The envelope of lines meeting a fixed line and tangent to two spheres

Gábor Megyesi; Frank Sottile

doi:10.1007/s00454-005-1160-8

The envelope of lines meeting a fixed line and tangent to two spheres

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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. © 2005 Springer Science+Business Media, Inc.

Original language	English
Pages (from-to)	617-644
Number of pages	27
Journal	Discrete & Computational Geometry
Volume	33
Issue number	4
DOIs	https://doi.org/10.1007/s00454-005-1160-8
Publication status	Published - Apr 2005

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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. {\textcopyright} 2005 Springer Science+Business Media, Inc.",

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AB - 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. © 2005 Springer Science+Business Media, Inc.

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JO - Discrete & Computational Geometry

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The envelope of lines meeting a fixed line and tangent to two spheres

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