Orthogonal Convex Hull
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In Euclidean geometry, a set KsubsetR^n is defined to be orthogonally convex if, for every line L that is parallel to one of the axes of the Cartesian coordinate system, the intersection of K with L is empty, a point, or a single interval. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected. The orthogonal convex hull of a set SsubsetR^n is the intersection of all connected orthogonally convex supersets of S. These definitions are made…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In Euclidean geometry, a set KsubsetR^n is defined to be orthogonally convex if, for every line L that is parallel to one of the axes of the Cartesian coordinate system, the intersection of K with L is empty, a point, or a single interval. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected. The orthogonal convex hull of a set SsubsetR^n is the intersection of all connected orthogonally convex supersets of S. These definitions are made by analogy with the classical theory of convexity, in which K is convex if, for every line L, the intersection of K with L is empty, a point, or a single interval. Orthogonal convexity restricts the lines for which this property is required to hold, so every convex set is orthogonally convex but not vice versa.