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- W2057578919 abstract "In this paper, we show that the $L_1$ geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the $L_1$ geodesic balls, that is, the metric balls with respect to the $L_1$ geodesic distance. More specifically, in this paper we show that any family of $L_1$ geodesic balls in any simple polygon has Helly number two, and the $L_1$ geodesic center consists of midpoints of shortest paths between diametral pairs. These properties are crucial for our linear-time algorithms, and do not hold for the Euclidean case." @default.
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- W2057578919 date "2015-08-01" @default.
- W2057578919 modified "2023-09-24" @default.
- W2057578919 title "Computing the L1 geodesic diameter and center of a simple polygon in linear time" @default.
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- W2057578919 doi "https://doi.org/10.1016/j.comgeo.2015.02.005" @default.
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