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- Orthogonal_convex_hull abstract "In geometry, a set K ⊂ Rn is defined to be orthogonally convex if, for every line L that is parallel to one of standard basis vectors, the intersection of K with L is empty, a point, or a single segment. The term "orthogonal" refers to corresponding Cartesian basis and coordinates in Euclidean space, where different basis vectors are perpendicular, as well as corresponding lines. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected. The orthogonal convex hull of a set S ⊂ Rn 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 segment (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. For the same reason, the orthogonal convex hull itself is a subset of the convex hull of the same point set. A point p belongs to the orthogonal convex hull of S if and only if each of the closed axis-aligned orthants having p as apex has a nonempty intersection with S.The orthogonal convex hull is also known as the rectilinear convex hull, or, in two dimensions, the x-y convex hull.".
- Orthogonal_convex_hull thumbnail Orthogonal-convex-hull.svg?width=300.
- Orthogonal_convex_hull wikiPageExternalLink restricted-convexity.pdf.
- Orthogonal_convex_hull wikiPageExternalLink restricted-halfspaces.pdf.
- Orthogonal_convex_hull wikiPageID "7847685".
- Orthogonal_convex_hull wikiPageRevisionID "603821891".
- Orthogonal_convex_hull hasPhotoCollection Orthogonal_convex_hull.
- Orthogonal_convex_hull last "Fink".
- Orthogonal_convex_hull last "Rawlins".
- Orthogonal_convex_hull last "Wood".
- Orthogonal_convex_hull year "1987".
- Orthogonal_convex_hull year "1988".
- Orthogonal_convex_hull year "1996".
- Orthogonal_convex_hull year "1998".
- Orthogonal_convex_hull subject Category:Convex_hulls.
- Orthogonal_convex_hull type ConvexHulls.
- Orthogonal_convex_hull type Covering109257949.
- Orthogonal_convex_hull type Hull113139918.
- Orthogonal_convex_hull type Husk113139647.
- Orthogonal_convex_hull type NaturalObject100019128.
- Orthogonal_convex_hull type Object100002684.
- Orthogonal_convex_hull type PhysicalEntity100001930.
- Orthogonal_convex_hull type Sheath105238036.
- Orthogonal_convex_hull type Whole100003553.
- Orthogonal_convex_hull comment "In geometry, a set K ⊂ Rn is defined to be orthogonally convex if, for every line L that is parallel to one of standard basis vectors, the intersection of K with L is empty, a point, or a single segment. The term "orthogonal" refers to corresponding Cartesian basis and coordinates in Euclidean space, where different basis vectors are perpendicular, as well as corresponding lines. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected.".
- Orthogonal_convex_hull label "Orthogonal convex hull".
- Orthogonal_convex_hull sameAs m.026g350.
- Orthogonal_convex_hull sameAs Q7104528.
- Orthogonal_convex_hull sameAs Q7104528.
- Orthogonal_convex_hull sameAs Orthogonal_convex_hull.
- Orthogonal_convex_hull wasDerivedFrom Orthogonal_convex_hull?oldid=603821891.
- Orthogonal_convex_hull depiction Orthogonal-convex-hull.svg.
- Orthogonal_convex_hull isPrimaryTopicOf Orthogonal_convex_hull.
