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Straightening polygonal arcs and convexifying polygonal cycles
 DISCRETE & COMPUTATIONAL GEOMETRY
, 2000
"... Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles ..."
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Cited by 87 (31 self)
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Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles
Convexifying Polygons in 3D: a Survey
"... To convexify a polygon is to reconfigure it with respect to a given set of operations until the polygon becomes convex. The problem of convexifying polygons has had a long history in a variety of fields, including mathematics, kinematics and physical chemistry. We survey its history throughout these ..."
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Cited by 1 (0 self)
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To convexify a polygon is to reconfigure it with respect to a given set of operations until the polygon becomes convex. The problem of convexifying polygons has had a long history in a variety of fields, including mathematics, kinematics and physical chemistry. We survey its history throughout
Convexifying Polygons Without Losing Visibilities
 CCCG 2011
, 2011
"... We show that any simple nvertex polygon can be made convex, without losing internal visibilities between vertices, using n moves. Each move translates a vertex of the current polygon along an edge to a neighbouring vertex. In general, a vertex of the current polygon represents a set of vertices of ..."
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Cited by 5 (3 self)
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We show that any simple nvertex polygon can be made convex, without losing internal visibilities between vertices, using n moves. Each move translates a vertex of the current polygon along an edge to a neighbouring vertex. In general, a vertex of the current polygon represents a set of vertices
Reconfigurations of polygonal structures
, 2005
"... This thesis contains new results on the subject of polygonal structure reconfiguration. Specifically, the types of structures considered here are polygons, polygonal chains, triangulations, and polyhedral surfaces. A sequence of vertices (points), successively joined by straight edges, is a polygona ..."
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Cited by 6 (2 self)
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This thesis contains new results on the subject of polygonal structure reconfiguration. Specifically, the types of structures considered here are polygons, polygonal chains, triangulations, and polyhedral surfaces. A sequence of vertices (points), successively joined by straight edges, is a
Locked and Unlocked Polygonal Chains in 3D
, 1999
"... In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are main ..."
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Cited by 25 (14 self)
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In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain
Deflating Polygons to the Limit
"... In this paper we study polygonal transformations through an operation called deflation. It is known that some families of polygons deflate infinitely for given deflation sequences. Here we show that every infinite deflation sequence of a polygon P has a unique limit, and that this limit is flat if a ..."
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In this paper we study polygonal transformations through an operation called deflation. It is known that some families of polygons deflate infinitely for given deflation sequences. Here we show that every infinite deflation sequence of a polygon P has a unique limit, and that this limit is flat
Partial Inflation of Closed Polygons in the Plane
, 1993
"... . Inflation for simply closed regular curves in the plane has been investigated first by S. A. Robertson [4] and studied in some more detail in [5]. It consists of an infinite iteration of reflections of parts of the curve at supporting double tangents, hopefully leading to a convex limit curve w ..."
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Cited by 9 (0 self)
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which has the same arc length as the original curve. The same procedure easily can be defined for simply closed polygons. It provides a special construction of chordstretched versions of the given curve. The aim of this note is to show that the behaviour of inflation is more comfortable
Results 1  10
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117