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In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by . The alpha-shape associated with a set of points is a generalization of the concept of the convex hull, i.e. every convex hull is an alpha-shape but not every alpha shape is a convex hull. == Characterization == For each real number ''α'', define the concept of a ''generalized disk of radius'' 1/''α'' as follows: * If ''α'' = 0, it is a closed half-plane; * If ''α'' > 0, it is closed disk of radius 1/''α''; * If ''α'' < 0, it is the closure of the complement of a disk of radius −1/''α''. Then an edge of the alpha-shape is drawn between two members of the finite point set whenever there exists a generalized disk of radius 1/''α'' containing the entire point set and which has the property that the two points lie on its boundary. If ''α'' = 0, then the alpha-shape associated with the finite point set is its ordinary convex hull. 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「Alpha shape」の詳細全文を読む スポンサード リンク
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