Publication detail

Geometric Data Structures and Their Selected Applications

ŠEDA, M.

Original Title

Geometric Data Structures and Their Selected Applications

Type

journal article - other

Language

English

Original Abstract

Finding the shortest path between two positions is a fundamental problem in transportation, routing, and communications applications. In robot motion planning, the robot should pass around the obstacles touching none of them, i.e. the goal is to find a collision-free path from a starting to a target position. This task has many specific formulations depending on the shape of obstacles, allowable directions of movements, knowledge of the scene, etc. Research of path planning has yielded many fundamentally different approaches to its solution, mainly based on various decomposition and roadmap methods. In this paper, we show a possible use of visibility graphs in point-to-point motion planning in the Euclidean plane and an alternative approach using Voronoi diagrams that decreases the probability of collisions with obstacles. The second application area, investigated here, is focused on problems of finding minimal networks connecting a set of given points in the plane using either only straight connections between pairs of points (minimum spanning tree) or allowing the addition of auxiliary points to the set to obtain shorter spanning networks (minimum Steiner tree).

Keywords

Voronoi diagram, Delaunay triangulation, visibility graph

Authors

ŠEDA, M.

RIV year

2006

Released

1. 2. 2006

ISBN

1305-5313

Periodical

Transactions on Engineering, Computing and Technology

Year of study

11

Number

2

State

Republic of Turkey

Pages from

61

Pages to

66

Pages count

6

BibTex

@article{BUT43697,
  author="Miloš {Šeda}",
  title="Geometric Data Structures and Their Selected Applications",
  journal="Transactions on Engineering, Computing and Technology",
  year="2006",
  volume="11",
  number="2",
  pages="6",
  issn="1305-5313"
}