On the degree of standard geometric predicates for line transversals in 3D (Q1025306)

The authors first study the degree of standard procedures for determining the number of line transversals to four lines or four segments in 3D [cf. \textit{H. Brönnimann, H. Everett, S. Lazard, F. Sottile}, and \textit{S. Whitesides}, Discrete Comput. Geom. 34, No.~3, 381--390 (2005; Zbl 1083.52003)]. They also consider the predicate for determining whether a minimal segment transversal to four line segments is intersected by a triangle. These predicators are ubiquitous in 3D visibility problems The predicate for ordinary planes through two fixed points, each plane containing a third rational point or a line transversal to four segments or lines is also studied [cf. \textit{H. Brönnimann, O. Devillers, V. Dujmović, H. Everett, M. Glisse, X. Goaoc, S. Lazard, H.-S. Na}, and \textit{S. Whitesides} SIAM J. Comput. 37, No.~2, 522--551 (2007; Zbl 1138.65019)].