نتایج جستجو برای: non convex polygon

تعداد نتایج: 1367003  

2001
Tetsuo Asano Yasuyuki Kawamura Reinhard Klette Koji Obokata

The paper introduces a new approximation scheme for planar digital curves. This scheme defines an approximating sausage ‘around’ the given digital curve, and calculates a minimum-length polygon in this approximating sausage. The length of the polygon is taken as an estimator for the length of the curve being the (unknown) preimage of the given digital curve. Assuming finer and finer grid resolu...

Journal: :I. J. Robotics Res. 2007
Subhash Suri Elias Vicari Peter Widmayer

We consider problems of geometric exploration and selfdeployment for simple robots that can only sense the combinatorial (non-metric) features of their surroundings. Even with such a limited sensing, we show that robots can achieve complex geometric reasoning and perform many non-trivial tasks. Specifically, we show that one robot equipped with a single pebble can decide whether the workspace e...

2001
Stephan Eidenbenz Peter Widmayer

The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex polygons is known to be NP -hard, even for polygons without holes [3]. We propose a polynomial-time approximation algorithm for this problem for polygons with or without holes that achieves an approximation ratio of O(logn), where n is the number of vertices in the input polygon. ...

Journal: :Discrete & Computational Geometry 2013
János Geleji Tibor Jordán

A tensegrity polygon is a planar cable-strut tensegrity framework in which the cables form a convex polygon containing all vertices. The underlying edgelabeled graph, in which the cable edges form a Hamilton cycle, is an abstract tensegrity polygon. It is said to be robust if every convex realization as a tensegrity polygon has an equilibrium stress which is positive on the cables and negative ...

2001
Oswin Aichholzer Erik D. Demaine Jeff Erickson Ferran Hurtado Mark Overmars Michael Soss Godfried T. Toussaint

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 canonical configuration like a subdivided triangle) in the sense that each angle changes monotonically throughout t...

Journal: :Comput. Geom. 1991
David Eppstein

We show that the planar dual to the Euclidean farthest point Voronoi diagram for the set of vertices of a convex polygon has the lexicographic minimum possible sequence of triangle angles, sorted from sharpest to least sharp. As a consequence, the sharpest angle determined by three vertices of a convex polygon can be found in linear time.

2011
Kevin Buchin Wouter Meulemans Bettina Speckmann

We define an edge-move operation for polygons and prove that every simple non-convex polygon P has a non-conflicting pair of complementary edge-moves that reduces the number of edges of P while preserving its area. We use this result to generate areapreserving C-oriented schematizations of polygons.

Journal: :Applied Mathematics Letters 1993

Journal: :Comput. Geom. 2008
Franz Aurenhammer

We introduce the concept of weighted skeleton of a polygon and present various decomposition and optimality results for this skeletal structure when the underlying polygon is convex.

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