2012
DOI: 10.1007/s00453-012-9679-6
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Relative Convex Hulls in Semi-Dynamic Arrangements

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Cited by 4 publications
(3 citation statements)
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“…Toussaint gave an O(n log n) time algorithm to compute the relative convex hull of a set of points in a simple polygon [52], and studied properties of such convex hulls [53]. Ishaque and Tóth [34] considered the case of line segments that separate the plane into simply connected regions (thus forming a CAT(0) space) and gave an semi-dynamic algorithm to maintain the convex hull of a set of points as line segments are added and points are deleted.…”
Section: Convex Hullsmentioning
confidence: 99%
“…Toussaint gave an O(n log n) time algorithm to compute the relative convex hull of a set of points in a simple polygon [52], and studied properties of such convex hulls [53]. Ishaque and Tóth [34] considered the case of line segments that separate the plane into simply connected regions (thus forming a CAT(0) space) and gave an semi-dynamic algorithm to maintain the convex hull of a set of points as line segments are added and points are deleted.…”
Section: Convex Hullsmentioning
confidence: 99%
“…The relative convex hull (RCH), also called geodesic convex hull, recently has received increasing attention in Computational Geometry [25], in particular related to shortest path problems which appear in a variety of applications as in robotics, industrial manufacturing, networking, or processing of geographical data [26], [13]. It was earlier defined in the context of Digital Geometry and Topology and their applications in Digital Image Analysis, where the RCH and related structures based on geodesic metrics have been proposed as approximations of digital curves and surfaces and for multi-grid convergent estimations of curve length or surface area [20], [9], [10], [22], [23], [8], [11], [1], [2], [17], [28], [27].…”
Section: Introductionmentioning
confidence: 99%
“…In this paper we study the RCH for simple polygons S,T . In [2], the RCH was considered for the more general situation where S is a finite point set and T is a polygonal domain. A distinct definition of RCH applies to disjoint simple polygons S, T , then CH T (S) is the weakly simple polygon formed by the shortest closed polygonal path without self-crossings which circumscribes S but excludes T [26], see Figure 1b).…”
Section: Introductionmentioning
confidence: 99%