 
Summary: ALGORITHMS FOR HIGH DIMENSIONAL STABBING
PROBLEMS
David Avis
Mike Doskas
School of Computer Science
McGill University
805 Sherbrooke St. W.
Montreal, Canada, H3A 2K6
ABSTRACT
Given a set of geometric objects in R d , the hyperplane transversal or
stabbing problem is to determine if there exists a hyperplane that simulta
neously intersects all of the objects. We give algorithms based on linear
programming for various hyperplane stabbing problems where the objects
are line segments or convex polyhedra. A hyperplane stabber for n seg
ments in R d can be found in O(n d ) time. In R d , a plane stabber for a set
of m polyhedra with a total of n edges can be found in O(n d1 m) time and
space. Given a query hyperplane, a list of polyhedra intersected by the
hyperplane can be determined in O(log n + m) time.
Keywords: Computational Geometry, Stabbing Problems, Transversals,
Intersections, Polyhedra, Geometric Algorithms
