Robust Point-Location in Generalized Voronoi Diagrams

2006 ◽  
Author(s):  
S. Bereg
Keyword(s):  
Voronoi Diagrams ◽  
Point Location ◽  
Generalized Voronoi Diagrams

scholarly journals Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Quanjun Yin ◽  
Long Qin ◽  
Xiaocheng Liu ◽  
Yabing Zha
Keyword(s):  
Voronoi Diagrams ◽  
Surrounding Area ◽  
Repair Mechanism ◽  
Local Repair ◽  
Order Of Magnitude ◽  
Generalized Voronoi Diagrams ◽  
Incremental Construction ◽  
Coarse To Fine ◽  
Multiple Granularities ◽  
Magnitude Improvement

In robotics, Generalized Voronoi Diagrams (GVDs) are widely used by mobile robots to represent the spatial topologies of their surrounding area. In this paper we consider the problem of constructing GVDs on discrete environments. Several algorithms that solve this problem exist in the literature, notably the Brushfire algorithm and its improved versions which possess local repair mechanism. However, when the area to be processed is very large or is of high resolution, the size of the metric matrices used by these algorithms to compute GVDs can be prohibitive. To address this issue, we propose an improvement on the current algorithms, using pointerless quadtrees in place of metric matrices to compute and maintain GVDs. Beyond the construction and reconstruction of a GVD, our algorithm further provides a method to approximate roadmaps in multiple granularities from the quadtree based GVD. Simulation tests in representative scenarios demonstrate that, compared with the current algorithms, our algorithm generally makes an order of magnitude improvement regarding memory cost when the area is larger than210×210. We also demonstrate the usefulness of the approximated roadmaps for coarse-to-fine pathfinding tasks.

Approximations of 2D and 3D generalized Voronoi diagrams

2008 ◽  
Vol 85 (7) ◽  
pp. 1003-1022 ◽  
Author(s):  
Imma Boada ◽  
Narcís Coll ◽  
Narcís Madern ◽  
J. Antoni Sellarès
Keyword(s):  
Voronoi Diagrams ◽  
Generalized Voronoi Diagrams ◽  
2D And 3D
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