Untangling Planar Curves
نویسندگان
چکیده
منابع مشابه
Untangling Planar Curves
Any generic closed curve in the plane can be transformed into a simple closed curve by a finite sequence of local transformations called homotopy moves. We prove that simplifying a planar closed curve with n self-crossings requires Θ(n3/2) homotopy moves in the worst case. Our algorithm improves the best previous upper bound O(n2), which is already implicit in the classical work of Steinitz; th...
متن کامل2 Untangling Planar Curves
6 Any generic closed curve in the plane can be transformed into a simple closed curve by a finite 7 sequence of local transformations called homotopy moves. We prove that simplifying a planar 8 closed curve with n self-crossings requires Θ(n3/2) homotopy moves in the worst case. Our 9 algorithm improves the best previous upper bound O(n2), which is already implicit in the classical 10 work of S...
متن کاملUntangling a Planar Graph
A straight-line drawing δ of a planar graph G need not be plane, but can be made so by untangling it, that is, by moving some of the vertices of G. Let shift(G, δ) denote the minimum number of vertices that need to be moved to untangle δ. We show that shift(G, δ) is NP-hard to compute and to approximate. Our hardness results extend to a version of 1BendPointSetEmbeddability, a well-known graph-...
متن کاملUntangling Two Systems of Noncrossing Curves
We consider two systems (α1, . . . , αm) and (β1, . . . , βn) of simple curves drawn on a compact two-dimensional surface M with boundary. Each αi and each βj is either an arc meeting the boundary of M at its two endpoints, or a closed curve. The αi are pairwise disjoint except for possibly sharing endpoints, and similarly for the βj . We want to “untangle” the βj from the αi by a self-homeomor...
متن کاملArrangements 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2017
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-017-9907-6