Line transversals to disjoint balls

Authors:
Ciprian Borcea;Xavier Goaoc;Sylvain Petitjean
Affiliations:
Rider University, Lawrenceville, NJ;Loria - INRIA Lorraine, Nancy, France;Loria - CNRS, Nancy, France
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

Citing 3
Cited 0

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Computational Geometry: Theory and Applications - Special issue on the thirteenth canadian conference on computational geometry - CCCG'01
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Geometric permutations of disjoint unit spheres

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Abstract

We prove that the set of directions of lines intersecting three disjoint balls in R3 in a given order is a strictly convex subset of S2. We then generalize this result to n disjoint balls in Rd. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.