2006/10/12 by Frank Sottile, Sottile, Frank, Thorsten Theobald +1
Computer Science · Mathematics · #14N99 #14Q15 #52C45 #68U05 #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #math.AG #math.MG #msc:14N99 #msc:14Q15 #msc:52C45 #msc:68U05
paper · pdf · doi:10.48550/arxiv.math/0610407
22 pages, 13 color figures
openalex publication_date 2006/10/12 · arxiv created 2007/04/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first review some topics in the classical computational geometry of lines, in particular the O(n3+ε) bounds for the combinatorial complexity of the set of lines in R3 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.