The number of transversals to line segments in R^3

نویسندگان

  • Hervé Brönnimann
  • Hazel Everett
  • Sylvain Lazard
  • Frank Sottile
  • Sue Whitesides
چکیده

We completely describe the structure of the connected components of transversals to a collection of n line segments in R. We show that n > 3 arbitrary line segments in R admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.

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

Transversals to Line Segments in Three-Dimensional Space

We completely describe the structure of the connected components of transversals to a collection of n line segments in R. Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that n > 3 arbitrary line segments in R admit at most n connected components of line transversals, and that this bound can be achieved in certain conf...

متن کامل

Transversals to line segments in R3

We completely describe the structure of the connected components of transversals to a collection of n arbitrary line segments in R. We show that n 3 line segments in R admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.

متن کامل

LINE-SEGMENTS CRITICAL SLIP SURFACE IN EARTH SLOPES USING AN OPTIMIZATION METHOD

In this paper the factor of safety (FS) and critical line-segments slip surface obtained by the Alternating Variable Local Gradient (AVLG) optimization method was presented as a new topic in 2D. Results revealed that the percentage of reduction in the FS obtained by switching from a circular shape to line segments was higher with the AVLG method than other methods. The 2D-AVLG optimization meth...

متن کامل

Predicates for Line Transversals in 3D

In this paper we study various predicates concerning line transversals to lines and segments in 3D. We compute the degrees of standard methods of evaluating these predicates. The degrees of some of these methods are surprisingly high, which may explain why computing line transversals with finite precision is prone to error. Our results suggest the need to explore alternatives to the standard me...

متن کامل

On the Helly Number for Hyperplane Transversals to Unit Balls

We prove some results about the Hadwiger problem of nding the Helly number for line transversals of disjoint unit disks in the plane, and about its higher-dimensional generalization to hyperplane transversals of unit balls in d-dimensional Euclidean space. These include (a) a proof of the fact that the Helly number remains 5 even for arbitrarily large sets of disjoint unit disks|thus correcting...

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:
  • CoRR

دوره math.MG/0306401  شماره 

صفحات  -

تاریخ انتشار 2003