Lines tangent to four triangles in three-dimensional space

Hervé Brönnimann; Olivier Devillers; Sylvain Lazard; Frank Sottile

inria-00000598, version 1

Lines tangent to four triangles in three-dimensional space

Hervé Brönnimann ¹, Olivier Devillers () ², Sylvain Lazard () ³, Frank Sottile ⁴

Discrete and Computational Geometry 37, 3 (2007) 369-380

Résumé : We investigate the lines tangent to four triangles in $\mathbb{R}^3$. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.

1 : Department of Computer and Information Science
Polytechnic University of New York
2 : GEOMETRICA (INRIA Sophia Antipolis)
INRIA
3 : VEGAS (INRIA Lorraine - LORIA)
INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
4 : Department of Mathematics [Texas] (TAMU)
Texas A&M University

inria-00000598, version 1
http://hal.inria.fr/inria-00000598
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Contributeur : Sylvain Lazard <>
Soumis le : Vendredi 4 Novembre 2005, 16:23:39
Dernière modification le : Dimanche 20 Décembre 2009, 16:05:00

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DOI : 10.1007/s00454-006-1278-3

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