An Enumerative Geometry Framework for Algorithmic Line Problems in $\mathbb R^3$

  title={An Enumerative Geometry Framework for Algorithmic Line Problems in \$\mathbb R^3\$},
  author={Thorsten Theobald},
  journal={SIAM J. Comput.},
  • T. Theobald
  • Published 1 April 2002
  • Mathematics
  • SIAM J. Comput.
We investigate the enumerative geometry aspects of algorithmic line problems when the admissible bodies are balls or polytopes. For this purpose, we study the common tangent lines/transversals to k balls of arbitrary radii and 4-k lines in ${\mathbb R}^3$. In particular, we compute tight upper bounds for the maximum number of real common tangents/transversals in these cases. Our results extend the results of Macdonald, Pach, and Theobald who investigated common tangents to four unit balls in… 

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