Three-dimensional strong convexity and visibility
journal contributionposted on 01.01.2003 by Eugene Fink, Derick Wood
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We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties of standard convex sets: (1) Every two points of a convex set are visible to each other. (2) The intersection of convex sets is a convex set. (3) For every point in the boundary of a convex set, there exists a supporting plane through this point. (4) A closed convex set in three dimensions is the intersection of all halfspaces that contain it.