An enumerative geometry framework or algorithmic line problems in R-3
W 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 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 R-3 [ Discrete Comput. Geom., 26 (2001), pp. 1-17].
enumerative geometry lines balls tangents transversals real solutions computational geometry