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AN O(n log log n)TIME ALGORITHM FOR TRIANGULATING A SIMPLE POLYGON
, 1988
"... Given a simple nvertex polygon, the triangulation problem is to partition the interior of the polygon into n2 triangles by adding n3 nonintersecting diagonals. We propose an O(n log logn)time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that tria ..."
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Cited by 37 (4 self)
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Given a simple nvertex polygon, the triangulation problem is to partition the interior of the polygon into n2 triangles by adding n3 nonintersecting diagonals. We propose an O(n log logn)time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that triangulation is not as hard as sorting. Improved algorithms for several other computational geometry problems, including testing whether a polygon is simple, follow from our result.
A computational basis for conic arcs and Boolean operations on conic polygons
 IN ESA 2002, LNCS 2461
, 2002
"... We give an exact geometry kernel for conic arcs, algorithms for exact computation with lowdegree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon ..."
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Cited by 29 (15 self)
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We give an exact geometry kernel for conic arcs, algorithms for exact computation with lowdegree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces ( = the set of points where a linear or quadratic function is nonnegative) by regularized boolean operations. The algorithm and its implementation are complete (they can handle all cases), exact (they give the mathematically correct result), and efficient (they can handle inputs with several hundred primitives).
Implementing a generalpurpose edge router
 Proceedings of Graph Drawing 97, LNCS 1353
, 1997
"... Abstract. Although routing is a wellstudied problem in various contexts, there remain unsolved problems in routing edges for graph layouts. In contrast with techniques from other domains such as VLSI CAD and robotics, where physical constraints play a major role, aesthetics play the more important ..."
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Cited by 17 (2 self)
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Abstract. Although routing is a wellstudied problem in various contexts, there remain unsolved problems in routing edges for graph layouts. In contrast with techniques from other domains such as VLSI CAD and robotics, where physical constraints play a major role, aesthetics play the more important role in graph layout. For graphs, we seek paths that are easy to follow and add meaning to the layout. We describe a collection of aesthetic attributes applicable to drawing edges in graphs, and present a general approach for routing individual edges subject to these principles. We also give implementation details and survey di culties that arise in an implementation. 1
Computing the Combinatorial Structure of Arrangements of Curves Using Polygonal Approximations
, 1998
"... In this paper, we present a method for computing the incidence graph of an arrangement of curves. The main idea of our approach is to avoid algebraic equations resolution, for the reason that this resolution cannot be performed precisely. To reach our goal, we use two polygonal approximations for ea ..."
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Cited by 4 (0 self)
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In this paper, we present a method for computing the incidence graph of an arrangement of curves. The main idea of our approach is to avoid algebraic equations resolution, for the reason that this resolution cannot be performed precisely. To reach our goal, we use two polygonal approximations for each of the curves of the arrangement and we establish sufficient conditions of equivalence for the three arrangements obtained. This provides not only two polygonal arrangements having the same incidence graph as the arrangement of curves, but also an approximation of this last arrangement in terms of distance. The method is made concrete by an algorithm and numerical results and examples are presented. Keywords: computational geometry, arrangement, B'ezier curve, combinatorial equivalence 1. Introduction The arrangements problem represents one of the most important topics in Computational Geometry. The arrangements find numerous applications, going from the design of 2D drawing tools [11...