A compact piecewise-linear voronoi diagram for convex sites in the plane
نویسندگان
چکیده
منابع مشابه
A Compact Piecewise-Linear Voronoi Diagram for Convex Sites in the Plane
I n the plane, the post-ofice problem, which asks for the closest site to a query site, and retraction motion planning, which asks for a one-dimensional retract of the free space of a robot, are both classtcally solved by computing a Voronoi diagram. When the sites are k disjoint convex sets, we give a compact representation of the Voronoi diagram, using O ( k ) line segments, that is suficient...
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This paper presents a dynamic algorithm for the construction of the Euclidean Voronoi diagram of a set of convex objects in the plane. We consider first the Voronoi diagram of smooth convex objects forming pseudo-circles set. A pseudo-circles set is a set of bounded objects such that the boundaries of any two objects intersect at most twice. Our algorithm is a randomized dynamic algorithm. It d...
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Lee and Drysdale [13] and Sharir [16] have given suboptimal algorithms for computing the Voronoi diagrams of line-segments or discs in the plane. This paper adapts their methods to constructing the Voronoi diagram for disjoint convex sites in three dimensions. Let be an upper bound on the number of features in any diagram involving sites in three dimensions. Even for point sites, is , so it is ...
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K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
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The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1996
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02716580