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Title: Visibility in semi-convex spaces
Authors: Schuierer, Sven
Wood, Derick
Issue Date: Jun-1995
Series/Report no.: Computer Science Technical Report ; HKUST-CS95-39
Abstract: We introduce the notion of a semi-convex space as a unifying framework for the treatment of various notions of convexity in the plane Semi-convex spaces are a generalization of convexity spaces that are more appropriate for investigating issues of visibility We deline the notion of visibility within the general framework of semi-convex spaces, and investigate the relationship between visibility,,kernels, and skulls. We prove the Kernel Theorem and the Cover Kernel Theorem, both of which relate kernels and skulls. Based on these results for semi-convex spaces we prove a theorem about metrics in the plane and demonstrate the utility of our theory with two examples of semi-convex spaces based on geodesic convexity and staircase convexity.
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