منابع مشابه
Farthest-Polygon Voronoi Diagrams
Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log n) time algorithm to compute it. We also prove a number of structural properties of this ...
متن کاملOn the Farthest Line-Segment Voronoi Diagram
The farthest line-segment Voronoi diagram shows properties surprisingly different than the farthest point Voronoi diagram: Voronoi regions may be disconnected and they are not characterized by convexhull properties. In this paper we introduce the farthest line-segment hull, a cyclic structure that relates to the farthest line-segment Voronoi diagram similarly to the way an ordinary convex hull ...
متن کاملRealizing Farthest-Point Voronoi Diagrams
1 The farthest-point Voronoi diagram of a set of n sites 2 is a tree with n leaves. We investigate whether arbi3 trary trees can be realized as farthest-point Voronoi di4 agrams. Given an abstract ordered tree T with n leaves 5 and prescribed edge lengths, we produce a set of n sites 6 S in O(n) time such that the farthest-point Voronoi di7 agram of S represents T . We generalize this algorithm...
متن کاملFarthest line segment Voronoi diagrams
The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restr...
متن کاملThe weighted farthest color Voronoi diagram on trees and graphs
! " # %$ & #' )(* +, ( *. # $/( #0 213 4 " #65/ )( 7986 $. /$ : %(* ; % ;% %$ % " =<> %(* ? @ A B$ ;% # 7DC E F % $ , =$ ;% GIH KJ L@ @ M F# 4 F F = N $ % : ;%(* # /+O #, P$ * ) Q # $ % * L@ + ) SR9 # * ) * ) ) ( #0 -T % </ ) $0 B $. ' * % U + 1V ;% * )(* W P ) # (* % * A +W @ / =</ %$0 X % / ?$ ;% Q P +W P+Y )# ) Q ,$ *;% # 7
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2019
ISSN: 0024-3795
DOI: 10.1016/j.laa.2019.09.002