The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres

Authors:
Gábor Megyesi;Frank Sottile
Affiliations:
Department of Mathematics, UMIST, P.O. Box 88, Manchester, M60 1QD, England;Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
Venue:
Discrete & Computational Geometry
Year:
2005

Citing 0
Cited 1

On the complexity of sets of free lines and line segments among balls in three dimensions

Proceedings of the twenty-sixth annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the set of lines that meet a fixed line and are tangent to two spheres and classify the configurations consisting of a single line and three spheres for which there are infinitely many lines tangent to the three spheres that also meet the given line. All such configurations are degenerate. The path to this result involves the interplay of some beautiful and intricate geometry of real surfaces in 3-space, complex projective algebraic geometry, explicit computation and graphics.