An improved algorithm for reconstructing a simple polygon from its visibility angles

Authors:
Danny Z. Chen;Haitao Wang
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2012

Citing 7
Cited 1

Orthogonal polygon reconstruction from stabbing information

Computational Geometry: Theory and Applications
Hard Tasks for Weak Robots: The Role of Common Knowledge in Pattern Formation by Autonomous Mobile Robots

ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Simple Robots with Minimal Sensing: From Local Visibility to Global Geometry

International Journal of Robotics Research
A polygon is determined by its angles

Computational Geometry: Theory and Applications
Reconstructing polygons from scanner data

Theoretical Computer Science
Reconstructing a simple polygon from its angles

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Reconstructing visibility graphs with simple robots

SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity

Perspective: Simple agents learn to find their way: An introduction on mapping polygons

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the visible vertices of v in P, we study the problem of reconstructing the polygon P (up to similarity). An O(n^3logn) time algorithm has been proposed for this problem (by Disser, Mihalak, and Widmayer in 2011 [5]). We show in this paper that the running time of the algorithm in the previous work can be reduced to O(n^2) time by new observations on the geometric structures of the problem.