the planar subdivision is contained inside a square bounding box.
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「Point location」の詳細全文を読む
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