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Results 1 - 10
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1,687
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 Erdős-Nagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counter-example to this conjecture by exhibiting a family ..."
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Cited by 1 (0 self)
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Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the Erdős-Nagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counter-example 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 ..."
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Cited by 4 (0 self)
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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 n-sided 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 ..."
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Cited by 48 (3 self)
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It is well known that, given two simple n-sided 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
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 NP-complete to nd ..."
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Cited by 6 (1 self)
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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
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 NP-complete to find a minimum we ..."
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Cited by 2 (0 self)
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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 NP-complete to find a minimum
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
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Cited by 6 (1 self)
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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 bn/2c − 1. Light reflecting diffusely leaves a surface in all directions, rather than at an identical angl ..."
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Cited by 1 (1 self)
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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
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 ..."
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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
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 ..."
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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 point-sets in simple polygons P endowed with geodesic
Trees in simple Polygons
"... We prove that every simple polygon contains a degree 3 tree encompassing a prescribed set of vertices. We give tight bounds on the minimal number of degree 3 vertices. We apply this result to reprove a result from Bose et al. [3] that every set of disjoint line segments in the plane admits a binary ..."
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We prove that every simple polygon contains a degree 3 tree encompassing a prescribed set of vertices. We give tight bounds on the minimal number of degree 3 vertices. We apply this result to reprove a result from Bose et al. [3] that every set of disjoint line segments in the plane admits a binary
Results 1 - 10
of
1,687
