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

@article{Megyesi2005TheEO, title={The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres}, author={G{\'a}bor Megyesi and Frank Sottile}, journal={Discrete & Computational Geometry}, year={2005}, volume={33}, pages={617-644} }

- Published 2005 in Discrete & Computational Geometry
DOI:10.1007/s00454-005-1160-8

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.