Abstract
Let S be a set of n points in the plane and CH(S) be the convex hull of S. An ε-strongly convex δ-superhull is a polygon P satisfying the following conditions: (1) P has at most O(n) vertices, (2) P contains all the points of S, (3) no vertex of P lies farther than δ outside CH(S), and (4) P is convex and remains convex even if its vertices are perturbed by as much as ε (when ε = δ = 0, P is equal to CH(S)). In this paper, we give the first method for finding such a generalized convex hull. We construct an ε-strongly convex (2 + 4√2)ε-superhull with at most n + 1 vertices in O (n log n) time for any ε ≥ 0.
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© 1997 Springer-Verlag Berlin Heidelberg
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Chen, W., Deng, X.W., Wada, K., Kawaguchi, K. (1997). Constructing a strongly convex superhull of points. In: Jiang, T., Lee, D.T. (eds) Computing and Combinatorics. COCOON 1997. Lecture Notes in Computer Science, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0045071
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DOI: https://doi.org/10.1007/BFb0045071
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