Editing Convex set (section)

=== Orthogonal convexity ===
{{main|Orthogonal convex hull}}
An example of generalized convexity is '''orthogonal convexity'''.<ref>Rawlins G.J.E. and Wood D, "Ortho-convexity and its generalizations",  in: ''Computational Morphology'', 137-152. [[Elsevier]], 1988.</ref>

A set {{mvar|S}} in the Euclidean space is called '''orthogonally convex''' or '''ortho-convex''', if any segment parallel to any of the coordinate axes connecting two points of {{mvar|S}} lies totally within {{mvar|S}}. It is easy to prove that an intersection of any collection of orthoconvex sets is orthoconvex. Some other properties of convex sets are  valid as well.