On local transformation of polygons with visibility properties

Authors:
Carmen Hernando;Michael E. Houle;Ferran Hurtado
Affiliations:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya ( UPC), Avda. Diagonal 647, 08028 Barcelona, Spain;IBM Tokyo Research Laboratory, Yamato, Kanagawa 242-8502, Japan and Basser Department of Computer Science, The University of Sydney, Sydney, NSW 2006, Australia;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya (UPC), Pau Gargallo 5, 08028 Barcelona, Spain
Venue:
Theoretical Computer Science
Year:
2002

Citing 13
Cited 5

Art gallery theorems and algorithms

Art gallery theorems and algorithms
Combinatorial face enumeration in arrangements and oriented matroids

Discrete Applied Mathematics
Construction of three-dimensional Delaunay triangulations using local transformations

Computer Aided Geometric Design
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra

Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Combinatorial face enumeration in convex polytopes

Computational Geometry: Theory and Applications
R(4,5)=25

Journal of Graph Theory
Computing the visibility graph via pseudo-triangulations

Proceedings of the eleventh annual symposium on Computational geometry
Reverse search for enumeration

Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Generating random polygons with given vertices

Computational Geometry: Theory and Applications
The four-colour theorem

Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Geometric tree graphs of points in convex position

Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Graph of triangulations of a convex polygon and tree of triangulations

Computational Geometry: Theory and Applications
Mental imagery in program design and visual programming

International Journal of Human-Computer Studies - Best of empirical studies of programmers 7

VC-Dimension of Exterior Visibility

IEEE Transactions on Pattern Analysis and Machine Intelligence
On planar path transformation

Information Processing Letters
Flips in planar graphs

Computational Geometry: Theory and Applications
Planar tree transformation: Results and counterexample

Information Processing Letters
Enumerating edge-constrained triangulations and edge-constrained non-crossing geometric spanning trees

Discrete Applied Mathematics

Quantified Score

Hi-index	5.23

Visualization

Abstract

One strategy for the enumeration of a class of objects is local transformation, in whch new objects of the class are produced by means of a small modification of a previously-visited object in the same class. When local transformation is possible, the operation can be used to generate objects of the class via random walks, and as the basis for such optimization heuristics as simulated annealing.For general simple polygons on fixed point sets, it is still not known whether the class of polygons on the set is connected via a constant-size local transformation. In this paper, we exhibit a simple local transformation for which the following polygon classes are connected: monotone, x-monotone, star-shaped, (weakly) edge-visible and (weakly) externally visible. The latter class is particularly interesting as it is the most general polygon class known to be connected under local transformation. For each of the polygon classes, we also provide asymptotically-tight worst-case upper bounds on the minimum number of operations required to transform one member of the class to any other.