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Conference ProceedingsOPEN ACCESS

Line transversals to disjoint balls

Discrete and Computational Geometry (2008) 39(1-3) 158-173
DOI: 10.1007/s00454-007-9016-z
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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 2. 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. © 2007 Springer Science+Business Media, LLC.

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Borcea, C., Goaoc, X., & Petitjean, S. (2008). Line transversals to disjoint balls. In Discrete and Computational Geometry (Vol. 39, pp. 158–173). Springer New York. https://doi.org/10.1007/s00454-007-9016-z

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