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Danilov, V. I., Koshevoj, G. A.
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Convexity without convex combinations
Journal of Geometry, 2015The paper studies the convex geometry of Beckenbach structures into the context of an axiomatic setting, using some of the axioms of the geometry proposed by Hilbert (the axioms of incidence, of betweenness and the axiom of half-plane). Sandwich results are proved for functions which are convex with respect to Beckenbach families.
Bessenyei, Mihály, Popovics, Bella
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Digital Convexity, Straightness, and Convex Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1982New schemes for digitizing regions and arcs are introduced. It is then shown that under these schemes, Sklansky's definition of digital convexity is equivalent to other definitions. Digital convex polygons of n vertices are defined and characterized in terms of geometric properties of digital line segments.
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