Investigating Recursive Point Voronoi Diagrams

Geographic Information Science - Lecture Notes in Computer Science ◽

10.1007/3-540-45799-2_1 ◽

2002 ◽

pp. 1-21 ◽

Cited By ~ 1

Author(s):

Barry Boots ◽

Robert Feick ◽

Narushige Shiode ◽

Steven Roberts

Keyword(s):

Voronoi Diagrams

Download Full-text

Polygon visibility ordering via Voronoi diagrams

The Visual Computer ◽

10.1007/s00371-007-0121-z ◽

2007 ◽

Vol 23 (7) ◽

pp. 503-511 ◽

Cited By ~ 1

Author(s):

Shinichi Fukushige ◽

Hiromasa Suzuki

Keyword(s):

Voronoi Diagrams ◽

Visibility Ordering

Download Full-text

Convex-Straight-Skeleton Voronoi Diagrams for Segments and Convex Polygons

Algorithmica ◽

10.1007/s00453-021-00824-9 ◽

2021 ◽

Author(s):

Gill Barequet ◽

Minati De ◽

Michael T. Goodrich

Keyword(s):

Voronoi Diagrams ◽

Convex Polygons

Download Full-text

Influence-based Voronoi diagrams of clusters

Computational Geometry ◽

10.1016/j.comgeo.2021.101746 ◽

2021 ◽

Vol 96 ◽

pp. 101746

Author(s):

Ziyun Huang ◽

Danny Z. Chen ◽

Jinhui Xu

Keyword(s):

Voronoi Diagrams

Download Full-text

Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees

Mathematical Problems in Engineering ◽

10.1155/2014/456739 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 1

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.

Download Full-text