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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 wikiPageLength "6736".
- Orthogonal_convex_hull wikiPageOutDegree "25".
- Orthogonal_convex_hull wikiPageRevisionID "672542424".
- Orthogonal_convex_hull wikiPageWikiLink Big_O_notation.
- Orthogonal_convex_hull wikiPageWikiLink Cartesian_coordinate_system.
- Orthogonal_convex_hull wikiPageWikiLink Category:Convex_hulls.
- Orthogonal_convex_hull wikiPageWikiLink Connectedness.
- Orthogonal_convex_hull wikiPageWikiLink Convex_hull.
- Orthogonal_convex_hull wikiPageWikiLink Convex_set.
- Orthogonal_convex_hull wikiPageWikiLink Euclidean_space.
- Orthogonal_convex_hull wikiPageWikiLink Geometry.
- Orthogonal_convex_hull wikiPageWikiLink Integer.
- Orthogonal_convex_hull wikiPageWikiLink Intersection_(set_theory).
- Orthogonal_convex_hull wikiPageWikiLink Line_(geometry).
- Orthogonal_convex_hull wikiPageWikiLink Line_segment.
- Orthogonal_convex_hull wikiPageWikiLink Logarithm.
- Orthogonal_convex_hull wikiPageWikiLink Lp_space.
- Orthogonal_convex_hull wikiPageWikiLink Manhattan_distance.
- Orthogonal_convex_hull wikiPageWikiLink Orthant.
- Orthogonal_convex_hull wikiPageWikiLink Perpendicular.
- Orthogonal_convex_hull wikiPageWikiLink Perpendicularity.
- Orthogonal_convex_hull wikiPageWikiLink Polygon.
- Orthogonal_convex_hull wikiPageWikiLink Real_coordinate_space.
- Orthogonal_convex_hull wikiPageWikiLink Standard_basis.
- Orthogonal_convex_hull wikiPageWikiLink Taxicab_geometry.
- Orthogonal_convex_hull wikiPageWikiLink Tight_span.
- Orthogonal_convex_hull wikiPageWikiLink Two-dimensional_space.
- Orthogonal_convex_hull wikiPageWikiLink Visibility_(geometry).
- Orthogonal_convex_hull wikiPageWikiLink File:Orthogonal-convex-hull.svg.
- Orthogonal_convex_hull wikiPageWikiLinkText "Orthogonal convex hull".
- Orthogonal_convex_hull wikiPageWikiLinkText "orthogonal convex hull".
- 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 wikiPageUsesTemplate Template:Citation.
- Orthogonal_convex_hull wikiPageUsesTemplate Template:Harvs.
- Orthogonal_convex_hull wikiPageUsesTemplate Template:Harvtxt.
- Orthogonal_convex_hull wikiPageUsesTemplate Template:Math.
- Orthogonal_convex_hull wikiPageUsesTemplate Template:Mvar.
- 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 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.".
- Orthogonal_convex_hull label "Orthogonal convex hull".
- Orthogonal_convex_hull sameAs m.026g350.
- Orthogonal_convex_hull sameAs Ортогональна_опукла_оболонка.
- Orthogonal_convex_hull sameAs Q7104528.
- Orthogonal_convex_hull sameAs Q7104528.
- Orthogonal_convex_hull wasDerivedFrom Orthogonal_convex_hull?oldid=672542424.
- Orthogonal_convex_hull depiction Orthogonal-convex-hull.svg.
- Orthogonal_convex_hull isPrimaryTopicOf Orthogonal_convex_hull.