Results 1  10
of
109,197
Simple Polygons that Cannot be Deflated
, 2000
"... Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the ErdősNagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counterexample to this conjecture by exhibiting a family ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the ErdősNagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counterexample to this conjecture by exhibiting a family
DETERMINING THE SEPARATION OF SIMPLE POLYGONS
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS
, 1993
"... Given simple polygons P and Q, their separation, denoted by (P; Q), is de ned to be the minimum distance between their boundaries. We present a parallel algorithm for finding a closest pair among all pairs (p; q), p 2 P and q 2 Q. The algorithm runs in O(log n) time using O(n) processors on a CREW P ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Given simple polygons P and Q, their separation, denoted by (P; Q), is de ned to be the minimum distance between their boundaries. We present a parallel algorithm for finding a closest pair among all pairs (p; q), p 2 P and q 2 Q. The algorithm runs in O(log n) time using O(n) processors on a CREW
On Compatible Triangulations of Simple Polygons
 Computational Geometry: Theory and Applications
, 1993
"... It is well known that, given two simple nsided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices ..."
Abstract

Cited by 50 (3 self)
 Add to MetaCart
It is well known that, given two simple nsided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional
Area Optimization of Simple Polygons
, 1997
"... We discuss problems of optimizing the area of a simple polygon for a given set of vertices P and show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P . We prove that it is NPcomplete to find a minimum we ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We discuss problems of optimizing the area of a simple polygon for a given set of vertices P and show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P . We prove that it is NPcomplete to find a minimum
On Simple Polygonizations with Optimal Area
, 1999
"... We discuss the problem of nding a simple polygonalization for a given set of vertices P that has optimal area. We show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P and prove that it is NPcomplete to nd ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We discuss the problem of nding a simple polygonalization for a given set of vertices P that has optimal area. We show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P and prove that it is NP
Visibility in Simple Polygons
, 1991
"... We present a new method of decomposing a simple polygon which allows the preprocessing of the polygon to efficiently answer queries of various forms. Using ) space, we can, given a query point q inside or outside the polygon, recover the number of vertices visible from q in O(log n) time. Also, ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We present a new method of decomposing a simple polygon which allows the preprocessing of the polygon to efficiently answer queries of various forms. Using ) space, we can, given a query point q inside or outside the polygon, recover the number of vertices visible from q in O(log n) time. Also
Diffuse Reflections in Simple Polygons
"... We prove a conjecture of Aanjaneya, Bishnu, and Pal that the maximum number of diffuse reflections needed for a point light source to illuminate the interior of a simple polygon with n walls is ⌊n/2 ⌋ − 1. Light reflecting diffusely leaves a surface in all directions, rather than at an identical an ..."
Abstract
 Add to MetaCart
We prove a conjecture of Aanjaneya, Bishnu, and Pal that the maximum number of diffuse reflections needed for a point light source to illuminate the interior of a simple polygon with n walls is ⌊n/2 ⌋ − 1. Light reflecting diffusely leaves a surface in all directions, rather than at an identical
Diffuse Reflections in Simple Polygons
"... We prove a conjecture of Aanjaneya, Bishnu, and Pal that the maximum number of diffuse reflections needed for a point light source to illuminate the interior of a simple polygon with n walls is bn/2c − 1. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angl ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We prove a conjecture of Aanjaneya, Bishnu, and Pal that the maximum number of diffuse reflections needed for a point light source to illuminate the interior of a simple polygon with n walls is bn/2c − 1. Light reflecting diffusely leaves a surface in all directions, rather than at an identical
Efficient Triangulation of Simple Polygons
 The Visual Computer
, 1991
"... This paper considers the topic of efficiently triangulating a simple polygon with emphasis on practical and easytoimplement algorithms. It also describes a new adaptive algorithm for triangulating a simple nsided polygon. The algorithm runs in time O(n(1+t 0 )), with t 0 < n. The quantity ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
This paper considers the topic of efficiently triangulating a simple polygon with emphasis on practical and easytoimplement algorithms. It also describes a new adaptive algorithm for triangulating a simple nsided polygon. The algorithm runs in time O(n(1+t 0 )), with t 0 < n
Pareto envelopes in simple polygons
, 2008
"... For a set T of n points in a metric space (X, d), a point y ∈ X is dominated by a point x ∈ X if d(x, t) ≤ d(y, t) for all t ∈ T and there exists t ′ ∈ T such that d(x, t ′ ) < d(y, t ′). The set of nondominated points of X is called the Pareto envelope of T. H. Kuhn (1973) established that in ..."
Abstract
 Add to MetaCart
that in Euclidean spaces, the Pareto envelopes and the convex hulls coincide. Chalmet et al. (1981) characterized the Pareto envelopes in the rectilinear plane (R2, d1) and constructed them in O(n log n) time. In this note, we investigate the Pareto envelopes of pointsets in simple polygons P endowed with geodesic
Results 1  10
of
109,197