On stabbing triangles by lines in 3-space

نویسندگان

  • Boris Aronov
  • Jiř́ı Matoušek
چکیده

We give an example of a set P of 3n points in R3 such that, for any partition of P into triples, there exists a line stabbing Ω( √ n) of the triangles determined by the triples.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lower Bounds on Stabbing Lines in 3-space

A stabbing line for a set of convex polyhedra is extremal if it passes through four edges and is tangent to the polyhedra containing those edges. In this paper we present three constructions of convex polyhedra with many extremal lines. The rst construction shows (n 2) extremal stabbing lines constrained to meet two skew lines. The second shows (n 4) extremal lines which are tangent to two poly...

متن کامل

CS - 1993 - 09 On Stabbing Lines for Convex Polyhedra in 3

Given a set B of convex polyhedra in R 3 , a linè in R 3 is called a stabbing line for B if it intersects all polyhedra of B. This paper presents an upper bound of O(n 3 logn) on the complexity of the space of stabbing lines for B. We solve a more general problem which counts the number of faces in a set of convex polyhedra, which are implicitly deened by a set of half-spaces and an arrangement...

متن کامل

Ray-Shooting on Triangles in 3-Space1

We present a uniform approach to problems involving lines in 3-space. This approach is based on mapping lines in R 3 into points and hyperplanes in 5-dimensional projective space (Pl ucker space). We obtain new results on the following problems: 1. Preprocess n triangles so as to eeciently answer the query: \Given a ray, which is the rst triangle hit?" (Ray-shooting problem). We discuss the ray...

متن کامل

Maximum line-pair stabbing problem and its variations

We study the Maximum Line-Pair Stabbing Problem: Given a planar point set S, find a pair of parallel lines within distance 6 from each others such that the number of points of S that intersect (stab) the area in between the two lines is maximized. There exists an algorithm that computes maximum stabbing in O(|S|2) time and space. We give a more space-efficient solution; the time complexity incr...

متن کامل

Constan Ratio Approximation Algorithms for the Rectangle Stabbing Problem and the Rectilinear Partitioning Problem

We provide constant ratio approximation algorithms for two NP-hard problems, the rectangle stabbing problem and the rectilinear partitioning problem. In the rectangle stabbing problem, we are given a set of rectangles in two-dimensional space, with the objective of stabbing all rectangles with the minimum number of lines parallel to the x and y axes. We provide a 2-approximation algorithm, whil...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010