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

  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},
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. 

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and S

  • C. Borcea, X. Goaoc, S. Lazard
  • Petitjean Common tangents to spheres in R3
  • 2004

Common transversal and tangents to two lines and two spheres in P n , Discrete Comput

  • F. Sottile G. Megyesi, T. Theobald
  • Geom .
  • 2003

Computational line geometry

  • H. Pottmann, J. Wallner
  • Springer-Verlag, Berlin
  • 2001

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