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In mathematics, a set in the Euclidean space R''n'' is called a star domain (or star-convex set, star-shaped or radially convex set) if there exists ''x''0 in ''S'' such that for all ''x'' in ''S'' the line segment from ''x''0 to ''x'' is in ''S''. This definition is immediately generalizable to any real or complex vector space. Intuitively, if one thinks of ''S'' as of a region surrounded by a wall, ''S'' is a star domain if one can find a vantage point ''x''0 in ''S'' from which any point ''x'' in ''S'' is within line-of-sight. ==Examples== * Any line or plane in R''n'' is a star domain. * A line or a plane with a single point removed is not a star domain. * If ''A'' is a set in R''n'', the set :: : obtained by connecting all points in ''A'' to the origin is a star domain. * Any non-empty convex set is a star domain. A set is convex if and only if it is a star domain with respect to any point in that set. * A cross-shaped figure is a star domain but is not convex. * A star-shaped polygon is a star domain whose boundary is a sequence of connected line segments. 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「Star domain」の詳細全文を読む スポンサード リンク
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