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

@article{Theobald2002AnEG,
title={An Enumerative Geometry Framework for Algorithmic Line Problems in \$\mathbb R^3\$},
author={Thorsten Theobald},
journal={SIAM J. Comput.},
year={2002},
volume={31},
pages={1212-1228}
}
• 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…
13 Citations

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