Algorithms for line transversals in space
SCG '87 Proceedings of the third annual symposium on Computational geometry
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Arrangements of lines in 3-space: a data structure with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Stabbing and ray shooting in 3 dimensional space
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Linear programming and convex hulls made easy
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Visibility preprocessing for interactive walkthroughs
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Finding stabbing lines in 3-dimensional space
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Stabbing Isothetic Boxes and Rectangles in O(nlgn) Time
Stabbing Isothetic Boxes and Rectangles in O(nlgn) Time
Helly theorems and generalized linear programming
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Interactive update of global illumination using a line-space hierarchy
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
3-D to 2-D Pose Determination with Regions
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Shape sensitive geometric permutations
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On Neighbors in Geometric Permutations
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Near-Linear Time Approximation Algorithms for Curve Simplification
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
On neighbors in geometric permutations
Discrete Mathematics
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An axial object in E3 is a box or rectangle, all of whose edges are parallel to the coordinate axes. A line transveral of a set of axial objects is a line that intersects every object. We present an algorithm which finds a line transversal, if one exists, in expected linear time. In the process, we generalize a randomized linear programming algorithm, and prove that the set of line transversals of axial objects has a constant number of connected components.