منابع مشابه
Arrangements of Planar Curves
Computing arrangements of curves is a fundamental and challenging problem in computational geometry as leading to many practical applications in a wide range of fields, especially in robot motion planning and computer vision. In this survey paper we present the state of the art for computing the arrangement of planar curves, considering various classes of curves, from lines to arbitrary curves.
متن کاملComputing Arrangements of Implicit Curves
We examine the problem of determining, when possible, the exact topological adjacency structure of the planar subdivision induced on a rectangle by a set of curves given in implicit form. This means finding the number of points of intersection of the curves and the way curve segments are linked to determine regions. We use a recursive method based on estimates given by interval arithmetic, toge...
متن کاملOsculation Vertices in Arrangements of Curves
In 1897 de Rocquigny [18] raised the problem of determining the maximal number of points of tangency possible in a system of n mutually non-crossing circles in the plane. The problem seems to have been forgotten until an analogous question concerning 'Apollonian arrangements' of curves was raised and the solution indicated in [11]. The aim of the present note is to indicate the easy solutions t...
متن کاملArrangements of Curves and Algebraic Surfaces
We show a close relation between Chern and logarithmic Chern numbers of complex algebraic surfaces. The method is a “random” p-th root cover which exploits a large scale behavior of Dedekind sums and continued fractions. We use this to construct smooth projective surfaces with Chern ratio arbitrarily close to the logarithmic Chern ratio of a given arrangement of curves. For certain arrangements...
متن کاملOn Levels in Arrangements of Curves
Analyzing the worst-case complexity of the k-level in a planar arrangement of n curves is a fundamental problem in combinatorial geometry. We give the first subquadratic upper bound (roughly O(nk1 2=3s)) for curves that are graphs of polynomial functions of an arbitrary fixed degree s. Previously, nontrivial results were known only for the case s = 1 and s = 2. We also improve the earlier bound...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2007
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216507005245