Line problems in nonlinear computational geometry Institutional Repository Document uri icon

abstract

  • We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+epsilon}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description complexity. The main part of this survey is recent work on a core algebraic problem--studying the lines tangent to k spheres that also meet 4-k fixed lines. We give an example of four disjoint spheres with 12 common real tangents.

author list (cited authors)

  • Sottile, F., & Theobald, T.

complete list of authors

  • Sottile, Frank||Theobald, Thorsten

publication date

  • October 2006