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Guarding galleries and terrains
 Information Processing Letters
, 2006
"... Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P. In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one ..."
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Cited by 17 (1 self)
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Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P. In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one point of G, and the points of G are constrained to be belong to the set of vertices of an arbitrarily dense grid. We also present similar algorithms for terrains and polygons with holes. 1
Conformal mapping in linear time
, 2006
"... Abstract. Given any ɛ> 0 and any planar region Ω bounded by a simple ngon P we construct a (1 + ɛ)quasiconformal map between Ω and the unit disk in time C(ɛ)n. One can take C(ɛ) = C + C log 1 ɛ log log ..."
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Cited by 13 (11 self)
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Abstract. Given any ɛ> 0 and any planar region Ω bounded by a simple ngon P we construct a (1 + ɛ)quasiconformal map between Ω and the unit disk in time C(ɛ)n. One can take C(ɛ) = C + C log 1 ɛ log log
An Output Sensitive Algorithm for Discrete Convex Hulls
 Comput. Geom. Theory Appl
, 1997
"... Given a convex body C in the plane, its discrete hull is C 0 = ConvexHull(C " L), where L = ZZ \Theta ZZ is the integer lattice. We present an O(jC 0 j log ffi(C))time algorithm for calculating the discrete hull of C, where jC 0 j denotes the number of vertices of C 0 , and ffi(C) is the ..."
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Cited by 8 (2 self)
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Given a convex body C in the plane, its discrete hull is C 0 = ConvexHull(C " L), where L = ZZ \Theta ZZ is the integer lattice. We present an O(jC 0 j log ffi(C))time algorithm for calculating the discrete hull of C, where jC 0 j denotes the number of vertices of C 0 , and ffi(C) is the diameter of C. Actually, using known combinatorial bounds, the running time of the algorithm is O(ffi(C) 2=3 log ffi(C)). In particular, this bound applies when C is a disk. 1 Introduction Let C be a planar convex body which we assume to be sufficiently round, in the sense that the following condition holds: Let L = ZZ \Theta ZZ denote the planar integer lattice. We require that C " L is latticeconnected; that is, the union of all the horizontal and vertical unit line segments that connect between pairs of points in C " L is connected; see Figure 1. The discrete hull C 0 of C is defined as the convex hull of C " L; see figure 2 for an illustration. The discrete hull arises in sever...
Constructing Pairwise Disjoint Paths with Few Links
, 1997
"... Let P be a simple polygon and let f(u i ; u 0 i )g be m pairs of distinct vertices of P where for every distinct i; j m, there exist pairwise disjoint paths connecting u i to u 0 i and u j to u 0 j . We wish to construct m pairwise disjoint paths in the interior of P connecting u i to u ..."
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Cited by 3 (1 self)
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Let P be a simple polygon and let f(u i ; u 0 i )g be m pairs of distinct vertices of P where for every distinct i; j m, there exist pairwise disjoint paths connecting u i to u 0 i and u j to u 0 j . We wish to construct m pairwise disjoint paths in the interior of P connecting u i to u 0 i for i = 1; : : : ; m, with minimal total number of line segments. We give an approximation algorithm which in O(n log m + M log m) time constructs such a set of paths using O(M) line segments where M is the number of line segments in the optimal solution.
SpaceEfficient Outlines from Image Data via Vertex Minimization and Grid Constraints
 CVGIP: Graphical Models and Image Processing
, 1997
"... This paper proposes a twostage pipeline that provides separate control over the twin goals of smoothness and conciseness: the first stage produces a specification for a set of closed curves that minimize the number of inflections subject to a specified error bound; the second stage produces polygon ..."
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Cited by 1 (0 self)
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This paper proposes a twostage pipeline that provides separate control over the twin goals of smoothness and conciseness: the first stage produces a specification for a set of closed curves that minimize the number of inflections subject to a specified error bound; the second stage produces polygonal outlines that obey the specifications, have vertices on a given grid, and have nearly the minimum possible number of vertices. Both algorithms are reasonably fast in practice, and can be implemented largely with lowprecision integer arithmetic. 1 Introduction
Robustness Issues in Computational Geometry
"... this paper, I will give a brief survey of the issues involved with each of these classes of problems, and discuss some of the solutions that have been proposed for dealing with them. In particular, I will draw on examples from the field of geometric and solid modeling, as an area where many of these ..."
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Cited by 1 (0 self)
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this paper, I will give a brief survey of the issues involved with each of these classes of problems, and discuss some of the solutions that have been proposed for dealing with them. In particular, I will draw on examples from the field of geometric and solid modeling, as an area where many of these problems have been seen and these techniques applied.
and
"... We exhibit efficient algorithms to perform the following task: Given a function f defined on a finite subset E ⊂ R n, compute a C m function F on R n,witha ..."
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We exhibit efficient algorithms to perform the following task: Given a function f defined on a finite subset E ⊂ R n, compute a C m function F on R n,witha