Finding stabbing lines in 3-space
نویسندگان
چکیده
منابع مشابه
On stabbing triangles by lines in 3-space
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.
متن کاملLower 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 کاملStabbing Orthogonal Objects in 3-Space
David M. Mount Fan-Tao Pu Department of Computer Science University of Maryland College Park, MD 20742 fmount,[email protected] 1 Motivation Computer graphics is the source of many interesting and challenging applications for the design of geometric algorithms and data structures. Applications in global illumination simulation and radiosity [7] have motivated our study of problems involving line...
متن کامل3 Stabbing segments
In this paper, we answer the question: Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection? We prove that already when the sets are segments in the plane, deciding existence of a convex stabber is NP-complete. On the positive side, we give a polynomial-time algorithm (in the full paper) to...
متن کاملCS - 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...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1992
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02293043