Results 1  10
of
96,010
Telling convex from reflex allows to map a polygon
"... We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e. if the line segment connecting them lies insid ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e. if the line segment connecting them lies
AMapping simple polygons: The power of telling convex from reflex
"... We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e., if the line segment connecting them lies insi ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
be distinguished by a robot from G by its observations alone, no matter how it moves. Combining this result with various other techniques allows to show that a robot exploring a polygon P with the above capabilities is always capable of reconstructing the visibility graph of P. We also show that multiple identical
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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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
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. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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.
ALGORITHM FOR GRAPH VISIBILITY OBTAINMENT FROM A MAP OF NONCONVEX POLYGONS
"... Visibility graphs are basic planning algorithms,widely used in mobile robotics and other disciplines. The construction of a visibility graph can be considered a tool based on geometry that provides support to planning strategies in mobile robots. Visually, the method is used to solve that planning, ..."
Abstract
 Add to MetaCart
, it is obligatory to know whether the area where one vertex of the polygon is found, is located in a convex or nonconvex area, being desirable to distinguish between both situations in a simple way, issue that was not possible up to now. To obtain the visibility of nonconvex polygons, the authors have developed a
Minimum Strictly Convex Quadrangulations of Convex Polygons
 PROC. 13TH SYMP. COMPUTATIONAL GEOMETRY
, 1996
"... We present a lineartime algorithm that decomposes a convex polygon conformally into a minimum number of strictly convex quadrilaterals. Moreover, we characterize the polygons that can be decomposed without additional vertices inside the polygon, and we present a lineartime algorithm for such decom ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We present a lineartime algorithm that decomposes a convex polygon conformally into a minimum number of strictly convex quadrilaterals. Moreover, we characterize the polygons that can be decomposed without additional vertices inside the polygon, and we present a lineartime algorithm
Novruzi: Polygons as optimal shapes with convexity constraint
 SIAM J. Control Optim
"... In this paper, we focus on the following general shape optimization problem: min{J(Ω), Ω convex, Ω ∈ Sad}, where Sad is a set of 2dimensional admissible shapes and J: Sad → R is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality conditions ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
In this paper, we focus on the following general shape optimization problem: min{J(Ω), Ω convex, Ω ∈ Sad}, where Sad is a set of 2dimensional admissible shapes and J: Sad → R is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality
The Limit Shape of Convex Lattice Polygons*
"... Abstract. It is proved here that, as n ~ 0 % almost all convex (1/n)2~21attice polygons lying in the square [ 1, 1] 2 are very close to a fixed convex set. ..."
Abstract
 Add to MetaCart
Abstract. It is proved here that, as n ~ 0 % almost all convex (1/n)2~21attice polygons lying in the square [ 1, 1] 2 are very close to a fixed convex set.
Results 1  10
of
96,010