Publication detail

A Construction of the 2D Generalized Voronoi Diagram, Part I: An Approximation Algorithm

ŠVEC, P.

Original Title

A Construction of the 2D Generalized Voronoi Diagram, Part I: An Approximation Algorithm

Type

conference paper

Language

English

Original Abstract

This paper proposes a new approximation algorithm for constructing the Generalized Voronoi diagram (GVD) for point, line, or polygonal generators based on Fortune’s plane sweep technique. The algorithm approximates a line generator or polygonal edge generators by a sequence of point generator with a given precision. This approach attempts to detect edges of narrow corridors, which are approximated with more points than others, thereby the computation is faster than in case of the uniform distribution with the same precision in these narrow corridors. The worst-time complexity of the computation is O(n log n), where n is the number of approximation point generators. This approximation algorithm is suitable for generating the GVD serving as a base for sampling-based robot motion planning methods, especially for robots with many degrees of freedom, by assuring the maximal clearance distance from surrounding obstacles.

Keywords

Generalized Voronoi diagram, Fortune’s plane sweep algorithm

Authors

ŠVEC, P.

RIV year

2006

Released

1. 5. 2006

Publisher

Brno University of Technology

Location

Brno

ISBN

80-214-3195-4

Book

Proceedings of the 12th International Conference on Soft Computing MENDEL 2006

Pages from

124

Pages to

134

Pages count

11

BibTex

@inproceedings{BUT24983,
  author="Petr {Švec}",
  title="A Construction of the 2D Generalized Voronoi Diagram, Part I: An Approximation Algorithm",
  booktitle="Proceedings of the 12th International Conference on Soft Computing MENDEL 2006",
  year="2006",
  volume="2006",
  pages="11",
  publisher="Brno University of Technology",
  address="Brno",
  isbn="80-214-3195-4"
}