Common Transversals and Tangents to Two Lines and Two Quadrics in P

G�bor Megyesi, Frank Sottile, Thorsten Theobald
2003 Discrete & Computational Geometry  
We solve the following geometric problem, which arises in several threedimensional applications in computational geometry: For which arrangements of two lines and two spheres in R 3 are there infinitely many lines simultaneously transversal to the two lines and tangent to the two spheres? We also treat a generalization of this problem to projective quadrics: Replacing the spheres in R 3 by quadrics in projective space P 3 , and fixing the lines and one general quadric, we give the following
more » ... lete geometric description of the set of (second) quadrics for which the 2 lines and 2 quadrics have infinitely many transversals and tangents: In the nine-dimensional projective space P 9 of quadrics, this is a curve of degree 24 consisting of 12 plane conics, a remarkably reducible variety.
doi:10.1007/s00454-003-0789-4 fatcat:pdny6lgoz5djpetc3fdspgserq