Results 1  10
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1,543
TwoConvex Polygons
, 2009
"... We introduce a notion of kconvexity and explore some properties of polygons that have this property. In particular, 2convex polygons can be recognized in O(n log n) time, and kconvex polygons can be triangulated in O(kn) time. ..."
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Cited by 2 (0 self)
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We introduce a notion of kconvexity and explore some properties of polygons that have this property. In particular, 2convex polygons can be recognized in O(n log n) time, and kconvex polygons can be triangulated in O(kn) time.
Convex polygons in geometric triangulations
, 2014
"... We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029n). This improves an earlier bound of O(1.6181n) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of Ω(1.5028n) due to the same authors. Give ..."
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We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029n). This improves an earlier bound of O(1.6181n) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of Ω(1.5028n) due to the same authors
Reconfiguring Convex Polygons
, 2000
"... We prove that there is a motion from any convex polygon to any convex polygon with the same counterclockwise sequence of edge lengths, that preserves the lengths of the edges, and keeps the polygon convex at all times. Furthermore, the motion is "direct" (avoiding any intermediate canon ..."
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Cited by 8 (4 self)
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We prove that there is a motion from any convex polygon to any convex polygon with the same counterclockwise sequence of edge lengths, that preserves the lengths of the edges, and keeps the polygon convex at all times. Furthermore, the motion is "direct" (avoiding any intermediate
Convex Polygons are SelfCoverable
, 2014
"... We introduce a new notion for geometric families called selfcoverability and show that homothets of convex polygons are selfcoverable. As a corollary, we obtain several results about coloring point sets such that any member of the family with many points contains all colors. This is dual (and in ..."
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Cited by 2 (1 self)
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We introduce a new notion for geometric families called selfcoverability and show that homothets of convex polygons are selfcoverable. As a corollary, we obtain several results about coloring point sets such that any member of the family with many points contains all colors. This is dual (and
On kConvex Polygons ∗
, 2011
"... We introduce a notion of kconvexity and explore polygons in the plane that have this property. Polygons which are kconvex can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUMhard problem. We give a characterization of 2convex polygons, a particularl ..."
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Cited by 3 (2 self)
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We introduce a notion of kconvexity and explore polygons in the plane that have this property. Polygons which are kconvex can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUMhard problem. We give a characterization of 2convex polygons, a
Implicit Convex Polygons
 JOURNAL OF MATHEMATICAL MODELLING AND ALGORITHMS 1: 57–85, 2002
, 2002
"... Convex polygons in the plane can be defined explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as facility location, robotics and computer graphics. In this paper, we inve ..."
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Cited by 4 (4 self)
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Convex polygons in the plane can be defined explicitly as an ordered list of vertices, or given implicitly, for example by a list of linear constraints. The latter representation has been considered in several fields such as facility location, robotics and computer graphics. In this paper, we
Dissections of polygons into convex polygons
"... Abstract In the paper we present purely combinatorial conditions that allow us to recognize the topological equivalence (or nonequivalence) of two given dissections. Using a computer program based on this result, we are able to generate a set which contains all topologically nonequivalent dissect ..."
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equivalent dissections of a p0gon into convex pigons, i = 1, ..., n, where n, p0, ..., pn are integers such that n ≥ 2, pi ≥ 3. By analyzing generated structures, we are able to find all (up to similarity) dissections of a given type. Since the number of topologically nonequivalent dissections is huge even
Convex Polygon Intersection Graphs
, 2010
"... Geometric intersection graphs are graphs determined by the intersections of certain geometric objects. We study the complexity of visualizing an arrangement of objects that induces a given intersection graph. We give a general framework for describing classes of geometric intersection graphs, using ..."
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Cited by 1 (0 self)
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arbitrary finite base sets of rationally given convex polygons and rationallyconstrained affine transformations as similarity maps. We prove that for every class of intersection graphs that fits this framework, the graphs in this class have a representation in integers using only polynomially many bits
SCATTERING BY CONVEX POLYGONS
, 2012
"... Abstract. In this paper we propose and analyse a hybrid hp boundary element method for the solution of problems of high frequency acoustic scattering by soundsoft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high freque ..."
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Abstract. In this paper we propose and analyse a hybrid hp boundary element method for the solution of problems of high frequency acoustic scattering by soundsoft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high
Hilbert geometry for convex polygonal domains
, 2008
"... We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane. ..."
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Cited by 11 (5 self)
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We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane.
Results 1  10
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1,543