α-visibility

Authors:
Mohammad Ghodsi;Anil Maheshwari;Mostafa Nouri;Jörg-Rüdiger Sack;Hamid Zarrabi-Zadeh
Affiliations:
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran,Institute for Research in Fundamental Sciences (IPM), Tehran, Iran;School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Venue:
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Year:
2012

Citing 14
Cited 0

Visibility of disjoint polygons

Algorithmica
Worst-case optimal algorithms for constructing visibility polygons with holes

SCG '86 Proceedings of the second annual symposium on Computational geometry
An output-sensitive algorithm for computing visibility

SIAM Journal on Computing
Shortest paths help solve geometric optimization problems in planar regions

SIAM Journal on Computing
An Optimal Algorithm for Computing Visibility in the Plane

SIAM Journal on Computing
The Robot Localization Problem

SIAM Journal on Computing
Succinct Representation of Balanced Parentheses and Static Trees

SIAM Journal on Computing
The Visibility Diagram: a Data Structure for Visibility Problems and Motion Planning

SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
Computational geometry in a curved world (algorithm)

Computational geometry in a curved world (algorithm)
Visibility Algorithms in the Plane

Visibility Algorithms in the Plane
Query point visibility computation in polygons with holes

Computational Geometry: Theory and Applications
Weak visibility of two objects in planar polygonal scenes

ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Optimal partition trees

Proceedings of the twenty-sixth annual symposium on Computational geometry
Planar visibility: testing and counting

Proceedings of the twenty-sixth annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments $\ensuremath{{\cal S}}$ in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility, weak and complete segment visibility, and the construction of the visibility graph. We also investigate the natural query versions of these problems, when α is either fixed or specified at query time.